Off-highway truck setup influence on vehicle dynamics and frame durability

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E. Dantas, M. T.C. Faria This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5010781/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Dec, 2024 Read the published version in Multibody System Dynamics → Version 1 posted 9 You are reading this latest preprint version Abstract The unpaved roads of mining sites can not only lead to health problems on haul truck’s driver but also reduce its frame useful life and provide worse handling performance. This study investigates the influence of different suspension-tire setups on the behaviour of a 64-ton mining haul truck, focusing on the initial gas volume of the hydropneumatic suspension (HPS) and tire inflation pressure. Using a multibody model, typical manoeuvres were simulated to assess handling, comfort, and frame durability. Results suggested that softer suspension and tire setups could enhance ride comfort and frame durability without substantially affecting handling. Haul truck Multibody dynamics Durability Handling Comfort Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 INTRODUCTION Off-highway trucks have a crucial role in the mining process, being widely used in excavation areas due to their low investment cost and high adaptability to new mining spots. These areas are characterized by unpaved roads with significant irregularities, which can be attributed to unproper maintenance, constant route improvisation, and intensive truck traffic. Combining with their heavy load transportation capacity, these irregularities result in severe impact and overload conditions on tyres and suspensions. Consequently, it can generate health issues for drivers due to vibration levels transmitted to the cabin (comfort), premature mechanical component failures (durability) and reduced productivity, since drivers need to slow down on curves and in obstacles avoidance manoeuvres (handling). Most papers concerning off-highway trucks focus primarily on driver’s comfort. It has been found that excessive levels of cabin vibration occurs when the truck is empty, descending grade or sliding on a wet and slippery road surface (MAYTON et al., 2018 ). Mining haul trucks are typically equipped with hydropneumatic suspensions (HPS) which enhance wheel load distribution through their nonlinear stiffness characteristics. These suspensions use inert gas whose compression and expansion generate restoring forces in accordance with the ideal gas law. Energy dissipation is achieved via oil flow through orifice and check valves. Hien et al. ( 2021 ) conducted a parametric analysis using a 2- degree-of-freedom (DOF) lumped mass model, revealing that initial gas volume and pressure, along with valve diameter, significantly affect driver's comfort. They found that combining changes in initial gas volume and valve diameter resulted in the most effective reduction of vertical cabin acceleration. Using a 10 (DOF) lumped mass model, Long et al ( 2021 ) demonstrated that vertical cabin acceleration can increase exponentially with worse ISO 8608:2016 class roads. Durability of off-highway trucks has been studied by several authors interested on their component useful lifetime. However, most papers focus on tyre wear rate instead of structural components, such as the vehicle’s frame. Haul truck frames are typically manufactured by combining cast and welded steel parts. Welds are certainly the structure most critical regions regarding fatigue life due to the microstructure modification. Gady e Craig (1989) showed that events such as loaded vehicle cornering and loading/unloading operations significantly contribute to structural damage. Later, Prem ( 1998 ) stated that road roughness is a determining factor on structural fatigue life. More recently, Savkin (2016) and Mi et al. ( 2023 ) employed multibody dynamics and finite element model validated by experimental data to estimate the frame’s peak stresses and welded parts fatigue life. Mi et al. ( 2023 ) multibody simulations were based on three different fully loaded working conditions: flat rough road, turning uphill and pothole road surface. It can be seen in the literature that most of the existing studies about truck handling dynamics concentrate on rolling and stability. Yin et al. ( 2016 ) found that the lateral acceleration Root Mean Square (RMS) during the sustained period of unity lateral-load-transfer-ratio (LTR) is an effective criterion for evaluating the rollover threshold. Kang et al. ( 2015 ) extended the analysis beyond roll dynamics by using a multibody model to determine the understeer gradients of a mining haul truck with four different suspension geometries, investigating their influence on driver’s handling experience. Both Kang et al. ( 2015 ) and Loo (2003) noted that the these trucks tend to exhibit a very strong understeering behaviour. Compared to on-road vehicles, the performance of off-road vehicles on curves has not received the same attention from researchers, likely due to their relatively low transportation speed. Consequently, studies on the influence of road roughness on on-road vehicle dynamics have become a valuable source of knowledge for mining haul truck research. Li et al. ( 2013 ) used different coherence functions applied to stochastic road profiles to demonstrate that higher lateral stability increases the risk of rollover, and that low coherence at low frequencies in left and right road profiles has a greater influence on rollover stability than on lateral stability. Cosme et al. ( 1999 ) conducted constant steering and double lane change manoeuvres using a multibody model with a flexible chassis of a heavy-duty articulated truck to investigate the influence of chassis stiffness on sprung mass roll angle. They found that frame flexibility can significantly increase the peak value of the roll angle. Mining companies often get vehicles with standardized setups from manufacturers, which may not be applicable for the specific operational conditions of a given site. To enhance the truck's ride comfort, handling, and durability, companies typically have two main options: (i) improve the haul road maintenance routine or (ii) perform field adjustments to vehicle parameters. The first option can be costly, particularly in tropical regions where extended rainy seasons need high-quality road materials and extensive drainage systems (TANNANT AND REGENSBURG, 2001). Conversely, defining new suspension setups is relatively straightforward and customizable. While the technical literature of mining haul trucks includes some studies on the impact of hydropneumatic suspension on vehicle dynamics, the influence of tyre pressure is rarely explored. Thus, it is presented in this work a study of the influence of different suspension-tyre setups on the behaviour of a mining haul truck frame. The initial HPS gas volume and the tyre pressure were the parameters of interest, being varied in each setup to create stiffer and softer interaction with the road. These two parameters were chosen for their feasibility and ease of adjustment. The assessment of ride comfort, handling and chassis durability for each suspension setup was conducted using multibody and finite element models of a 64-ton capacity off-highway truck. Different manoeuvres were simulated with the multibody model, including constant speed turning (CST) and double lane change (DLC), to examine the impact of stiffness on the vehicle’s handling characteristics. Roll dynamics are significantly influenced by road roughness conditions (BOGSJÖ, 2008 ; LI et al., 2013 ; YIN et al., 2016 ), thus the DLC manoeuvre was performed over a rough road surface. The evaluation of ride comfort and chassis durability was based on a straight-line constant speed manoeuvre (SLCS) using the same rough road profile as the DLC manoeuvre. MULTIBODY MODEL Numerical multibody analysis described in this paper comprise rigid and flexible parts. After defining mass, damping and stiffness properties of each body and establishing all joints constraint equations ( \(\:\varOmega\:\) ), the initial conditions of generalized coordinates q are determined. \(\:q={\left(x,y,z,\phi\:,\theta\:,\psi\:,{\xi\:}_{i}\right)}^{T}\) (Eq. 1) From Eq. (1), \(\:x\) , \(\:y\) , and \(\:z\) represent the positions of the local coordinate systems relative to the global coordinate system, while \(\:\phi\:\) , \(\:\theta\:\) , and \(\:\psi\:\) are the Euler angles of the local coordinate systems relative to the global coordinate system, and \(\:{\xi\:}_{i}\) is the modal displacement of a flexible body corresponding to mode i . The equations of motion (EOMs) of the system are then derived based on Euler-Lagrange mechanics. Their general form applied to flexible multibody dynamics is presented in Eq. (2). \(\:M\ddot{q}+\dot{M\dot{q}}-\frac{1}{2}{\left(\frac{\partial\:M}{\partial\:q}\dot{q}\right)}^{T}\dot{q}+Kq+{f}_{g}+C\dot{q}+{\left(\frac{\partial\:{\Omega\:}}{\partial\:q}\right)}^{T}{\lambda\:}_{Lag.}=Q\) (Eq. 2) The first term accounts for the inertial effects, while the second and third terms predict the changes in the mass matrices as a function of time and generalized coordinates. \(\:Kq\) and \(\:C\dot{q}\) represent the stiffness restoring forces and damping dissipative forces, respectively. \(\:{f}_{g}\) represents the gravitational forces, and \(\:{\left(\frac{\partial\:{\Omega\:}}{\partial\:q}\right)}^{T}{\lambda\:}_{Lag.}\) represents the constraint forces imposed by joints and restrictions. \(\:Q\) includes the applied external forces. In general, the EOMs derived from Eq. (2) can be classified as either stiff or non-stiff. Stiff problems are essentially those associated with systems that exhibit both low and high-frequency excitations and responses simultaneously. This is the case, for example, of vehicle systems evaluated in terms of ride comfort, as road roughness cover a wide frequency spectrum. When combined with low-frequency inputs such as steering and acceleration, these irregularities can excite both low and high-frequency vibration modes of the vehicle. The solution of stiff dynamic problems typically requires the use of implicit integrators due to their unconditional stability, which allows solving problems with a high degree of nonlinearity without the need for excessively small-time step increments. To solve the multibody dynamic equations this paper uses the variable-order and variable-step integration algorithm GSTIFF-I3 (Generalized STIFF Integration Method – Index 3), implemented in ADAMS/Solver®. This algorithm utilizes information from multiple previous time steps (multi-steps) rather than relying only on the current or most recent state. An integration error tolerance of 0.1 is assigned and the maximum time step is defined as 0.01s. Vehicle characteristics The full vehicle multibody model is a representation of a CAT 775G truck. This model is built using the ADAMS Car platform and consists of 94 free degrees of freedom (DOFs). This includes the frame, modelled as a flexible component with 10 vibration modes. The front wheels are connected to the chassis via an independent sliding pillar hidropneumatic suspension system. At the rear axle, the wheels are interconnected by a rigid axle, which is attached to the chassis through trailing arms, Panhard rod and hydropneumatic suspensions. Unlike the flexible frame, dump body and payload work as a single component rigidly fixed to each other. Their inertial load is transferred to the chassis through revolute joints and hoist cylinders. The model main parts are illustrated in Fig. 1 . Resulting mass and inertia properties are shown in Table 1 Geometric and inertial properties for the multibody model. Parameters Unloaded Loaded Wheelbase – L (m) 4.2 Front track width – t d (m) 3.2 Rear track width – t t (m) 2.15 Mass distribution (front : rear) 50:50 34:66 Vehicle mass – m (t) 48.2 112.2 CG height – h (m) 1.72 2.35 Total vehicle roll inertia – Iφ (t.m²) 106.6 251.7 Total vehicle pitch inertia – Iθ (t.m²) 264.0 498.2 Total vehicle yaw inertia – Iψ (t.m²) 328.0 608.3 Sprung mass distribution (front : rear) 66:34 40:60 Sprung mass – m s (t) 32.0 96.0 Sprung mass CG height – h s (m) 2.05 2.57 Sprung mass roll inertia – Iφ s (t.m²) 69.4 192.1 Sprung mass pitch inertia – Iθ s (t.m²) 180.1 407.5 Sprung mass yaw inertia – Iψ s (t.m²) 229.4 525.0 Front axle unsprung mass – m d (t) 4.6 Front axle unsprung mass CG height – h d (m) 1.04 Rear axle unsprung mass – m t (t) 11.6 Rear axle unsprung mass CG height – h t (m) 1.06 Flexible body frame A finite element (FE) model of the truck frame is developed by using tetrahedral solid elements. The discrete model leads to the eigenvalue problem that permits to obtain the frame free vibration modes. Incorporating all DOFs from this model to the multibody analysis would be extremely high demanding, thus applying model dynamic reduction through component mode synthesis (CMS) techniques can be very helpful. This is achieved by the Craig-Bampton technique, which effectively represents rigid body modes through a linear combination of static deformations. This method comprises internal DOFs ( a ) and interface DOFs ( b ) that are connected to the multibody model parts. The reduction process involves calculating the normal mode matrix of the m modes defined by the user with the b DOFs restrained ( \(\:{{\Phi\:}}_{a\times\:m}\) ). It also calculates the static modes matrix ( \(\:{G}_{a\times\:b}\) ) by applying unit displacements to b DOFs individually while restraining internal a DOFs. The Craig-Bampton reduction matrix \(\:{T}_{fj}\) is defined as \(\:{u}_{f}={T}_{fj}{u}_{j}\:\to\:\left\{\begin{array}{c}{u}_{a}\\\:{u}_{b}\end{array}\right\}=\:\left[\begin{array}{cc}{{\Phi\:}}_{a\times\:m}&\:{G}_{a\times\:b}\\\:{0}_{a\times\:m}&\:{I}_{a\times\:a}\end{array}\right]\left\{\begin{array}{c}{\eta\:}_{m}\\\:{u}_{b}\end{array}\right\}\) Eq. (3) where \(\:{u}_{f}\) is the displacement vector of internal ( \(\:{u}_{a}\) ) and interface DOFs ( \(\:{u}_{b}\) ) and \(\:{\eta\:}_{m}\) is the modal participation vector reduced to the predefined m modes. From Eq. 3.5 an eigensolution is performed to fully describe the reduced system in terms of modal coordinates. The resulting data, such as the interface nodes' positions and generalized mass and stiffness matrices, are then exported to a Modal Neutral File (MNF) compatible with ADAMS Car®. For simplification, the flexible frame is considered in the multibody analysis by including only the first 10 reduced system modes. As shown in Table 2 , all major vehicle movements, such as torsion and bending, are captured in these first 10 modes. These modes natural frequencies calculated by the full finite element and the reduced dynamic models are also presented in Table 2 . Reduced model showed that it can represent the full structure dynamics through with a very good agreement with full finite element model. Table 2 Comparative values of natural frequencies for the truck frame. ID Mode description FE (Hz) CMS (Hz) 1 1st Torsional 23.9 23.9 2 1st Lateral bending 28.1 28.2 3 1st Vertical bending 31.5 31.5 4 2nd Lateral bending 39.3 39.4 5 2nd Torsional 48.1 48.1 6 3rd Torsional 54.1 54.1 7 3rd Lateral bending 67.2 67.3 8 2nd Vertical bending 69.6 69.7 9 4th Lateral bending 74.7 74.8 10 4th Torsional 77.3 77.4 HPS equations As defined by Bauer ( 2011 ) the hydropneumatic suspension (HPS) forces combine gas elastic restoration force ( F g ) and viscous damping force resultant from oil flow through valves ( F h ). From the ideal gas law, F g is mathematically expressed as: \(\:{F}_{g}={P}_{0}{\left(\frac{{V}_{0}}{V}\right)}^{r}{A}_{h}={P}_{0}\left[{\left(\frac{{V}_{0}}{{V}_{0}\:+\:{A}_{h}\:({z}_{b}-{z}_{a})}\right)}^{r}-1\right]{A}_{h}\) Eq. (4) where P 0 and V 0 are the initial pressure and volume of the gas when the rod is extended (the nominal values are denoted as P 0N and V 0N in this work), r is the polytropic coefficient, A h is the cross-sectional area of the rod, and z a and z b are the longitudinal positions of the rod at instants a and b . HPSs tend to behave as an adiabatic system under high-frequency excitations ( r ≈ 1.40) and can approximate the isothermal regime at low frequencies ( r ≈ 1.00). Given that road roughness imposes mainly high-frequency excitations, a polytropic coefficient of 1.40 was estimated. A widely used equation to relate the pressure drop ( ∆P ) with the fluid flow rate through resistors ( Q res ) is given in Eq. (5). In this equation, ρ denotes the mass density of the oil, A r is the area of the resistor, and C d its discharge coefficient (BAUER, 2011 ). \(\:{\varDelta\:P}_{res}=\frac{\rho\:\:{{Q}_{res}}^{2}}{2\:{\left({C}_{d}{A}_{r}\right)}^{2}}\) Eq. (5) The orifice and check valves of a HPS connect the same chambers of the system, and thus experience the same pressure drop. Applying Eq. (5) to a HPS, where these valves act as the resistors, leads to: \(\:{F}_{h}=\frac{\rho\:{A}_{c}}{2}{\left(\frac{\dot{x}{A}_{c}}{{n}_{dv}{\alpha\:}_{dv}{A}_{dv}+{n}_{cv}{\alpha\:}_{cv}{A}_{cv}}\right)}^{2}\text{s}\text{i}\text{g}\text{n}\left(\dot{x}\right)\) Eq. (6) where ẋ is the rod compression/extension velocity, A is the oil chamber area, n dv and n cv are the quantities of orifice and check valves, α dv and α cv their discharge coefficient and A dv and A cv their cross-sectional area. The signal function in terms of rod velocity is 1 during compression and − 1 during extension. It is also important to note that check valves are unidirectional and do not allow oil flow during rod extension, meaning n cv must be assumed as null when sign (ẋ) = -1. Table 3 shows values employed to calculate the hydropneumatic restoration and dissipative forces, F g and F h . Table 3 Parameters used in the HPS force calculation. Parameter Front Rear Nominal initial gas volume – V 0N (l) 5.19 3.11 Nominal initial gas pressure – P 0N (kPa) 2600 1800 Rod cross-section area – A h (m²) 0.025 0.025 Oil chamber cross-section area – A c (m²) 0.0077 0.012 Number of orifice valves – n dv 2 1 Discharge coefficient of orifice valves – α dv 0.70 0.70 Orifice valves diameter – D dv (mm) 19.1 19.1 Number of orifice valves – n dv 1 1 Discharge coefficient of orifice valves – α dv 0.70 0.70 Orifice valves diameter – D dv (mm) 15.9 15.9 Oil density – ρ (kg/m³) 800 800 Tyre model The off-highway truck is equipped with 24.00R35 tyres represented in the multibody model by PAC 2002 semi-empirical model with 3D enveloping contact. Cornering characteristics of large tyres are not usually available due to their size and load capacity. Thus, cornering stiffness is estimated using procedures encountered in the technical literature (FRIMPONG et al., 2012 ; KANG et al., 2015 ). Figure 2 shows cornering force in terms of slip-angle estimated for three different vertical loads. Fz = 117 kN and Fz = 58 kN are the nominal normal load on front and rear tyres in unloaded truck, respectively. In loaded condition, all tyres have 185 kN of normal force equally. Table 4 provides the tyres main parameters. Table 4 Main tyre characteristics (FRIMPONG et al., 2012 ; KANG et al., 2015 ). Parameter Value Nominal radius 1082 mm Static radius 975,4 mm Tread width 665,5 mm Nominal rated load 210,9 kN Nominal inflation pressure – TP N 724,0 kPa Cornering stiffness ( F z = 58 kN) ~ 11 kN/° Cornering stiffness ( F z = 117 kN) ~ 21 kN/° Cornering stiffness ( F z = 185 kN) ~ 32 kN/° Damping coefficient 470 Ns/m Tyres vertical stiffness is significantly affected by their inflation pressure. Prem & Dickerson ( 1992 ) established a polynomial regression relationship for vertical load versus deflection for different tyres manufacturers and various sizes. This equation is also employed in this work to estimate the 24.00R35 tyre normal force. Suspension-tyres setup To simulate the manoeuvres described in this paper, seven total suspension-tyre setups are defined by varying HPS initial gas volume ( V 0 ) and tyres inflation pressure ( TP ). The former can be simply adjusted by managing gas/oil ratio in the main suspension chamber. Maximum variation of ± 15% of V 0N is selected since very low oil volume may cause component overheating. Similarly, tyres inflation pressure is defined in a range of ± 10% to avoid excessive tyre wear during loaded transportation. Table 5 summarizes the selected parameters for each setup identified from A to G. In this table, the percentages correspond to the differences relative to nominal suspension parameters. Setup A considers less initial gas volume combined with more tyre inflation pressure providing the stiffest adjustment whereas setup G consists in the softest one. Setup D only comprises nominal values of V 0 and TP . Subscripts u and l are added in setups ID to unloaded and loaded conditions. Table 5 Initial gas volume and tyre inflation for each setup. Setup ID A B C D E F G Front HPS initial gas volume – V 0F (l) 4.67 (-10%) 4.67 (-10%) 5.19 (-%) 5.19 (-%) 5.19 (-%) 5.71 (+ 10%) 5.71 (+ 10%) Rear HPS initial gas volume – V 0R (l) 2.64 (-15%) 2.64 (-15%) 3.11 (-%) 3.11 (-%) 3.11 (-%) 3.57 (+ 15%) 3.57 (+ 15%) Tyre inflation pressure – TP (kPa) 796.4 (+ 10%) 724 (-%) 796.4 (+ 10%) 724 (-%) 651.6 (-10%) 724 (-%) 651.6 (-10%) Figure 3 shows suspension curves obtained through Eq. (4) and Eq. (6). Gas restoration forces ( F g ) in terms of rod’s displacement are presented for each V 0 considered in setups A to G. By applying polynomial regression described by Prem & Dickerson ( 1992 ), Fig. 4 exhibits tyre stiffness curves for the inflation pressures of setups A to G. Road profile and validation For the dynamic analysis of off-road vehicles, the road roughness is represented as an undeformable stochastic profile describe by Power Spectrum Density (PSD) functions. Similar to ISO 8608:2016, Sayers ( 1988 ) describes Eq. (7) to build PSD functions of rough terrains, including additional high and low wavenumbers contributions through G e and G a variables, respectively. \(\:{G}_{d}\left({\nu\:}\right)={G}_{e}+\frac{{G}_{s}}{{\left(2\pi\:\nu\:\right)}^{2}}+\frac{{G}_{a}}{{\left(2\pi\:\nu\:\right)}^{4}}\) Eq. (7) The road profiles are generated by ADAMS Car by combining gaussian random signals with values of G e , G s and G a equal to 1,0E-6 m³/cycle, 5,0E-4 m/cycle e 0 m -1 cycle -1 , respectively, corresponding to an ISO 8608:2016 class D road. The resulting left and right road profiles over a 300 m length are shown in Fig. 5 . Their resultant PSDs and coherence are presented in Fig. 6 . The average coherence obtained between wavenumbers of 10 − 1 to 10 1 m -1 is approximately 0.18. Off-highway trucks are usually equipped with monitoring systems that provide instantaneous performance data of the vehicle speed, suspension pressure and payload. To validate the selected values of G e , G s and G a , experimental data of the suspension pressure of five trucks CAT 775G is collected under loaded and unloaded conditions at 20 ± 1 km/h travelling speed. These experimental data are compared with numerical values rendered by the multibody model with nominal setup D obtained during a straight-line manoeuvre at constant speed of 20 km/h. Comparison of experimental and computational data are presented in Fig. 7 for right side front and rear suspensions in both payload conditions (0-ton and 64-ton). RMS values showed a very good agreement for each suspension, indicating that the mining site of the studied vehicle is indeed very close to an ISO 8608:2016 class D road. HANDLING ASSESSMENT Constant speed cornering Based on the steady-state cornering manoeuvres in ISO 4138:2021, the constant speed can be the most representative of the actual behaviour of a vehicle in a turn, since drivers usually maintain a near constant speed when cornering. To assess the response of each setup at this condition, the multibody model maintains a constant controlled speed of 25 km/h with an increasing steering wheel angle input sufficient to provide a lateral acceleration rate of 0.01 g/s. The manoeuvre ends when the vehicle can not generate additional lateral acceleration. Resulting steering wheel angle rate ( δ stw ) for each suspension setup is shown in Fig. 8 . Unloaded vehicle does not indicate significant difference of response. However, loaded vehicle presents a slightly better handling response for stiffer suspensions. Setups A and B need almost 7% less steering angle to reach the same lateral acceleration in relation to the angle attained for softer setups F and G. Understeer gradient ( K ), calculated as the derivative of the difference between the front and rear slip angles \(\:\left({\alpha\:}_{f-}{\alpha\:}_{r}\right)\) with respect to lateral acceleration (Eq. 8)), is shown in Fig. 9 for each setup. \(\:K=\:\frac{{\Delta\:}\left({\alpha\:}_{f}-{\alpha\:}_{r}\right)}{{\Delta\:}\:{a}_{y}}\) Eq. (8) Similar to steering wheel angle rate, no significant difference in the understeer gradient has been observed for each setup at unloaded condition. The vehicle with no payload exhibits understeer behaviour (K > 0) within a lateral acceleration range of 0 < a y ≤ 0.3 g. At loaded condition, oversteering ( K < 0) can be found for small values of lateral acceleration ( a y ≤ 0.15 g) due to the mass centre offset towards the rear axle. However, understeer becomes predominant within the range of 0.15 < a y ≤ 0.25 g. Within this range, significant differences of 𝐾 values are observed for each suspension setup, with stiffer suspensions resulting in higher understeering. Compared to setup G, setup A could reach an understeer gradient twice larger. At both loading conditions the driver controller attempts to input an increasing throttle value when the maximum steering angle is reached in order to recover the 25 km/h speed that is slightly reduced during the manoeuvre. Hence, strong oversteering behaviour occurs due to the increased torque on the rear axle causing tyre slippage. This event occurs at a y = 0.35 g for the unloaded condition and at a y = 0.30 g for the loaded vehicle. Double lane change manoeuvre In order to assess the vehicle transient handling behaviour, a double lane change manoeuvre according to ISO 3888-1:2018 is performed by the multibody model. This manoeuvre is simulated at a speed of 35 km/h, which is very usual for the trucks analysed in this work. Figure 10 shows the roll angle estimated for rough terrain for loaded and unloaded vehicle conditions. Only setups A, D and G have the curves depicted for better visualization. On Fig. 10 , it is shown that setups A u , D u and G u present slightly different peak values of roll angle, whereas setups A l , D l and G l show larger differences for those angles. Compared to nominal setup D l , G l achieves a maximum peak value 20% higher. Rollover stability is evaluated by the Lateral Load Transfer Ratio (LTR) defined by Eq. (9). Unit value of LTR reflects a vehicle at a rollover threshold, since it designates that internal wheels lose soil contact. \(\:LTR=\:\frac{\left({F}_{zFL}+{F}_{zROL}+{F}_{zRIL}\right)-({F}_{zFR}+{F}_{zROR}+{F}_{zRIR})}{{F}_{zFL}+{F}_{zROL}+{F}_{zRIL}+{F}_{zFR}+{F}_{zROR}+{F}_{zRIR}}\) Eq. (9) Only the curves of LTR versus time for setups A, D and G are shown in Fig. 11 . Although it is not shown in this figure, LTR reaches 1.0 at 15s of manoeuvre time for setups E, F and G at loaded condition. Noteworthy to say that this condition likely does not last for enough time to produce vehicle rollover. Figure 12 shows the RMS values of roll angle and LTR for each setup in terms of front and rear suspension initial gas volume. Setups A u and B u show nearly 5% reduction in the RMS value of the roll angle in comparison to the nominal setup D u , while setups F u and G u exhibit an increase of approximately 10%. The stiffness of the suspension-tyre