Innovative Process Control Methods for Complex Geometrical Sheet Metal Parts
A cobalt-based elastic alloy corrugated spring was used as the focus of the research. An orthogonal test was designed to investigate its new deep drawing process. The main factors considered were the blank holder force, die clearance, and drawing height. A three-factor, three-level orthogonal test scheme was implemented to comprehensively evaluate the forming results, specifically looking at the thinning rate and springback of the workpiece.
Additionally, the performance analysis of the material utilized the Johnson-Cook model to generate a more accurate stress-strain curve. The software Dynaform was employed to simulate each of the designed test combinations individually. Through mean analysis, the optimal process parameter combination was identified.
Following actual production verification, the resultant product exhibited a satisfactory appearance, and its dimensional accuracy met the design specifications, closely aligning with the simulation results.
01 Preface
In aircraft engines, corrugated springs work in conjunction with graphite sealing rings to create an effective seal at the shaft end through elastic compression. It is crucial that these springs maintain high stability in elastic force and consistency in wave height. 3J21 refers to a cobalt-based chromium-nickel elastic alloy, known for its high elastic modulus, impressive elastic limit, and extremely low elastic aftereffect, making it ideal for producing elastic components in modern aircraft engines.
To achieve the desired properties, we utilize a deep drawing process during the press bending correction of the springs in their annealed state (see Figure 1). The design features a deep drawing flange on the curved surface of the corrugated spring, where the circumferential compressive stress and radial tensile stress induce plastic deformation and work hardening. This process enhances the dimensional accuracy and adjustable elastic force of the springs. However, effectively predicting the deformation and springback of the workpiece remains challenging, necessitating repeated trimming of the mold. This paper applies the orthogonal test method and conducts finite element analysis using Dynaform to improve the forming dimensional accuracy of the corrugated spring.
02 Workpiece analysis and finite element model establishment
As shown in Figure 2, a specific type of corrugated spring is made from a Co40NiCrMn strip with a wall thickness of 0.25 mm. The spring features four 3 mm waves that are evenly distributed around its circumference, resulting in minimal deformation at the peaks and troughs. To meet the design requirements, it is crucial to maintain strict control over springback during the forming process. The asterisk (*) in Figure 2 indicates that the angle dimensions are preserved throughout the forming and subsequent assembly processes of the corrugated spring.
2.1 Material Analysis
To effectively perform simulation calculations, it is essential to obtain the mechanical properties and constitutive relations of the relevant materials. For the cobalt-based high elastic alloy designated as 3J21, the simplified Johnson–Cook model can be used for its constitutive equation, expressed as follows:
σ = A + Bε^n (1)
In this equation:
- A represents the yield stress (in MPa),
- B is the strain hardening parameter (in MPa),
- ε denotes the equivalent plastic strain, and
- n is the hardening index.
The material performance parameters for the B-grade strip in the cold-rolled state are provided in Table 1. By substituting the relevant parameters into formula (1), the true stress-strain curve can be generated, as illustrated in Figure 3.
2.2 Establishment of finite element model
To enhance calculation accuracy and solution rates, a shell unit mesh size of 0.5 mm is utilized for the blank, considering the thin wall thickness and small size of the workpiece. The tool body is defined as a rigid body, and the outer diameter of the blank holder is set at 67.5 mm. Additionally, the friction model employed is the Coulomb model. The geometric model of the corrugated spring in Dynaform is illustrated in Figure 4.
03 Experimental design and simulation results
The final performance of the corrugated spring is influenced by the shape and wall thickness of the material after it has been formed. During the drawing process, the material flow at the flange edge is primarily affected by several factors, including the blank holder force, die gap, drawing height, stamping speed, and friction factor. In this case, the stamping speed is set at 1000 mm/s, and the friction factor is 0.125. By comprehensively evaluating the various factors that impact the thinning rate and springback of the CNC turning components, Minitab software is used to determine the optimal process parameters.
3.1 Orthogonal factors and levels
Through calculations and practical experience, we designed three parameters—blank holder force, die gap, and drawing height—into a 3×3 orthogonal experimental factor and level table (refer to Table 2). The different drawing heights correspond to three blanks with increasing outer diameters: φ54 mm, φ59 mm, and φ64 mm.
3.2 Orthogonal test design and result analysis
Nine uniform and random combinations were selected to create the L9 (34) orthogonal table for simulation calculations. Both the thinning rate and springback of the workpiece after forming exhibit directionality. The combination with the largest absolute value is chosen, and both factors are scored comprehensively to determine the final indicator. The weight ratio of the thinning rate to springback is set at 1:4, and the range normalization method is applied to standardize the dimensions. The results of the orthogonal test are presented in Table 3.
The Taguchi design module in Minitab was used to analyze the standard deviation and mean of the data, with the results for the comprehensive score mean analysis presented in Figure 5. It is evident that under the A3B2C1 condition, both the workpiece thinning rate and springback achieve optimal solutions. The corresponding simulation results are displayed in Figure 6.
The forming limit diagram indicates that the workpiece is free of cracks; however, there is a slight tendency for wrinkling in certain areas. This tendency arises from the deformation and work hardening of the flange, which creates challenges for material flow. As a result, substantial circumferential compressive stress occurs, coupled with the fact that the wall thickness of the workpiece is thin. Consequently, there is a risk of wrinkling near the outer ring of the workpiece, especially under a large blank holder force.
As shown in Figure 6b, the maximum thinning rate of the workpiece occurs in four symmetrical red areas close to the inner ring, with a thinning rate of approximately 8.35%. This thinning is most pronounced at the peaks of the workpiece’s corrugation, where the drawing height is 3 mm greater than at the troughs, making thinning more severe than in other regions.
Regarding the rebound results of the workpiece, the maximum rebound occurs at the adjacent peaks and troughs, measuring about 0.25 mm in the opposite direction. This observation aligns with expectations; however, it does not exhibit a symmetrical distribution trend. This lack of symmetry is attributed to the complex deformation that occurs in the middle area of the sheet after contact with the wavy blank holder ring, resulting in unbalanced stress in the drawing direction once the punch descends.
04 Production and processing verification
The actual mold is depicted in Figure 7a. Alumina grease was applied during the processing. The equipment used was a 315-ton four-column hydraulic press. The process utilized the A3B2C1 combination of parameters. The workpiece after deep drawing is shown in Figure 7b, while Figure 7c displays the workpiece after trimming. There were no issues with wrinkling or cracking during the metal stamping process.
Using blue light detection to scan the surface of the workpiece (see Figure 8), it can be observed that the surface deviations occur at adjacent peaks and valleys, but in opposite directions. The peak deviation measures 0.21 mm, while the valley deviation is 0.14 mm. Additionally, the wall thickness of the CNC custom machining workpiece is measured using a wall thickness micrometer, revealing that the minimum wall thickness is located within the inner circle of the four peaks, ranging from 0.20 mm to 0.23 mm. Overall, the actual processing results are largely consistent with the optimal simulation outcomes obtained through orthogonal test design.
05 Conclusion
This paper presents the design of an orthogonal test for the deep drawing process of a cobalt-based elastic alloy corrugated spring. By examining three factors—blank holder force, die clearance, and deep drawing height—and using a comprehensive evaluation index that includes thinning rate and springback, we employed Minitab software for mean analysis to determine the optimal combination of process parameters. The results were validated through actual production, demonstrating high surface quality with no occurrence of wrinkling or cracking, and the dimensional accuracy met the specified requirements.
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