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.

Time-varying mesh stiffness (TVMS) of the internal mesh transmission is a significant source of excitation that causes vibration and noise in planetary gear systems, and is also an important parameter in dynamics analysis. Currently, the calculation of mesh stiffness for internal gear pairs primarily relies on finite element simulation, and there still lacks a mesh stiffness analytical model that accounts for tooth surface nonlinear contact. Therefore, this paper proposes an analytical model for nonlinear contact mesh stiffness that comprehensively accounts for tooth surface modification and the flexibility of the ring gear. Firstly, a mesh stiffness calculation model for a sliced tooth pair was established using the potential energy method, which accounted for the influence of gear ring flexibility. Secondly, the tooth deviation ease-off diagram was derived from the modified tooth surface equations, which provided data support for the nonlinear contact analysis. On this basis, slicing element pairs that met the contact conditions were identified by combining elastic deformation with mesh clearance. The comprehensive mesh stiffness in nonlinear contact was calculated by integrating the deformation coordination equation with the principle of minimum potential energy. Finally, using a group of internal helical gear pairs as an example, the validity of the proposed method was verified through finite element simulation. The effects of load, modification amount, and face width on the TVMS and load transmission error (LTE) of an internal helical gear pair were investigated by the analytical model. The results show that the analytical model can provide a reference for the optimal design of internal gear transmission.

Interfacial bonding strength between the substrate and its coating is one of the important indexes affecting the service life of parts. To reduce the manufacturing cost, a mathematical model can be established to quantitatively describe the microscopic surface roughness and its anti-corrosion coating adhesion strength. Anti-corrosion life could be improved by controlling the surface roughness of the substrate. In this study, a model of interfacial bond strength and roughness, which was calibrated using the substrate surface and closely related to the cell spacing and length of the support, was established. Under the same condition as the coating, component materials and the coating thickness, results were obtained that the coating strength changed along with the substrate roughness. When roughness changed between 37.1 μm and 48.4 μm, the bonding strength showed a decreasing trend. The larger the value of the roughness, the more conducive it was to the bonding between the arc spraying layer and the substrate. The adhesion between the coating and substrate was not always increased with the higher roughness on the same surface. It should be evaluated based on the surface roughness and its evaluation parameters, and there was an optimal roughness evaluation and selection range. The experimental results were consistent with the theoretical predictions.

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.

During large-size gear topological modification by form grinding, the helical gear tooth surface geometrical shape will be complex and it is difficult for the traditional scanning measurement to characterize the whole tooth surface. Therefore, in order to characterize the actual tooth surfaces, an on-machine topography measurement approach is proposed for topological modification helical gears on the five-axis CNC gear form grinding machine that can measure the modified gear tooth deviations on the machine immediately after grinding. Combined with gear form grinding kinematics principles, the mathematical model of topography measurements is established based on the polar coordinate method. The mathematical models include calculating trajectory of the centre of measuring probe, defining gear flanks by grid of points, and solving coordinate values of topology measurement. Finally, a numerical example of on-machine topography measurement is presented. By establishing the topography diagram and the contour map of tooth error, the tooth surface modification amount and the tooth flank errors are separated, respectively. Research results can serve as foundation for topological modification and tooth surface errors closed-loop feedback correction.