system has a significant impact on the roll response, especially when the truck is loaded, since it presents an almost linear relationship with the RMS value of the roll angle. The stiffest (A l ) and softest (G l ) suspensions present approximately ± 20% of variation on the RMS values of the roll angle. Regarding LTR, the trends differ notably between unloaded and loaded conditions. When unloaded, the RMS values of LTR follow the expected behaviour, since stiffer configurations (A u and B u ) result in higher value of LTR due to increased load transfer. However, at loaded condition, the roll of the sprung masses becomes a dominant factor, potentially reversing that behaviour. Therefore suspensions with higher stiffness (A l and B l ) exhibit lower LTR, due to the increased influence of roll in the vehicle dynamics when loaded. STRAIGHT-LINE CONSTANT SPEED (SLCS) Ride comfort assessment Experimental data of truck speed are grouped into ranges of 0.5 km/h and separated into unloaded and loaded conditions. The resulting data are used to generate the histograms shown in Fig. 13 , where a total distance travelled is depicted for each range of vehicle speed. Dashed lines in both histograms divide the data into three speed classes: low, intermediate, and high. These classes are used as reference to establish vehicle speed to be controlled in SLCS manoeuvre. Figure 14 shows the vertical acceleration at the driver’s seat position for setups A, D and G obtained at each speed class weighted average. RMS values of the seat’s vertical acceleration are estimated and used as a parameter to assess the vehicle ride comfort. The resultant values for each setup are presented in Fig. 15 . Soft setups F and G generate a reduction about 10% in the RMS values of acceleration at intermediate and high speeds for both loaded and unloaded conditions. It can also be highlighted that the RMS values of acceleration obtained at intermediate and high speeds for every setup can be considered very uncomfortable according to ISO 2631:1997. Therefore, reducing the vertical acceleration of the vehicle driver’s seat is extremely desirable. Frame durability Suspension forces calculated at each speed class is then exported to a chassis finite element model, which accounts for the interaction between the dump body and the main frame (Fig. 16 ). Using inertia relief tool available on the package FEMAP/NASTRAN, the model requires no constraints. The numerical procedure reaches a condition of equilibrium by applying inertial acceleration to each finite element, resulting in a toral force of zero. Thus, for every local and minimum suspension force, this quasi-static analysis is conducted to calculate frame’s global displacements. In a different analysis performed using the finite element model, dumping and loading events are also evaluated. The effects of different vehicles setups are negligible at those events and the suspension-frame joints can have the translational degrees of freedom (DOFs) constrained. The dumping force primarily consists of the necessary force exerted by the hoist cylinder to lift the fully loaded dump body. Loading impact forces are estimated based on the linear momentum variation presented in Eq. (10), with corresponding parameter values shown in Table 6 . Experimental data provide the average number of shovel operations per loading process and the amount of material per shovel operation. The impulse duration is estimated as 1.28 seconds, according to Ali & Frimpong ( 2018 ). \(\:{F}_{i}=\:\frac{\sqrt{2g{H}_{t}}{m}_{i}}{ϵ}\) Eq. (10) Table 6 Parameters used for the loading forces computation. Shovel operation Material dumped – m i (ton) Impact force – F i (kN) Total force – F t (kN) 1st 19.7 10.7 204.0 2nd 11.3 5.7 116.6 3rd 9.9 4.6 101.7 4th 7.2 3.1 73.7 5th 6.5 2.5 66.3 6th 6.2 2.0 62.8 7th 3.3 0.9 33.3 Two welded joints are selected to assess fatigue life due to their high stress range. For better stress estimation, local model of these regions with refined mesh are developed, as shown in Fig. 17 . Displacements calculated by the global finite element model are then applied to those local models. Maximum principal stresses are used to build stress spectra based on the six speed classes at the loading and dumping events. These spectra are extrapolated using experimental total time of each speed class. Rainflow counting grouped the tress cycle spectrum into 1 MPa stress ranges. Using Palmgren-miner cumulative damage theory and the S-N curve for butt-welded joints with axial stresses from IIW (HOBBACHER, 2016 ), the total damage can be estimated of each welded joint for each suspension setup. Results show that traveling of the loaded vehicle under intermediate and high speeds contribute to 60 until 70% of total weld damage. Combined dumping and loading events represent 18 to 32% of the total damage depending on the suspension setup. Figure 18 illustrates the estimated life in years based on the damage results. It can be observed that stiffer suspension setups (A and B) may reduce welded joints life in almost 40%. Soft setups (F and G) could considerably improve the welds life by 25%. CONCLUSIONS An analysis of the influence of the tyre inflation pressure and of the initial gas volume of the hydropneumatic suspension (HPS) on the handling, ride comfort, and frame´s durability of an off-highway mining truck is performed by employing a numerical procedure based on the multibody dynamics and finite element method. Some remarks can be drawn from this analysis: Stiffness setups showed insignificant influence on steady-state cornering in unloaded condition. However, when the vehicle was loaded, stiffer setups demonstrated a slightly better capacity for generating lateral acceleration and a significantly increased understeer behaviour at lateral acceleration values above 0.15 g. Below 0.15 g, the driver may not perceive a noticeable difference in handling experience. Transient cornering assessed through a double lane change manoeuvre showed that enhanced/reduced stiffness setups can largely decrease/increase body roll angle especially in loaded condition. According to Uys et al. ( 2006 ), this can be a very solid indicator of handling performance. Rollover stability was not significantly influenced overall. Lateral Load Transfer Ratio (LTR) Root Mean Square (RMS) was very similar in every setup. A moderate influence in ride comfort was revealed for intermediate and high traveling speeds. Least rigid setup could improve driver’s Root Mean Square (RMS) vertical acceleration in almost 10% compared to nominal setup. However, this reduction is not sufficient to fit the vehicle in a comfortable range according to ISO 2631:1997. Significant influence on frame durability was found. Both welded joints showed a very large increase in fatigue life when the softest setup was considered. The results rendered in this work indicate that it will be worthwhile to perform experimental tests on field with different suspension setups and tyre pressures to confirm some of the findings described in this analysis. It should be highlighted that the softest setup may be very costly due to increased tyre wear with less inflation pressure. Thus, setup with nominal tyre inflation pressure and higher initial HPS gas volume, providing the second softest setup, can be the most promising adjustment, particularly if the mining road does not induce lateral accelerations exceeding 0.15 g Declarations Author Contribution This work is part of A.E. master thesis under the supervision of professor M.T.C. A.E. wrote the manuscript and M.T.C reviewed and provided additional input. ACKNOWLEDGEMENTS This work has been supported by a research project financed by Vale SA. Financial support by “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001” is also acknowledged. References ALI, D.; FRIMPONG, S. Impulse force reductions and their effects on WBV exposures in high impact shovel loading operations. International Journal of Mining Science and Technology , v. 28, n. 3, p. 423–435, maio 2018. BAUER, W. Spring and Damping Characteristics of Hydropneumatic Suspension Systems. Em: BAUER, W. (Ed.). Hydropneumatic Suspension Systems . Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. p. 19–66. BOGSJÖ, K. Coherence of road roughness in left and right wheel-path. Vehicle System Dynamics , v. 46, n. sup1, p. 599–609, set. 2008. COSME, C.; GHASEMI, A.; GANDEVIA, J. Application of Computer Aided Engineering in the Design of Heavy-Duty Truck Frames . . Em: INTERNATIONAL TRUCK & BUS MEETING & EXPOSITION. 15 nov. 1999. Disponível em: . Acesso em: 12 mar. 2024 FRIMPONG, S. et al. Dump truck tire stress simulation for extended service life. v. 332, 2012. GADY, R. E.; CRAIG, A. J. The NEOCON strut: A major breakthrough in suspension technology. Off-Highway Haulage in Surface Mines , Proceedings Of The International Symposium On Off-Highway Haulage in Surface Mines. maio 1989. HIEN, V. T. et al. EFFECT ANALYSIS OF THE PARAMETERS OF HYDRO-PNEUMATIC SUSPENSION SYSTEM ON VEHICLE RIDE COMFORT. International Journal of Advanced Research in Engineering and Technology , v. 12, n. 1, p. 422–430, 2021. HOBBACHER, A. F. Recommendations for Fatigue Design of Welded Joints and Components . Villepinte, FranceSpringer International Publishing, , 2016. KANG, Y.; ZHANG, W.; RAKHEJA, S. Relative kinematic and handling performance analyses of independent axle suspensions for a heavy-duty mining truck. International Journal of Heavy Vehicle Systems , v. 22, n. 2, p. 114, 2015. LI, Y. et al. Effect of vertical and lateral coupling between tyre and road on vehicle rollover. Vehicle System Dynamics , v. 51, n. 8, p. 1216–1241, ago. 2013. LONG, L. X. et al. Effect of operating conditions on a heavy truck ride comfort with hydro-pneumatic suspension system. E3S Web of Conferences , v. 304, p. 02011, 2021. MAYTON, A. G. et al. Investigation of human body vibration exposures on haul trucks operating at U.S. surface mines/quarries relative to haul truck activity. International Journal of Industrial Ergonomics , v. 64, p. 188–198, mar. 2018. MI, C. et al. An energy-based fatigue life estimation and optimization of an electric mining dump truck welded frame. Journal of the Brazilian Society of Mechanical Sciences and Engineering , v. 45, n. 2, p. 117, fev. 2023. PREM, H. Off-Highway Mine Haul Truck Dynamics Simulation . . Em: INTERNATIONAL OFF-HIGHWAY & POWERPLANT CONGRESS & EXPOSITION. 14 set. 1998. Disponível em: . Acesso em: 12 mar. 2024 PREM, H.; DICKERSON, A. W. A Study of the Steady State Roll-Response of a Large Rear-Dump Mining Truck . . Em: INTERNATIONAL OFF-HIGHWAY & POWERPLANT CONGRESS & EXPOSITION. 1 set. 1992. Disponível em: . Acesso em: 12 mar. 2024 SAVKIN, A. N.; GOROBTSOV, A. S.; BADIKOV, K. A. Estimation of Truck Frame Fatigue Life under Service Loading. Procedia Engineering , v. 150, p. 318–323, 2016. SAYERS, M. W. Dynamic Terrain Inputs to Predict Structural Integrity of Ground Vehicles. p. 114, 1988. TANNANT, D. D.; REGENSBURG, B. Guidelines for mine haul road design. 2001. UYS, P. E.; ELS, P. S.; THORESSON, M. J. Criteria for handling measurement. Journal of Terramechanics , v. 43, n. 1, p. 43–67, jan. 2006. VAN DE LOO, P. The Development of the Smart Strut Improved Sliding Pillar Front Active Suspension System for Mining Trucks. Birrana Engineering Pty Ltd. , 2003. YIN, Y.; RAKHEJA, S.; BOILEAU, P.-E. A roll stability performance measure for off-road vehicles. Journal of Terramechanics , v. 64, p. 58–68, abr. 2016. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 13 Dec, 2024 Read the published version in Multibody System Dynamics → Version 1 posted Editorial decision: Revision requested 14 Oct, 2024 Reviews received at journal 14 Oct, 2024 Reviews received at journal 16 Sep, 2024 Reviewers agreed at journal 07 Sep, 2024 Reviewers agreed at journal 06 Sep, 2024 Reviewers invited by journal 04 Sep, 2024 Editor assigned by journal 02 Sep, 2024 Submission checks completed at journal 02 Sep, 2024 First submitted to journal 31 Aug, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5010781","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":357106245,"identity":"6144dff4-1d50-4c00-9562-35d10e7dc468","order_by":0,"name":"A. E. Dantas","email":"data:image/png;base64,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","orcid":"","institution":"Universidade Federal de Minas Gerais","correspondingAuthor":true,"prefix":"","firstName":"A.","middleName":"E.","lastName":"Dantas","suffix":""},{"id":357106246,"identity":"f4dcdd85-56af-464f-a6b1-4ab7190cbc5b","order_by":1,"name":"M. T.C. Faria","email":"","orcid":"","institution":"Universidade Federal de Minas Gerais","correspondingAuthor":false,"prefix":"","firstName":"M.","middleName":"T.C.","lastName":"Faria","suffix":""}],"badges":[],"createdAt":"2024-09-01 00:45:00","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5010781/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5010781/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11044-024-10045-x","type":"published","date":"2024-12-13T15:57:54+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":65868002,"identity":"3ea4c6c2-1535-48b5-b47b-e3bba92bfd1c","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2697365,"visible":true,"origin":"","legend":"\u003cp\u003eOff-highway truck multibody model.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/3df41dd9b05e650fab05531c.png"},{"id":65867627,"identity":"c509d9b7-29d6-47f4-a561-2717d63ad4be","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":245487,"visible":true,"origin":"","legend":"\u003cp\u003eCornering force estimated from PAC 2002 tyre model (FRIMPONG et al., 2012; KANG et al., 2015).