Modeling and dynamic analysis of belt drive systems using a harmonic balance and alternating frequency/time domain method

Purpose To guarantee smooth transmission and develop digital twins for status monitoring of belt drive systems (BDSs), this research aims to develop a physical model and perform dynamic analysis for BDSs. Design/methodology/approach A mathematical model of a three-pulley BDS is first developed in both the time and frequency domains, considering the hysteresis characteristics of the automatic tensioner. Then, a harmonic balance and alternating frequency/time domain (HB-AFT) method is proposed to calculate the dynamic characteristics of BDSs. For dynamic analysis, the frequency response function (FRF) and energy dissipation characteristics of automatic tensioners, as well as their influencing factors, are calculated and analyzed. Finally, the digital twins development and fault diagnosis methods of BDSs are proposed using the dynamic analysis results. Findings The dynamic characteristics of the BDS calculated by the HB-AFT method and traditional numerical methods are compared, and the comparison results show that the HB-AFT method has a calculation speed more than 40 times faster than the numerical iteration method. The FRF and energy dissipation characteristics of tensioners are related to the torsional vibration amplitude of the driving pulley and the sliding frictional torque of the tensioner, and the fault in tensioners can be detected by their oscillation amplitude calculated by digital twins. Originality/value The proposed HB-AFT method can be used to calculate the dynamic characteristics of BDSs with high accuracy and efficiency, while considering the hysteresis characteristics of the tensioner. It can also be used for status monitoring and fault diagnosis in digital twins of BDSs.