Experimental-numerical framework integrated analysis for a study of multi-plate incremental forming (MPIF)

Experimental-numerical framework integrated analysis for a study of multi-plate incremental forming (MPIF) | 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 Experimental-numerical framework integrated analysis for a study of multi-plate incremental forming (MPIF) Ming-Chang Wu, Jyun-Wei Lai, Shang-Rong Cai, Chung-Chen Tsao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9410748/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Traditional single-point incremental forming (SPIF) requires no mold and allows flexible manufacturing of small quantities and variety but the surface quality of the workpieces after processing is poor, so it is not commonly used. Multi-plate incremental forming (MPIF) reduces tool wear on the workpiece surface so machining quality is increased. MPIF is complex and exhibits nonlinear characteristics so numerical simulation software is required. ABAQUS is a numerical simulation tool for the analysis of complex and nonlinear problems and is widely used in research and industry. This study uses an experimental-numerical framework to determine the forming characteristics of MPIF on AL1050 aluminum alloy plates and compares it with traditional SPIF. The results show that step depth and tool diameter significantly affect the forming characteristics of MPIF. The results also demonstrate that MPIF can be used to manufacture thin-plate parts with smooth surfaces and minimal waviness and efficiency is significantly increased. Numerical simulation tools address the forming force analysis problem for MPIF and can be used to analyze complex and nonlinear problems. Single-point incremental forming Surface quality Multi-plate incremental forming Forming characteristic Numerical simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Sheet metal processing (SMP) is a manufacturing technology that uses molds and an external force to shape thin metal plates. It allows high-volume, rapid production, excellent formability, high strength-to-weight ratio and flexible production so it is currently widely used in the manufacture of plate metal parts in the machinery, electronics, aerospace and automotive industries. However, it is not always used to manufacture plate metal parts in small batches or for developmental parts. Single-point incremental forming (SPIF) eliminates the need for the design and fabrication of molds because it uses a non-sharp ball tool, machining paths and a CNC machine to manufacture customized plate metal part and processing time is significantly reduced. SPIF is being developed by the plate metal forming industry. Duflou et al. [ 1 ] demonstrated that the forming force for SPIF on metal plates increases with the values for four common processing parameters (step depth, tool diameter, wall angle and plate thickness). Step depth has the least effect on the forming force for metal plates but in terms of process efficiency, moderately increasing step depth reduces the processing time. SPIF requires no lubricant so tool wear is significant and the tool and plate surface can crack. Le et al. [ 2 ] demonstrated that step depth and tool diameter have a significant effect on the formability of thermoplastic materials during SPIF. Reducing step depth and feed rate and increasing spindle speed improves formability. There is a significant interaction between step depth, feed rate and tool diameter. Bagudanch et al. [ 3 ] confirmed that a larger tool diameter and step depth produces a larger contact area and increases forming force with the plate during SPIF. However, as the spindle speed increases, the friction between the contact areas for the tool and the plate increases, which moderately improves the plastic deformation of the workpiece and the forming force is reduced. Rosca et al. [ 4 ] studied the effect of step depth and tool diameter on spring-back, thickness variation and forming force for SPIF. The results show that increasing step depth reduces variation in the finished product thickness and increases the forming force and spring-back. Increasing the tool diameter reduces plate thickness and increases forming force, but spring-back is less affected by tool diameter. Grimm and Mears [ 5 ] used SPIF for a workpiece by moving the tool path radially along the workpiece center, instead of along its periphery to give a more uniform thickness profile and increase formability by 21%. As the wall angle increases, single-step SPIF can cause local thinning and cracking of the material. Wu et al. [ 6 ] used a parametric multi-step forming strategy to eliminate local thinning and stepped features for large wall angle shapes. This strategy improves the formability of large wall angle shapes by avoiding local over-thinning and redistributing material thickness and minimizes geometric deviation that is caused by stepped features. Behera et al. [ 7 ] provided a concise overview of the current applications of SPIF for different hardware platforms, forming mechanics, failure mechanisms, force estimation, toolpath and tool strategy applications, the development of process planning tools, process simulation and sustainable manufacturing, and provided a roadmap for its future research directions. SPIF does not require costly stamping dies to achieve excellent performance in small and medium batch production but compared with stamping, traditional SPIF can produce excessively thin walls and premature fractures in single workpieces and leaves obvious machining marks on the contact surface between it and the tool, so it is not widely used. Skjoedt et al. [ 8 ] added a disposable plate to the plate metal to be formed to avoid contact between the machining tool and the workpiece during SPIF. The plate slightly reduces the forming efficiency of SPIF and eliminates wear on the workpiece surface and improves processing quality. Chang and Chen [ 9 ] confirmed that the three-plate incremental forming (TSIF) process produces parts with smooth surfaces and no obvious ripples and the forming efficiency is significantly improved. The forming limit and fracture strain for AA2024 and AA7075 plates are significantly improved after TSIF, which is of great significance for the manufacturing of low ductility plate metal parts. MPIF increases the forming limit and surface quality of the workpiece but its overall forming behavior is a complex and involves nonlinear change. In terms of manufacturing system control, MPIF is exponentially more difficult than SPIF and computer-aided engineering (CAE) is required for its study. Finite element analysis (FEA) is the core mathematical theory of CAE and predicts the microstructural evolution of machining deformation. Comparison with experimental results to verify the effectiveness of the model allows analysis of the forming force for SPIF on the workpiece and demonstrates the microstructural evolution during processing, which creates a theoretical basis for process optimization [ 10 – 12 ]. Kumar and Reddy [ 11 ] used the Taguchi method, ABAQUS software and SPIF process parameters (plate thickness, step depth, tool radius and friction coefficient) to study the forming performance for the manufacturing of parabolic cups of AA6082 alloy. The results show that the process parameters that most significantly affect the forming of parabolic cups by SPIF are plate thickness and step length. Abdelkader et al. [ 12 ] studied the process parameters for SPIF (tool path vertical step length, initial plate thickness and truncated cone wall angle) to predict the forming force and thickness variation for a double-layer material, compared to a single-layer plate. A double-layer plate is a low-cost material for SPIF and has important practical application significance. Cappellini [ 13 ] used the results of FEA simulations to show that SPIF achieves higher accuracy and more uniform material thickness distribution in the roughing-finishing strategy (ModeMD) and reduces spring-back. An experimental test on aluminum alloys (AA1050 H24 and AA5754 H111) with different tool radii verified the simulation results and showed that the use of multi-step trajectory increases the accuracy of