Improving Geometric Accuracy in Multi-Axis Machining of Thin-Walled Turbine Blades: Practical Methods for Minimizing Error and Online Compensation

Improving Geometric Accuracy in Multi-Axis Machining of Thin-Walled Turbine Blades: Practical Methods for Minimizing Error and Online Compensation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Improving Geometric Accuracy in Multi-Axis Machining of Thin-Walled Turbine Blades: Practical Methods for Minimizing Error and Online Compensation Shahab Moradi Kelardeh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6385585/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study aims to achieve the required geometric tolerance in the machining of the contact face surfaces on thin-walled rotary steam turbine blades to meet strict assembly requirements. The focus was on recognizing and reducing random errors contributing to dimensional deviation. Two methods were considered: (1) creating a U-notch at the end of the blade to relieve residual stress and bending forces due to fixture, tailstock system, and raw block misalignment, and (2) an online measurement and compensation method to estimate and correct elastic deformation during machining. Experimental tests on two five-axis CNC machining centers and finite element simulations were used to evaluate the impact of these methods. The results show that the U-notch method reduces the standard deviation and deviation range by approximately 37% and 42%, respectively, but the deviation range still exceeded the acceptable tolerance (0.09 mm > 0.06 mm). However, the online measurement and compensation method reached remarkable improvements, reducing the standard deviation by 71% and 78%, and improving the mean deviation by 76% and 97%, bringing the blade tip deviation within the acceptable tolerance range (0.028 mm, 0.045 mm < 0.06 mm). This technical study reveals the effectiveness of online compensation techniques as a highly efficient solution for reducing post-machining deformation and ensuring dimensional accuracy in turbine blades without extra operations such as grinding or fixture redesign. This practical method can be easily implemented in workshops, simplifying production processes and reducing costs. Multi-axis machining Turbine blades Geometrical accuracy Residual stress 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 1 Introduction In today’s development and advancement in industries, the demand for high-precision and complex parts using machining methods has rapidly increased, and without cost optimization, it will not be possible to survive in competitive global manufacturing [ 1 ]. Therefore, for sustainable production with high efficiency, the parameters affecting the cost price of products, including time (setup time, machining time, tool change time, etc.), number of reworked or scrap parts, energy consumption, tool deterioration and type of lubricant used should be optimized [ 2 ]. Multi-axis machines as the optimal method simplifies and offers a variety of reasonable advantages for machining sophisticated parts such as turbine blades, impellers, and airfoils. These machines with simultaneous multi-axis motions expand manufacturing capabilities and high efficiency, reduce the risk of misalignment without moving a workpiece from one fixture to another, and improve surface roughness by using shorter cutting tools and streamline programming efforts. They also develop precise positional adjustments with greater flexibility [ 3 ]. However, kinematic errors resulting from geometric inaccuracy of structural components can noticeably affect tool position and orientation relative to the workpiece [ 4 , 5 ]. Additionally, thermal gradients within the machine structure—caused by heat generated from moving axes and machining processes—lead to thermal expansion, bending, and reduced accuracy [ 6 ]. Machining forces and compensation errors play a significant role in tool positioning deviations [ 7 , 8 ]. Therefore, the tool position deviation caused by combined errors can be considered as a major challenge in precision machining. Since much effort has been made to minimize them, it is not possible to completely eliminate metrological errors. Studies also indicate that residual stress in the machining of thin-walled parts can cause deformation and reduce the accuracy after machining [ 9 , 10 ]. Predicting the distribution and effects of this stress is complex, often inconsistent due to various factors, and cannot be eliminated. Therefore, there are various strategies to mitigate these errors such as modifying the part geometry by applying toolpath compensation after measuring the first part deviation [ 11 ]. However, due to the costs of each part, achieving the correct initial part is essential. Additionally, random deviations may cause offsetting ineffective. To address this, modern machines are equipped with measuring probes for performing online offsets during production [ 12 ]. Blades are the key components in the energy and aviation industries, which directly affect the performance of turbines and jet engines. Therefore, many studies have been conducted to achieve high precision in their manufacturing. Liu et al. optimized the setup of the workpiece on a five-axis machine and succeeded in improving the surface quality and machining performance [ 13 ]. Similarly, Suri et al. succeeded in optimizing the machining parameters and improving the surface quality in five-axis machining of gas turbines using genetic algorithms [ 14 ]. Other studies try to predict the probable deviation and use compensating methods in machining programs [ 15 – 18 ]. However, accurately predicting dimensional and geometric deviations in thin-walled parts remains challenging and makes pre-offsetting impossible. Furthermore, Researchers found the clamping forces as a source of error that affected the final machining of thin-walled parts accuracy and try to eliminate it. Zha et al. investigated the dimensional deviations of blade airfoils. The results indicate that the major effective factor is the tailstock clamping force, and reducing this force from 10 kN to 1 kN, they achieved a repeatable dimensional accuracy of ± 0.125 mm [ 19 ]. Similarly, Yu et al. also studied the elimination of the torsion of thin-walled blades during machining. They design an adaptive dual-sphere fixture to minimize machining residual stress and finally corrective by a grinding process [ 20 ]. Researchers have also successfully used low-melting fixtures to eliminate clamping forces in machining thin-walled parts [ 21 , 22 ]; but they require fixture manufacturing and melting processes, which make complexity and extend production time. Despite substantial advances in computer numerical control (CNC) machines, the possibility of dimensional deviations during the machining process has been largely minimized; however, deformation and fluctuating deviations on the precision assembly surfaces of thin-walled parts (such as blades) after unclamping can greatly increase the times of rework, straightening, alignment, engineering inspections, etc. As previously mentioned, different approaches have been considered to eliminate such errors, including reducing the mechanical and thermal stress of the workpiece, symmetrical machining, multi-stage machining with stress relief between operations, using low-melting fixtures, straightening, and reworking each of them can complicate the production process, increase operational challenges, extend manufacturing time and costs. Additionally, many of these methods are not feasible depending on the type of part. Therefore, in this case study, the effect of various parameters that can be the root cause of dimensional errors in five-axis machining of compressor blades will be investigated, with focus on the influence of clamping. 2 Research Problem This study utilizes two five-axis machining centers with a SIEMENS 840D controller and travel range of 1700x600x500 mm. The machine has three linear axes (X, Y, and Z), with the Z-axis oriented vertically. The B-axis is located at the machine head, and the A-axis is located at the machine table. The A2 spindle moves freely without the U-axis (Fig. 1 ). In this research, the dimensional error of a steam compressor rotary blade with a length of 164 mm and material X22CrMoV12-1 has been investigated. This blade consists of a root and a tip that are connected by a long thin airfoil. The position of the blade tip relative to the root surface as the contact face is crucial, and if this deviation increases, it affects the permissible assembly gaps and complicates the assembly. Furthermore, in the case of assembly under stress, there is a possibility of reduced fatigue life and premature failure [ 23 , 24 ]. According to the positional tolerance specified in the design, the allowable deviation of the blade tip relative to the root’s reference surface (Datum A) must remain within ± 0.03 mm (Fig. 2 ). The low rigidity of the airfoil during final machining exposes the blade to deflections resulting from tailstock force, cutting force, clamping force, internal residual stress, etc., which can cause it to bend. By releasing the tailstock, this deformation becomes visible and measurable. As illustrated by the Coordinate measuring machine (CMM) results in Fig. 3 , the manufacturing deviations exhibit random errors outside the specified tolerance range. These deviations vary on different CNC machines. 3 Blade Manufacturing Process First, the raw block with dimensions of 60x52x260 mm 3 is setup on the machine between the fixture and the tailstock. The tightening torque of the fixture bolt is 70 N.m and the tailstock pressure is set to 90 kg. Then all machining operations are carried out sequentially. The roughing and flat surface finishing are performed using three-axis, while the airfoil is machined using five-axis operations. In the final step, both the start and end of the blade are cut off. Figure 4 illustrates the finishing toolpath, tool data, and cutting parameters. 4 Analysis of Variables Affecting Geometric Deviation The first approach to eliminating this deviation is straightening by pressing, but this process increases internal elastic stress, and therefore springback was observed over time, especially during storage. This method can be used when the blades are assembled in a short time, but the pressing will still be a manual operation with error, which has the risk of severe deformation, cracks, and rejection that limits the use of this method. In addition, this method requires non-destructive testing (NDT) to ensure the blades are free of damage. The second approach is to correct the blades by milling or grinding, which increases production time and cost. Therefore, it is necessary to analyze the distribution of deviations and identify the variable that has the greatest impact on the total dimensional accuracy. To investigate the root causes and reduce deviations, the following steps were examined: Analysis of dimensional changes over time due to residual stress Symmetric machining with reduced DOC to minimize residual stress Investigation of the Effect of Tailstock Force Examination of fixture and clamping conditions 4.1 Analysis of Dimensional Changes over Time Due to Residual Stress The performance of machined components significantly depends on surface integrity, particularly residual stress on or beneath the machined surface [ 10 , 25 ]. Residual stress is present in the part even without any external loads. They are generated by mechanical, thermal, and metallurgical effects during machining processes, or by the raw material's manufacturing process [ 26 ]. However, predicting the exact distribution of residual stress and its impact on components is challenging, as various influencing factors can lead to inconsistencies in repeatability. Considering that the final blades shows no dimensional deviations while clamped on the machine, errors caused by machine backlash, tool issues, and other factors are eliminated. After machining, the blade tip deviation was measured using a CMM at 20°C with a resolution of 0.1 µm (Fig. 5). The measurement was repeated multiple times at different intervals, and as shown in Table 1 , the measured values indicate minimal changes. Therefore, the deviation for each blade remains constant and is not dependent on the gradual relief of residual stress over time, occurring immediately upon unclamping. The direction and magnitude of this deviation vary between the blades. Table 1 Measurement of the blade tip position relative to Datum A at different times (CMM report) Row Measurement Time (hours) Deviation (mm) 1 0.1 -0.037 2 69 -0.041 3 156 -0.042 4 249 -0.038 5 380 -0.040 The measurement variations in Table 1 are very small; it seems that these deviations are probably due to measurement errors and not related to the relief of residual stress over time. 4.2 Symmetric Machining with Reduced DOC to Minimize Residual Stress In the machining of thick parts, the primary source of deviation is known to be bulk redistribution stress in rough machining, but in the machining of thin-walled parts, the main factor affecting deviations is the final machining. For complete control over the machining, it is necessary to consider both machining processes [ 27 ]. In the machining process plan, to control cutting loads and reduce stress, the roughing depth of cut (DOC) was reduced from 2 mm to 1 mm and an appropriate coolant flow rate was used. The roughing ​​was also performed in multiple stages and symmetrically. The results of both processes are shown in Fig. 6 . Accordingly, no improvement was observed in terms of the range and average deviations. 