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/594076e7cd67b1f2849e65b9.png"},{"id":65867628,"identity":"98b3e4ed-8c54-47df-97af-1f0b77cd5a0b","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2112973,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristic HPS curves – Nitrogen gas restoration force \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e of (a) front HPS (b) rear HPS; Dissipative oil damping force \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e of (c) front HPS (d) rear HPS;\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/a26a5cd47def9154bf2b9b8c.png"},{"id":65867999,"identity":"764d36b9-4964-4855-aa3b-06d7dc84eaf3","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":402377,"visible":true,"origin":"","legend":"\u003cp\u003e24.00R35 tyres estimated vertical force curve.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/ed7087d4290f50eabc1be6d4.png"},{"id":65868247,"identity":"272f155d-7962-4256-b0e5-0c4fa15a06d5","added_by":"auto","created_at":"2024-10-03 18:09:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":648478,"visible":true,"origin":"","legend":"\u003cp\u003eResultant road roughness.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/17ff5736704a625115c53e8a.png"},{"id":65868004,"identity":"692db21c-1513-41ac-bc34-06689bd8c252","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1966521,"visible":true,"origin":"","legend":"\u003cp\u003eInput road roughness (a) Comparison to input PSD function; (b) Coherence between left and right profiles.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/4d26ad3e01dbf0611937b42c.png"},{"id":65868000,"identity":"abbee7a0-8d43-47d0-a06b-cd4a899f26ed","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":3123243,"visible":true,"origin":"","legend":"\u003cp\u003eComparative values of experimental and numerical Nitrogen gas pressure: Front right HPS – FR (a) unloaded (b) loaded; Rear right HPS – RR (a) unloaded (b) loaded.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/0f05830921abea0123d09038.png"},{"id":65867642,"identity":"a3582163-386b-477e-afd9-99b5ea326c21","added_by":"auto","created_at":"2024-10-03 17:53:45","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":983851,"visible":true,"origin":"","legend":"\u003cp\u003eSteering wheel angle rate (δ\u003csub\u003estw\u003c/sub\u003e) at constant speed cornering. (a) Unloaded; (b) Loaded.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/95692d2033ff9564fc8bebfb.png"},{"id":65867629,"identity":"cca071c3-2e40-44da-aaeb-0bc33f0bd621","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":700299,"visible":true,"origin":"","legend":"\u003cp\u003eUndersteer gradient for different lateral acceleration. (a) Unloaded; (b) Loaded.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/5917e9dc3f0dd3866b0997b3.png"},{"id":65868491,"identity":"203fed02-6e37-47ee-9772-dfdfc6cf1cf7","added_by":"auto","created_at":"2024-10-03 18:17:44","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":990988,"visible":true,"origin":"","legend":"\u003cp\u003eSprung mass roll angle in DLC manoeuvre. (a) Unloaded; (b) Loaded.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/c518f55913f743e46e01a942.png"},{"id":65868003,"identity":"738ffd2f-e9be-4dbf-b29e-e364c6b6b995","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":1119263,"visible":true,"origin":"","legend":"\u003cp\u003eLateral load transfer ratio (LTR) in DLC manoeuvre. (a) Unloaded; (b) Loaded.\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/b9f3d9e8eaeda9c4f39a98be.png"},{"id":65867635,"identity":"e0af5881-237a-452d-a7da-e96a30e5071d","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":1019953,"visible":true,"origin":"","legend":"\u003cp\u003eRoot Mean Square (RMS) values of roll angle (φ) and LTR calculated for different initial gas volume of HPS. (a)(c) Unloaded; (b)(d) Loaded.\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/6c3126840461e0d2157af579.png"},{"id":65867640,"identity":"5548f837-6614-4556-b05e-8ec3a32bfc68","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1107229,"visible":true,"origin":"","legend":"\u003cp\u003eHistogram of the truck speed measured experimentally. (a) Unloaded; (b) Loaded.\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/59914c249df54868cd2e5b26.png"},{"id":65867638,"identity":"de772725-a272-459e-ad7f-e7e8dd850ac7","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":1114660,"visible":true,"origin":"","legend":"\u003cp\u003eVertical acceleration of the driver’s seat in straight-line constant speed manoeuvre. 1-(a) 10 km/h; 1-(b) 25 km/h; 1-(c) 38 km/h; 2-(a) 10 km/h; 2-(b) 20 km/h; 2-(c) 32 km/h.\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/a4a49813bcb642e480d487e2.png"},{"id":65867641,"identity":"742b73a8-6e0e-496e-b649-7b2e5ad2fcc7","added_by":"auto","created_at":"2024-10-03 17:53:44","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":1561504,"visible":true,"origin":"","legend":"\u003cp\u003eRoot Mean Square (RMS) values of driver’s seat vertical acceleration (a\u003csub\u003ecab.z\u003c/sub\u003e) calculated in different initial gas volume of HPS. 1-(a) 10 km/h; 1-(b) 25 km/h; 1-(c) 38 km/h; 2-(a) 10 km/h; 2-(b) 20 km/h; 2-(c) 32 km/h.\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/37abe624bbadf73d0266c1dd.png"},{"id":65868006,"identity":"51f7ea4a-a06a-45b5-a421-5a11ead76b62","added_by":"auto","created_at":"2024-10-03 18:01:44","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":554843,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element model with frame and dump body interaction. (a) Revolute pinned joint; (b) Hoist cylinder interaction with dump body and frame support; (c) Dump body cushion pad contact with the frame’s main beam.\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/bc85d717fe784caa557917bd.png"},{"id":65867644,"identity":"6979e807-eea2-4ef6-8cc4-e149d5c6e051","added_by":"auto","created_at":"2024-10-03 17:53:45","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":422991,"visible":true,"origin":"","legend":"\u003cp\u003eWelded joints selected to estimate fatigue life.\u003c/p\u003e","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/2d243182d49708a187d0084a.png"},{"id":65868007,"identity":"87b56836-40a7-44ca-b47a-68412d66f2b4","added_by":"auto","created_at":"2024-10-03 18:01:45","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":696190,"visible":true,"origin":"","legend":"\u003cp\u003eFatigue estimated life of welded joints of the (a) external and (b) internal side of the frame’s main beam.\u003c/p\u003e","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/5e204cd0f20a63f81b1d8cc1.png"},{"id":71552490,"identity":"bc216805-371a-4e9f-813b-c5ba3b1c16c4","added_by":"auto","created_at":"2024-12-16 16:06:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":22406802,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5010781/v1/30abebaf-ef06-475a-b7d3-fb7347a3b603.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Off-highway truck setup influence on vehicle dynamics and frame durability","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eOff-highway trucks have a crucial role in the mining process, being widely used in excavation areas due to their low investment cost and high adaptability to new mining spots. These areas are characterized by unpaved roads with significant irregularities, which can be attributed to unproper maintenance, constant route improvisation, and intensive truck traffic. Combining with their heavy load transportation capacity, these irregularities result in severe impact and overload conditions on tyres and suspensions. Consequently, it can generate health issues for drivers due to vibration levels transmitted to the cabin (comfort), premature mechanical component failures (durability) and reduced productivity, since drivers need to slow down on curves and in obstacles avoidance manoeuvres (handling).\u003c/p\u003e \u003cp\u003eMost papers concerning off-highway trucks focus primarily on driver\u0026rsquo;s comfort. It has been found that excessive levels of cabin vibration occurs when the truck is empty, descending grade or sliding on a wet and slippery road surface (MAYTON et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Mining haul trucks are typically equipped with hydropneumatic suspensions (HPS) which enhance wheel load distribution through their nonlinear stiffness characteristics. These suspensions use inert gas whose compression and expansion generate restoring forces in accordance with the ideal gas law. Energy dissipation is achieved via oil flow through orifice and check valves. Hien et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) conducted a parametric analysis using a 2- degree-of-freedom (DOF) lumped mass model, revealing that initial gas volume and pressure, along with valve diameter, significantly affect driver's comfort. They found that combining changes in initial gas volume and valve diameter resulted in the most effective reduction of vertical cabin acceleration. Using a 10 (DOF) lumped mass model, Long et al (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) demonstrated that vertical cabin acceleration can increase exponentially with worse ISO 8608:2016 class roads.\u003c/p\u003e \u003cp\u003eDurability of off-highway trucks has been studied by several authors interested on their component useful lifetime. However, most papers focus on tyre wear rate instead of structural components, such as the vehicle\u0026rsquo;s frame. Haul truck frames are typically manufactured by combining cast and welded steel parts. Welds are certainly the structure most critical regions regarding fatigue life due to the microstructure modification. Gady e Craig (1989) showed that events such as loaded vehicle cornering and loading/unloading operations significantly contribute to structural damage. Later, Prem (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) stated that road roughness is a determining factor on structural fatigue life. More recently, Savkin (2016) and Mi et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) employed multibody dynamics and finite element model validated by experimental data to estimate the frame\u0026rsquo;s peak stresses and welded parts fatigue life. Mi et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) multibody simulations were based on three different fully loaded working conditions: flat rough road, turning uphill and pothole road surface.\u003c/p\u003e \u003cp\u003eIt can be seen in the literature that most of the existing studies about truck handling dynamics concentrate on rolling and stability. Yin et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) found that the lateral acceleration Root Mean Square (RMS) during the sustained period of unity lateral-load-transfer-ratio (LTR) is an effective criterion for evaluating the rollover threshold. Kang et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) extended the analysis beyond roll dynamics by using a multibody model to determine the understeer gradients of a mining haul truck with four different suspension geometries, investigating their influence on driver\u0026rsquo;s handling experience. Both Kang et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and Loo (2003) noted that the these trucks tend to exhibit a very strong understeering behaviour.\u003c/p\u003e \u003cp\u003eCompared to on-road vehicles, the performance of off-road vehicles on curves has not received the same attention from researchers, likely due to their relatively low transportation speed. Consequently, studies on the influence of road roughness on on-road vehicle dynamics have become a valuable source of knowledge for mining haul truck research. Li et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) used different coherence functions applied to stochastic road profiles to demonstrate that higher lateral stability increases the risk of rollover, and that low coherence at low frequencies in left and right road profiles has a greater influence on rollover stability than on lateral stability. Cosme et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) conducted constant steering and double lane change manoeuvres using a multibody model with a flexible chassis of a heavy-duty articulated truck to investigate the influence of chassis stiffness on sprung mass roll angle. They found that frame flexibility can significantly increase the peak value of the roll angle.\u003c/p\u003e \u003cp\u003eMining companies often get vehicles with standardized setups from manufacturers, which may not be applicable for the specific operational conditions of a given site. To enhance the truck's ride comfort, handling, and durability, companies typically have two main options: (i) improve the haul road maintenance routine or (ii) perform field adjustments to vehicle parameters. The first option can be costly, particularly in tropical regions where extended rainy seasons need high-quality road materials and extensive drainage systems (TANNANT AND REGENSBURG, 2001). Conversely, defining new suspension setups is relatively straightforward and customizable.\u003c/p\u003e \u003cp\u003eWhile the technical literature of mining haul trucks includes some studies on the impact of hydropneumatic suspension on vehicle dynamics, the influence of tyre pressure is rarely explored. Thus, it is presented in this work a study of the influence of different suspension-tyre setups on the behaviour of a mining haul truck frame. The initial HPS gas volume and the tyre pressure were the parameters of interest, being varied in each setup to create stiffer and softer interaction with the road. These two parameters were chosen for their feasibility and ease of adjustment.