Gear grinding is a critical finishing process in gear manufacturing, directly impacting the service performance and lifespan of transmission systems. As the final cutting step in the “hobbing-heat treatment-grinding” workflow, gear grinding induces residual stresses on the tooth surface that significantly influence fatigue resistance, wear behavior, and susceptibility to grinding cracks. Traditional measurement methods, such as X-ray diffraction, often fail to account for the complex geometry of gear teeth, leading to inaccuracies. Moreover, the relationship between grinding parameters and residual stress remains unclear, particularly for gear profile grinding. This study addresses these gaps by proposing a novel measurement approach with specialized fixtures, developing a predictive model for residual stress based on grinding parameters, and investigating the effect of pre-grinding surface conditions. The findings offer practical guidance for optimizing gear grinding processes to minimize grinding cracks and enhance durability.
Residual stress measurement techniques are broadly categorized into destructive and non-destructive methods. Destructive approaches, like hole-drilling and sectioning, are traditional but invasive. Non-destructive methods, such as X-ray diffraction, leverage physical phenomena induced by residual stress to determine stress values without damaging the component. X-ray diffraction is widely adopted due to its speed, accuracy, and repeatability. However, its application to gear grinding surfaces is challenging because the method requires a near-planar surface and unobstructed X-ray paths—conditions rarely met by the curved tooth surfaces in gear profile grinding. For instance, adjacent teeth can block diffraction signals or focusing light paths, and maintaining the required probe-to-surface distance is difficult. To overcome these issues, we propose sectioning individual teeth via wire cutting to isolate the measurement area. This allows for precise orientation adjustments using a custom fixture that aligns the tooth surface tangent to the horizontal plane, ensuring accurate X-ray incidence and detection.
The fixture design incorporates a magnetic mounting plate to secure the sectioned tooth, a rotary mechanism for adjusting the tooth orientation, and an angle measurement plate to verify horizontal alignment. The coordinate transformation between the gear coordinate system and the global measurement system is achieved through this fixture. For a point on the involute tooth surface, the tangential vector is derived from the gear geometry. The rotation angle θ for alignment is calculated as:
$$ \theta = \frac{\pi}{2} – \sqrt{\left( \frac{d_a – 2r_{dm}}{2r_b} \right)^2 – 1 } $$
where \( d_a \) is the tip diameter, \( r_{dm} \) is the distance from the tip to the measurement point, and \( r_b \) is the base circle radius. This adjustment ensures the measurement point’s tangent is horizontal, minimizing errors. Experimental validation showed that a mere 6° deviation in orientation altered residual stress readings by over 100 MPa, underscoring the necessity of precise alignment in gear grinding measurements.
To establish a predictive model for residual stress in gear profile grinding, we conducted a series of experiments focusing on key grinding parameters: feed rate, wheel speed, and cutting depth. A L9(3^4) orthogonal array was designed, with parameters and levels summarized in Table 1. The workpiece material was steel, and the gear geometry included 20 teeth, a module of 4.75 mm, and a pressure angle of 20°. Each gear underwent a standardized grinding sequence: rough grinding followed by finish grinding with varying parameters in the reverse stroke. After grinding, three teeth per gear were sectioned, and residual stress was measured at 54 points per tooth (27 per flank) using the X-ray method. The average values of tangential and axial residual stresses were recorded.
| No. | Feed Rate (mm/min) | Wheel Speed (m/s) | Cutting Depth (mm) |
|---|---|---|---|
| 1 | 800 | 20 | 0.03 |
| 2 | 1500 | 20 | 0.06 |
| 3 | 2200 | 20 | 0.10 |
| 4 | 800 | 27 | 0.06 |
| 5 | 1500 | 27 | 0.10 |
| 6 | 2200 | 27 | 0.03 |
| 7 | 800 | 35 | 0.10 |
| 8 | 1500 | 35 | 0.03 |
| 9 | 2200 | 35 | 0.06 |
The measured residual stresses are presented in Table 2. Both tangential and axial stresses were compressive, with tangential stresses generally higher in magnitude. The data were analyzed using the range method to determine the influence of each parameter. The level average \( K_{ij} \) for parameter i at level j was computed as the mean of residual stresses for trials at that level. The influence factor \( D_i \) was derived as the difference between the maximum and minimum \( K_{ij} \) values for each parameter.
