Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.

齿轮驱动装置通常用于机械传动系统中。由于在制造，安装和操作中不可避免的随机误差，齿轮传动系统的动力会随机波动。为了揭示其动态特性，建立了单级正齿轮副的区间参数动力学模型，其中包括了位移激励，载荷激励和刚度激励的不确定性，并通过区间数学详细推导了它们的公式。 。通过将Chebyshev包含函数方法和Runge–Kutta方法结合起来，可以解决已建立的区间参数动力学模型的问题。最后，随机间隔参数对啮合刚度，输入扭矩，研究了齿轮传动系统的传动误差，齿隙对振动速度间隔和传动可靠性的影响。分析结果表明，三种激励方式对动力特性的影响不同。具体来说，不确定参数对动态特性的影响可以按照从最强到最弱的顺序依次划分为啮合刚度，输入扭矩，反冲和传动误差。本研究可以作为合理的理论基础，可以为正齿轮传动系统的设计和振动控制提供参考。不确定参数对动力特性的影响可以按照啮合刚度，输入扭矩，齿隙和传动误差从最强到最弱的顺序进行排序。本研究可以作为合理的理论基础，可以为正齿轮传动系统的设计和振动控制提供参考。不确定参数对动力特性的影响可以按照啮合刚度，输入扭矩，齿隙和传动误差从最强到最弱的顺序进行排序。本研究可以作为合理的理论基础，可以为正齿轮传动系统的设计和振动控制提供参考。