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Transmission error (TE) is an important parameter in gear dynamics that has a direct impact on the vibration and noise of gears. Under quasi-static conditions, gear elastic deformation and assembly errors amplify with increasing load, potentially contributing to noise and vibration. This paper presents a novel method for measuring the quasi-static transmission error (QSTE) of spur gears under quasi-static conditions. In particular, the study investigates the relationship between quasi-static transmission error, elastic deformation transmission error, and gear tangential acceleration. Gear elastic deformation transmission error was calculated from experimental data obtained with single-point, symmetrical dual-point, and orthogonal four-point configurations of tangential acceleration sensors. The orthogonal four-point sensor configuration greatly improves measurement accuracy when compared to theoretical values derived from material mechanics calculations. A dedicated on-machine acquisition system for spur gear tangential acceleration was constructed. Tangential acceleration tests were conducted across varying loads and rotational speeds. The acquired data underwent filtering and integration processing in order to obtain gear elastic deformation and quasi-static transmission error. The feasibility of the acceleration approach for measuring both gear elastic deformation and quasi-static transmission error is confirmed by a comparative analysis of the acceleration method results with transmission errors obtained via material mechanics calculations and magnetic grating detection.

The primary aim of the present study is to develop a micro-deformation method for measuring the quasi-static transmission error in gears. First, the micro-deformation method is introduced, based on which a transmission error measurement scheme is established. Following this, the measurement method is experimentally verified by measuring the quasi-static transmission error of spur gears. Strain data collected by a strain data acquisition system is processed to obtain the transmission error results. Finally, the credibility of the micro-deformation method is substantiated theoretically using material mechanics and transmission error results obtained from the magnetic gate detection method. This study contributes to the advancement of gear transmission research by proposing a novel approach to quantify pseudo-static gear transmission error.

The gearboxes of machines generally operate under a time-varying state rather than under steady-state conditions. However, it is difficult to investigate the nonlinear dynamics of a time-varying gear system. A gear system model of a railway vehicle was proposed in consideration of its time-varying mesh stiffness, nonlinear backlash, transmission error, time-varying external excitation, and rail irregularity. To obtain the nonlinear behaviors of a time-varying stochastic gear system, a quasi-static analysis was performed to observe its doubling-periodic bifurcation, chaotic motion, and transition from a lower to a higher power periodic motion. Based on the energy comparison results, the time-varying stochastic gear system was degraded to a time-varying system to simplify the calculation. Furthermore, the nonlinear response of the time-varying system was computed using the Runge–Kutta method and was compared with the results of a quasi-static analysis that employed a short-time Fourier transform method. The results of the quasi-static analysis were consistent with the results of the time–frequency analysis for the time-varying gear system except for the result at 3180 r/min, which represented a short period wherein the process transitioned to chaos. Hence, the comparison demonstrates the applicability of the quasi-static analysis for the nonlinear behavior analysis of a time-varying stochastic system.