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Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness. [ABSTRACT FROM AUTHOR]

Rough surfaces have a positive and important influence on the mechanical properties of the joint surface. Bolted joints are one of the common connection modes, whose assembly stiffness directly determines the machining accuracy of the machine tool. In this work, considering the joint stiffness between connectors, a mechanical model of the joint surface considering the asperity interaction is established based on fractal theory. On this basis, combined with the equivalent form of the bolted joint system, a new stiffness model depended on strain energy method is proposed. Then, the correctness of the proposed model is verified by experiments. Finally, through the application of FEA, the research on bolt tightening with different friction coefficients is completed. Results show that when the stiffness effect of the bolted joint surface is neglected, the equivalent stiffness of this system is too large, exceeding the accurate value by more than 20%. [ABSTRACT FROM AUTHOR]