\u003c/p\u003e \u003cp\u003eThe assessment of ride comfort, handling and chassis durability for each suspension setup was conducted using multibody and finite element models of a 64-ton capacity off-highway truck. Different manoeuvres were simulated with the multibody model, including constant speed turning (CST) and double lane change (DLC), to examine the impact of stiffness on the vehicle\u0026rsquo;s handling characteristics. Roll dynamics are significantly influenced by road roughness conditions (BOGSJ\u0026Ouml;, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; LI et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; YIN et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), thus the DLC manoeuvre was performed over a rough road surface. The evaluation of ride comfort and chassis durability was based on a straight-line constant speed manoeuvre (SLCS) using the same rough road profile as the DLC manoeuvre.\u003c/p\u003e"},{"header":"MULTIBODY MODEL","content":"\u003cp\u003eNumerical multibody analysis described in this paper comprise rigid and flexible parts. After defining mass, damping and stiffness properties of each body and establishing all joints constraint equations (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varOmega\\:\\)\u003c/span\u003e\u003c/span\u003e), the initial conditions of generalized coordinates \u003cem\u003eq\u003c/em\u003e are determined.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:q={\\left(x,y,z,\\phi\\:,\\theta\\:,\\psi\\:,{\\xi\\:}_{i}\\right)}^{T}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(Eq.\u0026nbsp;1)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eFrom Eq.\u0026nbsp;(1), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:x\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:y\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:z\\)\u003c/span\u003e\u003c/span\u003e represent the positions of the local coordinate systems relative to the global coordinate system, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\phi\\:\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\psi\\:\\)\u003c/span\u003e\u003c/span\u003e are the Euler angles of the local coordinate systems relative to the global coordinate system, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\xi\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the modal displacement of a flexible body corresponding to mode \u003cem\u003ei\u003c/em\u003e. The equations of motion (EOMs) of the system are then derived based on Euler-Lagrange mechanics. Their general form applied to flexible multibody dynamics is presented in Eq.\u0026nbsp;(2).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:M\\ddot{q}+\\dot{M\\dot{q}}-\\frac{1}{2}{\\left(\\frac{\\partial\\:M}{\\partial\\:q}\\dot{q}\\right)}^{T}\\dot{q}+Kq+{f}_{g}+C\\dot{q}+{\\left(\\frac{\\partial\\:{\\Omega\\:}}{\\partial\\:q}\\right)}^{T}{\\lambda\\:}_{Lag.}=Q\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(Eq.\u0026nbsp;2)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eThe first term accounts for the inertial effects, while the second and third terms predict the changes in the mass matrices as a function of time and generalized coordinates. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Kq\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:C\\dot{q}\\)\u003c/span\u003e\u003c/span\u003e represent the stiffness restoring forces and damping dissipative forces, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{g}\\)\u003c/span\u003e\u003c/span\u003e represents the gravitational forces, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\left(\\frac{\\partial\\:{\\Omega\\:}}{\\partial\\:q}\\right)}^{T}{\\lambda\\:}_{Lag.}\\)\u003c/span\u003e\u003c/span\u003e represents the constraint forces imposed by joints and restrictions. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\)\u003c/span\u003e\u003c/span\u003e includes the applied external forces.\u003c/p\u003e \u003cp\u003eIn general, the EOMs derived from Eq.\u0026nbsp;(2) can be classified as either stiff or non-stiff. Stiff problems are essentially those associated with systems that exhibit both low and high-frequency excitations and responses simultaneously. This is the case, for example, of vehicle systems evaluated in terms of ride comfort, as road roughness cover a wide frequency spectrum. When combined with low-frequency inputs such as steering and acceleration, these irregularities can excite both low and high-frequency vibration modes of the vehicle. The solution of stiff dynamic problems typically requires the use of implicit integrators due to their unconditional stability, which allows solving problems with a high degree of nonlinearity without the need for excessively small-time step increments.\u003c/p\u003e \u003cp\u003eTo solve the multibody dynamic equations this paper uses the variable-order and variable-step integration algorithm GSTIFF-I3 (Generalized STIFF Integration Method – Index 3), implemented in ADAMS/Solver®. This algorithm utilizes information from multiple previous time steps (multi-steps) rather than relying only on the current or most recent state. An integration error tolerance of 0.1 is assigned and the maximum time step is defined as 0.01s.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eVehicle characteristics\u003c/h2\u003e \u003cp\u003eThe full vehicle multibody model is a representation of a CAT 775G truck. This model is built using the ADAMS Car platform and consists of 94 free degrees of freedom (DOFs). This includes the frame, modelled as a flexible component with 10 vibration modes. The front wheels are connected to the chassis via an independent sliding pillar hidropneumatic suspension system. At the rear axle, the wheels are interconnected by a rigid axle, which is attached to the chassis through trailing arms, Panhard rod and hydropneumatic suspensions. Unlike the flexible frame, dump body and payload work as a single component rigidly fixed to each other. Their inertial load is transferred to the chassis through revolute joints and hoist cylinders. The model main parts are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Resulting mass and inertia properties are shown in\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeometric and inertial properties for the multibody model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnloaded\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLoaded\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWheelbase – \u003cem\u003eL\u003c/em\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFront track width – \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e3.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRear track width – \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e2.15\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMass distribution (front : rear)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50:50\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e34:66\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVehicle mass – \u003cem\u003em\u003c/em\u003e (t)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e48.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e112.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCG height – \u003cem\u003eh\u003c/em\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.72\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.35\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal vehicle roll inertia – \u003cem\u003eIφ\u003c/em\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e106.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e251.7\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal vehicle pitch inertia – \u003cem\u003eIθ\u003c/em\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e264.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e498.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal vehicle yaw inertia – \u003cem\u003eIψ\u003c/em\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e328.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e608.3\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass distribution (front : rear)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e66:34\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40:60\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass – \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (t)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e32.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e96.0\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass CG height – \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.05\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.57\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass roll inertia – \u003cem\u003eIφ\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e69.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e192.1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass pitch inertia – \u003cem\u003eIθ\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e180.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e407.5\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSprung mass yaw inertia – \u003cem\u003eIψ\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e (t.m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e229.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e525.0\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFront axle unsprung mass – \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e (t)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e4.6\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFront axle unsprung mass CG height – \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1.04\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRear axle unsprung mass – \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e (t)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e11.6\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRear axle unsprung mass CG height – \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e (m)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1.06\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eFlexible body frame\u003c/h2\u003e \u003cp\u003eA finite element (FE) model of the truck frame is developed by using tetrahedral solid elements. The discrete model leads to the eigenvalue problem that permits to obtain the frame free vibration modes. Incorporating all DOFs from this model to the multibody analysis would be extremely high demanding, thus applying model dynamic reduction through component mode synthesis (CMS) techniques can be very helpful.\u003c/p\u003e \u003cp\u003eThis is achieved by the Craig-Bampton technique, which effectively represents rigid body modes through a linear combination of static deformations. This method comprises internal DOFs (\u003cem\u003ea\u003c/em\u003e) and interface DOFs (\u003cem\u003eb\u003c/em\u003e) that are connected to the multibody model parts. The reduction process involves calculating the normal mode matrix of the \u003cem\u003em\u003c/em\u003e modes defined by the user with the \u003cem\u003eb\u003c/em\u003e DOFs restrained (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Phi\\:}}_{a\\times\\:m}\\)\u003c/span\u003e\u003c/span\u003e). It also calculates the static modes matrix (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{a\\times\\:b}\\)\u003c/span\u003e\u003c/span\u003e) by applying unit displacements to \u003cem\u003eb\u003c/em\u003e DOFs individually while restraining internal \u003cem\u003ea\u003c/em\u003e DOFs.\u003c/p\u003e \u003cp\u003eThe Craig-Bampton reduction matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{fj}\\)\u003c/span\u003e\u003c/span\u003e is defined as\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{f}={T}_{fj}{u}_{j}\\:\\to\\:\\left\\{\\begin{array}{c}{u}_{a}\\\\\\:{u}_{b}\\end{array}\\right\\}=\\:\\left[\\begin{array}{cc}{{\\Phi\\:}}_{a\\times\\:m}\u0026amp;\\:{G}_{a\\times\\:b}\\\\\\:{0}_{a\\times\\:m}\u0026amp;\\:{I}_{a\\times\\:a}\\end{array}\\right]\\left\\{\\begin{array}{c}{\\eta\\:}_{m}\\\\\\:{u}_{b}\\end{array}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(3)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{f}\\)\u003c/span\u003e\u003c/span\u003e is the displacement vector of internal (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{a}\\)\u003c/span\u003e\u003c/span\u003e) and interface DOFs (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{u}_{b}\\)\u003c/span\u003e\u003c/span\u003e) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\eta\\:}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the modal participation vector reduced to the predefined \u003cem\u003em\u003c/em\u003e modes. From Eq.\u0026nbsp;3.5 an eigensolution is performed to fully describe the reduced system in terms of modal coordinates. The resulting data, such as the interface nodes' positions and generalized mass and stiffness matrices, are then exported to a Modal Neutral File (MNF) compatible with ADAMS Car®.\u003c/p\u003e \u003cp\u003eFor simplification, the flexible frame is considered in the multibody analysis by including only the first 10 reduced system modes. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, all major vehicle movements, such as torsion and bending, are captured in these first 10 modes. These modes natural frequencies calculated by the full finite element and the reduced dynamic models are also presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Reduced model showed that it can represent the full structure dynamics through with a very good agreement with full finite element model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative values of natural frequencies for the truck frame.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eID\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMode description\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFE\u003c/p\u003e \u003cp\u003e(Hz)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCMS (Hz)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1st Torsional\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e23.9\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1st Lateral bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.2\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1st Vertical bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e31.5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e31.5\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2nd Lateral bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.4\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2nd Torsional\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e48.