4.3 Investigation of the Effect of Tailstock Force Based on the studies, the pressure of the tailstock can be another possible influencing parameter in the deformation of the workpiece. Therefore, the tailstock force and its repeatability were investigated. As shown in Fig. 7 , a compression load cell was used to calibrate the pressure. The input pressure values of the device were compared with the output pressure value. The calibration was performed at 30 kg, 90 kg, and 120 kg. According to Table 2 , the pressure had good accuracy and repeatability and was verified. After calibration, the tailstock force in the machining of the blades was reduced from 120 Kg to 30 Kg, but no improvement was observed which seems other factors may be influencing the results. Table 2 Tailstock Force Calibration Row Nominal Tailstock Force (kg) Measured Tailstock Force (kg) 1 30 29.5 2 90 89.5 3 120 119 4.4 Examination of Fixture and Clamping Conditions This section investigates the misalignment of the tailstock, clamping system, and raw block, as well as their effects on the final workpiece accuracy. The clamping procedure begins by setting up the raw block in the fixture with minimal bolt-tightening torque. The tailstock is then applied with a pressure of 10 kg to stabilize the block. Subsequently, the fixture jaws are loosened to allow natural alignment with the tailstock before being re-tightened to a torque of 70 N.m. Finally, the tailstock pressure is increased to 90 kg to ensure a firm and precise setup. Observations showed that after the complete clamping procedure, if the tailstock is unclamped, the fixture jaws tend to shift the block either upward or downward. The direction and magnitude of this shift are unique and repeatable for each block, and this effect is independent of the block’s weight or only has a minimal impact. With more detailed inspection observe that the blocks were sometimes setup with large misalignment. As a result, in some cases after clamping with tailstock, the position of the raw block was moved up to 0.3 mm, and after releasing, it returned to its previous position. At the same time, by placing the dial indicator on the fixture jaws and measuring their position, it was observed that this displacement of the block caused increased pressure on the jaws and they slightly opened, at the same time, it increased the amount of bolt preload and jaws pressure. Consequently, a restoring force was introduced, attempting to return both the jaws and the block to their original positions, which will cause bending stress in the block. After carefully considering the clamping of the raw block and checking the final blade's CMM report, it was inferred that the raw block with more displacement during setup resulted in more blade tip deviation. If this bending stress is significant, after rough machining and reducing the cross-section of the raw block, the blade will undergo elastic bending in the area that has the least strength and the final machining will be performed with error. Since the airfoil strength is less than the root, the blade tip exhibits the highest displacement and the root remains relatively fixed. Therefore, it seems that the workpiece is machined under an elastic deformation state and tends to return to its previous position when opened. Consequently, depending on the direction of bending, the blade tip is machined with verity, which is ultimately observed as a positional deviation in the CMM inspection report. To mitigate this phenomenon, potential sources that could cause misalignment were investigated. In this regard, the first focused on the effect of the center drill hole position. Due to surface irregularities on the raw blocks, it was not possible to accurately measure and control the position. Additionally, the limited engagement raw block and jaws (about 3mm) and the surface roughness caused the block’s position to vary with reclamping. The block displacement was measured after the tailstock clamped using a dial indicator as shown in Fig. 8 -A. To further evaluate the effect of the center drill hole position, a precisely machined block was prepared, and the position of the hole was accurately machined and controlled with an accuracy of Ø0.03 mm. This block was used to ensure stable clamping conditions and minimize positional deviations. However, despite the orthogonal surfaces and the correct position of the hole, the tailstock still tended to shift the position of the block. The results showed that the position of the block center drill hole is not perfectly aligned with the tailstock axis, which could be affected by the accuracy of the fixture or the position of the tailstock system. Therefore, a dimensional inspection of the fixture was conducted. As shown in Fig. 8 -B, by measuring the same point on the fixture and 180 degrees rotation, it was observed that the fixture had an axial runout of 0.02 mm. Then, the parallelism of the jaws with each other and its parallelism with the Y axis was examined. The non-parallelism of the two jaws with each other was 0.02 mm. The maximum non-parallelism of the jaws with the Y-axis was 0.04 mm (Fig. 8 -C). Further analysis of the midplane of the jaws revealed that the midplane shifted by 0.1 mm (Fig. 8 -D). The parallelism deviation of the jaws with each other in the XY plane is 0.05 mm. These findings confirm fixture inaccuracies that contribute to misalignment, potentially affecting the overall machining precision and final workpiece accuracy. Figure 9 schematically shows the factors that can cause bending stress in the blade after the tailstock clamp including; deviation of jaws midplane relative to the fixture midplane, the deviation of the tailstock position, the angular state of the raw material block in clamping, and the deviation of the center drill hole relative to the block midplane. In practice, it is not possible to eliminate and monitor all of these deviations in the company’s production line. The second hypothesis is that the displacement of the blade tip occurs due to machining residual stress, or a combination of both factors, ultimately resulting in the blade tip shifting. 5 Finite Element Simulation The simulation aims to validate the initial assumptions derived from experimental measurements. Based on the finite element analysis results, it is also possible to estimate how deflection will cause errors on the workpiece. For this purpose, ABAQUS 6.14 software was employed to perform the simulation. The three-dimensional assembly model used for simulation is shown in Fig. 10 . The workpiece is clamped using fixture jaws and applying preload via the bolt force. Also, the displacement applied to the reference point (RP) at the center of the drill hole is connected to the workpiece with a coupling constraint. The simulation was solved in one step. Due to the nature of the problem and low deformation, the material was considered pure elastic and the standard solver was used. The step time was set to 1. Due to the geometric complexity, the second-order Tet element (C3D10), a 3D continuum element with 10 integration points, was selected for meshing. The properties of the X22CrMoV12-1 material were considered isotropic according to Table 3 . Table 3 Material Properties of X22CrMoV12-1 Property Value Density 7.8 g/cm³ Young's Modulus 190 GPa Poisson's Ratio 0.28 In this analysis, according to the torque of 70 N.m applied to the M16 bolt, the bolt preload force was calculated to be 23 kN. The blade root was firmly clamped using the fixture jaws and a displacement of RP = 0.2 mm was applied to the blade tip. Figure 11 (scaled 200 times for visualization) shows that the fixture jaws effectively constrained the root and the blade bends. In practice, the blade is machined along the Actual level line. After machining is completed and the tailstock is released, the position of the blade tip will shift, and points P 1 and P 2 will be on the Expected level line according to Fig. 11 and Table 4 . Therefore, it is expected that the value of P 3 with a displacement of 0.07 mm will also be on this line; but based on simulation, due to the bending effect, the displacement of the blade tip has reached P 3 = 0.14 mm. This results in a deviation of 0.07 mm from the expected value, which is ultimately reflected in the final machined part. Table 4 Position of Points After Applying a 0.2 mm Displacement to the RP Row Position X (mm) Z (mm) 1 P 1 0.0 0.00 2 P 2 66.7 0.025 3 P 3 181.1 0.144 6 Proposed Methods for Improving Precision in Multi-Axis Machining Considering the source of error, the following solutions can be proposed for further investigation: Method 1: Machining a U-notch at the end of the blade to transfer residual stress to the outside of the blade Method 2: Measuring the magnitude and direction of displacement with a probe and applying offset online 6.1 Evaluation of Method 1 In this method, before final machining, a U-notch is created in the outer area of the blade to relief the residual stress and bending moment caused by fixture misalignment. The notch width was 11 mm and the thickness was 6 mm. In Fig. 12, the notch position is shown, along with the stress distribution and bending before and after the notch was created, evaluated by finite element simulation. As shown, the stress distribution is transferred from the airfoil to the outer part of the blade, and as a result, the root reference surface alignment with the blade tip is relatively maintained. According to Fig. 12, machining a U-notch and applying displacement to the center drill hole by RP = 0.1 mm shifted the blade tip about P 3 = 0.077 mm. Final machining under this condition is expected to result in approximately 0.01 mm deviation in the blade tip, which will ultimately improve the accuracy. This method will need to be further investigated by experimental tests for validation and stability. 