| Due to its superior performance,harmonic drive(HD)has become a kind of precision transmission in modern industry,widely used as reducers in robot joints.The parameters of its tooth profile greatly affect the transmission performance and the ease of processing.Based on the huge industrial potential of double-circular-arc tooth profile(DTP),this paper takes the DTP of HD as the research object,and focuses on key issues including the flow design of its conjugate tooth profile,the analysis of its meshing characteristics,the establishment of its tooth profile and the processing,by means of theoretical analysis,numerical simulation and Matlab visualization simulation to optimize the tooth profile parameters.The content is as follows:Firstly,the basic principles of HD are described,including the main components and the transmission ratio calculation.Based on the motion transformation between moving frames and the deformation of the neutral layer,an elastic kinematic and geometric model of HD is investigated,and the relative movement and trajectory of components/points are described;The fixed centrode and moving centrode are derived by differential geometry method,with their properties discussed.The conjugating tooth profile equation is set up based on the motion of instantaneous center line,which can explain the phenomenon of twice engagement and double conjugation,and at the same time the superiority of DTP in the conjugation aspect.Secondly,a planar profile design approach for HD with nice meshing performance is introduced.Based on the kinematic geometry of a pair of teeth,the cause of the tip interference is explored,then a criteria for tip interference judge,interference zone determination and sample points consisting of conjugate points and tip motion points in the interference region,which will achieve the tooth profile design procedure well,are proposed.Combined with the unilateral fitting of arcs,adjustments of the relative position of the two arcs of DTP and the new coordinate system,a curve fitting method used to the conjugate profile of DTP is presented.The evaluation of meshing qualities including analysis of fitting error,backlash distribution,contact ratio and engaging depth to prove the feasibility of the profile design approach for HD.Then,the multi-parameter optimal design with the maximum conjugation interval for the DTP of long cup-type flexible spline is solved by the genetic algorithm,realizing the full utilization of the twice engagement.With the consideration of the craftsmanship and strength,the feature points to control the rate tooth thickness and the transition radius of the tooth root to decrease the stress concentration are added to form a complete reference tooth profile parameter model of the DTP.The bad solution domain is set up to distinguish the non-optimized direction;The independent tooth parameters of the flexible spline and the addendum and dedendum of the circular spline are selected as the design variables;The constraints are discussed from various aspects of strength,generating methods,meshing requirements and tooth geometry,and disposed by serial methods including the external penalty function method,strictness classification of constraints and boundary translation of strong constrains;An optimization mathematical model of single-objective with multiple constraints is established.In addition,a comprehensive evaluation system for the validity of the solution and the meshing performance is built for the optimization results.The validity and superiority of the optimization model and method are verified through a case study.Finally,the design method of the tooth profile for spatial engagement of HD is put forward due to the axial deflection phenomenon of the short cylinder flexible spline after assembly.Its main ideal is that discrete the spacial elastic conjugate problem into a series of planar conjugate problems and complete three major design goals of tooth profile including interference elimination,nice generating processing and high utilization.The influence of the radial deformation,the angle of common tangent line,radius of convex and concave arcs,and tooth addendum in DTP,on the position of the first and second conjugate curves of the flexible spline,are studied.According to the influence law found above,adjust the studied parameters to achieve the effective conjugate profiles in ordered cross sections,and then splice curve periods with the largest horizontal coordinate among sections.Redefine the calculation method of the special meshing performance for HD.The feasibility of the profile design method adapted to the spatial engagement is verified by the case design. |
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