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e48.1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3rd Torsional\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e54.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e54.1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3rd Lateral bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e67.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e67.3\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2nd Vertical bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e69.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e69.7\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4th Lateral bending\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e74.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e74.8\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4th Torsional\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e77.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e77.4\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eHPS equations\u003c/h2\u003e \u003cp\u003eAs defined by Bauer (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) the hydropneumatic suspension (HPS) forces combine gas elastic restoration force (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e) and viscous damping force resultant from oil flow through valves (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e). From the ideal gas law, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e is mathematically expressed as:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{g}={P}_{0}{\\left(\\frac{{V}_{0}}{V}\\right)}^{r}{A}_{h}={P}_{0}\\left[{\\left(\\frac{{V}_{0}}{{V}_{0}\\:+\\:{A}_{h}\\:({z}_{b}-{z}_{a})}\\right)}^{r}-1\\right]{A}_{h}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(4)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e are the initial pressure and volume of the gas when the rod is extended (the nominal values are denoted as \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0N\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0N\u003c/em\u003e\u003c/sub\u003e in this work), \u003cem\u003er\u003c/em\u003e is the polytropic coefficient, \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e is the cross-sectional area of the rod, and \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e are the longitudinal positions of the rod at instants \u003cem\u003ea\u003c/em\u003e and \u003cem\u003eb\u003c/em\u003e. HPSs tend to behave as an adiabatic system under high-frequency excitations (\u003cem\u003er\u003c/em\u003e ≈ 1.40) and can approximate the isothermal regime at low frequencies (\u003cem\u003er\u003c/em\u003e ≈ 1.00). Given that road roughness imposes mainly high-frequency excitations, a polytropic coefficient of 1.40 was estimated.\u003c/p\u003e \u003cp\u003eA widely used equation to relate the pressure drop (\u003cem\u003e∆P\u003c/em\u003e) with the fluid flow rate through resistors (\u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e) is given in Eq.\u0026nbsp;(5). In this equation, \u003cem\u003eρ\u003c/em\u003e denotes the mass density of the oil, \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e is the area of the resistor, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e its discharge coefficient (BAUER, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:P}_{res}=\\frac{\\rho\\:\\:{{Q}_{res}}^{2}}{2\\:{\\left({C}_{d}{A}_{r}\\right)}^{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(5)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eThe orifice and check valves of a HPS connect the same chambers of the system, and thus experience the same pressure drop. Applying Eq.\u0026nbsp;(5) to a HPS, where these valves act as the resistors, leads to:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{h}=\\frac{\\rho\\:{A}_{c}}{2}{\\left(\\frac{\\dot{x}{A}_{c}}{{n}_{dv}{\\alpha\\:}_{dv}{A}_{dv}+{n}_{cv}{\\alpha\\:}_{cv}{A}_{cv}}\\right)}^{2}\\text{s}\\text{i}\\text{g}\\text{n}\\left(\\dot{x}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(6)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eẋ\u003c/em\u003e is the rod compression/extension velocity, \u003cem\u003eA\u003c/em\u003e is the oil chamber area, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecv\u003c/em\u003e\u003c/sub\u003e are the quantities of orifice and check valves, \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003ecv\u003c/em\u003e\u003c/sub\u003e their discharge coefficient and \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003ecv\u003c/em\u003e\u003c/sub\u003e their cross-sectional area. The signal function in terms of rod velocity is 1 during compression and − 1 during extension. It is also important to note that check valves are unidirectional and do not allow oil flow during rod extension, meaning \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecv\u003c/em\u003e\u003c/sub\u003e must be assumed as null when sign (ẋ) = -1. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows values employed to calculate the hydropneumatic restoration and dissipative forces, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters used in the HPS force calculation.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFront\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRear\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNominal initial gas volume – \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0N\u003c/em\u003e\u003c/sub\u003e (l)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.19\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNominal initial gas pressure – \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0N\u003c/em\u003e\u003c/sub\u003e (kPa)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2600\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1800\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRod cross-section area – \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e (m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.025\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.025\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOil chamber cross-section area – \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e (m²)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0077\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of orifice valves – \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDischarge coefficient of orifice valves – \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOrifice valves diameter – \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e (mm)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of orifice valves – \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDischarge coefficient of orifice valves – \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOrifice valves diameter – \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003edv\u003c/em\u003e\u003c/sub\u003e (mm)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.9\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOil density – \u003cem\u003eρ\u003c/em\u003e (kg/m³)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eTyre model\u003c/h2\u003e \u003cp\u003eThe off-highway truck is equipped with 24.00R35 tyres represented in the multibody model by PAC 2002 semi-empirical model with 3D enveloping contact. Cornering characteristics of large tyres are not usually available due to their size and load capacity. Thus, cornering stiffness is estimated using procedures encountered in the technical literature (FRIMPONG et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; KANG et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows cornering force in terms of slip-angle estimated for three different vertical loads. \u003cem\u003eFz\u003c/em\u003e = 117 kN and \u003cem\u003eFz\u003c/em\u003e = 58 kN are the nominal normal load on front and rear tyres in unloaded truck, respectively. In loaded condition, all tyres have 185 kN of normal force equally. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e provides the tyres main parameters.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMain tyre characteristics (FRIMPONG et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; KANG et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNominal radius\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1082 mm\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatic radius\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e975,4 mm\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTread width\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e665,5 mm\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNominal rated load\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e210,9 kN\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNominal inflation pressure – TP\u003csub\u003eN\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e724,0 kPa\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCornering stiffness (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e = 58 kN)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e~ 11 kN/°\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCornering stiffness (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e = 117 kN)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e~ 21 kN/°\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCornering stiffness (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e = 185 kN)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e~ 32 kN/°\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDamping coefficient\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e470 Ns/m\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eTyres vertical stiffness is significantly affected by their inflation pressure. Prem \u0026amp; Dickerson (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1992\u003c/span\u003e) established a polynomial regression relationship for vertical load versus deflection for different tyres manufacturers and various sizes. This equation is also employed in this work to estimate the 24.00R35 tyre normal force.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eSuspension-tyres setup\u003c/h2\u003e \u003cp\u003eTo simulate the manoeuvres described in this paper, seven total suspension-tyre setups are defined by varying HPS initial gas volume (\u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e) and tyres inflation pressure (\u003cem\u003eTP\u003c/em\u003e). The former can be simply adjusted by managing gas/oil ratio in the main suspension chamber. Maximum variation of ± 15% of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0N\u003c/em\u003e\u003c/sub\u003e is selected since very low oil volume may cause component overheating. Similarly, tyres inflation pressure is defined in a range of ± 10% to avoid excessive tyre wear during loaded transportation. Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e summarizes the selected parameters for each setup identified from A to G. In this table, the percentages correspond to the differences relative to nominal suspension parameters. Setup A considers less initial gas volume combined with more tyre inflation pressure providing the stiffest adjustment whereas setup G consists in the softest one. Setup D only comprises nominal values of \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eTP\u003c/em\u003e. Subscripts \u003cem\u003eu\u003c/em\u003e and \u003cem\u003el\u003c/em\u003e are added in setups ID to unloaded and loaded conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInitial gas volume and tyre inflation for each setup.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSetup ID\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eE\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eG\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFront HPS initial gas volume – \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0F\u003c/em\u003e\u003c/sub\u003e (l)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.67\u003c/p\u003e \u003cp\u003e(-10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.67\u003c/p\u003e \u003cp\u003e(-10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.19\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.19\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.19\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.71\u003c/p\u003e \u003cp\u003e(+ 10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.71\u003c/p\u003e \u003cp\u003e(+ 10%)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRear HPS initial gas volume – \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0R\u003c/em\u003e\u003c/sub\u003e (l)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.64\u003c/p\u003e \u003cp\u003e(-15%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.64\u003c/p\u003e \u003cp\u003e(-15%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.11\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.57\u003c/p\u003e \u003cp\u003e(+ 15%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.57\u003c/p\u003e \u003cp\u003e(+ 15%)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTyre inflation pressure – \u003cem\u003eTP\u003c/em\u003e (kPa)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e796.4\u003c/p\u003e \u003cp\u003e(+ 10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e724\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e796.4\u003c/p\u003e \u003cp\u003e(+ 10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e724\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e651.6\u003c/p\u003e \u003cp\u003e(-10%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e724\u003c/p\u003e \u003cp\u003e(-%)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e651.6\u003c/p\u003e \u003cp\u003e(-10%)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows suspension curves obtained through Eq.