6.2 Evaluation of Method 2 The measurement process and an example of measuring data as shown in Fig. 13 . To assess the feasibility of this method, the blade was measured on the machine with a probe in three steps: 1- tailstock clamp, 2- tailstock unclamp, and 3- tailstock reclamp. According to Eq. 1, first, the expected correct position P z was calculated. Then, in Eq. 2, the position of the blade tip is evaluated as T z . The results consider whether the position of the blade tip is in the right place after reclamping and take any deviation into account. Based on experiments the blades return to the right position with high repeatability (Fig. 13 ; P 1_3 ≈ P 3_3 ). Then, in Eq. 3, the compensation value is extracted as the tool offset Z (Offset) . Considering the measuring data in Fig. 13 , the final deviation value and the necessary offset were estimated to be 0.051 mm. Next, the final machining of the blade was performed without compensation. The CMM report showed a 0.043 mm deviation, which differed by 0.009 mm from the values calculated by the machine probe and Eq. 3. This result confirm that this method is practical to compensate for the deviation with high accuracy. The flowchart detailing online blade correction is presented in Fig. 14 . (1) \(\:\frac{{P}_{2\_2}-{P}_{1\_2}}{{X}_{1}}=\frac{{\varvec{P}}_{\varvec{z}}}{{X}_{1}+{X}_{2}}\) (1) (2) \(\:{\varvec{T}}_{\varvec{z}}=({P}_{3\_1}-{P}_{3\_3})\) (2) (3) \(\:{\varvec{Z}}_{\left(\varvec{O}\varvec{f}\varvec{f}\varvec{s}\varvec{e}\varvec{t}\right)}={P}_{1\_2}-{P}_{3\_2}-{P}_{z}+{T}_{z}\) (3 7 Results 7.1 Method 1 To experimentally compare the effect of U-notch on blade tip deviation, two machining programs—one with a notch and one without—were developed, and the results were analyzed on machines 1 and 2. According to Fig. 15 , the mean and range deviation for 27 blades with and without notch (Conventional method) were − 0.009 mm, -0.027 mm, -0.09 mm, and − 0.15 mm, respectively. Similarly, in Fig. 16 , these values for 27 blades were − 0.009 mm, -0.039 mm, -0.09 mm, and − 0.16 mm. Additionally, the standard deviation for the blades with and without notch in Figs. 15 and 16 was calculated as 0.026 mm, 0.027 mm, and 0.039 mm, 0.045 mm, respectively. The results indicated that the mean and range deviation were close in both machines. By creating the U-notch machining, the mean and range deviations were reduced by approximately 73% and 42%, respectively. However, the deviation range remained around 0.09 mm which is out of the acceptable tolerance limit. This deviation range is unsatisfactory. Consequently, the notch thickness was reduced from 6 mm to 4 mm and 3 mm. While this reduction caused more declaration in deviation, it also introduced instability, increasing the risk of angular misalignment, surface quality deterioration, and other defects. In general, this method can relatively improve the deviation condition, but notch thickness is a key parameter and structural stability is crucial. 7.2 Method 2 In Fig. 17 , the deviation of the blade tip that is machined using the online control method on machines 1 and 2 is presented. The results show a substantial reduction in deviation, from 0.15 mm and 0.16 mm to 0.028 mm and 0.045 mm—a fourfold improvement—while good repeatability is achieved. Figure 18 provides additional insight into the effect of the notch and probing methods as opposed to conventional machining. With the notch method, the standard deviations produced on machines 1 and 2 are 33% and 41%, respectively, and the mean deviation are %67 and 77%. However, due to the range of deviations, there is the probability and risk of producing a part outside the acceptable tolerance limits. While, on the other hand, the probing method showed higher accuracy with standard deviation and mean deviation improvements in the range of 76–97% and 71–78% for machines 1 and 2, respectively. Considering the range of deviations within 0.028 mm and 0.045 mm and high repeatability, this technique was extremely successful. Thus, the application of an online control method using a Renishaw OMP60 probe provides a reliable solution to decrease the deviations without corrective grinding or redesign of fixtures. Not only does this technique enhance machining accuracy, but also simplifies production processes, lowers dependence on operators, minimizes processing times, and saves overall costs. 8 Conclusion In this study, the aim is to achieve acceptable geometric tolerance in machining the contact face surfaces of thin-walled blades (steam turbine rotary blades) to meet assembly requirements. Therefore, efforts were made to identify and eliminate the source of random error. An attempt was also made to make the methods easily applicable in manufacturing workshops without major modifications in the preparation and machining process. For this purpose, several error sources were evaluated and finite element simulation was performed. It was determined that various types of errors may cause deviation in the workpiece. In addition, the magnitude and direction of each error can increase or decrease the overall deviation and cannot be predicted. Therefore, geometric deviation results from a sum of different errors, and eliminating them is highly difficult or impossible. By root cause analysis, two primary sources of deviation were revealed: 1. Bending stress due to fixture, tailstock system, and raw block misalignment. 2. Machining residual stress causes elastic deformation after releasing the tailstock. Finally, two methods were presented to improve geometric accuracy: · Notch Machining for Stress Relief (Method 1): A U-Notch was created at the end of the blade to relief residual machining stress and bending forces caused by fixture misalignment. · Online Measurement and Compensation (Method 2): Geometric deviation compensation was achieved by online measurement and estimation of the elastic deformation of the blade in the unclamped state of the tailstock. To assess the effectiveness of these methods, the blades were machined on two five-axis machining centers using the techniques. The results revealed that: 1. Elastic deformation occurs immediately after the tailstock is released, and its magnitude and direction cannot be predicted. · The contact face surfaces are machined correctly and without deviation in the clamped state. Immediately after the tailstock is released, elastic deformation occurs and it is not time-dependent. · These deviations on thin-walled parts such as blades are common, and it’s one of the machining challenges and considered a random error. 2. No noticeable change was observed in deviations with reduced DOC in roughing and decreased tailstock force. · The roughing DOC was reduced from 2 mm to 1 mm, and an appropriate coolant flow was used roughing was performed in several stages and symmetrically. · The amount of tailstock force was calibrated and its pressure was reduced to 30 kg, but no noticeable change was observed in the deviations. 3. Based on experiments, fixture misalignment was identified as a main source of deviation. · Axial runout, parallelism, and jaw symmetry were measured on the CNC machine, confirmed that the fixture has deviations. · Misalignment of the tailstock system, deviation in the position of the center drill hole of the raw material, surface irregularities, and rough surfaces, will cause bending stress to the block. · With machining and reduced stiffness in the airfoil, this bending can be applied to the blade airfoil as the thin wall causes elastic deformation. Machining the blade under these conditions will cause errors. Eliminating all these factors in workshop is neither practical nor cost-effective. Two methods were proposed to reduce dimensional error: 1. Transfer the residual machining stress and bending force to the outside of the blade by creating a U-notch at the end of the blade. · Blades were machined with and without a notch on two different CNC machines. · The results showed that the standard deviation and the range of deviations were improved by approximately 37% and 42%, respectively. · Further reducing the thickness of the notch from 6 to 4 and 3 mm, the deviations were reduced, destabilized blade fixturing, and parameters such as angle, surface quality, etc. were out of control. This method can generally improve the deviations relatively, but choosing the notch thickness must be carefully considered. · The notch method was improved (range of deviations 0.09 mm) but insufficient for achieving the acceptable tolerance limit (0.06 mm). 2. The online measurement and compensation method. · A mathematical model was developed to estimate the blade’s elastic deformation during machining. This was achieved by unclamping the tailstock and measuring the elastic deformation of the blade during the machining process with a Renishaw OMP60 probe. The estimated error was then directly compensated in the machining program. · Experimental tests show a good reduction in deviations, and 30 blades were successfully produced with a deviation range of 0.028 mm and 0.045 mm, well within the tolerance. · Using this method, standard deviation and mean deviation improved from 76% to 97% and 71% to 78%, respectively. · Due to its high repeatability to produce blades within tolerance (< 0.06 mm), this method can be used as an effective solution to eliminate random error in thin-walled blades. By comparing the results obtained with the study of Jian-Hua et al., although their process and parts are different, they also focused on the importance of the clamping method to design and manufacture the fixture and finally produced the correct part by grinding [14]. In the present study, it was also possible to produce the correct part by grinding, but an attempt was made to produce the correct blades in one step without redesigning the standard LANG fixture or adding a correction process. Li et al. and Juan Zha et al. also focused on the analysis of clamping forces and the importance of the clamping method, which is essential for manufacturing parts within the allowable tolerance range [13-28]. Declarations Acknowledgements I would like to express my sincere appreciation for the invaluable support from my colleagues at TUGA company, whose continuous encouragement and assistance—both technical and moral—have been critical throughout this project, with particular mention of Javad Bigdeli and Dr. Masoud Saberi. Funding The author did not receive any direct financial support for this research. However, the technical equipment and facilities of MAPNA Turbine Engineering and Manufacturing Company (TUGA) were used during the research process. Competing Interests The author declare no conflict of interest. Author Contributions Not applicable. References Soori M, Asmael M (2022) A review of the recent development in machining parameter optimization. Jordan J Mech Ind Eng 16(2):205–223 Apro K (2008) Secrets of 5 Axis Machining, New York Soori M, et al (n.d.) A review in capabilities and challenges of 5-axis CNC milling machine tool operations Uddin MS, Mian AJ, Rahman M, Senthil Kumar A, Bashir S (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Precis Eng 33(2):194–201 Ibaraki S, Matsubara A, Sato H, Yamaji I (2010) Machining tests to identify kinematic errors on five-axis machine tools. Precis Eng 34(3):387–398 Mayr J, Jedrzejewski J, Uhlmann E, Donmez A, Härtig F, Wendt K, Schmitt R, Weikert S, Kunzmann H (2012) Thermal issues in machine tools. CIRP Ann 61(2):771–791 Zhao D, Bi Y, Ke Y (2017) An efficient error compensation method for coordinated CNC five-axis machine tools. Int J Mach Tools Manuf 123:105–115 Bohez EL (2002) Compensating for systematic errors in 5-axis NC machining. Comput Aided Des 34(5):391–403 Huang X, Sun J, Li J (2015) Effect of initial residual stress and machining-induced residual stress on the deformation of aluminium alloy plate. Stroj Vestn J Mech Eng 61(2):131–137 Masoudi S, Asnafi N, Movahhedy MR, Hosseini M (2015) Effect of machining-induced residual stress on the distortion of thin-walled parts. Int J Adv Manuf Technol 76:597–608 Astakhov V, Basak A, Dixit US (2016) Metal Cutting Technologies: Progress and Current Trends. Vol. 1. Walter de Gruyter GmbH & Co KG Zhuang Q, Liu H, Tang W, Wang L, Zhao G, Gao T (2023) A novel pre-travel error compensation strategy for five-axis on-machine measurement with a touch-trigger probe. IEEE Trans Instrum Meas Liu X, Yang Y, Xu K, Xu J (2024) A workpiece setup optimization method for 5-axis machining with motion coherence and stiffness enhancement. Precis Eng 88:867–883 