基于光纤光栅的直齿圆柱齿轮应力修正系数优化

Stress Concentration Factor Optimization of Spur Gear Based on FBG Strain Measurement

利用光纤光栅传感器截面直径小的优势,将光纤光栅粘贴在直齿圆柱齿轮齿根过渡曲线处,测量弯曲应力将会得到比较好的测量效果。文中利用光纤光栅传感器测量了直齿圆柱齿轮弯曲应力,并对直齿圆柱齿轮弯曲应力解析计算的应力修正系数进行了优化。首先根据弹性理论的两个平面假设,提出在齿根表面一点上沿齿宽方向应力与该点至端面的距离有关,并且沿齿宽方向应力与弯曲应力的比值,在齿宽方向上服从指数函数变化规律;然后利用光纤光栅传感器,测量直齿圆柱齿轮弯曲应力;最后根据光纤光栅测量,优化直齿圆柱齿轮弯曲应力解析计算的应力修正系数。研究结果表明,直齿圆柱齿轮弯曲应力解析计算的应力修正系数取值偏大,比测量得到的应力修正系数大21.8%。直齿圆柱齿轮是最常见的传动装置基本零件,基于光纤光栅测量对直齿圆柱齿轮弯曲应力修正系数进行优化,可提高直齿圆柱齿轮强度设计的可靠性。

With a small cross-section diameter, FBG has the advantage to be pasted on the fillet in the narrow non- intermeshing space of spur gear root. It would be suitable to measure the spur gear bending stress with FBG. In this paper, the spur gear bending stress is measured using FBGs, and the stress concentration factor in the analytic calculation of spur gear bending stress is optimized. Firstly, based on the 2 hypothesis about plane problem in the theory of elasticity, we put forward a hypothesis that the stress in the tooth width direction on a point on the surface of the gear root is related to the distance between that point to the gear end-face and the ratio of the stress in the tooth width direction to the bending stress accords with the law of exponential function; Secondly, the spur gear bending stress is measured using FBGs; Lastly, based on the FBG measurement, the stress concentration factor of spur gear bending stress analytic calculation is optimized. The result of study shows： the value of stress concentration factor in the spur gear bending stress analytic formula is 21.8 percent larger than that obtained from the bending stress test based on FBG. Spur gear is the most common part in the driving device. The reliability in the spur gear strength design can be improved by the optimization to the spur gear bending stress concentration factor basing on the FBG measurement.