Order tracking has been widely used to diagnose failures of variable speed rotating machines. The performance of the TOT (Time-Frequency Domain Tacholess Order Tracking) methods is based on the correct separation of the target component strictly related to the shaft rotation frequency. Currently, most of the methods have focused on obtaining the instantaneous frequency with accuracy. In this paper, a new TOT method has been proposed that combines the inverse short-time Fourier transform (ISTFT) with singular value decomposition (SVD). The target component closely related to the shaft rotation frequency is selected and filtered approximately in the time-frequency domain. Hence, the ISTFT is adopted to reverse the target component into the time domain. Next, SVD is used to refine the roughly filtered target component. Finally, the phase of the refined signal is extracted to resample the original signal. The performance of the method was tested using real vibration signals collected from a large-scale test rig of a high-speed train traction system.

Rotate vector (RV) reducers have widely been used in high-performance precision drives for industrial robots. However, the current nonlinear dynamic studies on RV reducers are not extensive and require a deeper focus. To bridge this gap, a translational–torsional nonlinear dynamic model for an RV reducer transmission system is proposed. The gear backlash, time-varying mesh stiffness, and comprehensive meshing errors are taken into account in the model. The dimensionless vibration differential equations of the system were derived and solved numerically. By means of bifurcation diagrams, phase trajectories, Poincaré sections, and the power spectrum, the motion state of the system was studied with the bifurcation parameters’ variation, including excitation frequency and meshing damping. The results demonstrate that this system presents enriched nonlinear dynamic characteristics under different parameter combinations. The motion state of the system is more susceptible to change at lower frequencies. Increasing the meshing damping coefficient proves effective in suppressing the occurrence of chaos and reducing vibration amplitudes, significantly enhancing the stability of the transmission system.

Transmission error (TE) and backlash are important parameters used to evaluate the transmission accuracy of cycloid-pin drives. Existing calculation methods are mostly based on two-dimensional tooth profile models, and these methods ignore the influence of some abnormal meshing phenomena caused by profile modifications (PMs), manufacturing errors (MEs), and assembly errors (AEs), such as the instantaneous mesh-apart of tooth pairs and the eccentric load on the tooth surface. To fill this gap, a novel approach to accurately calculating the TE and backlash of a cycloid-pin gear pair based on the error tooth surfaces is proposed, and its feasibility and effectiveness are validated by comparison with the theoretical analyses and the results from the literature. Based on this, the effects of the PMs, MEs, and AEs on the transmission accuracy are studied, which will be helpful in optimizing the tooth profile design of a cycloid gear and the tolerance allocation during the installation of a gear pair. The proposed method is also expected to provide accurate error excitation data for the dynamic analysis of cycloid-pin drives.

Tooth surface wear is an essential factor that affects gear transmission system dynamic characteristics and must be considered in monitoring the health status of gear systems. In this study, a coupled bending and torsion dynamic model is first established. The internal excitation changes under the influence of tooth surface wear and geometric errors, including the time‐varying meshing stiffness and comprehensive meshing error, are calculated using the method proposed by the authors in a previously published paper. Subsequently, a quasi‐static wear model of a tooth surface is established based on the Archard wear formula. The two proposed models are combined to simulate the changes in the wear area and depth of involute gear pairs and to investigate the influence of tooth surface wear on gear system dynamic characteristics. Several sets of simulation results are used to demonstrate the relationship between the tooth surface wear and gear system dynamic characteristics. The coupled analysis method and findings presented in this study are of great significance for the fault diagnosis and health monitoring of gear transmission systems.

As a core component of industrial robots, the transmission accuracy life (TAL) of rotary vector (RV) reducers constitutes a primary factor determining the high-precision operation of robotic systems. However, current life evaluation methods for RV reducers predominantly rely on conventional bearing strength life calculations, while neglecting its transmission accuracy degradation during operation. To address this limitation, a static analysis model of RV reducers is established, through which a calculation method for transmission accuracy and TAL is presented. Simultaneously, tooth surface and bearing wear models are developed based on Archard’s wear theory. Through coupled analysis of the aforementioned models, the transmission accuracy degradation law of RV reducers is revealed. The results show that during the operation of the RV reducer, the transmission error (TE) maintains relative stability over time, whereas the lost motion (LM) exhibits a continuous increase. Based on this observation, LM is defined as the evaluation metric for TAL, and a novel TAL estimation model is proposed. The feasibility of the developed TAL estimation model is ultimately validated through accelerated transmission accuracy degradation tests on RV reducers. The error between the predicted and experimental results is 11.06%. The proposed TAL estimation model refines the life evaluation methodology for RV reducers, establishing a solid foundation for real-time transmission accuracy compensation in reducer operation.