\u0026nbsp;(4) and Eq.\u0026nbsp;(6). Gas restoration forces (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e) in terms of rod’s displacement are presented for each \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e considered in setups A to G. By applying polynomial regression described by Prem \u0026amp; Dickerson (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1992\u003c/span\u003e), Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e exhibits tyre stiffness curves for the inflation pressures of setups A to G.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eRoad profile and validation\u003c/h2\u003e \u003cp\u003eFor the dynamic analysis of off-road vehicles, the road roughness is represented as an undeformable stochastic profile describe by Power Spectrum Density (PSD) functions. Similar to ISO 8608:2016, Sayers (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1988\u003c/span\u003e) describes Eq.\u0026nbsp;(7) to build PSD functions of rough terrains, including additional high and low wavenumbers contributions through \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e variables, respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{d}\\left({\\nu\\:}\\right)={G}_{e}+\\frac{{G}_{s}}{{\\left(2\\pi\\:\\nu\\:\\right)}^{2}}+\\frac{{G}_{a}}{{\\left(2\\pi\\:\\nu\\:\\right)}^{4}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(7)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eThe road profiles are generated by ADAMS Car by combining gaussian random signals with values of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e equal to 1,0E-6 m³/cycle, 5,0E-4 m/cycle e 0 m\u003csup\u003e-1\u003c/sup\u003ecycle\u003csup\u003e-1\u003c/sup\u003e, respectively, corresponding to an ISO 8608:2016 class D road. The resulting left and right road profiles over a 300 m length are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Their resultant PSDs and coherence are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The average coherence obtained between wavenumbers of 10\u003csup\u003e− 1\u003c/sup\u003e to 10\u003csup\u003e1\u003c/sup\u003e m\u003csup\u003e-1\u003c/sup\u003e is approximately 0.18.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOff-highway trucks are usually equipped with monitoring systems that provide instantaneous performance data of the vehicle speed, suspension pressure and payload. To validate the selected values of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e, experimental data of the suspension pressure of five trucks CAT 775G is collected under loaded and unloaded conditions at 20 ± 1 km/h travelling speed. These experimental data are compared with numerical values rendered by the multibody model with nominal setup D obtained during a straight-line manoeuvre at constant speed of 20 km/h. Comparison of experimental and computational data are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e for right side front and rear suspensions in both payload conditions (0-ton and 64-ton). RMS values showed a very good agreement for each suspension, indicating that the mining site of the studied vehicle is indeed very close to an ISO 8608:2016 class D road.\u003c/p\u003e\n\n\u003c/div\u003e"},{"header":"HANDLING ASSESSMENT","content":"\u003ch2\u003eConstant speed cornering\u003c/h2\u003e\u003cp\u003eBased on the steady-state cornering manoeuvres in ISO 4138:2021, the constant speed can be the most representative of the actual behaviour of a vehicle in a turn, since drivers usually maintain a near constant speed when cornering. To assess the response of each setup at this condition, the multibody model maintains a constant controlled speed of 25 km/h with an increasing steering wheel angle input sufficient to provide a lateral acceleration rate of 0.01 g/s. The manoeuvre ends when the vehicle can not generate additional lateral acceleration.\u003c/p\u003e\u003cp\u003eResulting steering wheel angle rate (\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003estw\u003c/em\u003e\u003c/sub\u003e) for each suspension setup is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. Unloaded vehicle does not indicate significant difference of response. However, loaded vehicle presents a slightly better handling response for stiffer suspensions. Setups A and B need almost 7% less steering angle to reach the same lateral acceleration in relation to the angle attained for softer setups F and G.\u003c/p\u003e\u003cp\u003eUndersteer gradient (\u003cem\u003eK\u003c/em\u003e), calculated as the derivative of the difference between the front and rear slip angles \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\alpha\\:}_{f-}{\\alpha\\:}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003e with respect to lateral acceleration (Eq.\u0026nbsp;8)), is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e for each setup.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabh\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:K=\\:\\frac{{\\Delta\\:}\\left({\\alpha\\:}_{f}-{\\alpha\\:}_{r}\\right)}{{\\Delta\\:}\\:{a}_{y}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(8)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eSimilar to steering wheel angle rate, no significant difference in the understeer gradient has been observed for each setup at unloaded condition. The vehicle with no payload exhibits understeer behaviour (K \u0026gt; 0) within a lateral acceleration range of 0 \u0026lt; \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e ≤ 0.3 g.\u003c/p\u003e\u003cp\u003eAt loaded condition, oversteering (\u003cem\u003eK\u003c/em\u003e \u0026lt; 0) can be found for small values of lateral acceleration (\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e ≤ 0.15 g) due to the mass centre offset towards the rear axle. However, understeer becomes predominant within the range of 0.15 \u0026lt; \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e ≤ 0.25 g. Within this range, significant differences of 𝐾 values are observed for each suspension setup, with stiffer suspensions resulting in higher understeering. Compared to setup G, setup A could reach an understeer gradient twice larger.\u003c/p\u003e\u003cp\u003eAt both loading conditions the driver controller attempts to input an increasing throttle value when the maximum steering angle is reached in order to recover the 25 km/h speed that is slightly reduced during the manoeuvre. Hence, strong oversteering behaviour occurs due to the increased torque on the rear axle causing tyre slippage. This event occurs at \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e = 0.35 g for the unloaded condition and at \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e = 0.30 g for the loaded vehicle.\u003c/p\u003e\u003ch2\u003eDouble lane change manoeuvre\u003c/h2\u003e\u003cp\u003eIn order to assess the vehicle transient handling behaviour, a double lane change manoeuvre according to ISO 3888-1:2018 is performed by the multibody model. This manoeuvre is simulated at a speed of 35 km/h, which is very usual for the trucks analysed in this work. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the roll angle estimated for rough terrain for loaded and unloaded vehicle conditions. Only setups A, D and G have the curves depicted for better visualization.\u003c/p\u003e\u003cp\u003eOn Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, it is shown that setups A\u003csub\u003eu\u003c/sub\u003e, D\u003csub\u003eu\u003c/sub\u003e and G\u003csub\u003eu\u003c/sub\u003e present slightly different peak values of roll angle, whereas setups A\u003csub\u003el\u003c/sub\u003e, D\u003csub\u003el\u003c/sub\u003e and G\u003csub\u003el\u003c/sub\u003e show larger differences for those angles. Compared to nominal setup D\u003csub\u003el\u003c/sub\u003e, G\u003csub\u003el\u003c/sub\u003e achieves a maximum peak value 20% higher.\u003c/p\u003e\u003cp\u003eRollover stability is evaluated by the Lateral Load Transfer Ratio (LTR) defined by Eq.\u0026nbsp;(9). Unit value of LTR reflects a vehicle at a rollover threshold, since it designates that internal wheels lose soil contact.\u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabi\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:LTR=\\:\\frac{\\left({F}_{zFL}+{F}_{zROL}+{F}_{zRIL}\\right)-({F}_{zFR}+{F}_{zROR}+{F}_{zRIR})}{{F}_{zFL}+{F}_{zROL}+{F}_{zRIL}+{F}_{zFR}+{F}_{zROR}+{F}_{zRIR}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEq.\u0026nbsp;(9)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e\u003cp\u003eOnly the curves of LTR versus time for setups A, D and G are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e. Although it is not shown in this figure, LTR reaches 1.0 at 15s of manoeuvre time for setups E, F and G at loaded condition. Noteworthy to say that this condition likely does not last for enough time to produce vehicle rollover.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the RMS values of roll angle and LTR for each setup in terms of front and rear suspension initial gas volume. Setups A\u003csub\u003eu\u003c/sub\u003e and B\u003csub\u003eu\u003c/sub\u003e show nearly 5% reduction in the RMS value of the roll angle in comparison to the nominal setup D\u003csub\u003eu\u003c/sub\u003e, while setups F\u003csub\u003eu\u003c/sub\u003e and G\u003csub\u003eu\u003c/sub\u003e exhibit an increase of approximately 10%. The stiffness of the suspension-tyre system has a significant impact on the roll response, especially when the truck is loaded, since it presents an almost linear relationship with the RMS value of the roll angle. The stiffest (A\u003csub\u003el\u003c/sub\u003e) and softest (G\u003csub\u003el\u003c/sub\u003e) suspensions present approximately ± 20% of variation on the RMS values of the roll angle.\u003c/p\u003e\u003cp\u003eRegarding LTR, the trends differ notably between unloaded and loaded conditions. When unloaded, the RMS values of LTR follow the expected behaviour, since stiffer configurations (A\u003csub\u003eu\u003c/sub\u003e and B\u003csub\u003eu\u003c/sub\u003e) result in higher value of LTR due to increased load transfer. However, at loaded condition, the roll of the sprung masses becomes a dominant factor, potentially reversing that behaviour. Therefore suspensions with higher stiffness (A\u003csub\u003el\u003c/sub\u003e and B\u003csub\u003el\u003c/sub\u003e) exhibit lower LTR, due to the increased influence of roll in the vehicle dynamics when loaded.\u003c/p\u003e"},{"header":"STRAIGHT-LINE CONSTANT SPEED (SLCS)","content":"\u003ch2\u003eRide comfort assessment\u003c/h2\u003e\u003cp\u003eExperimental data of truck speed are grouped into ranges of 0.5 km/h and separated into unloaded and loaded conditions. The resulting data are used to generate the histograms shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, where a total distance travelled is depicted for each range of vehicle speed. Dashed lines in both histograms divide the data into three speed classes: low, intermediate, and high. These classes are used as reference to establish vehicle speed to be controlled in SLCS manoeuvre. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the vertical acceleration at the driver’s seat position for setups A, D and G obtained at each speed class weighted average.\u003c/p\u003e\u003cp\u003eRMS values of the seat’s vertical acceleration are estimated and used as a parameter to assess the vehicle ride comfort. The resultant values for each setup are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e. Soft setups F and G generate a reduction about 10% in the RMS values of acceleration at intermediate and high speeds for both loaded and unloaded conditions. It can also be highlighted that the RMS values of acceleration obtained at intermediate and high speeds for every setup can be considered very uncomfortable according to ISO 2631:1997. Therefore, reducing the vertical acceleration of the vehicle driver’s seat is extremely desirable.\u003c/p\u003e\u003ch2\u003eFrame durability\u003c/h2\u003e\u003cp\u003eSuspension forces calculated at each speed class is then exported to a chassis finite element model, which accounts for the interaction between the dump body and the main frame (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e). Using inertia relief tool available on the package FEMAP/NASTRAN, the model requires no constraints. The numerical procedure reaches a condition of equilibrium by applying inertial acceleration to each finite element, resulting in a toral force of zero. Thus, for every local and minimum suspension force, this quasi-static analysis is conducted to calculate frame’s global displacements.\u003c/p\u003e\u003cp\u003eIn a different analysis performed using the finite element model, dumping and loading events are also evaluated. The effects of different vehicles setups are negligible at those events and the suspension-frame joints can have the translational degrees of freedom (DOFs) constrained. The dumping force primarily consists of the necessary force exerted by the hoist cylinder to lift the fully loaded dump body. Loading impact forces are estimated based on the linear momentum variation presented in Eq.\u0026nbsp;(10), with corresponding parameter values shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Experimental data provide the average number of shovel operations per loading process and the amount of material per shovel operation. The impulse duration is estimated as 1.28 seconds, according to Ali \u0026amp; Frimpong (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003ctable id=\"Tab6\" border=\"1\"\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{i}=\\:\\frac{\\sqrt{2g{H}_{t}}{m}_{i}}{ϵ}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003eEq.