process geometry for SPIF. Nguyen et al. [ 14 ] used experimental-numerical comprehensive analysis to show that the vertical step length (58.6%) has the greatest effect on the forming wall thickness for SPIF using AA1050 aluminum alloy, followed by the feed rate (27.8%) and the tool radius (12.5%). A smaller wall angle significantly increases the forming height for SPIF in the workpiece and the simulation and experimental deviation is the least, at only 1.17%. Defects that are caused by using only a single-plate for SPIFs, such as excessively thin walls, premature fracture and uneven surface roughness (SR), have been the subject of studies. Some studies use upper and lower plates to separate the workpiece, tool and bearing. This reduces some SPIF defects but crates problems between the plates and the workpiece. This study uses ABAQUS software and experiments to compare the surface quality and forming limit of SPIF and MPIF. Numerical simulation is used to determine the causes of specific instability defects in MPIF and to address these defects and improve surface finish. A robust experimental-numerical framework is established for this process to give a theoretical basis and practical guidelines for improving product quality and manufacturing efficiency. 2. Methodology To compare SPIF and MPIFs, this study uses an axisymmetric conical part with a top diameter of 70 mm, a depth of 25 mm, a bottom diameter of 20 mm and a wall angle of 45° (Fig. 1 ). Experiments used AL1050 aluminum alloy plates and a three-axis CNC machine (Tungtai Machinery TMV-850QⅡ) with a maximum spindle horsepower of 11 kW and a maximum speed of 10,000 rpm, as shown in Fig. 2 . The workpiece dimensions are 100 mm ⋅ 100 mm ⋅ 1.0 mm and the thickness of the upper and lower plates is 0.5 mm. The machining path for the multi-plate axisymmetric conical model part was generated using HYPERMILL software with a clockwise oblique 3D contour-lowering machining method and a spindle speed of 0 rpm and a feed rate of 1,000 mm/min. To determine variation in the forming during MPIF, this study uses a piezoelectric rotary dynamometer (Type 9170A) this is manufactured by Kistler, Switzerland. This dynamometer measures the torque that is applied by the tool to the workpiece and the loads in three orthogonal directions (X, Y and Z axes). Machining data for the X and Y axial forces and torque shows that the Z axial force has the most significant effect on SPIF so this study uses the Fz data to determine the quality of the forming force. The workpiece thickness changes only slightly after SPIF so a digital thickness gauge (Qualitot-21752, China) with an accuracy of 0.001 mm was used for measurement. This study uses step depth (three levels) and tool diameter (four levels), as shown in Table 1 . The tool material was tungsten carbide steel with a length of 100 mm to construct a ball end mill without a cutting edge. The MPIF fixture and its experimental flowchart are shown in Figs. 3 and 4 . To prevent slippage between the workpiece and the upper and lower plates during MPIF, this study places it inside a 1.0 mm thick brass shim. The shim measures 115 mm ⋅ 115 mm and has four rounded corners with a radius of 6 mm. 5 mm-diameter holes were drilled at the four corners of the 100 mm ⋅ 100 mm rectangle in the center of the brass shim and then a 100 mm ⋅ 100 mm hollow rectangle was milled out to hold the workpiece, as shown in Fig. 5 . To reduce friction and heat that are generated during prolonged contact between the cutting tool and the workpiece in the SPIF process, this study used SW-68 Hercules® Slideway Oil for lubrication and cooling. The SR measurements for the conical finished product's wall angle and four points 90° apart on the inner wall surface after MPIF machining used a 2° graduated gauge (SHINWA-62995) and a 0.001µm SR meter (Mitutoyo SURFTEST SV-3100H4) to determine the effect of experimental parameters on SR variations in the conical finished product's wall angle and inner wall surface. The average SR value for the workpiece before machining was 0.6225 µm. Table 1 Experimental parameters for MPIF Processing conditions Value Spindle Speed (rpm) 0 Upper plate thickness (mm) 0.5 Feed Rate (mm/min) 1,000 Experimental parameter Level 1 Level 2 Level 3 Level 4 Step depth (mm) 0.5 1.0 1.5 Tool diameter (mm) 8 10 12 14 The presence of the plates changes the machining path for MPIF, depending on the thickness of the finished product. To ensure the accuracy of the final product shape, the machining path for MPIF must undergo inward compensation. For an upper plate thickness of 0.5 mm, the tolerance in the XY plane is 0.21 mm, as shown in Fig. 6 . The MPIF path is shortened inward so its distance (7160.9 mm) is 286.9 mm shorter than that for SPIF (7447.8 mm). When machining large parts or forming thicker upper plates, MPIF uses a significantly shorter machining time than SPIF. 3. Finite element method (FEM) To determine the variation in the forming load for MPIF on AL1050 aluminum alloy sheets, this study uses FEA to model the load based on the following assumptions: (1) The model (bulk and upper and lower plates) is homogeneous, isotropic and conforms to the von-Mises yield criterion; (2) the model exhibits isotropic hardening and plastic incompressibility; (3) the fixture and tool are considered to be perfectly rigid bodies and (4) the effect of the frictional temperature due to sliding between the tool and the plate and grain slip of the material during the forming process are ignored. During the SPIF process, the magnitude and fluctuation of the forming force are directly related to the forming state of the material, the generation of defects and the quality of the final product [ 15 ]. Forming force has a significant effect so it is accurately measured to ensure the success of SPIF. In experiments and practical applications, a dynamometer (such as piezoelectric platforms) is used to monitor the force changes in the forming process in real time. This data is used to verify the theoretical model and to allow online control. If abnormal forming force is detected, the process parameters (workpiece thickness, tool diameter, wall angle) are adjusted or processing is suspended to avoid scrap [ 16 ]. To determine the changes in the forming force for MPIF on AL1050 aluminum alloy plates, ABAQUS software is used. The ABAQUS simulation analysis model uses a surface-to-surface contact mode. The master-surface is the outer surface of the tool and the slave-surface is the three surfaces of the sheet metal. The data from the finite element model is shown in Table 2 . The actual stress-strain curves for the AL1050 sheet metal are shown in Fig. 7 . As plastic deformation increases, the stress in the AL1050 sheet metal increases slowly, which shows that it is very ductile. The Coulomb friction coefficient (µp) between the tool and the workpiece is 0.1. The workpiece is firmly fixed between the support plate and the pressure plate to prevent slippage. Table 2 Data for the FEM model Workpiece Young’s modulus Poisson ratio Initial yield stress Density AL1050 69 GPa 0.33 165 MPa 2,700 kg/m 3 . To determine the forming force for MPIF in an axisymmetric conical product, this study initially uses 80,000 meshes and increases the mesh count in increments of 10,000. The convergence of the numerical calculation results is used to select the most suitable mesh for finite element simulation. The minimum forming force for MPIF converges at 120,000 meshes so this study uses 120,000 meshes for FEA, as shown in Fig. 8 . 