林小燕，魏静，赖育彬，秦大同，张爱强，汝学斌

(1.重庆大学 机械传动国家重点实验室，重庆 400044; 2.太原重工股份有限公司 齿轮传动分公司，山西 太原 030024)

齿轮的剩余强度模型及其动态可靠度

林小燕1，魏静1，赖育彬1，秦大同1，张爱强1，汝学斌2

(1.重庆大学 机械传动国家重点实验室，重庆 400044; 2.太原重工股份有限公司 齿轮传动分公司，山西 太原 030024)

针对现有剩余强度模型不适用于体积大、寿命长、造价高的齿轮传动的寿命预测问题，本文应用非线性疲劳损伤累积理论建立剩余强度预测模型，该模型的参数由S- N曲线确定，以避免进行大量破坏性实验。结合损伤等效理论推导二级加载剩余强度预测公式，并将模型预测结果与材料实验结果进行比较，以验证模型的合理性。考虑齿轮传动强度及所受载荷随机性的特点，以应力-强度干涉理论为基础，建立齿轮传动动态可靠度功能函数；并利用摄动法及Rackwitz- Fiessler法(JC验算点法)得到齿轮传动服役过程中可靠度指标及可靠度动态变化曲线。研究表明：齿轮服役前期，应关注齿面接触疲劳强度可靠度；齿轮服役中后期，应关注齿面接触疲劳强度可靠度及齿根弯曲疲劳强度可靠度。

非线性疲劳损伤； 齿轮传动； 剩余强度； 损伤等效； 动态可靠度； 接触疲劳； 弯曲疲劳； 正态分布

Abstract：Existing residual strength models are inapplicable in the life forecast of a transmission gear with large volume, long life, and high cost. Thus, a new residual strength model is proposed to address this shortcoming. The proposed model is based on the nonlinear fatigue damage accumulation theory and its parameters are extrapolated from the S- N curve of materials to avoid massive and destructive experiments. The formula for residual strength prediction under two- stage loading is derived through the damage equivalent theory. Then, the model prediction result is compared with experimental data to verify the feasibility of the model. Considering the drive strength of the gear and the randomness of the load, the dynamic reliability function of the gear drive is established on the basis of the theory of stress- strength interference. In addition, the perturbation method and JC design point method are utilized to obtain the reliability index and the dynamic change curve of reliability in the drive process of the gear. Research shows that the reliability of the contact fatigue strength of the tooth surface in the early stage of gear service should receive more attention. By contrast, the fatigue- strength reliability of the tooth- surface contact and that of the tooth- root bending in the mid and late stage of gear service should receive more attention.

Keywords：nonlinear fatigue damage; gear drive; residual strength; damage equivalent; dynamic reliability; contacting fatigue; bending fatigue; normal distribution

齿轮是航空航天、能源、交通及机器人等领域中极其重要的基础零部件，齿轮的可靠性关系到整个传动系统甚至整个机械系统的安全。其剩余强度与可靠度预测是齿轮传动研究的重要内容。……