| Harmonic drive has the advantages of small size, light weight, large transmission ratio, high transmission precision, large carrying capacity and so on. But there is only a small area near the major axis of the wave generator in which the harmonic gears with involute tooth profile can meshed in conjugate condition, and most of the teeth are in tooth-tip meshing state. Therefore, the study of the tooth profile especially the design of a new profile is expected to improve the present situation.Cycloidal gear was born in horological industry, and had been widely used. It has advantages such as long contacting line, smooth transmission, uniform wear, large area of tooth contact, low contact stress and so on. If these advantages can be combined with the advantages of harmonic drive, a new available tooth profile for harmonic drive will be provided which can improve the conjugate meshing performance, and a new direction for the application of cycloidal gear will be opened up.The analysis and simulation of the traditional cycloid tooth profile’s conjugate solution and motion in harmonic drive which based on envelope method show that, even though the envelope is much better, there also exist some shortcomings relate to the fixed zero tooth profile angle. Thus, the equations of cycloid tooth profile have been modified in this paper with the thinkings of cycloid tooth profile with non-zero profile angles. The best tooth profile angle can be determined after the analysis of the influence on the tooth’s conjugate meshing features by changing the profile angle.Composite cycloid tooth profile can be expressed by two parametric equations with three parameters, in which, the tooth profile angle was shared. Choose the composite cycloid tooth profile on flexspline as the original tooth profile of conjugate equations. The solutions, meanwhile, the theoretical tooth profile of circular spline are appeared as discrete points. In order to fit the theoretical tooth profile to express it better, an optimization algorithm based on complex method to get a composite cycloid fitting tooth profile was proposed. The objective function was built as the standard deviation of the distance between discrete points and the fitting curve and the goal is to find its minimum value.To get the backlash of the meshing teeth accompanying its position, the tooth was divided equally along the tooth depth and dichotomy was used to find the value that can be more exact. Not only the backlash can verify whether the interference between the meshing teeth occurred, but also its regularities of distribution can evaluate the harmonic drive’s motion precision under static load and meshing state during load rotation. Therefore, the cons and pros of the tooth profile design can be directly reflected.In order to ensure the theoretical design method is feasible, a FEM with shell elements of flexspline with wave generator was built in ANASYS, in which the APDL modular was used. After simulation analysis of contact, the deformation of flexspline was obtained. Use the FEM solution as the actual location of the teeth on flexspline to establish the solid model of harmonic drive under assembly conditions in SolidWorks. Through the interference inspection and clearance measurement of the model, the theoretical method of backlash calculation and the meshing state between the teeth of flexspline and circular spline can be verified.
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