Soori M, Asmael M, et al (2023) Minimization of surface roughness in 5-axis milling of turbine blades. Mech Based Des Struct Mach 51(9):5213–5230 Li ZL, Wang Z, Zhu LM (2018) Surface form error prediction in five-axis flank milling of thin-walled parts. Int J Mach Tools Manuf 128:21–32 Chen D, Zhang X, Liu Y, Feng P, Wang J (2015) Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool. Int J Mach Tools Manuf 94:74–87 Ding G, Liu Y, Zhang X, Wang Q, Wang Y (2014) Prediction of machining accuracy based on a geometric error model in five-axis peripheral milling process. Proc Inst Mech Eng Part B J Eng Manuf 228(10):1226–1236 Li ZL, Zhu LM (2019) Compensation of deformation errors in five-axis flank milling of thin-walled parts via tool path optimization. Precis Eng 55:77–87 Zha J, Hu L, Yan Y, Jiang C (2023) An accuracy evolution method applied to five-axis machining of curved surfaces. Int J Adv Manuf Technol 125(7):3475–3487 Yu JH, Chen ZT, Jiang ZP (2016) A control process for machining distortion by using an adaptive dual-sphere fixture. Int J Adv Manuf Technol 86:3463–3470 Wang H, Li H, Yao C, Kou M, Wang W, Huang B, Zheng W (2015) Integrated analysis method of thin-walled turbine blade precise machining. Precis Eng Manuf 16:1011–1019 Wang T, Liu Y, Wu B, Zhang Y, Yang D (2016) Application of low-melting alloy in the fixture for machining aeronautical thin-walled component. Int J Adv Manuf Technol 87:2797–2807 Moradi Kelardeh S, Shafiei E, Hemmati R, Bagheri M (2022) An investigation on the effect of interference clearance of bushing on fatigue strength in triangle suspension. J Engine Res 67(67):30–41 Kadhom HK, Mohammed AJ, Sillanpää M (2024) The influence of thickness and interference fit ratio on fatigue phenomenon: an empirical study. Math Model Eng Probl 11(1) Lin K, Sun J, Zhang J (2017) A numerical study on the redistribution of residual stress after machining. In: ASME Int Mech Eng Congr Expo. American Society of Mechanical Engineers Thakur A, Gangopadhyay S (2016) State-of-the-art in surface integrity in machining of nickel-based super alloys. Int J Mach Tools Manuf 100:25–54 Akhtar W, Lazoglu I, Liang SY (2022) Prediction and control of residual stress-based distortions in the machining of aerospace parts: a review. J Manuf Process 76:106–122 Li B, Melkote S (2001) Fixture clamping force optimisation and its impact on workpiece location accuracy. Int J Adv Manuf Technol 17:104–113 Cite Share Download PDF Status: Posted Version 1 posted 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-6385585","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":448161118,"identity":"0f5d5ea9-915a-4fbe-98ff-956f46dbaa6b","order_by":0,"name":"Shahab Moradi Kelardeh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/klEQVRIiWNgGAWjYBACgwNAgscAyJB/2PjgA5DDxk5AiyVcC0PyYcMZIC3MBLTYg7WArGNIS5MGMRgIaTE73vvww5sCBntzhjMG0ja/tsnzMTMwfviYg0fLmePGknMMGBJ3NvYYGOf23TZsY2Zglpy5DY+WG2kM0kC/JBgc5jFIzu25zQjUwsbMi0eLwY005t9ALfYGx3gMDlv23LYnRgsbyBbGDWfYEpsZftxOJKzlzDE2yzkGEokbbjAfZuxtuJ3cxszYjNcvBsfbmG+8+WNjb3CDsf3Hjz+3bee3Nx/88BGPFiiQgFCMbWCygaB6JPCHFMWjYBSMglEwUgAAfyZQ0B/DYawAAAAASUVORK5CYII=","orcid":"","institution":"MAPNA Group","correspondingAuthor":true,"prefix":"","firstName":"Shahab","middleName":"Moradi","lastName":"Kelardeh","suffix":""}],"badges":[],"createdAt":"2025-04-06 08:23:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6385585/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6385585/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81645254,"identity":"1f40a534-58c4-4647-986c-1529810467af","added_by":"auto","created_at":"2025-04-29 14:25:49","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":763922,"visible":true,"origin":"","legend":"\u003cp\u003eAxes of the five-axis machining center\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/24c3245ca5fe397fc2833a50.png"},{"id":81645659,"identity":"f5541158-4397-4907-bfa1-87e1b13b7313","added_by":"auto","created_at":"2025-04-29 14:33:49","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":272166,"visible":true,"origin":"","legend":"\u003cp\u003eAssembly of the blades – Contact faces and tip position tolerance relative to Datum A\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/56336e38ca79220a4ae1234d.png"},{"id":81644543,"identity":"0196a3d4-29ac-4cef-ba0c-05f7933fbf46","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":173397,"visible":true,"origin":"","legend":"\u003cp\u003eDeviation of the blade tip position relative to Datum A\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/1baf315dfcdfb7de11afb8bd.png"},{"id":81644557,"identity":"a55cb56a-a48c-4822-ae5a-b2938c8e1e50","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":373973,"visible":true,"origin":"","legend":"\u003cp\u003eBlade machining setup, finishing toolpath, Tool and cutting data\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/0215995fec980fc4859d231c.png"},{"id":81644544,"identity":"b801183b-721e-43ec-ba72-9637d45c6fd7","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":338706,"visible":true,"origin":"","legend":"\u003cp\u003eBlade measurement with CMM\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNote\u003c/strong\u003e: To ensure the measurements are repeatable and reproducible, the Gauge repeatability and reproducibility (GR\u0026amp;R) was evaluated. It was determined to be an acceptable measurement system.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/be9d7baea9ede8311d23258b.png"},{"id":81646442,"identity":"9f316ac2-51b7-46e6-9caa-29884cc553e5","added_by":"auto","created_at":"2025-04-29 14:41:49","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":175881,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Final Blade Tip Deflections with Varying DOC in Rough Machining\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/8c09c2ee4e379329951c07fa.png"},{"id":81645664,"identity":"687c7f09-786d-4149-8739-354ed99ddd79","added_by":"auto","created_at":"2025-04-29 14:33:49","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":836962,"visible":true,"origin":"","legend":"\u003cp\u003eCalibration of tailstock force using a compression load cell.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/08613287696fc6be03016987.png"},{"id":81646445,"identity":"ba521f83-496e-46bb-9cfc-abe80037127d","added_by":"auto","created_at":"2025-04-29 14:41:49","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":976697,"visible":true,"origin":"","legend":"\u003cp\u003eMeasurement of the block position under tailstock clamping and unclamping (A), measurement of fixture axial runout (B), measurement of jaws parallelism (C), and measurement of Midplane position of jaws (D).\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/30b208eff2086a7d5d892127.png"},{"id":81645657,"identity":"766abf7d-040a-4c82-a867-8d9b92ba4fee","added_by":"auto","created_at":"2025-04-29 14:33:49","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":82785,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of factors (a) contributing to misalignment of the raw block and (b) unbalanced fixturing forces\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/9cb0d324e9c843aebb866737.png"},{"id":81645662,"identity":"37b63730-97c4-445a-9bf9-8465dd57e16f","added_by":"auto","created_at":"2025-04-29 14:33:49","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":94337,"visible":true,"origin":"","legend":"\u003cp\u003eAssembly Model in Finite Element Simulation\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/94945544cbd77ffe32efe592.png"},{"id":81646443,"identity":"600a0b1a-3597-4f31-b304-206fd2998d32","added_by":"auto","created_at":"2025-04-29 14:41:49","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":125988,"visible":true,"origin":"","legend":"\u003cp\u003eElastic Deformation of the Blade (Z Direction) and Prediction of Tip deviation (Scaled by 200x)\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/b2f694dd1d02d30d4dd8f5a6.png"},{"id":81644571,"identity":"07de9633-48e1-4a87-91e9-211db2174ceb","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":494937,"visible":true,"origin":"","legend":"\u003cp\u003eStress Distribution and Blade Deformation Before and After Notch Creation\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/686d13bcdafb096b1f307e49.png"},{"id":81645666,"identity":"1ddfc4c5-8b41-4345-8fd4-bc3c16336fa1","added_by":"auto","created_at":"2025-04-29 14:33:49","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":82770,"visible":true,"origin":"","legend":"\u003cp\u003eOnline Measurement Method Using a Probe on a CNC Machining Center\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/0e5b973a0372608406441505.png"},{"id":81645265,"identity":"6b3677d9-f41a-4ccc-8286-f5abc0ab646d","added_by":"auto","created_at":"2025-04-29 14:25:49","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":108629,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart for Online Blade Deviation ompensation\u003c/p\u003e","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/ec30dc93c9bde12237db600a.png"},{"id":81644560,"identity":"9eb86f36-904f-4e53-9153-95b080eb16a9","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":83154,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Blade Tip Position Deviation in Conventional Machining vs. Notch Method on Machine 1\u003c/p\u003e","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/6201133577160e52476d30cf.png"},{"id":81645269,"identity":"aa4bbd51-acd7-435a-9ecb-d498b6eea25f","added_by":"auto","created_at":"2025-04-29 14:25:49","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":83823,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Blade Tip Position Deviation in Conventional Machining vs. Notch Method on Machine 2\u003c/p\u003e","description":"","filename":"floatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/f3505c23ae35d573321d1072.png"},{"id":81644569,"identity":"8ffe3986-2e57-4392-a303-a73d7bc57b48","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":514259,"visible":true,"origin":"","legend":"\u003cp\u003eError reduction on Blade Tip Position with Online Compensation on Machine 1 and 2\u003c/p\u003e","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/317b6ab8d7c0b07cd5173bc2.png"},{"id":81644570,"identity":"8eaa8131-4e1a-4db6-9438-7d212d3a5f7f","added_by":"auto","created_at":"2025-04-29 14:17:49","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":136145,"visible":true,"origin":"","legend":"\u003cp\u003eHistogram Comparison of Standard Deviation and Average Tip Displacement in Conventional Machining vs. Online Compensation Method\u003c/p\u003e","description":"","filename":"floatimage21.png","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/0ed430b103ff443510b2e15c.png"},{"id":85568015,"identity":"24cfcf5f-ca53-434c-bd0c-844a63c03ace","added_by":"auto","created_at":"2025-06-27 15:09:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8541842,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6385585/v1/dd824ed6-292a-4eae-a27f-5b30a2fdd4b2.pdf"}],"financialInterests":"","formattedTitle":"Improving Geometric Accuracy in Multi-Axis Machining of Thin-Walled Turbine Blades: Practical Methods for Minimizing Error and Online Compensation","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eIn today\u0026rsquo;s development and advancement in industries, the demand for high-precision and complex parts using machining methods has rapidly increased, and without cost optimization, it will not be possible to survive in competitive global manufacturing [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Therefore, for sustainable production with high efficiency, the parameters affecting the cost price of products, including time (setup time, machining time, tool change time, etc.), number of reworked or scrap parts, energy consumption, tool deterioration and type of lubricant used should be optimized [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Multi-axis machines as the optimal method simplifies and offers a variety of reasonable advantages for machining sophisticated parts such as turbine blades, impellers, and