4. Results and Discussion 4.1 Forming force During MPIF, the tool must first overcome its elastic or plastic deformation resistance and compress before it can apply sufficient forming force to the workpiece to shape it. Figure 9 compares the forming forces for SPIF and MPIF for different processing parameters (step depth and tool diameter). The results in Fig. 9 show that the forming force for MPIF is greater than that for SPIF. The forming forces for both increase as step depth and tool diameter increase but these differ by a magnitude of three. If the tool diameter is fixed, the deformation volume, local bending moment and tensile strain for the material also increase as step depth increases. If the step depth is fixed, the contact area and deformation range also increase as the tool diameter increases. To maintain the required deformation pressure per unit area, the forming force for MPIF must increase. During MPIF, the tool contacts the workpiece through a partition that deforms a surface or region, rather than through direct point contact (SPIF). To drive plastic flow across this larger and more uniform area of material, MPIF requires a greater forming force. Elastomeric separators wrap more tightly around the cutting tool during SPIF, which creates a normal constraint pressure on the sheet metal below. This constraint force causes the sheet metal to accumulate and flow around the cutting tool, which causes wrinkles, so MPIF must overcome greater friction and the forming force is greater. Figure 10 compares the forming forces obtained using ABAQUS software and for practical MPIF for an 8 mm tool diameter and a 0.5 mm step depth. Both are very accurate and errors are less than 5%, so FEM software allows reliable analysis of MPIF. 4.2 Plate thickness During SPIF, forming conditions significantly affect the overall workpiece thickness distribution. Figure 11 compares the finished product thickness distribution for SPIF and MPIF for an 8 mm tool diameter and different step depths. Figure 11 (a) shows that the least thickness for SPIF is 32-38.5 mm from the zero point and a smaller step depth increases forming thickness. The least thickness for MPIF is 27.5–32 mm from the zero point and larger step depths increases forming thickness, as shown in Fig. 11 (b). During SPIF, the thickness deformation is highly concentrated near the contact point between the tool and the sheet metal. Due to the workpiece geometry (axisymmetric cone), the material experiences the greatest biaxial tensile stress in the middle section of its sidewalls. This creates localized strain concentration and insufficient material replenishment so some locations experience a rapid reduction in thickness. During SPIF, a smaller step depth means a larger forming thickness but during MPIF, the tool must first compress the upper plate to transfer the forming force to the workpiece, so the upper plate evenly distributes the concentrated load of the cutting tool to a larger contact pressure area and the workpiece is formed over a wider range. The upper plate compresses and constrains so the plastic deformation zone for the material moves closer to the bottom rounded corner area on the formed part. The upper plate restricts free bulging or the accumulation of material in the middle section of the sidewall so maximum deformation is concentrated near the bottom. Figure 12 compares the finished product thickness for SPIF and MPIF for different processing parameters. For MPIF, a smaller step depth (0.5 mm) results in a smaller forming thickness and the opposite is true for SPIF, as shown in Fig. 12 . During MPIF, the tool applies normal constraint pressure to the material, which restricts the workpiece from free bulging or wrinkling in the thickness direction. For a smaller step depth (0.5 mm) during MPIF, the tool's movement per step is small. However, the upper plate continuously presses against the workpiece so it is repeatedly compressed in localized areas. Friction and the constraint of the upper plate prevents the material from flowing smoothly outwards if a smaller step depth is used for MPIF: there is a localized accumulation in front of the tool so this area is thinner because compression is greater. A smaller step depth for MPIF increases the number of processing passes (longer processing time), so the workpiece endures prolonged repeated compression and friction and remains in a state of work hardening (rapid heat dissipation), so accumulated local deformation increases thinning. 4.3 Surface roughness (SR) The SR of the workpiece after SPIF directly affects its mechanical properties (fatigue strength, wear resistance and contact rigidity) and application value. Figure 13 shows a comparison of the SR for SPIF and MPIF for different values for processing parameters. For SPIF, if the step depth is fixed, SR decreases as the tool diameter increases. For a step depth of 0.5 mm, Ra decreases from 1.13 µm for an φ8 mm tool to 0.50 µm for a φ14 mm tool, as shown in Fig. 13 (a). During SPIF, a larger diameter tool has a larger contact area with the workpiece (i.e., the pressure per unit area is reduced), so there are fewer surface scratches and ripples and surface quality increases. If the tool diameter is fixed, the SR increases as the step depth increases. For an φ8 mm tool, Ra increases from 1.13 µm for a 0.5 mm step depth to 1.78 µm for a 1.5 mm step depth. Increasing the step depth increases the vertical descent (deformation) of the tool per layer, so stepped marks are more noticeable and localized uneven deformation occurs on the workpiece surface. For this study, the optimal surface quality (Ra = 0.50 µm) is achieved for SPIF using a φ14 mm tool and a step depth of 0.5 mm. For MPIF, if the step depth is fixed, the SR decreases as tool diameter increases but there are local fluctuations. If the step depth is 0.5 mm, Ra decreases from 1.07 µm for an φ8 mm tool to 0.78 µm for a φ14 mm tool, but the Ra for a φ10 mm tool (Ra = 0.66 µm) is slightly less than that for a φ12 mm tool (Ra = 0.83 µm) and a φ14 mm tool (Ra = 0.78 µm), as shown in Fig. 13 (b). A larger tool diameter increases the surface quality of the workpiece but due to the influence of the upper plate, the Ra trend is not as stable as that for SPIF without an upper plate. If the tool diameter is fixed, the relationship between SR and step depth is less clear. In particular, the change in Ra is particularly significant for a φ10 mm tool. The value for Ra increases from 0.66 µm for a step depth of 0.5 mm to 1.15 µm for a step depth of 1.0 mm. The Ra value decreases from 1.15 µm to 0.97 µm if the step depth increased to 1.5 mm, probably because there is a smaller overlap in the step between toolpaths with a φ10 mm tool at a step depth of 1.0 mm and the upper plate is in the nonlinear compression transition zone. In terms of the overall workpiece surface finish, the Ra value for MPIF is mostly lower the value for SPIF, so SPIF gives lower SR. 4.4 Wall angle Multiple plates are stacked for MPIF (upper plate + workpiece + lower plate) so the wall angle is more complex than for SPIF. Figure 14 compares the wall angle for SPIF and MPIF for different values for processing parameters. The results in Fig. 14 show that SPIF shapes the wall angle of the workpiece to 45° for different values of processing parameters because MPIF uses multi-plate stacking, which increases the overall bending stiffness. The upper plate absorbs some of the deformation energy during MPIF so there is less strain on the workpiece and the final wall angle is affected. If a lower step depth is used for MPIF, the workpiece accumulates frictional heat and becomes elastic-plastic. When the external force is released and the heat dissipates, the workpiece recovers elastically, which can increase the wall angle deviation, as shown in Fig. 14 (b). 