Uncertainty Estimator-Based Sliding Mode Control For a Novel Spherical Robot With Cable Transmission Mechanism

This paper presents a new spherical robot with a cable transmission mechanism. Cable transmission mechanism replaces conventional gear train to eliminate the influence of gear backlash, lower the costs on mechanical customization, and can be arranged flexibly. By projection method, the 3D robot dynamic model with structural asymmetry is decoupled into balance subsystem and velocity subsystem, and the kinetics equations are established based on Newton-Euler's law. To estimate the unknown structural dynamics in the balance subsystem and external disturbance in the velocity subsystem, adaptive law containing both control and estimation error information is proposed for the uncertainty estimator (UE) design. Then, an uncertainty estimator-based sliding mode controller (UESMC) is introduced for balance and velocity control, leading to enhanced disturbance rejection capability and a reduced steady-state error. Simulations and experiments on a real spherical robot are conducted to demonstrate the efficacy of the proposed control strategies.

Study on Gear Contact Stiffness and Backlash of Harmonic Drive Based on Fractal Theory

Contact stiffness and backlash model of harmonic reducer is related to robot’s positioning accuracy and vibration characteristics. Harmonic reducer tooth pair height is typically less than 1 mm. Thus, backlash and contact stiffness measurement and modeling are relatively complex. In this paper, contact stiffness and backlash model is proposed by establishing a relationship between fractal parameters and tooth contact load. Non-contact optical profiler and RMS method are combined to obtain fractal roughness parameters of real machined tooth surface. Finally, the effect of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash is studied. The results indicate that surface topography parameters and contact force have significant effects on contact stiffness and backlash. By increasing the fractal dimension, a decrease of gear backlash and contact stiffness is observed. However, the opposite is true for the fractal roughness parameter. Lastly, an increase in contact force improves the contact stiffness.

Modeling and fault identification of the gear tooth surface wear failure system

In order to detect the gear tooth surface wear fault, this paper presents a new fault diagnosis method based on Symlets wavelet family multi-structure element difference morphological denoising and frequency slice wavelet transform (FSWT). Besides considering the gear backlash, time-varying mesh stiffness, gear error and bearing longitudinal response, and low frequency excitation caused by the torque fluctuation, random disturbance of damping gear ratio, gear backlash, excitation frequency, and meshing stiffness are also considered. Dynamics equations of a three degrees of freedom spur gear transmission system with tooth surface wear fault are established according to Newton’s laws. The 4–5 order variable step Runge–Kutta method has been used for solving the equations to get the vibration signal of the system. Then, the proposed method is applied to extract the wear fault signal, which verifies the feasibility and effectiveness of the proposed method.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

Dynamic characteristics analysis of locomotive traction gear pair system under internal and external excitations

Purpose As the transmission component of a locomotive, the traction gear pair system has a direct effect on the stability and reliability of the whole machine. This paper aims to provide a detailed dynamic analysis for the traction system under internal and external excitations by numerical simulation. Design/methodology/approach A non-linear dynamic model of locomotive traction gear pair system is proposed, where the comprehensive time-varying meshing stiffness is obtained through the Ishikawa formula method and verified by the energy method, and then the sliding friction excitation is analyzed based on the location of the contact line. Meantime, the adhesion torque is constructed as a function of the adhesion-slip feature between wheelset and rail. Through Runge–Kutta numerical method, the system responses are studied with varying bifurcation parameters consisting of exciting frequency, load fluctuation, gear backlash, error fluctuation and friction coefficient. The dynamic behaviors of the system are analyzed and discussed from bifurcation diagram, time history, spectrum plot, phase portrait, Poincaré map and three-dimensional frequency spectrum. Findings The analysis results reveal that as control parameters vary the system experiences complex transition among a diverse range of motion states such as one-periodic, multi-periodic and chaotic motions. Specifically, the significant difference in system bifurcation characteristics can be observed under different adhesion conditions. The suitable gear backlash and error fluctuation can avoid the chaotic motion, and thus, reduce the vibration amplitude of the system. Similarly, the increasing friction coefficient can also suppress the unstable state and improve the stability of the system. Originality/value The numerical results may provide a systemic understanding of dynamic characteristics and present some available information to design and optimize the transmission performance of the locomotive traction system.