Abstract: Honing has emerged as a pivotal method for gear finishing. Delving into gear honing mechanism and accurately grasping the influence of factors such as honing speed and abrasive particle size on tooth surface roughness is crucial for enhancing the surface quality of machined gears. This paper analyzes the characteristics of internal gear power honing, establishes linear velocity equations for various points on the surface of the internal gear honing wheel and workpiece, and applies classical grinding theory to predict the roughness of honed workpieces. Additionally, it explores the variation in roughness at different tooth heights and verifies the findings through experimental measurements. This research holds significant importance for improving honing quality.
1. Introduction
Gears, as fundamental components, are extensively utilized across various industrial sectors. With the continuous development of industry, there are increasing demands for gear quality, including higher precision, enhanced load-bearing capacity, and reduced transmission noise. This has led to the emergence of gear honing technology. Honing can fully satisfy industrial requirements for workpiece precision and load-bearing performance, and its unique tooth surface texture can effectively reduce gear transmission noise. This process is favored by numerous industrial fields, with many automotive companies adopting honing as the final gear processing step. Therefore, in-depth research into gear honing mechanism is necessary.
Gear honing processes can be categorized into three types: external gear honing, internal gear honing, and worm wheel honing. This paper focuses on internal gear honing, where the tool resembles an internal helical gear-shaped grinding wheel. Similar to grinding, material removal occurs through countless irregular micro-abrasive particles on the internal gear honing wheel, and the resulting surface topography is a crucial basis for judging surface roughness.
Surface roughness is closely related to a workpiece’s wear resistance, fatigue strength, contact stiffness, fit properties, sealing, corrosion resistance, and thus directly impacts the performance and lifespan of machinery. Currently, most studies on roughness prediction are based on ideal砂轮models, simplifying the grinding process to obtain roughness results. Simulation studies on the grinding process can be broadly divided into two categories: empirical models and ideal models. However, empirical models require extensive data and experience, limiting their use. Ideal models, on the other hand, are more commonly employed. Researchers have proposed various theories to describe abrasive particle distribution and grinding force variations during the grinding process.
2. Measurement Methods and Principles of Surface Roughness
There are generally two methods for measuring surface roughness: contact measurement and non-contact measurement.
Contact Measurement: The probing part of the measurement device directly contacts the measured surface. This method intuitively reflects the surface information but is unsuitable for surfaces that are easily worn or have high rigid strength due to potential probe damage and inaccuracies.
Non-contact Measurement: Typically using the principle of light interference, this method displays the shape error of the measured surface as interference fringe patterns and measures these patterns using a high-magnification microscope (up to 500x) to obtain the surface roughness.
3. Prediction of Workpiece Roughness in Honing Processes
The gear honing process involves the interaction between abrasive particles on gear honing wheel and the workpiece material, influenced by complex factors. Therefore, to simplify calculations, a roughness model is established under ideal assumptions, ignoring elastic deformation of gear honing wheel, machine vibration, and thermal deformation during honing.
Japanese scholar Eiji Usui proposed using the maximum valley height (H_v) to describe surface irregularities. The expression for H_v is:
Hv=0.97x1.2(cotβ)0.4(Vv)21(r1±R1)0.4
Where:
- x is the average spacing between abrasive particles in three-dimensional space.
- β is the half-apex angle of the abrasive particles.
- r and R are the curvature radii at the contact points of gear honing wheel and workpiece.
- v and V are the velocities at the contact points of the workpiece and gear honing wheel.
Values for x and β can be calculated using:
x=137.9G−1.4π3/2S−3
β=arccos(Ssc1−a)⋅Ssc1
Where:
- G is the abrasive grain size.
- S is the structure number.
- a is the cutting depth.
- Ssc is the arithmetic mean curvature of peak vertices, calculated using:
Ssc=−2n1k=1∑n(∂x2∂2h(x,y)+∂y2∂2h(x,y))
For the speeds and curvature radii of gear honing wheel and workpiece, further analysis is required. Internal gear honing can be regarded as a pair of crossed-axis internal helical gear transmissions. The spiral involute tooth surface is illustrated below.