\u0026nbsp;(10)\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003cdiv\u003eTable 6 Parameters used for the loading forces computation.\u0026nbsp;\u003c/div\u003e\u003ctable id=\"Tabj\" border=\"1\"\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eShovel operation\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial dumped – \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e(ton)\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eImpact force – F\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e\n \u003cp\u003e(kN)\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eTotal force – F\u003csub\u003et\u003c/sub\u003e (kN)\u003c/p\u003e\n \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e1st\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e19.7\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e10.7\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e204.0\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e2nd\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e11.3\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e5.7\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e116.6\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e3rd\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e9.9\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e4.6\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e101.7\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e4th\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e7.2\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e3.1\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e73.7\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e5th\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e6.5\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e66.3\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e6th\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e6.2\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e62.8\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e7th\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e3.3\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.9\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e33.3\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003cp\u003eTwo welded joints are selected to assess fatigue life due to their high stress range. For better stress estimation, local model of these regions with refined mesh are developed, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e17\u003c/span\u003e. Displacements calculated by the global finite element model are then applied to those local models. Maximum principal stresses are used to build stress spectra based on the six speed classes at the loading and dumping events. These spectra are extrapolated using experimental total time of each speed class.\u003c/p\u003e\u003cp\u003eRainflow counting grouped the tress cycle spectrum into 1 MPa stress ranges. Using Palmgren-miner cumulative damage theory and the S-N curve for butt-welded joints with axial stresses from IIW (HOBBACHER, \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e), the total damage can be estimated of each welded joint for each suspension setup. Results show that traveling of the loaded vehicle under intermediate and high speeds contribute to 60 until 70% of total weld damage. Combined dumping and loading events represent 18 to 32% of the total damage depending on the suspension setup.\u003c/p\u003e\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e18\u003c/span\u003e illustrates the estimated life in years based on the damage results. It can be observed that stiffer suspension setups (A and B) may reduce welded joints life in almost 40%. Soft setups (F and G) could considerably improve the welds life by 25%.\u003c/p\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eAn analysis of the influence of the tyre inflation pressure and of the initial gas volume of the hydropneumatic suspension (HPS) on the handling, ride comfort, and frame\u0026acute;s durability of an off-highway mining truck is performed by employing a numerical procedure based on the multibody dynamics and finite element method. Some remarks can be drawn from this analysis:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eStiffness setups showed insignificant influence on steady-state cornering in unloaded condition. However, when the vehicle was loaded, stiffer setups demonstrated a slightly better capacity for generating lateral acceleration and a significantly increased understeer behaviour at lateral acceleration values above 0.15 g. Below 0.15 g, the driver may not perceive a noticeable difference in handling experience.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTransient cornering assessed through a double lane change manoeuvre showed that enhanced/reduced stiffness setups can largely decrease/increase body roll angle especially in loaded condition. According to Uys et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), this can be a very solid indicator of handling performance. Rollover stability was not significantly influenced overall. Lateral Load Transfer Ratio (LTR) Root Mean Square (RMS) was very similar in every setup.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eA moderate influence in ride comfort was revealed for intermediate and high traveling speeds. Least rigid setup could improve driver\u0026rsquo;s Root Mean Square (RMS) vertical acceleration in almost 10% compared to nominal setup. However, this reduction is not sufficient to fit the vehicle in a comfortable range according to ISO 2631:1997.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSignificant influence on frame durability was found. Both welded joints showed a very large increase in fatigue life when the softest setup was considered.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe results rendered in this work indicate that it will be worthwhile to perform experimental tests on field with different suspension setups and tyre pressures to confirm some of the findings described in this analysis.\u003c/p\u003e \u003cp\u003eIt should be highlighted that the softest setup may be very costly due to increased tyre wear with less inflation pressure. Thus, setup with nominal tyre inflation pressure and higher initial HPS gas volume, providing the second softest setup, can be the most promising adjustment, particularly if the mining road does not induce lateral accelerations exceeding 0.15 g\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThis work is part of A.E. master thesis under the supervision of professor M.T.C. A.E. wrote the manuscript and M.T.C reviewed and provided additional input.\u003c/p\u003e\u003cp\u003eACKNOWLEDGEMENTS\u003c/p\u003e\n\u003cp\u003eThis work has been supported by a research project financed by Vale SA. Financial support by \u0026ldquo;Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior - Brasil (CAPES) - Finance Code 001\u0026rdquo; is also acknowledged.\u0026nbsp;\u003cbr\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eALI, D.; FRIMPONG, S. Impulse force reductions and their effects on WBV exposures in high impact shovel loading operations. \u003cstrong\u003eInternational Journal of Mining Science and Technology\u003c/strong\u003e, v. 28, n. 3, p. 423\u0026ndash;435, maio 2018. \u003c/li\u003e\n\u003cli\u003eBAUER, W. Spring and Damping Characteristics of Hydropneumatic Suspension Systems. Em: BAUER, W. (Ed.). \u003cstrong\u003eHydropneumatic Suspension Systems\u003c/strong\u003e. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. p. 19\u0026ndash;66. \u003c/li\u003e\n\u003cli\u003eBOGSJ\u0026Ouml;, K. 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The NEOCON strut: A major breakthrough in suspension technology. \u003cstrong\u003eOff-Highway Haulage in Surface Mines\u003c/strong\u003e, Proceedings Of The International Symposium On Off-Highway Haulage in Surface Mines. maio 1989. \u003c/li\u003e\n\u003cli\u003eHIEN, V. T. et al. EFFECT ANALYSIS OF THE PARAMETERS OF HYDRO-PNEUMATIC SUSPENSION SYSTEM ON VEHICLE RIDE COMFORT. \u003cstrong\u003eInternational Journal of Advanced Research in Engineering and Technology\u003c/strong\u003e, v. 12, n. 1, p. 422\u0026ndash;430, 2021. \u003c/li\u003e\n\u003cli\u003eHOBBACHER, A. F. \u003cstrong\u003eRecommendations for Fatigue Design of Welded Joints and Components\u003c/strong\u003e. Villepinte, FranceSpringer International Publishing, , 2016. \u003c/li\u003e\n\u003cli\u003eKANG, Y.; ZHANG, W.; RAKHEJA, S. Relative kinematic and handling performance analyses of independent axle suspensions for a heavy-duty mining truck. \u003cstrong\u003eInternational Journal of Heavy Vehicle Systems\u003c/strong\u003e, v. 22, n. 2, p. 114, 2015. \u003c/li\u003e\n\u003cli\u003eLI, Y. et al. Effect of vertical and lateral coupling between tyre and road on vehicle rollover. \u003cstrong\u003eVehicle System Dynamics\u003c/strong\u003e, v. 51, n. 8, p. 1216\u0026ndash;1241, ago. 2013. \u003c/li\u003e\n\u003cli\u003eLONG, L. X. et al. Effect of operating conditions on a heavy truck ride comfort with hydro-pneumatic suspension system. \u003cstrong\u003eE3S Web of Conferences\u003c/strong\u003e, v. 304, p. 02011, 2021. \u003c/li\u003e\n\u003cli\u003eMAYTON, A. G. et al. Investigation of human body vibration exposures on haul trucks operating at U.S. surface mines/quarries relative to haul truck activity. \u003cstrong\u003eInternational Journal of Industrial Ergonomics\u003c/strong\u003e, v. 64, p. 188\u0026ndash;198, mar. 2018. \u003c/li\u003e\n\u003cli\u003eMI, C. et al. An energy-based fatigue life estimation and optimization of an electric mining dump truck welded frame. \u003cstrong\u003eJournal of the Brazilian Society of Mechanical Sciences and Engineering\u003c/strong\u003e, v. 45, n. 2, p. 117, fev. 2023. \u003c/li\u003e\n\u003cli\u003ePREM, H. \u003cstrong\u003eOff-Highway Mine Haul Truck Dynamics Simulation\u003c/strong\u003e. . Em: INTERNATIONAL OFF-HIGHWAY \u0026amp; POWERPLANT CONGRESS \u0026amp; EXPOSITION. 14 set. 1998. Dispon\u0026iacute;vel em: \u0026lt;https://www.sae.org/content/981982/\u0026gt;. Acesso em: 12 mar. 2024\u003c/li\u003e\n\u003cli\u003ePREM, H.; DICKERSON, A. 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Criteria for handling measurement. \u003cstrong\u003eJournal of Terramechanics\u003c/strong\u003e, v. 43, n. 1, p. 43\u0026ndash;67, jan. 2006. \u003c/li\u003e\n\u003cli\u003eVAN DE LOO, P. The Development of the Smart Strut Improved Sliding Pillar Front Active Suspension System for Mining Trucks. \u003cstrong\u003eBirrana Engineering Pty Ltd.\u003c/strong\u003e, 2003. \u003c/li\u003e\n\u003cli\u003eYIN, Y.; RAKHEJA, S.; BOILEAU, P.-E. A roll stability performance measure for off-road vehicles. \u003cstrong\u003eJournal of Terramechanics\u003c/strong\u003e, v. 64, p. 58\u0026ndash;68, abr. 2016. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Haul truck, Multibody dynamics, Durability, Handling, Comfort","lastPublishedDoi":"10.21203/rs.3.rs-5010781/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5010781/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The unpaved roads of mining sites can not only lead to health problems on haul truck’s driver but also reduce its frame useful life and provide worse handling performance. This study investigates the influence of different suspension-tire setups on the behaviour of a 64-ton mining haul truck, focusing on the initial gas volume of the hydropneumatic suspension (HPS) and tire inflation pressure. Using a multibody model, typical manoeuvres were simulated to assess handling, comfort, and frame durability. Results suggested that softer suspension and tire setups could enhance ride comfort and frame durability without substantially affecting handling.","manuscriptTitle":"Off-highway truck setup influence on vehicle dynamics and frame durability","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-03 17:53:39","doi":"10.21203/rs.3.rs-5010781/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-14T07:47:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-14T07:03:52+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-16T17:32:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"24411492673264125726136818148356595670","date":"2024-09-07T06:01:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"95454970887200046064417728335898693989","date":"2024-09-06T17:10:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-04T12:27:36+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-02T15:15:16+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-09-02T13:26:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Multibody System Dynamics","date":"2024-09-01T00:43:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"multibody-system-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mubo","sideBox":"Learn more about [Multibody System Dynamics](http://link.springer.com/journal/11044)","snPcode":"11044","submissionUrl":"https://submission.nature.com/new-submission/11044/3","title":"Multibody System Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"1af1be05-0c2c-4017-aa6a-cef220fb942c","owner":[],"postedDate":"October 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-12-16T16:02:42+00:00","versionOfRecord":{"articleIdentity":"rs-5010781","link":"https://doi.org/10.1007/s11044-024-10045-x","journal":{"identity":"multibody-system-dynamics","isVorOnly":false,"title":"Multibody System Dynamics"},"publishedOn":"2024-12-13 15:57:54","publishedOnDateReadable":"December 13th, 2024"},"versionCreatedAt":"2024-10-03 17:53:39","video":"","vorDoi":"10.1007/s11044-024-10045-x","vorDoiUrl":"https://doi.org/10.1007/s11044-024-10045-x","workflowStages":[]},"version":"v1","identity":"rs-5010781","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5010781","identity":"rs-5010781","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}