airfoils. These machines with simultaneous multi-axis motions expand manufacturing capabilities and high efficiency, reduce the risk of misalignment without moving a workpiece from one fixture to another, and improve surface roughness by using shorter cutting tools and streamline programming efforts. They also develop precise positional adjustments with greater flexibility [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. However, kinematic errors resulting from geometric inaccuracy of structural components can noticeably affect tool position and orientation relative to the workpiece [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Additionally, thermal gradients within the machine structure\u0026mdash;caused by heat generated from moving axes and machining processes\u0026mdash;lead to thermal expansion, bending, and reduced accuracy [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMachining forces and compensation errors play a significant role in tool positioning deviations [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Therefore, the tool position deviation caused by combined errors can be considered as a major challenge in precision machining. Since much effort has been made to minimize them, it is not possible to completely eliminate metrological errors. Studies also indicate that residual stress in the machining of thin-walled parts can cause deformation and reduce the accuracy after machining [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Predicting the distribution and effects of this stress is complex, often inconsistent due to various factors, and cannot be eliminated. Therefore, there are various strategies to mitigate these errors such as modifying the part geometry by applying toolpath compensation after measuring the first part deviation [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. However, due to the costs of each part, achieving the correct initial part is essential. Additionally, random deviations may cause offsetting ineffective. To address this, modern machines are equipped with measuring probes for performing online offsets during production [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eBlades are the key components in the energy and aviation industries, which directly affect the performance of turbines and jet engines. Therefore, many studies have been conducted to achieve high precision in their manufacturing. Liu et al. optimized the setup of the workpiece on a five-axis machine and succeeded in improving the surface quality and machining performance [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Similarly, Suri et al. succeeded in optimizing the machining parameters and improving the surface quality in five-axis machining of gas turbines using genetic algorithms [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Other studies try to predict the probable deviation and use compensating methods in machining programs [\u003cspan additionalcitationids=\"CR16 CR17\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. However, accurately predicting dimensional and geometric deviations in thin-walled parts remains challenging and makes pre-offsetting impossible. Furthermore, Researchers found the clamping forces as a source of error that affected the final machining of thin-walled parts accuracy and try to eliminate it. Zha et al. investigated the dimensional deviations of blade airfoils. The results indicate that the major effective factor is the tailstock clamping force, and reducing this force from 10 kN to 1 kN, they achieved a repeatable dimensional accuracy of \u0026plusmn;\u0026thinsp;0.125 mm [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Similarly, Yu et al. also studied the elimination of the torsion of thin-walled blades during machining. They design an adaptive dual-sphere fixture to minimize machining residual stress and finally corrective by a grinding process [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Researchers have also successfully used low-melting fixtures to eliminate clamping forces in machining thin-walled parts [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]; but they require fixture manufacturing and melting processes, which make complexity and extend production time.\u003c/p\u003e \u003cp\u003eDespite substantial advances in computer numerical control (CNC) machines, the possibility of dimensional deviations during the machining process has been largely minimized; however, deformation and fluctuating deviations on the precision assembly surfaces of thin-walled parts (such as blades) after unclamping can greatly increase the times of rework, straightening, alignment, engineering inspections, etc. As previously mentioned, different approaches have been considered to eliminate such errors, including reducing the mechanical and thermal stress of the workpiece, symmetrical machining, multi-stage machining with stress relief between operations, using low-melting fixtures, straightening, and reworking each of them can complicate the production process, increase operational challenges, extend manufacturing time and costs. Additionally, many of these methods are not feasible depending on the type of part. Therefore, in this case study, the effect of various parameters that can be the root cause of dimensional errors in five-axis machining of compressor blades will be investigated, with focus on the influence of clamping.\u003c/p\u003e"},{"header":"2 Research Problem","content":"\u003cp\u003eThis study utilizes two five-axis machining centers with a SIEMENS 840D controller and travel range of 1700x600x500 mm. The machine has three linear axes (X, Y, and Z), with the Z-axis oriented vertically. The B-axis is located at the machine head, and the A-axis is located at the machine table. The A2 spindle moves freely without the U-axis (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this research, the dimensional error of a steam compressor rotary blade with a length of 164 mm and material X22CrMoV12-1 has been investigated. This blade consists of a root and a tip that are connected by a long thin airfoil. The position of the blade tip relative to the root surface as the contact face is crucial, and if this deviation increases, it affects the permissible assembly gaps and complicates the assembly. Furthermore, in the case of assembly under stress, there is a possibility of reduced fatigue life and premature failure [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. According to the positional tolerance specified in the design, the allowable deviation of the blade tip relative to the root\u0026rsquo;s reference surface (Datum A) must remain within \u0026plusmn;\u0026thinsp;0.03 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The low rigidity of the airfoil during final machining exposes the blade to deflections resulting from tailstock force, cutting force, clamping force, internal residual stress, etc., which can cause it to bend. By releasing the tailstock, this deformation becomes visible and measurable. As illustrated by the Coordinate measuring machine (CMM) results in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the manufacturing deviations exhibit random errors outside the specified tolerance range. These deviations vary on different CNC machines.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3 Blade Manufacturing Process","content":"\u003cp\u003eFirst, the raw block with dimensions of 60x52x260 mm\u003csup\u003e3\u003c/sup\u003e is setup on the machine between the fixture and the tailstock. The tightening torque of the fixture bolt is 70 N.m and the tailstock pressure is set to 90 kg. Then all machining operations are carried out sequentially. The roughing and flat surface finishing are performed using three-axis, while the airfoil is machined using five-axis operations. In the final step, both the start and end of the blade are cut off. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the finishing toolpath, tool data, and cutting parameters.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4 Analysis of Variables Affecting Geometric Deviation","content":"\u003cp\u003eThe first approach to eliminating this deviation is straightening by pressing, but this process increases internal elastic stress, and therefore springback was observed over time, especially during storage. This method can be used when the blades are assembled in a short time, but the pressing will still be a manual operation with error, which has the risk of severe deformation, cracks, and rejection that limits the use of this method. In addition, this method requires non-destructive testing (NDT) to ensure the blades are free of damage.\u003c/p\u003e \u003cp\u003eThe second approach is to correct the blades by milling or grinding, which increases production time and cost. Therefore, it is necessary to analyze the distribution of deviations and identify the variable that has the greatest impact on the total dimensional accuracy.\u003c/p\u003e \u003cp\u003eTo investigate the root causes and reduce deviations, the following steps were examined:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAnalysis of dimensional changes over time due to residual stress\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSymmetric machining with reduced DOC to minimize residual stress\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eInvestigation of the Effect of Tailstock Force\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eExamination of fixture and clamping conditions\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Analysis of Dimensional Changes over Time Due to Residual Stress\u003c/h2\u003e \u003cp\u003eThe performance of machined components significantly depends on surface integrity, particularly residual stress on or beneath the machined surface [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Residual stress is present in the part even without any external loads. They are generated by mechanical, thermal, and metallurgical effects during machining processes, or by the raw material's manufacturing process [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. However, predicting the exact distribution of residual stress and its impact on components is challenging, as various influencing factors can lead to inconsistencies in repeatability. Considering that the final blades shows no dimensional deviations while clamped on the machine, errors caused by machine backlash, tool issues, and other factors are eliminated. After machining, the blade tip deviation was measured using a CMM at 20\u0026deg;C with a resolution of 0.1 \u0026micro;m (Fig.\u0026nbsp;5).\u003c/p\u003e \u003cp\u003eThe measurement was repeated multiple times at different intervals, and as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the measured values indicate minimal changes. Therefore, the deviation for each blade remains constant and is not dependent on the gradual relief of residual stress over time, occurring immediately upon unclamping. The direction and magnitude of this deviation vary between the blades.\u003c/p\u003e\u003cp\u003e \u003cdiv class=\"gridtable\"\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\u003eMeasurement of the blade tip position relative to Datum A at different times (CMM report)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeasurement Time (hours)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDeviation (mm)\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\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.037\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\u003e69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.041\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\u003e156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.042\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\u003e249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.038\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\u003e380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.040\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe measurement variations in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e are very small; it seems that these deviations are probably due to measurement errors and not related to the relief of residual stress over time.