Backlash And Load Distribution Analyzing Between The Teeth Of Flexspline Of Harmonic Drivewith Double Circular-arc Tooth Profile

The load distribution between tooth of flexspline and the coordinativedeformationwas researched in the paper. And the load distribution was calculated by the mean of thefinite element and mathematics methods. And then, the theory how the load distributionwas effected by the parameters of tooth profile and the structure parameters offlexspline and wave generator was analyzed.Firstly, the coordinate systems of the parts of harmonic drive were analyzed. Andthe polar equation of the midcourt line of flexspline acted by four roller wave generatorwas proposed. The profile equation of flexspline and rigidspline were derived. It was allthe base of the theoretical analysis.Different with the method of calculating the backlash of involute tooth profile, themethod suited to double circular-arctoothprofile’s was applied. The shortest distancebetween tooth profile was found first, and then the backlash could be worked out. Theinitial backlash distribution when the wave generator, load torque and parameters oftooth profile were variable was analyzed, and the changing law was generalized.The deformation of flexspline was caused by wave generator and load torque. So,the deformation of flexspline include torsional deformation of the body of flexsplineand contact deformation of tooth. The flexspline tooth come into contact with therigidspline when the deformation of flexspline could offset the backlash. Based on thistheory, the mathematics model about couples of contact pairs was established. And then,the load distribution of flexspline was calculated with the mathematics model when thewave generator, the load torque, the parameters of tooth profile were variable. Thechanging law was generalized.The three-dimensional model of the harmonic gear drive system was established,thenimport into ANSYS to meshing and define contact relationship, and analysisflexspline with the theory of geometric nonlinear shell finite element. Research the loaddistribution between the flexspline tooth within the shape of the wave generator, loadtorque, tooth profile parameters as independent variables respectively, and studythedifferences and relations of load distribution between the actual conditions and thetheoretical calculation results.Conclusion follows：Because of the difference in thecirculation algorithms and modelingideas between the actual working conditions andtheoretical calculation, the theoretical calculationcould only calculatethe load distributionin a small meshing range.The results in the full range of teeth meshing wasinaccurate. Theoretical model need to be further improved.These could be good fundamentals for improving the design of harmonic drive intooth profile and meshing performance.