The gear test bench is important equipment for analyzing gear performance, detecting gear quality, and providing basic data for gear design and machining. In order to monitor the running state of the gear test bench, predict its running performance both timely and effectively, and guarantee its stable operation, a digital twin-based state monitoring method of the gear test bench is proposed in this paper. The state monitoring system of the gear test bench based on the digital twin model is constructed to simulate its normal running state in real time. On this basis, through the acquisition of physical information of the gear test bench, the developing of the state monitoring system, and the simulation of the digital twin model, the real-time state monitoring of the normal operation gear test bench is realized. The test results of the closed power flow gear test bench show that the digital twin simulation results of the gear test bench are basically consistent with it. The proposed state monitoring system can map the normal running state of the gear test bench, so as to realize the running state monitoring of the gear test bench.

In the manufacturing and production of hypoid gears, it is a necessary key problem to improve the tooth surface heat treatment precision and production efficiency of the hypoid gears. How to use advanced statistical theory and methods to evaluate the whole batch machining quality of the tooth surface after heat treatment is particularly urgent. In this connection, for the same batch of hypoid gears with the same gear material, numerical control gear milling method, and heat treatment specifications, a bootstrap-based statistics scheme of tooth surface errors after heat treatment is proposed in this paper. The bootstrap statistics model of the tooth surface errors for the batch hypoid gears is established. The bootstrap probability eigenvalues and confidence intervals of the measurement sequence points on the tooth surface errors are solved, and the optimizing selection of the single sampling numbers and the repeated sampling times is completed. On this basis, by applying the cubic NURBS surface fitting method, the mean value difference surface of the batch tooth surface errors data is constructed, the statistics laws of the whole batch tooth surface errors after heat treatment is determined, and the effective evaluation of the whole batch tooth surface accuracy is realized. Finally, the feasibility and correctness of the bootstrap-based statistics scheme are verified by the tooth surface errors bootstrap statistics application experiment of one kind of hypoid gear. The results show that with the help of the bootstrap statistics method proposed in this paper, it is not necessary to accurately measure the tooth surface errors of the whole batch of hypoid gears one by one. Only by randomly selecting 10 tooth surface samples and repeatedly sampling 2000 times, the original sample characteristic values of the whole batch tooth surface errors can be accurately estimated, and the heat treatment deformation statistics laws of the whole patch tooth surfaces can be also counted.