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Symmetric Machining with Reduced DOC to Minimize Residual Stress\u003c/h2\u003e \u003cp\u003eIn the machining of thick parts, the primary source of deviation is known to be bulk redistribution stress in rough machining, but in the machining of thin-walled parts, the main factor affecting deviations is the final machining. For complete control over the machining, it is necessary to consider both machining processes [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn the machining process plan, to control cutting loads and reduce stress, the roughing depth of cut (DOC) was reduced from 2 mm to 1 mm and an appropriate coolant flow rate was used. The roughing ​​was also performed in multiple stages and symmetrically. The results of both processes are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Accordingly, no improvement was observed in terms of the range and average deviations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Investigation of the Effect of Tailstock Force\u003c/h2\u003e \u003cp\u003eBased on the studies, the pressure of the tailstock can be another possible influencing parameter in the deformation of the workpiece. Therefore, the tailstock force and its repeatability were investigated. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e, a compression load cell was used to calibrate the pressure. The input pressure values of the device were compared with the output pressure value. The calibration was performed at 30 kg, 90 kg, and 120 kg. According to Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the pressure had good accuracy and repeatability and was verified. After calibration, the tailstock force in the machining of the blades was reduced from 120 Kg to 30 Kg, but no improvement was observed which seems other factors may be influencing the results.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\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\u003eTailstock Force Calibration\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNominal Tailstock Force (kg)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMeasured Tailstock Force (kg)\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=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.5\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=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89.5\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=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e119\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Examination of Fixture and Clamping Conditions\u003c/h2\u003e \u003cp\u003eThis section investigates the misalignment of the tailstock, clamping system, and raw block, as well as their effects on the final workpiece accuracy. The clamping procedure begins by setting up the raw block in the fixture with minimal bolt-tightening torque. The tailstock is then applied with a pressure of 10 kg to stabilize the block. Subsequently, the fixture jaws are loosened to allow natural alignment with the tailstock before being re-tightened to a torque of 70 N.m. Finally, the tailstock pressure is increased to 90 kg to ensure a firm and precise setup. Observations showed that after the complete clamping procedure, if the tailstock is unclamped, the fixture jaws tend to shift the block either upward or downward. The direction and magnitude of this shift are unique and repeatable for each block, and this effect is independent of the block\u0026rsquo;s weight or only has a minimal impact.\u003c/p\u003e \u003cp\u003eWith more detailed inspection observe that the blocks were sometimes setup with large misalignment. As a result, in some cases after clamping with tailstock, the position of the raw block was moved up to 0.3 mm, and after releasing, it returned to its previous position. At the same time, by placing the dial indicator on the fixture jaws and measuring their position, it was observed that this displacement of the block caused increased pressure on the jaws and they slightly opened, at the same time, it increased the amount of bolt preload and jaws pressure. Consequently, a restoring force was introduced, attempting to return both the jaws and the block to their original positions, which will cause bending stress in the block. After carefully considering the clamping of the raw block and checking the final blade's CMM report, it was inferred that the raw block with more displacement during setup resulted in more blade tip deviation.\u003c/p\u003e \u003cp\u003eIf this bending stress is significant, after rough machining and reducing the cross-section of the raw block, the blade will undergo elastic bending in the area that has the least strength and the final machining will be performed with error. Since the airfoil strength is less than the root, the blade tip exhibits the highest displacement and the root remains relatively fixed. Therefore, it seems that the workpiece is machined under an elastic deformation state and tends to return to its previous position when opened. Consequently, depending on the direction of bending, the blade tip is machined with verity, which is ultimately observed as a positional deviation in the CMM inspection report.\u003c/p\u003e \u003cp\u003eTo mitigate this phenomenon, potential sources that could cause misalignment were investigated. In this regard, the first focused on the effect of the center drill hole position. Due to surface irregularities on the raw blocks, it was not possible to accurately measure and control the position. Additionally, the limited engagement raw block and jaws (about 3mm) and the surface roughness caused the block\u0026rsquo;s position to vary with reclamping. The block displacement was measured after the tailstock clamped using a dial indicator as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e-A.\u003c/p\u003e \u003cp\u003eTo further evaluate the effect of the center drill hole position, a precisely machined block was prepared, and the position of the hole was accurately machined and controlled with an accuracy of \u0026Oslash;0.03 mm. This block was used to ensure stable clamping conditions and minimize positional deviations. However, despite the orthogonal surfaces and the correct position of the hole, the tailstock still tended to shift the position of the block. The results showed that the position of the block center drill hole is not perfectly aligned with the tailstock axis, which could be affected by the accuracy of the fixture or the position of the tailstock system.\u003c/p\u003e \u003cp\u003eTherefore, a dimensional inspection of the fixture was conducted. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e-B, by measuring the same point on the fixture and 180 degrees rotation, it was observed that the fixture had an axial runout of 0.02 mm. Then, the parallelism of the jaws with each other and its parallelism with the Y axis was examined. The non-parallelism of the two jaws with each other was 0.02 mm. The maximum non-parallelism of the jaws with the Y-axis was 0.04 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e-C). Further analysis of the midplane of the jaws revealed that the midplane shifted by 0.1 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e-D). The parallelism deviation of the jaws with each other in the XY plane is 0.05 mm. These findings confirm fixture inaccuracies that contribute to misalignment, potentially affecting the overall machining precision and final workpiece accuracy.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e schematically shows the factors that can cause bending stress in the blade after the tailstock clamp including; deviation of jaws midplane relative to the fixture midplane, the deviation of the tailstock position, the angular state of the raw material block in clamping, and the deviation of the center drill hole relative to the block midplane. In practice, it is not possible to eliminate and monitor all of these deviations in the company\u0026rsquo;s production line.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe second hypothesis is that the displacement of the blade tip occurs due to machining residual stress, or a combination of both factors, ultimately resulting in the blade tip shifting.\u003c/p\u003e \u003c/div\u003e"},{"header":"5 Finite Element Simulation","content":"\u003cp\u003eThe simulation aims to validate the initial assumptions derived from experimental measurements. Based on the finite element analysis results, it is also possible to estimate how deflection will cause errors on the workpiece. For this purpose, ABAQUS 6.14 software was employed to perform the simulation.\u003c/p\u003e \u003cp\u003eThe three-dimensional assembly model used for simulation is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e. The workpiece is clamped using fixture jaws and applying preload via the bolt force. Also, the displacement applied to the reference point (RP) at the center of the drill hole is connected to the workpiece with a coupling constraint.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe simulation was solved in one step. Due to the nature of the problem and low deformation, the material was considered pure elastic and the standard solver was used. The step time was set to 1. Due to the geometric complexity, the second-order Tet element (C3D10), a 3D continuum element with 10 integration points, was selected for meshing. The properties of the X22CrMoV12-1 material were considered isotropic according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\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\u003eMaterial Properties of X22CrMoV12-1\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProperty\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\u003eDensity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.8 g/cm\u0026sup3;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eYoung's Modulus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e190 GPa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePoisson's Ratio\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn this analysis, according to the torque of 70 N.m applied to the M16 bolt, the bolt preload force was calculated to be 23 kN. The blade root was firmly clamped using the fixture jaws and a displacement of RP\u0026thinsp;=\u0026thinsp;0.2 mm was applied to the blade tip. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e (scaled 200 times for visualization) shows that the fixture jaws effectively constrained the root and the blade bends.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn practice, the blade is machined along the Actual level line. After machining is completed and the tailstock is released, the position of the blade tip will shift, and points P\u003csub\u003e1\u003c/sub\u003e and P\u003csub\u003e2\u003c/sub\u003e will be on the Expected level line according to Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Therefore, it is expected that the value of P\u003csub\u003e3\u003c/sub\u003e with a displacement of 0.07 mm will also be on this line; but based on simulation, due to the bending effect, the displacement of the blade tip has reached P\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.14 mm. This results in a deviation of 0.07 mm from the expected value, which is ultimately reflected in the final machined part.