Abstract
The method to fundamentally address the imbalance in gear shaving for cylindrical gears with few teeth in transmissions. The MASTA software’s shaving dynamics simulation module was utilized to calculate and address issues in a Z12-tooth component of a transmission. The feasibility of resolving the concave defect by altering the shaving cutter’s profile shift coefficient was explored, providing a method and basis for optimizing the shaving cutter during the design phase.
Keywords: few teeth, concave defect, balanced shaving, dynamics simulation
Introduction
In automotive transmission products, each typically contains one to two cylindrical gears with few teeth. The concave defect in the finish shaving of these gears is a ubiquitous issue in gear processing. This defect often leads to increased transmission errors, causing noise, vibration, concentrated tooth surface contact stress, early pitting and cracking during life tests, as well as large-scale spalling and failure.
The primary cause of the concave defect on the tooth surface is the small meshing engagement between the shaving cutter and the gear, particularly when shaving gears with few teeth and large modulus straight teeth. The meshing engagement between the shaving cutter and the gear is usually less than 2 in terms of contact ratio. Therefore, during the meshing process between the gear and the shaving cutter, single-tooth and double-tooth contacts will alternately appear, leading to imbalanced shaving. This imbalance can manifest as uneven removal of material from the two tooth surfaces during shaving, typically with more material removed from the driving tooth surface, potentially causing tooth surface damage.
To fundamentally solve the problem of concave defects in shaving gears with few teeth, it is necessary to optimize the design of the shaving cutter and hob before shaving the gears with few teeth to ensure that the shaving cutter operates within the quasi-balanced shaving condition. When the gear parameters are determined, the length of the gear’s meshing line and the contact ratio are fixed. By changing the profile shift coefficient of the shaving cutter, the size of the unbalanced shaving area can be adjusted to reduce or eliminate the concave amount during shaving.
Dynamic Simulation Calculation of Gear Shaving Process for Gears with Few Teeth
To select reasonable shaving cutter and hob parameters before the occurrence of concave defects and ensure that the shaving cutter meets the quasi-balanced shaving conditions over a large range, simulation calculations are required for advance optimization.
In this paper, the dynamic simulation of the shaving process for a Z12-tooth reverse gear in a transmission was conducted using the MASTA software’s shaving dynamics simulation module. The feasibility of optimizing the shaving of gears with few teeth by changing the profile shift coefficient of the shaving cutter was determined. The shaving cutter’s regrinding parameters, including the amount of each regrinding and the size after the tooth tip is regrinded, were all input into the software strictly according to the manufacturer’s regrinding table. The calculations focused on the changes in the unbalanced shaving area caused by the regrinding of the shaving cutter.
The simulation results show that as the shaving cutter is regrinded, the calculated unbalanced development angle decreases, and the imbalance in shaving improves. When the shaving cutter is near the end of its life, the concave defect in shaving is eliminated.
When processing errors are included in the simulation calculations, the imbalance in shaving differs with changes in the positions of the SAP and EAP points, among which the SAP point has a more sensitive influence on the imbalance characteristics. During the initial stages of blade grinding, when the post-shaving SAP point is at the upper limit, the concave defect in shaving is smaller; when the SAP point is at the lower limit, the concave amount in shaving is larger. As the shaving cutter is regrinded, when the SAP point is at a certain value after shaving, the tooth surface is prone to concave defects.
Experimental Study on Gear Shaving for Gears with Few Teeth
To exclude the influence of the shaving cutter’s profile modification on the shaving results, the profile and lead modifications of the shaving cutter were kept consistent with the new cutter parameters during regrinding. The shaving process strictly followed the regrinding table for the shaving cutter’s tooth thickness and tooth tip circle.
The first cutting tool regrinding inspection report. Each error is approximately 2~3 micrometers, meeting the test requirements. Shaving was performed after grinding the gear according to its conjugate relationship with the new cutter, and shaving was carried out with the tooth thickness at the upper limit, median, and lower limit. The resulting SAP point positions were different, with the SAP point also biased towards the upper limit when the tooth thickness was biased towards the upper limit, to verify the calculation results of the shaving dynamics simulation with error values.
The test results showed that the change law of the concave defect with different tooth thicknesses after shaving was consistent with the simulation results. As the shaving cutter was regrinded, the concave amount in the shaved parts gradually decreased, approaching zero after the fifth regrinding. The detection results of the tooth shape of the gear after shaving with the shaving cutter regrinded once, showing the change law of the concave defect in shaving, which was consistent with the simulation results. After that, the cutting tool was regrinded according to the cutting tool regrinding table. The detection results of the gear tooth shape at different tooth thickness states after several stages of the cutting tool regrinding.
Conclusion
In summary, the dynamic simulation results of gear shaving for the Z12-tooth gear in the tested transmission were consistent with the test results of the shaving cutter regrinding. The test results indicated that during the design phase of gears with few teeth, the shaving dynamics simulation calculation could be used to confirm whether the shaving cutters provided by the tool manufacturer could achieve quasi-balanced shaving. Furthermore, it could further confirm the suitable regrinding range of the shaving cutter to meet the quasi-balanced shaving conditions, guiding the regrinding of the shaving cutter.
The size of the unbalanced shaving area is determined by the length of the meshing line during shaving and the positions of various characteristic points. Factors influencing its size include the design of the SAP and EAP points of the gear, the basic rack design of the hob, the shaving allowance, and the profile shift coefficient of the shaving cutter. To optimize the shaving process for gears with few teeth and reduce the unbalanced development angle, these three factors must be considered together for an integrated design of the gear, hob, and shaving cutter.