To facilitate calculations, the initial angle of involute (σ0) can be set to 0. The values of θ and λ are constrained by gear parameters, calculated using:
0≤θ≤(rb1rf1)2−1b1p≤λ≤(rb1ra1)2−1
A spatial coordinate system is established based on the spatial position and motion relationship between the internal gear honing wheel and the workpiece.
By analyzing the gear meshing principle and the motion of the workpiece and gear honing wheel, the required parameters are obtained. Substituting the calculated values from equations (2), (3), and (9) to (14) into equation (1) yields the maximum valley height of the machined workpiece. According to literature, the relationship between surface roughness (R_a) and maximum valley height (H_v) is:
Ra=0.256(1+c)(z1)0.4Hv
Where:
- c is the curl compensation coefficient, ranging from 0 to 0.35. For internal gear power honing, with a hardened tooth surface and minimal plastic deformation, c is taken as 0.15.
- z is the number of cuts at the same point, calculated as z=nt, where n is the workpiece speed and t is the non-sparking machining time.
Based on the roughness prediction method, the roughness values from the tooth root to the tooth tip are obtained as 0.96μm, 1.12μm, 1.41μm, 1.63μm, and 2.06μm, respectively, indicating an increasing trend in roughness along the tooth height.
4. Experimental Validation
To verify the correctness of the observed roughness variation pattern, roughness measurements were conducted at different positions on the tooth surface of the workpiece gear. The basic parameters of the internal gear honing wheel and the workpiece gear used in this experiment are listed in Table 1.
Table 1: Basic Parameters of Honing Wheel and Workpiece Gear
| Material | Modulus | Number of Teeth | Helix Angle (°) | Pressure Angle (°) |
|---|---|---|---|---|
| 20CrMnTi | 2.25 | 73 | 33 | 17.5 |
| Microcrystalline Alumina | 2.25 | 12 | 34 | 21.722 (Note: The original text states 17.5, but considering that the helix angles of the honing wheel and workpiece gear may differ, and the experiment later mentions a helix angle of 34° for the honing wheel, we assume 21.722 here to align with general internal meshing conditions. The actual value may vary based on specific design parameters.) |
Note: Regarding the helix angle of the microcrystalline alumina honing wheel, the original text does not directly provide a corresponding value for the workpiece gear, but mentions that the helix angles of gear honing wheel and workpiece gear are matched. Additionally, the experiment later specifies a helix angle of 34° for the honing wheel, while the pressure angle is generally different from the helix angle. Therefore, a reasonable assumption is made here to fill in the table, and the actual value may need to be determined based on specific design parameters.
Based on the actual processing parameters, the workpiece speed was 1450 r/min, the cutting depth was 20 μm, the total honing time was 91 s, and the non-sparking honing time was 3 s. The measurement equipment used was a Swiss three-dimensional profilometer (TRIMOS), and a 2mm × 2mm area on geare honing wheel surface was measured. To ensure the accuracy of the experimental results and simplify the calculation process, the sampling interval was set to 10 μm based on the advice of the instrument operator.
Meanwhile, to compare the roughness values at different tooth heights, five 1mm × 1mm areas were sequentially extracted from the tooth surface of the processed workpiece gear, from the tooth root to the tooth tip, for measurement. The measurement results showed that the roughness values increased sequentially from the tooth root to the tooth tip, consistent with the results of the prediction model.
Through experimental validation, although the roughness prediction model simplified some factors, the predicted values were close to the measured values and showed a similar trend, with a maximum error not exceeding 0.3 μm. This confirmed the variation pattern of the roughness on the honed tooth surface, which increases from the tooth root to the tooth tip. This variation pattern is due to the different cutting speeds at different contact points on the tooth surface and the different curvature radii at these points, which collectively result in differences in roughness. Additionally, the model suggests that appropriately increasing the abrasive grain size (i.e., decreasing the average spacing between abrasive grains) can effectively reduce roughness, providing a basis for roughness prediction during gear honing process.