5. Conclusions SPIF allows higher formability limits and easier toolpath modification than SPF so it is ideal for small-batch production, prototyping or customized sheet metal parts. MPIF gives better workpiece surface quality but the processing effects that are caused by multi-plate stacking create more complex problems than SPIF. ABAQUS software is ideal for nonlinear problems so it is used to simulate and analyze engineering problems. This study uses an experimental-numerical framework to determine the forming characteristics for AL1050 aluminum alloy plate for different step depths and tool diameters using SPIF and MPIF. The main conclusions are summarized as follows: Using a lower step depth and a larger tool diameter for SPIF yields a finer and smoother workpiece surface texture. During MPIF, the upper plate reduces the surface texture and a smaller step depth still produces path marks on the workpiece surface. The forming force for SPIF and MPIF increases as step depth and tool diameter increase but MPIF forms three plates simultaneously so the forming force is approximately 1.7 to 2.4 times greater than the force that is required for SPIF. Analysis of the forming force for MPIF using ABAQUS software yields highly accurate results (error within 5%), which confirms that it is a reliable tool for analysis. SPIF and MPIF paths decrease as step depth and tool diameter increase. The inward MPIF path uses a machining path that is approximately 4.0% shorter than the path for SPIF. The thickness distribution for SPIF for different values for processing parameters does not differ significantly. The minimum thickness is more constant than that for MPIF. For SPIF, a smaller the step size increases the forming thickness but for MPIF, a larger the step size increases the forming thickness. Changes in tool diameter have no significant effect on the forming thickness value for MPIF. Decreasing step depth and increasing tool diameter reduces the SR of the workpiece after SPIF but MPIF achieves a lower SR for the same SPIF forming conditions. SPIF uses multi-plate stacking so the forming wall angle is better than the angle for MPIF. For MPIF using a step depth of 0.5 mm and different tool diameters, a deviation wall angle of 5° is possible. Declarations Conflict of interest The authors state no conflict of interest. Ethics approval Not applicable. Consent to participate Not applicable. Consent for publication Not applicable. Acknowledgments The authors gratefully acknowledge the support of the National Science and Technology Council, Taiwan (ROC) through Grant Nos. NSTC 114-2622-E-262-002 and NSTC 114-2221-E-262-001. 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09:52:05","extension":"jpeg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":643546,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/e9a36524eed2b5645d723b5c.jpeg"},{"id":107713310,"identity":"c75066e4-6aa3-42c3-97cb-1c8d1efde9df","added_by":"auto","created_at":"2026-04-24 09:52:04","extension":"jpeg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":599847,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage14.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/6baa87e007431b30ff66300d.jpeg"},{"id":107714295,"identity":"86ea1e21-597e-49dc-95b2-76bed68173e2","added_by":"auto","created_at":"2026-04-24 09:56:08","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":52582,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental workpiece and relevant dimensions\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/988e99aa9e4339eea082076a.jpeg"},{"id":107713501,"identity":"3b12a82e-6a19-415a-88ba-f21bb66df728","added_by":"auto","created_at":"2026-04-24 09:52:34","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":124388,"visible":true,"origin":"","legend":"\u003cp\u003ePhotograph of the experimental setup\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/9a908d840228e028a21fa1a3.jpeg"},{"id":107713529,"identity":"c5641aea-dc87-4616-9a37-6fc35ddae6db","added_by":"auto","created_at":"2026-04-24 09:52:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":451413,"visible":true,"origin":"","legend":"\u003cp\u003eMPIF fixture\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/a1580e4de82289b9fa9f2f2e.png"},{"id":107713502,"identity":"fad1a877-98b5-4e87-9c05-34bf420490e6","added_by":"auto","created_at":"2026-04-24 09:52:34","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":58682,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart for the MPIF experiment\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/fd6fd035431fd28ec86beb7a.png"},{"id":107713313,"identity":"75b75be3-9867-4ffb-bae9-fce8b7e96959","added_by":"auto","created_at":"2026-04-24 09:52:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":95203,"visible":true,"origin":"","legend":"\u003cp\u003eDetailed design drawing of the brass shim\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/45008864ba826dd9bcfd19ea.png"},{"id":107713531,"identity":"4ea568e1-d9e7-4b3c-85f5-f3c9ac825541","added_by":"auto","created_at":"2026-04-24 09:52:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":293792,"visible":true,"origin":"","legend":"\u003cp\u003eThe dimensional error that is caused by using an upper plate with a thickness of 0.5 mm\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/d5adc0b324e48569865441f3.png"},{"id":107713312,"identity":"236ef83a-ae5d-4ac2-aabb-ef518a391778","added_by":"auto","created_at":"2026-04-24 09:52:04","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":97139,"visible":true,"origin":"","legend":"\u003cp\u003eStress-strain curves for AL1050\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/595c760a26f0886b53356b02.png"},{"id":107714378,"identity":"7324d9e1-7d52-46ca-942c-585d111d422b","added_by":"auto","created_at":"2026-04-24 09:56:35","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":104981,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence analysis for minimum forming force\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/59eed7b939dedab4610949a1.png"},{"id":107713311,"identity":"cf2fe161-d557-4ebf-9e84-604a2a920cea","added_by":"auto","created_at":"2026-04-24 09:52:04","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":90483,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of forming forces for SPIF and MPIF for different processing parameters (step depth and tool diameter)\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/f429f298eb14d20eaf3dc4fd.png"},{"id":108180882,"identity":"dd6634d3-82c8-49be-91f4-081185895b29","added_by":"auto","created_at":"2026-04-30 08:54:40","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1458353,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/7bd1f8c5-dc22-470d-95bc-f785a2631f16.pdf"},{"id":107713532,"identity":"df8ae65e-8abe-40e6-83e2-a9e23188c08b","added_by":"auto","created_at":"2026-04-24 09:52:36","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":44122,"visible":true,"origin":"","legend":"","description":"","filename":"Highlights.docx","url":"https://assets-eu.researchsquare.com/files/rs-9410748/v1/9bcee0a2e2de78b24e68d438.docx"}],"financialInterests":"","formattedTitle":"Experimental-numerical framework integrated analysis for a study of multi-plate incremental forming (MPIF)","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSheet metal processing (SMP) is a manufacturing technology that uses molds and an external force to shape thin metal plates. It allows high-volume, rapid production, excellent formability, high strength-to-weight ratio and flexible production so it is currently widely used in the manufacture of plate metal parts in the machinery, electronics, aerospace and automotive industries. However, it is not always used to manufacture plate metal parts in small batches or for developmental parts. Single-point incremental forming (SPIF) eliminates the need for the design and fabrication of molds because it uses a non-sharp ball tool, machining paths and a CNC machine to manufacture customized plate metal part and processing time is significantly reduced. SPIF is being developed by the plate metal forming industry.\u003c/p\u003e \u003cp\u003eDuflou et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] demonstrated that the forming force for SPIF on metal plates increases with the values for four common processing parameters (step depth, tool diameter, wall angle and plate thickness). Step depth has the least effect on the forming force for metal plates but in terms of process efficiency, moderately increasing step depth reduces the processing time. SPIF requires no lubricant so tool wear is significant and the tool and plate surface can crack. Le et al. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] demonstrated that step depth and tool diameter have a significant effect on the formability of thermoplastic materials during SPIF. Reducing step depth and feed rate and increasing spindle speed improves formability. There is a significant interaction between step depth, feed rate and tool diameter. Bagudanch et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] confirmed that a larger tool diameter and step depth produces a larger contact area and increases forming force with the plate during SPIF. However, as the spindle speed increases, the friction between the contact areas for the tool and the plate increases, which moderately improves the plastic deformation of the workpiece and the forming force is reduced. Rosca et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] studied the effect of step depth and tool diameter on spring-back, thickness variation and forming force for SPIF. The results show that increasing step depth reduces variation in the finished product thickness and increases the forming force and spring-back. Increasing the tool diameter reduces plate thickness and increases forming force, but spring-back is less affected by tool diameter. Grimm and Mears [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] used SPIF for a workpiece by moving the tool path radially along the workpiece center, instead of along its periphery to give a more uniform thickness profile and increase formability by 21%. As the wall angle increases, single-step SPIF can cause local thinning and cracking of the material. Wu et al. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] used a parametric multi-step forming strategy to eliminate local thinning and stepped features for large wall angle shapes. This strategy improves the formability of large wall angle shapes by avoiding local over-thinning and redistributing material thickness and minimizes geometric deviation that is caused by stepped features. Behera et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] provided a concise overview of the current applications of SPIF for different hardware platforms, forming mechanics, failure mechanisms, force estimation, toolpath and tool strategy applications, the development of process planning tools, process simulation and sustainable manufacturing, and provided a roadmap for its future research directions. SPIF does not require costly stamping dies to achieve excellent performance in small and medium batch production but compared with stamping, traditional SPIF can produce excessively thin walls and premature fractures in single workpieces and leaves obvious machining marks on the contact surface between it and the tool, so it is not widely used.\u003c/p\u003e \u003cp\u003eSkjoedt et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] added a disposable plate to the plate metal to be formed to avoid contact between the machining tool and the workpiece during SPIF. The plate slightly reduces the forming efficiency of SPIF and eliminates wear on the workpiece surface and improves processing quality. Chang and Chen [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] confirmed that the three-plate incremental forming (TSIF) process produces parts with smooth surfaces and no obvious ripples and the forming efficiency is significantly improved. The forming limit and fracture strain for AA2024 and AA7075 plates are significantly improved after TSIF, which is of great significance for the manufacturing of low ductility plate metal parts. MPIF increases the forming limit and surface quality of the workpiece but its overall forming behavior is a complex and involves nonlinear change. In terms of manufacturing system control, MPIF is exponentially more difficult than SPIF and computer-aided engineering (CAE) is required for its study.\u003c/p\u003e \u003cp\u003eFinite element analysis (FEA) is the core mathematical theory of CAE and predicts the microstructural evolution of machining deformation. Comparison with experimental results to verify the effectiveness of the model allows analysis of the forming force for SPIF on the workpiece and demonstrates the microstructural evolution during processing, which creates a theoretical basis for process optimization [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Kumar and Reddy [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] used the Taguchi method, ABAQUS software and SPIF process parameters (plate thickness, step depth, tool radius and friction coefficient) to study the forming performance for the manufacturing of parabolic cups of AA6082 alloy. The results show that the process parameters that most significantly affect the forming of parabolic cups by SPIF are plate thickness and step length. Abdelkader et al. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] studied the process parameters for SPIF (tool path vertical step length, initial plate thickness and truncated cone wall angle) to predict the forming force and thickness variation for a double-layer material, compared to a single-layer plate. A double-layer plate is a low-cost material for SPIF and has important practical application significance. Cappellini [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] used the results of FEA simulations to show that SPIF achieves higher accuracy and more uniform material thickness distribution in the roughing-finishing strategy (ModeMD) and reduces spring-back. An experimental test on aluminum alloys (AA1050 H24 and AA5754 H111) with different tool radii verified the simulation results and showed that the use of multi-step trajectory increases the accuracy of process geometry for SPIF. Nguyen et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] used experimental-numerical comprehensive analysis to show that the vertical step length (58.6%) has the greatest effect on the forming wall thickness for SPIF using AA1050 aluminum alloy, followed by the feed rate (27.8%) and the tool radius (12.5%). A smaller wall angle significantly increases the forming height for SPIF in the workpiece and the simulation and experimental deviation is the least, at only 1.17%.\u003c/p\u003e \u003cp\u003eDefects that are caused by using only a single-plate for SPIFs, such as excessively thin walls, premature fracture and uneven surface roughness (SR), have been the subject of studies. Some studies use upper and lower plates to separate the workpiece, tool and bearing. This reduces some SPIF defects but crates problems between the plates and the workpiece. This study uses ABAQUS software and experiments to compare the surface quality and forming limit of SPIF and MPIF. Numerical simulation is used to determine the causes of specific instability defects in MPIF and to address these defects and improve surface finish. A robust experimental-numerical framework is established for this process to give a theoretical basis and practical guidelines for improving product quality and manufacturing efficiency.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eTo compare SPIF and MPIFs, this study uses an axisymmetric conical part with a top diameter of 70 mm, a depth of 25 mm, a bottom diameter of 20 mm and a wall angle of 45\u0026deg; (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Experiments used AL1050 aluminum alloy plates and a three-axis CNC machine (Tungtai Machinery TMV-850QⅡ) with a maximum spindle horsepower of 11 kW and a maximum speed of 10,000 rpm, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The workpiece dimensions are 100 mm \u0026sdot; 100 mm \u0026sdot; 1.0 mm and the thickness of the upper and lower plates is 0.5 mm. The machining path for the multi-plate axisymmetric conical model part was generated using HYPERMILL software with a clockwise oblique 3D contour-lowering machining method and a spindle speed of 0 rpm and a feed rate of 1,000 mm/min. To determine variation in the forming during MPIF, this study uses a piezoelectric rotary dynamometer (Type 9170A) this is manufactured by Kistler, Switzerland. This dynamometer measures the torque that is applied by the tool to the workpiece and the loads in three orthogonal directions (X, Y and Z axes). Machining data for the X and Y axial forces and torque shows that the Z axial force has the most significant effect on SPIF so this study uses the Fz data to determine the quality of the forming force. The workpiece thickness changes only slightly after SPIF so a digital thickness gauge (Qualitot-21752, China) with an accuracy of 0.001 mm was used for measurement.