Abstract: Obtaining a simulated tooth surface that closely resembles the actual machined surface remains challenging with existing simulation methods. This paper proposes a high-precision gear shaping simulation approach. Based on the CATIA platform, by establishing models of the cutter and gear blank, analyzing the spatial motion relationship between them, and utilizing CATIA commands such as translation, rotation, Boolean operations, and secondary development functions, high-precision gear shaping simulation for cylindrical spur gear is achieved. By measuring the normal distance between the standard involute and the simulated tooth surface, tooth surface accuracy is assessed and verified against actual machining parameters. Furthermore, the simulation model is reconstructed, and finite element analyses are conducted on both the simulation and reconstructed models. By comparing the results, the validity of the simulation model obtained using the proposed method is verified.
1. Introduction
When the tooth surface is prone to poor running-in, initial pitting can gradually evolve into destructive pitting, which, if severe, can lead to tooth surface failure. To conduct finite element analysis for such poor tooth surface contact conditions, spur gear model that matches the actual gear tooth surface is required. Existing gear model creation methods can be broadly classified into two categories: direct modeling and simulation-based modeling. While direct modeling can quickly obtain a theoretical tooth surface, it lacks the tool mark characteristics present on actual tooth surfaces. Simulation, however, can address this by assigning the tool and gear blank models the same machining path and parameters as in actual processing, thereby obtaining a simulation model that closely approximates the actual tooth surface.
This paper proposes a high-precision gear shaping simulation method based on CATIA. The specific content is organized as follows: Section 2 introduces spur gear shaping simulation method based on CATIA; Section 3 presents the finite element analysis of the simulation and reconstructed models; and Section 4 summarizes the conclusions.
2. Gear Shaping Simulation Method Based on CATIA
2.1 Principle of Gear Shaping
Gear shaping involves the generation of spur gear through a process that can be viewed as a discontinuous meshing process between a pair of cylindrical spur gears. By assigning the same rake angle α and relief angle β to the teeth of one of spur gears to form cutting edges, this gear can be considered as spur gear shaping cutter, while the other gear can be regarded as the workpiece gear blank.
The main motion in spur gear shaping is the high-speed reciprocal linear motion of the cutter along the axial direction of spur gear blank; the generating motion is the non-slip rolling motion between the pitch circles of the cutter and spur gear blank; the tool retraction motion is the radial movement of the cutter away from spur gear blank when retracting; and the radial feed motion is the radial feed of the cutter until the full tooth height is machined.
2.2 Establishment of Cutter and Gear Blank Models
When spur gear shaping cutter moves reciprocally along the axial direction of spur gear blank at high speed, it visually resembles a cylindrical spur gear. To ensure simulation accuracy while reducing computational load, spur gear shaping cutter model with rake and relief angles can be simplified in the simulation. This involves projecting the high-precision gear shaping cutter model onto the base plane and stretching the closed curve obtained from the projection along the axial direction of the cutter to obtain a simplified gear shaping cutter model that meets simulation requirements.
After obtaining the original tooth profile angle an of spur gear shaping cutter, an accurate model of spur gear shaping cutter can be created in CATIA based on the parameters shown in Table 1.
Table 1: Main Parameters of Gear Shaping Cutter
| Parameter | Value (mm/°) |
|---|---|
| Module | 2 |
| Number of teeth | 38 |
| Maximum modification coefficient | 0.31 |
| Minimum modification coefficient | -0.91 |
| Rake angle | 5 |
| Relief angle | 6 |
| Addendum coefficient | 1.25 |
| Tooth top round | 0.15 |
Table 2: Parameters of Gear
| Parameter | Value (mm/°) |
|---|---|
| Module | 2 |
| Number of teeth | 20 |
| Pressure angle | 20 |
| Face width | 20 |
| Coefficient of top clearance | 0.25 |
| Addendum coefficient | 1 |
2.3 Gear Shaping Simulation Process
The spur gear shaping simulation process involves completing the establishment of the simplified gear shaping cutter and gear blank models in the CATIA part design environment. These models are then assembled in the assembly design environment with the standard center distance, and the assembly model is converted into a part model.
Due to CATIA’s memory reading mechanism limitations, when the memory read exceeds a certain value, it can impose a significant load on the computer’s CPU and memory, reducing computational efficiency and prolonging simulation time. Therefore, to improve simulation efficiency, a memory reading threshold can be set for CATIA.
2.4 VBA Macro Program Implementation
Given the regularity of the spatial position transformations between spur gear shaping cutter and gear blank during the simulation process, a loop statement is used to achieve continuous spatial position transformations, and a judgment statement is added to determine whether the memory exceeds the threshold and whether a complete gear has been machined.
The main elements of the loop statement controlling the spatial position transformation between spur gear shaping cutter and gear blank models include the number of cycles n and the circumferential feed step Δθ. The number of cycles n is determined by the circumferential feed step Δθ. The smaller Δθ is, the larger n is, resulting in more enveloping iterations and higher accuracy.
3. Finite Element Analysis of Simulation and Reconstructed Models
The simulation model with a representative feed parameter of Δθ=0.4mm is reconstructed into a model without tool marks using the B-spline curve fitting method proposed by Pu et al. [4]. For ease of observation, the simulation and reconstructed models are overlaid. The reconstructed tooth surface has slight undulations compared to the tool marks of the simulation model.
The simulation and reconstructed models are imported into Hypermesh for high-precision meshing. The finite element analysis accuracy in Abaqus directly depends on the model mesh size. For contact problems, which are highly nonlinear, excessively dense meshing can provide precise results but consume excessive computational power and extend calculation time [8].
The meshed models are then imported into Abaqus for finite element analysis. The material is 40Cr, with an elastic modulus of 211 GPa and a Poisson’s ratio of 0.277. The contact properties are set to general contact, with a hard contact surface and a friction coefficient of 0.1. To simulate a loaded condition, a fixed resistance torque is applied to the driven gear.
When the same resistance torque of 25 N·m is applied to both the simulation and reconstructed models, the maximum contact stresses are extracted for different rotation angles. Both models exhibit periodic variations in maximum stress. The maximum stress of the simulation model fluctuates around the maximum stress of the reconstructed model, with a fluctuation range of -30% to 40%.
In practical applications, pitting first appears near the pitch point due to single-tooth meshing in this region, causing the gear to experience higher forces. The finite element analysis results also show that the maximum contact stress occurs near the pitch point. The maximum contact stress for the simulation model is 868 MPa, while for the reconstructed model, it is only 716 MPa.
4. Conclusion
This paper studied the gear shaping simulation of cylindrical spur gears using secondary development technology in CATIA V5 based on the principle of conjugate tooth surface enveloping. By extracting the partially machined gear blank during the simulation, reassembling it, and continuing with spur gear shaping simulation, simulation under actual machining parameters was achieved. By comparing the simulation results with the theoretical involute for corresponding parameters, the correctness and accuracy of the models obtained using the proposed method were demonstrated. The simulation model was reconstructed, and finite element analyses were conducted on both the simulation and reconstructed models. By comparing their results, the validity of the simulation model obtained using the proposed method was verified. This method is also applicable to hobbing and grinding simulation processing, providing solutions for high-precision simulation processing and finite element analysis of simulation results for hobbing and grinding.