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\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\u003ePosition of Points After Applying a 0.2 mm Displacement to the RP\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\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=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRow\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePosition\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eX (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZ (mm)\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\u003eP\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.00\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\u003eP\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.025\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\u003eP\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e181.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"6 Proposed Methods for Improving Precision in Multi-Axis Machining","content":"\u003cp\u003eConsidering the source of error, the following solutions can be proposed for further investigation:\u003c/p\u003e\n\u003cp\u003eMethod 1: Machining a U-notch at the end of the blade to transfer residual stress to the outside of the blade\u003c/p\u003e\n\u003cp\u003eMethod 2: Measuring the magnitude and direction of displacement with a probe and applying offset online\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003e6.1 Evaluation of Method 1\u003c/h2\u003e\n \u003cp\u003eIn this method, before final machining, a U-notch is created in the outer area of the blade to relief the residual stress and bending moment caused by fixture misalignment. The notch width was 11 mm and the thickness was 6 mm. In Fig. 12, the notch position is shown, along with the stress distribution and bending before and after the notch was created, evaluated by finite element simulation. As shown, the stress distribution is transferred from the airfoil to the outer part of the blade, and as a result, the root reference surface alignment with the blade tip is relatively maintained.\u003c/p\u003e\n \u003cp\u003eAccording to Fig.\u0026nbsp;12, machining a U-notch and applying displacement to the center drill hole by RP\u0026thinsp;=\u0026thinsp;0.1 mm shifted the blade tip about P\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.077 mm. Final machining under this condition is expected to result in approximately 0.01 mm deviation in the blade tip, which will ultimately improve the accuracy. This method will need to be further investigated by experimental tests for validation and stability.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e6.2 Evaluation of Method 2\u003c/h2\u003e\n \u003cp\u003eThe measurement process and an example of measuring data as shown in Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e. To assess the feasibility of this method, the blade was measured on the machine with a probe in three steps: 1- tailstock clamp, 2- tailstock unclamp, and 3- tailstock reclamp. According to Eq.\u0026nbsp;1, first, the expected correct position P\u003csub\u003ez\u003c/sub\u003e was calculated. Then, in Eq. 2, the position of the blade tip is evaluated as T\u003csub\u003ez\u003c/sub\u003e. The results consider whether the position of the blade tip is in the right place after reclamping and take any deviation into account. Based on experiments the blades return to the right position with high repeatability (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e; P\u003csub\u003e1_3\u003c/sub\u003e \u0026asymp; P\u003csub\u003e3_3\u003c/sub\u003e).\u003c/p\u003e\n \u003cp\u003eThen, in Eq.\u0026nbsp;3, the compensation value is extracted as the tool offset Z\u003csub\u003e(Offset)\u003c/sub\u003e. Considering the measuring data in Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e, the final deviation value and the necessary offset were estimated to be 0.051 mm. Next, the final machining of the blade was performed without compensation. The CMM report showed a 0.043 mm deviation, which differed by 0.009 mm from the values calculated by the machine probe and Eq. 3. This result confirm that this method is practical to compensate for the deviation with high accuracy. The flowchart detailing online blade correction is presented in Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e.\u0026nbsp;\u003c/p\u003e\n \u003ctable id=\"Tabc\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{P}_{2\\_2}-{P}_{1\\_2}}{{X}_{1}}=\\frac{{\\varvec{P}}_{\\varvec{z}}}{{X}_{1}+{X}_{2}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(1)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{T}}_{\\varvec{z}}=({P}_{3\\_1}-{P}_{3\\_3})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(2)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{Z}}_{\\left(\\varvec{O}\\varvec{f}\\varvec{f}\\varvec{s}\\varvec{e}\\varvec{t}\\right)}={P}_{1\\_2}-{P}_{3\\_2}-{P}_{z}+{T}_{z}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e"},{"header":"7 Results","content":"\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e7.1 Method 1\u003c/h2\u003e \u003cp\u003eTo experimentally compare the effect of U-notch on blade tip deviation, two machining programs\u0026mdash;one with a notch and one without\u0026mdash;were developed, and the results were analyzed on machines 1 and 2. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e15\u003c/span\u003e, the mean and range deviation for 27 blades with and without notch (Conventional method) were \u0026minus;\u0026thinsp;0.009 mm, -0.027 mm, -0.09 mm, and \u0026minus;\u0026thinsp;0.15 mm, respectively. Similarly, in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e16\u003c/span\u003e, these values for 27 blades were \u0026minus;\u0026thinsp;0.009 mm, -0.039 mm, -0.09 mm, and \u0026minus;\u0026thinsp;0.16 mm. Additionally, the standard deviation for the blades with and without notch in Figs.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e15\u003c/span\u003e and \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e16\u003c/span\u003e was calculated as 0.026 mm, 0.027 mm, and 0.039 mm, 0.045 mm, respectively.\u003c/p\u003e \u003cp\u003eThe results indicated that the mean and range deviation were close in both machines. By creating the U-notch machining, the mean and range deviations were reduced by approximately 73% and 42%, respectively. However, the deviation range remained around 0.09 mm which is out of the acceptable tolerance limit. This deviation range is unsatisfactory. Consequently, the notch thickness was reduced from 6 mm to 4 mm and 3 mm. While this reduction caused more declaration in deviation, it also introduced instability, increasing the risk of angular misalignment, surface quality deterioration, and other defects.\u003c/p\u003e \u003cp\u003eIn general, this method can relatively improve the deviation condition, but notch thickness is a key parameter and structural stability is crucial.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e7.2 Method 2\u003c/h2\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e17\u003c/span\u003e, the deviation of the blade tip that is machined using the online control method on machines 1 and 2 is presented. The results show a substantial reduction in deviation, from 0.15 mm and 0.16 mm to 0.028 mm and 0.045 mm\u0026mdash;a fourfold improvement\u0026mdash;while good repeatability is achieved. Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e18\u003c/span\u003e provides additional insight into the effect of the notch and probing methods as opposed to conventional machining. With the notch method, the standard deviations produced on machines 1 and 2 are 33% and 41%, respectively, and the mean deviation are %67 and 77%. However, due to the range of deviations, there is the probability and risk of producing a part outside the acceptable tolerance limits.\u003c/p\u003e \u003cp\u003eWhile, on the other hand, the probing method showed higher accuracy with standard deviation and mean deviation improvements in the range of 76\u0026ndash;97% and 71\u0026ndash;78% for machines 1 and 2, respectively. Considering the range of deviations within 0.028 mm and 0.045 mm and high repeatability, this technique was extremely successful.\u003c/p\u003e \u003cp\u003eThus, the application of an online control method using a Renishaw OMP60 probe provides a reliable solution to decrease the deviations without corrective grinding or redesign of fixtures. Not only does this technique enhance machining accuracy, but also simplifies production processes, lowers dependence on operators, minimizes processing times, and saves overall costs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"8 Conclusion","content":"\u003cp\u003eIn this study, the aim is to achieve acceptable geometric tolerance in machining the contact face surfaces of thin-walled blades (steam turbine rotary blades) to meet assembly requirements. Therefore, efforts were made to identify and eliminate the source of random error. An attempt was also made to make the methods easily applicable in manufacturing workshops without major modifications in the preparation and machining process. For this purpose, several error sources were evaluated and finite element simulation was performed. It was determined that various types of errors may cause deviation in the workpiece. In addition, the magnitude and direction of each error can increase or decrease the overall deviation and cannot be predicted. Therefore, geometric deviation results from a sum of different errors, and eliminating them is highly difficult or impossible.\u003c/p\u003e \u003cp\u003eBy root cause analysis, two primary sources of deviation were revealed:\u003c/p\u003e\u003cp\u003e1.\u0026nbsp; \u0026nbsp;\u0026nbsp;Bending stress due to fixture, tailstock system, and raw block misalignment.\u003c/p\u003e\n\u003cp\u003e2.\u0026nbsp; \u0026nbsp;\u0026nbsp;Machining residual stress causes elastic deformation after releasing the tailstock.\u003c/p\u003e\n\u003cp\u003eFinally, two methods were presented to improve geometric accuracy:\u003c/p\u003e\n\u003cp\u003e\u0026middot; Notch Machining for Stress Relief (Method 1): A U-Notch was created at the end of the blade to relief residual machining stress and bending forces caused by fixture misalignment.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Online Measurement and Compensation (Method 2): Geometric deviation compensation was achieved by online measurement and estimation of the elastic deformation of the blade in the unclamped state of the tailstock.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo assess the effectiveness of these methods, the blades were machined on two five-axis machining centers using the techniques. The results revealed that:\u003c/p\u003e\n\u003cp\u003e1.\u0026nbsp; \u0026nbsp;\u0026nbsp;Elastic deformation occurs immediately after the tailstock is released, and its magnitude and direction cannot be predicted.\u003c/p\u003e\n\u003cp\u003e\u0026middot; The contact face surfaces are machined correctly and without deviation in the clamped state. Immediately after the tailstock is released, elastic deformation occurs and it is not time-dependent.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026middot; These deviations on thin-walled parts such as blades are common, and it\u0026rsquo;s one of the machining challenges and considered a random error.\u003c/p\u003e\n\u003cp\u003e2.\u0026nbsp; \u0026nbsp;\u0026nbsp;No noticeable change was observed in deviations with reduced DOC in roughing and decreased tailstock force.\u003c/p\u003e\n\u003cp\u003e\u0026middot; The roughing DOC was reduced from 2 mm to 1 mm, and an appropriate coolant flow was used roughing was performed in several stages and symmetrically.\u003c/p\u003e\n\u003cp\u003e\u0026middot; The amount of tailstock force was calibrated and its pressure was reduced to 30 kg, but no noticeable change was observed in the deviations.\u003c/p\u003e\n\u003cp\u003e3.\u0026nbsp; \u0026nbsp;\u0026nbsp;Based on experiments, fixture misalignment was identified as a main source of deviation.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Axial runout, parallelism, and jaw symmetry were measured on the CNC machine, confirmed that the fixture has deviations.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Misalignment of the tailstock system, deviation in the position of the center drill hole of the raw material, surface irregularities, and rough surfaces, will cause bending stress to the block.