\u003c/p\u003e \u003cp\u003eThis study uses step depth (three levels) and tool diameter (four levels), as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The tool material was tungsten carbide steel with a length of 100 mm to construct a ball end mill without a cutting edge. The MPIF fixture and its experimental flowchart are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. To prevent slippage between the workpiece and the upper and lower plates during MPIF, this study places it inside a 1.0 mm thick brass shim. The shim measures 115 mm \u0026sdot; 115 mm and has four rounded corners with a radius of 6 mm. 5 mm-diameter holes were drilled at the four corners of the 100 mm \u0026sdot; 100 mm rectangle in the center of the brass shim and then a 100 mm \u0026sdot; 100 mm hollow rectangle was milled out to hold the workpiece, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. To reduce friction and heat that are generated during prolonged contact between the cutting tool and the workpiece in the SPIF process, this study used SW-68 Hercules\u0026reg; Slideway Oil for lubrication and cooling. The SR measurements for the conical finished product's wall angle and four points 90\u0026deg; apart on the inner wall surface after MPIF machining used a 2\u0026deg; graduated gauge (SHINWA-62995) and a 0.001\u0026micro;m SR meter (Mitutoyo SURFTEST SV-3100H4) to determine the effect of experimental parameters on SR variations in the conical finished product's wall angle and inner wall surface. The average SR value for the workpiece before machining was 0.6225 \u0026micro;m.\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\u003eExperimental parameters for MPIF\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProcessing conditions\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"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\u003eSpindle Speed (rpm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUpper plate thickness (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeed Rate (mm/min)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003e1,000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExperimental parameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStep depth (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTool diameter (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e14\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 presence of the plates changes the machining path for MPIF, depending on the thickness of the finished product. To ensure the accuracy of the final product shape, the machining path for MPIF must undergo inward compensation. For an upper plate thickness of 0.5 mm, the tolerance in the XY plane is 0.21 mm, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The MPIF path is shortened inward so its distance (7160.9 mm) is 286.9 mm shorter than that for SPIF (7447.8 mm). When machining large parts or forming thicker upper plates, MPIF uses a significantly shorter machining time than SPIF.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3. Finite element method (FEM)","content":"\u003cp\u003eTo determine the variation in the forming load for MPIF on AL1050 aluminum alloy sheets, this study uses FEA to model the load based on the following assumptions: (1) The model (bulk and upper and lower plates) is homogeneous, isotropic and conforms to the von-Mises yield criterion; (2) the model exhibits isotropic hardening and plastic incompressibility; (3) the fixture and tool are considered to be perfectly rigid bodies and (4) the effect of the frictional temperature due to sliding between the tool and the plate and grain slip of the material during the forming process are ignored.\u003c/p\u003e \u003cp\u003eDuring the SPIF process, the magnitude and fluctuation of the forming force are directly related to the forming state of the material, the generation of defects and the quality of the final product [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Forming force has a significant effect so it is accurately measured to ensure the success of SPIF. In experiments and practical applications, a dynamometer (such as piezoelectric platforms) is used to monitor the force changes in the forming process in real time. This data is used to verify the theoretical model and to allow online control. If abnormal forming force is detected, the process parameters (workpiece thickness, tool diameter, wall angle) are adjusted or processing is suspended to avoid scrap [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. To determine the changes in the forming force for MPIF on AL1050 aluminum alloy plates, ABAQUS software is used.\u003c/p\u003e \u003cp\u003eThe ABAQUS simulation analysis model uses a surface-to-surface contact mode. The master-surface is the outer surface of the tool and the slave-surface is the three surfaces of the sheet metal. The data from the finite element model is shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The actual stress-strain curves for the AL1050 sheet metal are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. As plastic deformation increases, the stress in the AL1050 sheet metal increases slowly, which shows that it is very ductile. The Coulomb friction coefficient (\u0026micro;p) between the tool and the workpiece is 0.1. The workpiece is firmly fixed between the support plate and the pressure plate to prevent slippage.\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\u003eData for the FEM model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorkpiece\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYoung\u0026rsquo;s modulus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInitial yield stress\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAL1050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e69 GPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e165 MPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2,700 kg/m\u003csup\u003e3\u003c/sup\u003e.\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\u003e \u003c/p\u003e \u003cp\u003eTo determine the forming force for MPIF in an axisymmetric conical product, this study initially uses 80,000 meshes and increases the mesh count in increments of 10,000. The convergence of the numerical calculation results is used to select the most suitable mesh for finite element simulation. The minimum forming force for MPIF converges at 120,000 meshes so this study uses 120,000 meshes for FEA, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Results and Discussion","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Forming force\u003c/h2\u003e \u003cp\u003eDuring MPIF, the tool must first overcome its elastic or plastic deformation resistance and compress before it can apply sufficient forming force to the workpiece to shape it. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e compares the forming forces for SPIF and MPIF for different processing parameters (step depth and tool diameter). The results in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e show that the forming force for MPIF is greater than that for SPIF. The forming forces for both increase as step depth and tool diameter increase but these differ by a magnitude of three. If the tool diameter is fixed, the deformation volume, local bending moment and tensile strain for the material also increase as step depth increases. If the step depth is fixed, the contact area and deformation range also increase as the tool diameter increases. To maintain the required deformation pressure per unit area, the forming force for MPIF must increase. During MPIF, the tool contacts the workpiece through a partition that deforms a surface or region, rather than through direct point contact (SPIF). To drive plastic flow across this larger and more uniform area of material, MPIF requires a greater forming force. Elastomeric separators wrap more tightly around the cutting tool during SPIF, which creates a normal constraint pressure on the sheet metal below. This constraint force causes the sheet metal to accumulate and flow around the cutting tool, which causes wrinkles, so MPIF must overcome greater friction and the forming force is greater. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e compares the forming forces obtained using ABAQUS software and for practical MPIF for an 8 mm tool diameter and a 0.5 mm step depth. Both are very accurate and errors are less than 5%, so FEM software allows reliable analysis of MPIF.