The axial friction force (AFF) of automotive drive-shaft systems is an important nonlinear dynamic characteristic, which will directly cause the vibration and noise of vehicles. During the operation of drive-shaft systems, the AFF has great uncertainty. Taking a drive-shaft system as the research object, a hybrid random and interval uncertainties (HRIU) model of the AFF is proposed to study the AFF more effectively. In the HRIU model, the articulation angle and the pitch circle radius of tripod joints are regarded as random variables, while the input torque, the shaft angular position and the friction coefficient are regarded as interval variables. To enhance the efficiency and accuracy of the analysis and optimization, a novel method called as the perturbation-vertex method is proposed to calculate the responses of the HRIU model. Due to complex responses of the HRIU model, in order to optimize the AFF more effectively, a reliability-based optimization method for the AFF under the HRIU is proposed, and the lower bound of the AFF reliability is taken as the optimization objective to determine the best design parameters of drive-shaft systems. A test bench for measuring the AFF is subsequently established together with the model verification, as well the analysis and optimization of the AFF with the HRIU are performed through numerical examples. The results suggest that the proposed perturbation-vertex method is very suitable for the analysis and optimization with the HRIU, as well the influence of the HRIU on the AFF cannot be ignored when analyzing and optimizing the AFF.

汽车传动轴系统的轴向摩擦力（AFF）是一种重要的非线性动力学特性，它会直接引起汽车的振动和噪声。在传动轴系统运行过程中，AFF具有很大的不确定性。以传动轴系统为研究对象，提出了AFF的混合随机和区间不确定性（HRIU）模型，以更有效地研究AFF。在HRIU模型中，三脚架关节的铰接角和节圆半径被视为随机变量，而输入扭矩、轴角位置和摩擦系数被视为区间变量。为了提高分析和优化的效率和准确性，提出了一种称为扰动顶点法的新方法来计算 HRIU 模型的响应。由于HRIU模型响应复杂，为了更有效地优化AFF，提出了一种基于可靠性的HRIU下AFF优化方法，以AFF可靠性下界为优化目标，确定传动轴系统的最佳设计参数。随后建立了测量AFF的试验台，并进行了模型验证，并通过数值算例对带有HRIU的AFF进行了分析和优化。结果表明，本文提出的微扰顶点法非常适用于HRIU的分析和优化，在分析和优化AFF时，HRIU对AFF的影响也不容忽视。提出了HRIU下基于可靠性的AFF优化方法，以AFF可靠性下界为优化目标，确定传动轴系统的最佳设计参数。随后建立了测量AFF的试验台，并进行了模型验证，并通过数值算例对带有HRIU的AFF进行了分析和优化。结果表明，本文提出的微扰顶点法非常适用于HRIU的分析和优化，在分析和优化AFF时，HRIU对AFF的影响也不容忽视。提出了HRIU下基于可靠性的AFF优化方法，以AFF可靠性下界为优化目标，确定传动轴系统的最佳设计参数。随后建立了测量AFF的试验台，并进行了模型验证，并通过数值算例对带有HRIU的AFF进行了分析和优化。结果表明，本文提出的微扰顶点法非常适用于HRIU的分析和优化，在分析和优化AFF时，HRIU对AFF的影响也不容忽视。以AFF可靠性下界为优化目标，确定传动轴系统的最佳设计参数。随后建立了测量AFF的试验台，并进行了模型验证，并通过数值算例对带有HRIU的AFF进行了分析和优化。结果表明，本文提出的微扰顶点法非常适用于HRIU的分析和优化，在分析和优化AFF时，HRIU对AFF的影响也不容忽视。以AFF可靠性下界为优化目标，确定传动轴系统的最佳设计参数。随后建立了测量AFF的试验台，并进行了模型验证，并通过数值算例对带有HRIU的AFF进行了分析和优化。结果表明，本文提出的微扰顶点法非常适用于HRIU的分析和优化，在分析和优化AFF时，HRIU对AFF的影响也不容忽视。