\u003c/p\u003e\n\u003cp\u003e\u0026middot; With machining and reduced stiffness in the airfoil, this bending can be applied to the blade airfoil as the thin wall causes elastic deformation. Machining the blade under these conditions will cause errors. Eliminating all these factors in workshop is neither practical nor cost-effective.\u003c/p\u003e\n\u003cp\u003eTwo methods were proposed to reduce dimensional error:\u003c/p\u003e\n\u003cp\u003e1.\u0026nbsp; \u0026nbsp;\u0026nbsp;Transfer the residual machining stress and bending force to the outside of the blade by creating a U-notch at the end of the blade.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Blades were machined with and without a notch on two different CNC machines.\u003c/p\u003e\n\u003cp\u003e\u0026middot; The results showed that the standard deviation and the range of deviations were improved by approximately 37% and 42%, respectively.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Further reducing the thickness of the notch from 6 to 4 and 3 mm, the deviations were reduced, destabilized blade fixturing, and parameters such as angle, surface quality, etc. were out of control. This method can generally improve the deviations relatively, but choosing the notch thickness must be carefully considered.\u003c/p\u003e\n\u003cp\u003e\u0026middot; The notch method was improved (range of deviations 0.09 mm) but insufficient for achieving the acceptable tolerance limit (0.06 mm).\u003c/p\u003e\n\u003cp\u003e2.\u0026nbsp; \u0026nbsp;\u0026nbsp;The online measurement and compensation method.\u003c/p\u003e\n\u003cp\u003e\u0026middot; A mathematical model was developed to estimate the blade\u0026rsquo;s elastic deformation during machining. This was achieved by unclamping the tailstock and measuring the elastic deformation of the blade during the machining process with a Renishaw OMP60 probe. The estimated error was then directly compensated in the machining program.\u003c/p\u003e\n\u003cp\u003e\u0026middot; Experimental tests show a good reduction in deviations, and 30 blades were successfully produced with a deviation range of 0.028 mm and 0.045 mm, well within the tolerance.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026middot; Using this method, standard deviation and mean deviation improved from 76% to 97% and 71% to 78%, respectively.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026middot; Due to its high repeatability to produce blades within tolerance (\u0026lt; 0.06 mm), this method can be used as an effective solution to eliminate random error in thin-walled blades.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBy comparing the results obtained with the study of Jian-Hua et al., although their process and parts are different, they also focused on the importance of the clamping method to design and manufacture the fixture and finally produced the correct part by grinding [14]. In the present study, it was also possible to produce the correct part by grinding, but an attempt was made to produce the correct blades in one step without redesigning the standard LANG fixture or adding a correction process. Li et al. and Juan Zha et al. also focused on the analysis of clamping forces and the importance of the clamping method, which is essential for manufacturing parts within the allowable tolerance range [13-28].\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eI would like to express my sincere appreciation for the invaluable support from my colleagues at TUGA company, whose continuous encouragement and assistance\u0026mdash;both technical and moral\u0026mdash;have been critical throughout this project, with particular mention of Javad Bigdeli and Dr. Masoud Saberi.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author did not receive any direct financial support for this research. However, the technical equipment and facilities of MAPNA Turbine Engineering and Manufacturing Company (TUGA) were used during the research process.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eSoori M, Asmael M (2022) A review of the recent development in machining parameter optimization. Jordan J Mech Ind Eng 16(2):205\u0026ndash;223\u003c/li\u003e\n\u003cli\u003eApro K (2008) Secrets of 5 Axis Machining, New York\u003c/li\u003e\n\u003cli\u003eSoori M, et al (n.d.) A review in capabilities and challenges of 5-axis CNC milling machine tool operations\u003c/li\u003e\n\u003cli\u003eUddin MS, Mian AJ, Rahman M, Senthil Kumar A, Bashir S (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Precis Eng 33(2):194\u0026ndash;201\u003c/li\u003e\n\u003cli\u003eIbaraki S, Matsubara A, Sato H, Yamaji I (2010) Machining tests to identify kinematic errors on five-axis machine tools. Precis Eng 34(3):387\u0026ndash;398\u003c/li\u003e\n\u003cli\u003eMayr J, Jedrzejewski J, Uhlmann E, Donmez A, H\u0026auml;rtig F, Wendt K, Schmitt R, Weikert S, Kunzmann H (2012) Thermal issues in machine tools. CIRP Ann 61(2):771\u0026ndash;791\u003c/li\u003e\n\u003cli\u003eZhao D, Bi Y, Ke Y (2017) An efficient error compensation method for coordinated CNC five-axis machine tools. Int J Mach Tools Manuf 123:105\u0026ndash;115\u003c/li\u003e\n\u003cli\u003eBohez EL (2002) Compensating for systematic errors in 5-axis NC machining. Comput Aided Des 34(5):391\u0026ndash;403\u003c/li\u003e\n\u003cli\u003eHuang X, Sun J, Li J (2015) Effect of initial residual stress and machining-induced residual stress on the deformation of aluminium alloy plate. Stroj Vestn J Mech Eng 61(2):131\u0026ndash;137\u003c/li\u003e\n\u003cli\u003eMasoudi S, Asnafi N, Movahhedy MR, Hosseini M (2015) Effect of machining-induced residual stress on the distortion of thin-walled parts. Int J Adv Manuf Technol 76:597\u0026ndash;608\u003c/li\u003e\n\u003cli\u003eAstakhov V, Basak A, Dixit US (2016) Metal Cutting Technologies: Progress and Current Trends. Vol. 1. Walter de Gruyter GmbH \u0026amp; Co KG\u003c/li\u003e\n\u003cli\u003eZhuang Q, Liu H, Tang W, Wang L, Zhao G, Gao T (2023) A novel pre-travel error compensation strategy for five-axis on-machine measurement with a touch-trigger probe. IEEE Trans Instrum Meas\u003c/li\u003e\n\u003cli\u003eLiu X, Yang Y, Xu K, Xu J (2024) A workpiece setup optimization method for 5-axis machining with motion coherence and stiffness enhancement. Precis Eng 88:867\u0026ndash;883\u003c/li\u003e\n\u003cli\u003eSoori M, Asmael M, et al (2023) Minimization of surface roughness in 5-axis milling of turbine blades. Mech Based Des Struct Mach 51(9):5213\u0026ndash;5230\u003c/li\u003e\n\u003cli\u003eLi ZL, Wang Z, Zhu LM (2018) Surface form error prediction in five-axis flank milling of thin-walled parts. Int J Mach Tools Manuf 128:21\u0026ndash;32\u003c/li\u003e\n\u003cli\u003eChen D, Zhang X, Liu Y, Feng P, Wang J (2015) Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool. Int J Mach Tools Manuf 94:74\u0026ndash;87\u003c/li\u003e\n\u003cli\u003eDing G, Liu Y, Zhang X, Wang Q, Wang Y (2014) Prediction of machining accuracy based on a geometric error model in five-axis peripheral milling process. Proc Inst Mech Eng Part B J Eng Manuf 228(10):1226\u0026ndash;1236\u003c/li\u003e\n\u003cli\u003eLi ZL, Zhu LM (2019) Compensation of deformation errors in five-axis flank milling of thin-walled parts via tool path optimization. Precis Eng 55:77\u0026ndash;87\u003c/li\u003e\n\u003cli\u003eZha J, Hu L, Yan Y, Jiang C (2023) An accuracy evolution method applied to five-axis machining of curved surfaces. Int J Adv Manuf Technol 125(7):3475\u0026ndash;3487\u003c/li\u003e\n\u003cli\u003eYu JH, Chen ZT, Jiang ZP (2016) A control process for machining distortion by using an adaptive dual-sphere fixture. Int J Adv Manuf Technol 86:3463\u0026ndash;3470\u003c/li\u003e\n\u003cli\u003eWang H, Li H, Yao C, Kou M, Wang W, Huang B, Zheng W (2015) Integrated analysis method of thin-walled turbine blade precise machining. Precis Eng Manuf 16:1011\u0026ndash;1019\u003c/li\u003e\n\u003cli\u003eWang T, Liu Y, Wu B, Zhang Y, Yang D (2016) Application of low-melting alloy in the fixture for machining aeronautical thin-walled component. Int J Adv Manuf Technol 87:2797\u0026ndash;2807\u003c/li\u003e\n\u003cli\u003eMoradi Kelardeh S, Shafiei E, Hemmati R, Bagheri M (2022) An investigation on the effect of interference clearance of bushing on fatigue strength in triangle suspension. J Engine Res 67(67):30\u0026ndash;41\u003c/li\u003e\n\u003cli\u003eKadhom HK, Mohammed AJ, Sillanp\u0026auml;\u0026auml; M (2024) The influence of thickness and interference fit ratio on fatigue phenomenon: an empirical study. Math Model Eng Probl 11(1)\u003c/li\u003e\n\u003cli\u003eLin K, Sun J, Zhang J (2017) A numerical study on the redistribution of residual stress after machining. In: ASME Int Mech Eng Congr Expo. American Society of Mechanical Engineers\u003c/li\u003e\n\u003cli\u003eThakur A, Gangopadhyay S (2016) State-of-the-art in surface integrity in machining of nickel-based super alloys. Int J Mach Tools Manuf 100:25\u0026ndash;54\u003c/li\u003e\n\u003cli\u003eAkhtar W, Lazoglu I, Liang SY (2022) Prediction and control of residual stress-based distortions in the machining of aerospace parts: a review. J Manuf Process 76:106\u0026ndash;122\u003c/li\u003e\n\u003cli\u003eLi B, Melkote S (2001) Fixture clamping force optimisation and its impact on workpiece location accuracy. Int J Adv Manuf Technol 17:104\u0026ndash;113\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Multi-axis machining, Turbine blades, Geometrical accuracy, Residual stress","lastPublishedDoi":"10.21203/rs.3.rs-6385585/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6385585/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study aims to achieve the required geometric tolerance in the machining of the contact face surfaces on thin-walled rotary steam turbine blades to meet strict assembly requirements. The focus was on recognizing and reducing random errors contributing to dimensional deviation. Two methods were considered: (1) creating a U-notch at the end of the blade to relieve residual stress and bending forces due to fixture, tailstock system, and raw block misalignment, and (2) an online measurement and compensation method to estimate and correct elastic deformation during machining. Experimental tests on two five-axis CNC machining centers and finite element simulations were used to evaluate the impact of these methods. The results show that the U-notch method reduces the standard deviation and deviation range by approximately 37% and 42%, respectively, but the deviation range still exceeded the acceptable tolerance (0.09 mm\u0026thinsp;\u0026gt;\u0026thinsp;0.06 mm). However, the online measurement and compensation method reached remarkable improvements, reducing the standard deviation by 71% and 78%, and improving the mean deviation by 76% and 97%, bringing the blade tip deviation within the acceptable tolerance range (0.028 mm, 0.045 mm\u0026thinsp;\u0026lt;\u0026thinsp;0.06 mm). This technical study reveals the effectiveness of online compensation techniques as a highly efficient solution for reducing post-machining deformation and ensuring dimensional accuracy in turbine blades without extra operations such as grinding or fixture redesign. This practical method can be easily implemented in workshops, simplifying production processes and reducing costs.\u003c/p\u003e","manuscriptTitle":"Improving Geometric Accuracy in Multi-Axis Machining of Thin-Walled Turbine Blades: Practical Methods for Minimizing Error and Online Compensation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-29 14:17:44","doi":"10.21203/rs.3.rs-6385585/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0618c44d-e1e0-4c7c-8919-ce8f3c397f9b","owner":[],"postedDate":"April 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-27T15:01:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-29 14:17:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6385585","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6385585","identity":"rs-6385585","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}