Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears

Abstract

This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

On the analytical definition of profile modifications minimising transmission error variations in narrow-faced spur helical gears

“…The problem is then reduced to finding the relief amplitude Ẽ * minimising (11): Combining (7), (11) and (12) leads to the following equation:…”

“…Since tooth correction amplitudes depend on deflections, profile and lead modifications are usually calibrated for one specific design load whereas, in a number of applications, load can vary substantially. Numerous contributions are available in the literature showing the applications of tooth profile modifications to spur and helical gears with both low and high contact ratios [7][8][9][10][11][12][13][14][15][16][17][18]. However, most of the recent results are based on intensive numerical simulations which, if very accurate, do not necessarily lend themselves to a complete understanding of the effects of design parameters and operating conditions.…”

Multi-objective optimisation of profile modifications in spur and helical gears – an analytical approach

“…Based on [4], [8], , , [11] and [13], performance diagrams can be established as shown in Figure 5 which, for all low-contact ratio gear geometries, illustrate the design criterion evolutions when changing profile relief amongst the set of modifications along the master curve in Figure 2. It is observed, in particular, that the design criteria can be classified in two families: a) the maximum contact pressure and root stress which are reduced when longer optimum relief is used and, b) the loss factor and contact length reduction (or actual contact ratio) which increase as longer relief is considered.…”

“…who found that they were influential on off-lineof-action contacts and could strongly reduce the vibration and noise of spur gears at one particular load, coined 'design load' (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17). In this context, approximate design rules for profile relief in spur gears have been established (9-10), (12) whereas, for helical gear teeth, the definition of modifications mostly relies on extensive numerical simulations (11), (13)(14)(15)(16)(17) from which general trends can hardly be extrapolated.…”

“…In this context, approximate design rules for profile relief in spur gears have been established (9-10), (12) whereas, for helical gear teeth, the definition of modifications mostly relies on extensive numerical simulations (11), (13)(14)(15)(16)(17) from which general trends can hardly be extrapolated. Recently, some approximate analytical formulae have been proposed (21)(22) which correlate reasonably well with the results from specific software codes and make it possible to estimate the relevant profile modification parameters minimising transmission error fluctuations for both spur and helical gears.…”