Traditional reliability assessment of spindle systems of machine tools suffers from long testing time and high cost. Accelerated life testing is an alternative that overcomes the shortcomings of traditional reliability testing. In a life testing, identification of critical factors of service life and an accurate model are important. Based on the characteristic analysis and engineering experience, four reliability factors, which are the average power of spindle systems, the number of tool changing, the number of spindles restarting and environment temperature, are selected as accelerating environment variables. An accelerated failure time model is used to describe the inverse relationship between the variables and reliability for the catastrophic failure mode and the degradation failure mode separately. Then a competing risk model is built by considering competing risks of two modes. Parametric reliability models are proposed to capture the statistical independency and dependency separately, in which the Gumbel–Hougaard copula function is used to establish the joint cumulative distribution for dependency. Thereby the hypothesis testing is developed to determine the failure modes dependency. The reliability sensitivity of each environment variable is analyzed. Finally, the proposed model is illustrated with a real field case study.

A new compiling method based on cutting force model is proposed for an eight-block program-loading spectrum of a motorized spindle. In the proposed method, all loads exerted on the motorized spindle are dependent, which is accurate for loading in reliability tests. A cutting force measuring system is set up to obtain cutting forces accurately. Then, two concluded cutting force models are compared to choose the better one through fitting the measured cutting force signals under different machining process parameters. In accordance with the characteristic of the milling load, program-loading spectrum for the amplitude of radial force is compiled while neglecting other factors. Thereafter, the compiled spectrum is converted into a complete program-loading spectrum where torque and loads' correlation are calculated by the chosen cutting force model. Finally, the accelerated factor of the program-loading spectrum relative to actual machining conditions is solved.

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In the accelerated degradation test (ADT) of motorized spindles, it is necessary to apply a variety of stresses to simulate real working conditions. However, the traditional accelerated test scheme optimization method does not consider the weight of various stresses in the test, resulting in the evaluation accuracy of important stress parameters in the model being too low. In order to solve this problem, an optimal design method of the step stress accelerated degradation test (SSADT) scheme for motorized spindles is proposed based on Ds-optimality. Firstly, the fault tree analysis (FTA) method is used to analyze the collected fault data of motorized spindles and screen the main stress. Then, the accelerated degradation model is established by using drift Brownian motion. Based on the Ds-optimality, the optimization variables and constraints in the test are determined, and the optimization model is established with the objective of minimizing the estimated variance of the main stress parameters in the acceleration model; additionally, the optimization steps are given. Finally, an example is given to verify the effectiveness of the method. Sensitivity analysis of the optimization results shows that the method has good robustness.