Abstract: The existing gear hobbing simulation methods struggle to adhere to actual processing parameters and lack effective tooth surface accuracy measurements of the simulated models, thus failing to provide effective guidance for practical gear hobbing operations. To address this, a high-precision gear hobbing simulation and accuracy verification method is proposed. This method leverages the CATIA design platform, incorporating secondary development functions through commands such as translation, rotation, and Boolean operations in CATIA. By extracting a preliminary tooth groove model containing the main motion and generating motion characteristics and simulating the vertical feed motion between the preliminary tooth groove model and the tooth blank, high-precision gear hobbing simulation is achieved. By establishing a standard tooth surface point set to measure the accuracy of the simulated tooth surface, the error distribution of the simulated tooth surface is obtained. The highest tooth surface accuracy error in the obtained simulation model is below 1 μm, verifying the correctness of the gear hobbing simulation method and the accuracy of the simulation model.
Keywords: gear hobbing; CATIA; high-precision simulation; accuracy verification; tooth surface error
1. Introduction
With the development of modern computer technology, significant progress has been made in the field of gear hobbing simulation in China. However, existing research focuses on simulation cutting modeling and various software platforms and their applicable methods, without fully integrating gear hobbing simulation with actual processing parameters. Additionally, domestic researchers have not conducted in-depth discussions on the accuracy verification of simulation models. Consequently, the existing gear hobbing simulation methods cannot provide precise and effective guidance for actual processing. To address these issues, this paper proposes a high-precision gear hobbing simulation and accuracy verification method.
2. Gear Hobbing Simulation Based on CATIA
2.1 Principle of Gear Hobbing
Gear hobbing processes gears using the generating method. In gear hobbing, it can be considered as a seamless transmission between a gear and a rack. During the transmission, when the rack moves normally by one tooth, the hob rotates around its own axis for one week. When the hob rotates continuously, it can be regarded as a continuously straight-moving infinitely extended rack. In gear hobbing, the main motion is the rotational motion of the hob around its own axis; the generating motion is the motion that forces the tooth blank to maintain the meshing relationship between the gear and the rack; and the vertical feed motion is the straight-line motion of the hob moving up and down along the axial direction of the tooth blank to cut out the tooth shape on the tooth width of the tooth blank.
2.2 Establishment of Hob and Tooth Blank Models
When designing the hob, to ensure smooth cutting, chip removal, and heat dissipation during gear hobbing, a series of chip grooves need to be milled on the hob. The side of one of the chip grooves is the rake face of the hob. To produce the correct involute tooth shape, the surface created by the rake face during the main motion of gear hobbing should be the threaded surface of an involute worm.
In the gear hobbing simulation in this paper, the Boolean difference operation within CATIA is used to simulate the cutting of the tooth blank by the hob. Therefore, the influence of chip removal and heat dissipation does not need to be considered in hob design.
2.3 Gear Hobbing Simulation Process
The gear hobbing simulation process. After starting CATIA, the tooth blank and hob models are first established in the part design environment. To obtain the main motion and generating motion characteristics from the tooth blank to the greatest extent, the hob is then assembled to the midpoint of the tooth thickness of the tooth blank, After assembling the hob and tooth blank, the assembly model is converted into a part model, and the simulation of the main motion and generating motion is performed in the part design environment. After each segment of the main motion and generating motion simulation, the Boolean difference operation is used to remove the intersecting model of the tooth blank and hob from the tooth blank, thereby simulating the cutting of the tooth blank by the hob. The step size of the main motion and generating motion depends on the number of teeth on the hob.
Table 1: Required Processing Gear Parameters
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Number of teeth | 20 | Helix angle | 20° |
| Normal modulus | 2 mm | Head clearance coefficient | 0.25 |
| Spiral direction | Right | Modification coefficient | – |
| Normal pressure angle | 20° | Addendum height coefficient | 1 |
After obtaining the preliminary tooth groove model, it can be used to replace the hob to simulate the vertical feed motion of the tooth blank. This reduces the redundant features added to the tooth blank by the hob in the Boolean difference operation, decreases memory usage, eliminates repeated main motion and generating motion simulations, and improves the efficiency of gear hobbing simulations.
3. Accuracy Verification and Analysis of the Simulation Model
3.1 Accuracy Verification of the Simulated Tooth Surface
After obtaining the simulation model through gear hobbing simulation, the tooth surface accuracy of the simulation model needs to be verified to validate the correctness of the gear hobbing simulation method and the accuracy of the obtained simulation model. Wang et al. used a comparison between the theoretical involute and the simulation model for accuracy verification of the straight gear model obtained from gear hobbing simulation.
For the accuracy verification of helical gears, based on the above measurement method, combined with the tooth blank parameters and the Knowledge Engineering function in CATIA, a theoretical tooth profile coordinate equation can be established.
The accuracy verification of the helical gear simulation model obtained from gear hobbing simulation involves establishing a theoretical involute set along the tooth thickness direction of the tooth blank. The theoretical involute set is established by creating involutes at equally spaced benchmark planes along the tooth thickness direction of the tooth blank, with a fixed angle difference between adjacent involutes. For subsequent measurements, equidistant points can be obtained and established on one side of the involute set, forming a point set required for measurement on a single tooth surface.
3.2 Analysis of Simulation Model Accuracy
In gear hobbing simulations, the main feed parameters are the circumferential feed parameter Δθ and the vertical feed rate h. The circumferential feed parameter Δθ is determined by the number of teeth on the hob. In actual production and processing, 9-12-toothed hobs are suitable for general-purpose processing, 12-16-toothed hobs are used in precision processing, and hobs with more than 20 teeth per head are relatively rare in production and processing. Therefore, a 12-toothed hob, which is representative of processing, can be selected, and a 24-toothed hob with double the number of teeth can be selected as a comparison object. With the vertical feed rate h as the influencing factor, experiments are set up, and the maximum tooth surface error is studied to analyze the influence trend of the vertical feed rate h on the maximum tooth surface error.
Table 2: Maximum Error of Tooth Surface (μm)
| Number of Hob Teeth | Vertical Feed Rate (mm) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 12 | 1.58 | 4.71 | 9.5 | 20.36 | |
| 24 | 0.97 | 4.69 | 9.05 | 20.22 |
As shown in Table 2, when the number of hob teeth is constant and the vertical feed rate h increases, the maximum tooth surface error also increases, showing a trend of geometric progression close to 2 for each 1 mm increase in the vertical feed rate.