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Plate thickness\u003c/h2\u003e \u003cp\u003eDuring SPIF, forming conditions significantly affect the overall workpiece thickness distribution. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e compares the finished product thickness distribution for SPIF and MPIF for an 8 mm tool diameter and different step depths. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(a) shows that the least thickness for SPIF is 32-38.5 mm from the zero point and a smaller step depth increases forming thickness. The least thickness for MPIF is 27.5\u0026ndash;32 mm from the zero point and larger step depths increases forming thickness, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e(b). During SPIF, the thickness deformation is highly concentrated near the contact point between the tool and the sheet metal. Due to the workpiece geometry (axisymmetric cone), the material experiences the greatest biaxial tensile stress in the middle section of its sidewalls. This creates localized strain concentration and insufficient material replenishment so some locations experience a rapid reduction in thickness. During SPIF, a smaller step depth means a larger forming thickness but during MPIF, the tool must first compress the upper plate to transfer the forming force to the workpiece, so the upper plate evenly distributes the concentrated load of the cutting tool to a larger contact pressure area and the workpiece is formed over a wider range. The upper plate compresses and constrains so the plastic deformation zone for the material moves closer to the bottom rounded corner area on the formed part. The upper plate restricts free bulging or the accumulation of material in the middle section of the sidewall so maximum deformation is concentrated near the bottom.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e compares the finished product thickness for SPIF and MPIF for different processing parameters. For MPIF, a smaller step depth (0.5 mm) results in a smaller forming thickness and the opposite is true for SPIF, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. During MPIF, the tool applies normal constraint pressure to the material, which restricts the workpiece from free bulging or wrinkling in the thickness direction. For a smaller step depth (0.5 mm) during MPIF, the tool's movement per step is small. However, the upper plate continuously presses against the workpiece so it is repeatedly compressed in localized areas. Friction and the constraint of the upper plate prevents the material from flowing smoothly outwards if a smaller step depth is used for MPIF: there is a localized accumulation in front of the tool so this area is thinner because compression is greater. A smaller step depth for MPIF increases the number of processing passes (longer processing time), so the workpiece endures prolonged repeated compression and friction and remains in a state of work hardening (rapid heat dissipation), so accumulated local deformation increases thinning.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Surface roughness (SR)\u003c/h2\u003e \u003cp\u003eThe SR of the workpiece after SPIF directly affects its mechanical properties (fatigue strength, wear resistance and contact rigidity) and application value. Figure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows a comparison of the SR for SPIF and MPIF for different values for processing parameters. For SPIF, if the step depth is fixed, SR decreases as the tool diameter increases. For a step depth of 0.5 mm, Ra decreases from 1.13 \u0026micro;m for an φ8 mm tool to 0.50 \u0026micro;m for a φ14 mm tool, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e(a). During SPIF, a larger diameter tool has a larger contact area with the workpiece (i.e., the pressure per unit area is reduced), so there are fewer surface scratches and ripples and surface quality increases. If the tool diameter is fixed, the SR increases as the step depth increases. For an φ8 mm tool, Ra increases from 1.13 \u0026micro;m for a 0.5 mm step depth to 1.78 \u0026micro;m for a 1.5 mm step depth. Increasing the step depth increases the vertical descent (deformation) of the tool per layer, so stepped marks are more noticeable and localized uneven deformation occurs on the workpiece surface. For this study, the optimal surface quality (Ra\u0026thinsp;=\u0026thinsp;0.50 \u0026micro;m) is achieved for SPIF using a φ14 mm tool and a step depth of 0.5 mm.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor MPIF, if the step depth is fixed, the SR decreases as tool diameter increases but there are local fluctuations. If the step depth is 0.5 mm, Ra decreases from 1.07 \u0026micro;m for an φ8 mm tool to 0.78 \u0026micro;m for a φ14 mm tool, but the Ra for a φ10 mm tool (Ra\u0026thinsp;=\u0026thinsp;0.66 \u0026micro;m) is slightly less than that for a φ12 mm tool (Ra\u0026thinsp;=\u0026thinsp;0.83 \u0026micro;m) and a φ14 mm tool (Ra\u0026thinsp;=\u0026thinsp;0.78 \u0026micro;m), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e(b). A larger tool diameter increases the surface quality of the workpiece but due to the influence of the upper plate, the Ra trend is not as stable as that for SPIF without an upper plate. If the tool diameter is fixed, the relationship between SR and step depth is less clear. In particular, the change in Ra is particularly significant for a φ10 mm tool. The value for Ra increases from 0.66 \u0026micro;m for a step depth of 0.5 mm to 1.15 \u0026micro;m for a step depth of 1.0 mm. The Ra value decreases from 1.15 \u0026micro;m to 0.97 \u0026micro;m if the step depth increased to 1.5 mm, probably because there is a smaller overlap in the step between toolpaths with a φ10 mm tool at a step depth of 1.0 mm and the upper plate is in the nonlinear compression transition zone. In terms of the overall workpiece surface finish, the Ra value for MPIF is mostly lower the value for SPIF, so SPIF gives lower SR.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Wall angle\u003c/h2\u003e \u003cp\u003eMultiple plates are stacked for MPIF (upper plate\u0026thinsp;+\u0026thinsp;workpiece\u0026thinsp;+\u0026thinsp;lower plate) so the wall angle is more complex than for SPIF. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e compares the wall angle for SPIF and MPIF for different values for processing parameters. The results in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e show that SPIF shapes the wall angle of the workpiece to 45\u0026deg; for different values of processing parameters because MPIF uses multi-plate stacking, which increases the overall bending stiffness. The upper plate absorbs some of the deformation energy during MPIF so there is less strain on the workpiece and the final wall angle is affected. If a lower step depth is used for MPIF, the workpiece accumulates frictional heat and becomes elastic-plastic. When the external force is released and the heat dissipates, the workpiece recovers elastically, which can increase the wall angle deviation, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eSPIF allows higher formability limits and easier toolpath modification than SPF so it is ideal for small-batch production, prototyping or customized sheet metal parts. MPIF gives better workpiece surface quality but the processing effects that are caused by multi-plate stacking create more complex problems than SPIF. ABAQUS software is ideal for nonlinear problems so it is used to simulate and analyze engineering problems. This study uses an experimental-numerical framework to determine the forming characteristics for AL1050 aluminum alloy plate for different step depths and tool diameters using SPIF and MPIF. The main conclusions are summarized as follows:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eUsing a lower step depth and a larger tool diameter for SPIF yields a finer and smoother workpiece surface texture. During MPIF, the upper plate reduces the surface texture and a smaller step depth still produces path marks on the workpiece surface.