| No. | Tangential Residual Stress (MPa) | Axial Residual Stress (MPa) |
|---|---|---|
| 1 | -701.5 | -288.2 |
| 2 | -584.3 | -222.6 |
| 3 | -503.3 | -177.0 |
| 4 | -691.0 | -277.3 |
| 5 | -545.3 | -214.5 |
| 6 | -576.3 | -222.5 |
| 7 | -642.2 | -284.0 |
| 8 | -631.8 | -264.8 |
| 9 | -480.2 | -190.2 |
The calculated \( K_{ij} \) and \( D_i \) values are summarized in Tables 3-5. Feed rate exhibited the highest influence on both tangential and axial residual stresses, followed by cutting depth. Wheel speed had a negligible effect, likely due to efficient cooling and the limited speed range in gear profile grinding. The interaction between feed rate and cutting depth was weak, allowing for a linear superposition of their individual effects in the predictive model.
| Feed Rate (mm/min) | Tangential \( K_{ij} \) (MPa) | Axial \( K_{ij} \) (MPa) | Tangential \( D_i \) | Axial \( D_i \) |
|---|---|---|---|---|
| 800 | -678.2 | -283.2 | 158.3 | 86.6 |
| 1500 | -587.1 | -234.0 | ||
| 2200 | -519.9 | -196.6 |
| Wheel Speed (m/s) | Tangential \( K_{ij} \) (MPa) | Axial \( K_{ij} \) (MPa) | Tangential \( D_i \) | Axial \( D_i \) |
|---|---|---|---|---|
| 20 | -596.4 | -229.3 | 19.5 | 17.0 |
| 27 | -604.2 | -238.1 | ||
| 35 | -584.7 | -246.3 |
| Cutting Depth (mm) | Tangential \( K_{ij} \) (MPa) | Axial \( K_{ij} \) (MPa) | Tangential \( D_i \) | Axial \( D_i \) |
|---|---|---|---|---|
| 0.03 | -636.5 | -258.5 | 72.9 | 33.3 |
| 0.06 | -585.2 | -230.0 | ||
| 0.10 | -563.6 | -225.2 |
Based on the orthogonal results, we conducted additional experiments to quantify the relationship between residual stress and the dominant parameters: feed rate and cutting depth. Wheel speed was excluded due to its minimal impact. The experimental data were fitted using logarithmic and linear functions. The tangential residual stress \( y_1 \) relates to feed rate \( f \) and cutting depth \( a_p \) as:
$$ y_1 = 144.24 \ln f + 18.67 \ln a_p – 2433.17 $$
The axial residual stress \( y_2 \) is given by:
$$ y_2 = 0.1018 f + 788.94 a_p – 885.22 $$
Both equations exhibit high coefficients of determination (R² > 0.95), confirming their accuracy within the tested range. The models indicate that increasing feed rate or cutting depth reduces compressive residual stress, potentially elevating the risk of grinding cracks in gear profile grinding. This trend aligns with the higher thermal and mechanical loads at elevated parameters, which can induce tensile stresses if uncontrolled.
To assess the effect of pre-grinding surface conditions, we performed hobbing experiments with varied parameters (feed rate, cutter speed, and finishing allowance) on identical gears. After hobbing, residual stresses were measured, followed by heat treatment, shot blasting, and final grinding under constant parameters. The results, summarized in Table 6, show that pre-grinding residual stresses varied significantly due to hobbing parameters (standard deviations of 55.43 MPa tangential and 40.24 MPa axial). However, post-grinding stresses were consistent across all groups (standard deviations of 22.79 MPa tangential and 20.25 MPa axial), indicating that the grinding process overrides the initial state. This is attributed to the removal of the affected surface layer during gear grinding, which typically involves a 0.3 mm depth of cut, exceeding the penetration depth of hobbing-induced stresses.
| Process | Tangential Standard Deviation (MPa) | Axial Standard Deviation (MPa) |
|---|---|---|
| Hobbing | 55.43 | 40.24 |
| Heat Treatment | 66.43 | 67.35 |
| Grinding | 22.79 | 20.25 |
The predictive model and measurement approach have significant implications for industrial gear grinding. By selecting lower feed rates and cutting depths, manufacturers can enhance compressive residual stresses, thereby improving resistance to grinding cracks and fatigue. For instance, in gear profile grinding, a feed rate of 800 mm/min and cutting depth of 0.03 mm yielded tangential stresses of -701.5 MPa, whereas 2200 mm/min and 0.10 mm resulted in -480.2 MPa. The proposed fixture enables accurate residual stress mapping on complex geometries, facilitating quality control. Future work could integrate real-time monitoring to dynamically adjust parameters, minimizing residual stress variations and preventing defects in high-precision gears.
In conclusion, this study presents a comprehensive framework for residual stress management in gear grinding. The measurement method addresses geometric challenges through sectioning and fixturing, ensuring reliable data acquisition. The predictive model, based on feed rate and cutting depth, provides a practical tool for optimizing gear profile grinding processes. Experimental evidence confirms that pre-grinding conditions have minimal impact, emphasizing the dominance of grinding parameters. By implementing these findings, industries can achieve superior gear performance, reduced grinding cracks, and extended service life in demanding applications.