Abstract Gear transmission systems are widely used in mechanical equipment. Due to manufacturing and processing errors, material defects, wear and external environments, there are uncertain parameters such as mass, mesh stiffness and support stiffness. Parametric uncertainty plays an important role in response predictions of the gear transmission systems. In order to evaluate reasonably the dynamic characteristics of the gear transmission systems, a dynamic model of an uncertain single-stage gear system is established. The dynamic responses of the bounded uncertain gear transmission system are investigated by an interval analysis method based on the Chebyshev inclusion function. A matrix form of the least square method is applied to improve the calculation efficiency of the interval approach. The investigation reveals the effects of different uncertain parameters on amplitude-frequency responses of the gear system. It is the first time to design and to implement a test rig of an uncertain single-stage spur gear transmission system. The experimental results verify the accuracy and the effectiveness of the theoretical analysis results. The results demonstrate that the parametric uncertainty may propagate in the gear transmission system and the propagation results in significant variations of the dynamic responses.

中文翻译：

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不确定正齿轮系统的动力学分析

摘要 齿轮传动系统广泛应用于机械设备中。由于制造和加工误差、材料缺陷、磨损和外部环境，存在质量、网格刚度和支撑刚度等不确定参数。参数不确定性在齿轮传动系统的响应预测中起着重要作用。为了合理评价齿轮传动系统的动态特性，建立了不确定单级齿轮系统的动力学模型。采用基于切比雪夫包含函数的区间分析方法研究了有界不确定齿轮传动系统的动态响应。应用最小二乘法的矩阵形式来提高区间法的计算效率。研究揭示了不同不确定参数对齿轮系统幅频响应的影响。首次设计并实现了不确定单级直齿轮传动系统的试验台。实验结果验证了理论分析结果的准确性和有效性。结果表明，参数不确定性可能会在齿轮传动系统中传播，并且传播会导致动态响应的显着变化。