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe forming force for SPIF and MPIF increases as step depth and tool diameter increase but MPIF forms three plates simultaneously so the forming force is approximately 1.7 to 2.4 times greater than the force that is required for SPIF. Analysis of the forming force for MPIF using ABAQUS software yields highly accurate results (error within 5%), which confirms that it is a reliable tool for analysis.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSPIF and MPIF paths decrease as step depth and tool diameter increase. The inward MPIF path uses a machining path that is approximately 4.0% shorter than the path for SPIF.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe thickness distribution for SPIF for different values for processing parameters does not differ significantly. The minimum thickness is more constant than that for MPIF. For SPIF, a smaller the step size increases the forming thickness but for MPIF, a larger the step size increases the forming thickness. Changes in tool diameter have no significant effect on the forming thickness value for MPIF.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eDecreasing step depth and increasing tool diameter reduces the SR of the workpiece after SPIF but MPIF achieves a lower SR for the same SPIF forming conditions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSPIF uses multi-plate stacking so the forming wall angle is better than the angle for MPIF. For MPIF using a step depth of 0.5 mm and different tool diameters, a deviation wall angle of 5\u0026deg; is possible.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of interest\u003c/strong\u003e \u003cp\u003eThe authors state no conflict of interest.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eEthics approval\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to participate\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThe authors gratefully acknowledge the support of the National Science and Technology Council, Taiwan (ROC) through Grant Nos. NSTC 114-2622-E-262-002 and NSTC 114-2221-E-262-001.\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDuflou J, Tun\u0026ccedil;kol Y, Szekeres A, Vanherck P (2007) Experimental study on force measurements for single point incremental forming. J Mater Process Technol 189:65\u0026ndash;72\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLe VS, Ghiotti A, Lucchetta G (2008) Preliminary studies on single point incremental forming for thermoplastic materials. Int J Mater Form 1:1179\u0026ndash;1182\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBagudanch I, Centeno G, Vallellano C, Garcia-Romeu ML (2013) Forming force in single point incremental forming under different bending conditions. Procedia Eng 63:354\u0026ndash;360\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRosca N, Oleksik V, Pascu A, Oleksik M, Avrigean E (2019) Optical study for springback prediction, thickness reduction and forces variations on single point incremental forming. Mater Today Proc 12:213\u0026ndash;218\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGrimm TJ, Mears L (2020) Investigation of a radial toolpath in single point incremental forming. Procedia Manuf 48:215\u0026ndash;222\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu S, Ma Y, Gao L, Zhao Y, Rashed S, Ma N (2020) A novel multi-step strategy of single point incremental forming for high wall angle shape. J Manuf Process 56:697\u0026ndash;706\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBehera AK, de Sousa RA, Ingaraom G, Oleksik V (2017) Single point incremental forming: An assessment of the progress and technology trends from 2005 to 2015. J Manuf Process 27:37\u0026ndash;62\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSkjoedt M, Silva MB, Bay N, Martins PAF, Lenau TA (2007) Single point incremental forming using a dummy plate, 2 edn. Inter Conf New Form Technol Bremen, pp 20\u0026ndash;21\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChang Z, Chen J (2020) Investigations on the deformation mechanism of a novel three-plate incremental forming. J Mater Process Technol 281:116619\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAyll\u0026oacute;n J, Miguel V, Martinez A, Rodr\u0026iacute;guez-Alcaraz JL, Coello J (2017) Modelization of bending under tension tests with application to the SPIF processes. Procedia Manuf 13:299\u0026ndash;306\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar KSS, Reddy AC (2016) Die less single point incremental forming process of AA6082 plate metal to draw parabolic cups using ABAQUS. Int J Adv Technol Eng Sci 4(11):127\u0026ndash;134\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAbdelkader WB, Bahloul R, Arfa H (2020) Numerical investigation of the influence of some parameters in SPIF process on the forming forces and thickness distributions of a bimetallic plate CP-Titanium/low-carbon steel compared to an individual layer. Procedia Manuf 42:1319\u0026ndash;1327\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCappellini C (2025) FEM-based quality analysis of multi-stage tool paths in single point incremental forming. Eur J Mech A-Solid 114:105749\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNguyen DT, Mac TB, Hoang TK, Nguyen TH, Luyen TT (2026) Integrated experimental\u0026ndash;numerical analysis and optimization of wall thickness in single point incremental forming of AA1050 Aluminum alloy. J Braz Mech Sci Eng 48:56\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharma M, Bhattacharya A, Paul SK (2025) Failure behavior in single point incremental forming parts of AA6061-T6. Eng Fail Anal 177:109682\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDavarpanah MA, Mirkouei A, Yu X, Malhotra R, Pilla S (2015) Effects of incremental depth and tool rotation on failure modes and microstructural properties in single point incremental forming of polymers. J Mater Process Technol 222:287\u0026ndash;300\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Single-point incremental forming, Surface quality, Multi-plate incremental forming, Forming characteristic, Numerical simulation","lastPublishedDoi":"10.21203/rs.3.rs-9410748/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9410748/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTraditional single-point incremental forming (SPIF) requires no mold and allows flexible manufacturing of small quantities and variety but the surface quality of the workpieces after processing is poor, so it is not commonly used. Multi-plate incremental forming (MPIF) reduces tool wear on the workpiece surface so machining quality is increased. MPIF is complex and exhibits nonlinear characteristics so numerical simulation software is required. ABAQUS is a numerical simulation tool for the analysis of complex and nonlinear problems and is widely used in research and industry. This study uses an experimental-numerical framework to determine the forming characteristics of MPIF on AL1050 aluminum alloy plates and compares it with traditional SPIF. The results show that step depth and tool diameter significantly affect the forming characteristics of MPIF. The results also demonstrate that MPIF can be used to manufacture thin-plate parts with smooth surfaces and minimal waviness and efficiency is significantly increased. Numerical simulation tools address the forming force analysis problem for MPIF and can be used to analyze complex and nonlinear problems.\u003c/p\u003e","manuscriptTitle":"Experimental-numerical framework integrated analysis for a study of multi-plate incremental forming (MPIF)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-24 09:38:29","doi":"10.21203/rs.3.rs-9410748/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2026-04-25T10:38:31+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-16T12:38:02+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-16T06:08:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2026-04-14T01:25:27+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5be6882c-5dce-4ab4-a8e8-24d3428566d2","owner":[],"postedDate":"April 24th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-24T09:38:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-24 09:38:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9410748","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9410748","identity":"rs-9410748","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}