Contact Characteristics Analysis And Experimental Investigations On Cycloid-Pin Planetary Drives With Mesh Clearance

The cycloid-pin planetary drive has been used widely in many industrial areas for power transmission,such as metallurgical machinery,hoisting and conveying machinery,construction machinery,chemical machinery and textile machinery,etc.,due to its superior characteristics: large transmission ratio,compact structure,small size,light weight,high transmission efficiency and high load capacity,etc..In recent years,because of its outstanding averaging effect of errors which can lead to high precision caused by the multi-tooth meshing,its 2KV type cycloid-pin speed reducer with the involute gear planetary drive as the first stage has been also used more and more widely in precision transmission,such as the areas of aerospace,CNC machine tools,robot and medical equipment,etc..Theoretically,for one tooth difference cycloid speed reducer,all the cycloid gear teeth remain in contact with subsequent pins and half of them are considered participating in torque transmission at any instance.However,in practice,to accommodate the interferences caused by manufacturing errors,tooth deformations and thermal influence,to provide better lubrication conditions and to accomplish easier assembling and disassembling,the cycloid gear tooth profile is usually modified to obtain a mesh clearance.The existence of mesh clearance,assembling error,clearances between elements and contact deformation in the cycloid-pin planetary drive system significantly influences the performances of this type of speed reducer,such as the load capability,service life and noise and vibration.Therefore,it has the theoretical significance and engineering practice value to deeply and systematically study on the tooth contact characteristics and the elements force behavior for the optimal design of this type of gear drive and for the performance evaluation of this speed reducer with considering the effects of the above factors.In this paper,the research is mainly focused on the conjugated mesh geometry,loaded tooth contact analysis,systematical force analysis and the trial-manufacture of new type prototypes of cycloid-pin planetary drives on the gear and system levels.The main contents are as follows:The geometry of the cycloid-pin planetary drive with mesh clearance is studied in details by using the differential geometry and the theory of gearing.Based on its practical application,four feasible types of modified cycloid gear profiles are proposed and the constrain of the modification amount is discussed.Base on the double-enveloping method used in the planetary gear drive with small tooth difference,the new elliptical and parabolic types of gear drive with mesh clearance are proposed,and their modification methods for the tooth profiles are determined.Numerical examples are provided for the illustration and validation.Based on the gear tooth contact analysis(TCA),the TCA model of cycloid-pin pair with mesh clearance is proposed.The time-varying output angle of cycloid gear and backlash angles between gear pairs are determined.Based on the Hertz contact theory,the nonlinear Hertz contact stiffness is introduced to establish the loaded TCA model of the cycloid-pin pair by enforcing the deformation compatibility,and force and moment equilibrium conditions.With this,the actual potential number of gear pairs in contact are determined,and the transmission error,mesh stiffness and variations of gear ratio are calculated by using the variation of output angle of the cycloid gear due to the contact deformation.The proposed model can be used to simulate the mesh process and evaluate the contact characteristics of the cycloid-pin gear pair.This serves for further study on the system-level static and dynamic characteristics analysis of this gear drive.Based on the proposed loaded TCA model of the cycloid-pin pair,the force characteristics analysis model of the cycloid-pin planetary drive system with small teeth difference is established with considering the modification of cycloid gear profile,output mechanism clearance,assembly error and contact deformation.The forces,Hertz contact stress and stiffness on various elements are calculated.The transmission error,variations of gear ratio of the speed reducer are also obtained.Based on the energy method,the rolling element bearing stiffness matrix model are proposed.The components of time-varying bearing stiffness are calculated with the obtained force,which is for the further study on the dynamic analysis model of the cycloid-pin planetary drive system with small teeth difference.The parametric studies show that the gear mesh and pin-hole clearances as well as eccentricity errors have significate effects on some key design factors,such as contact stress,transmission error,gear ratio and load on bearing.Based on the working principle and structure of the 2KV type cycloid-pin speed reducer,the differential relationship and force analysis are studied in details.Based on the Timoshenko beam theory,the force on the crankshaft are calculated by using the finite element method.The bending deflection of crankshaft and the force on the supporting bearing are obtained.Based on Weber energy method,the time-varying involute gear mesh stiffness model is established with considering its deflections of the tooth and body parts as well as the contact deformation.Then,the time-varying torsional stiffness model of the 2KV type speed reducer is proposed considering the deformations of the involute gear pair,cycloid-pin pair,planetary carrier,crankshaft and bearings.The obtained results show the periodic fluctuation of the time-varying torsional stiffness of the speed reducer along the crankshaft angles,and the crankshaft bearing is the main contributory factor.A new 2KV type cycloid-pin speed reducer with double-arc ring gear,modified cycloid gear,integrated input and output supporting mechanisms.Its prototype is designed and manufactured and its performances are tested by using self-designed experimental equipment,including the transmission efficiency,transmission precision,torsional stiffness and hysteresis error.The experimental results show that the new speed reducer has better performances.The experimental data lay a good foundation for its industrialization and application.