Research On The Inner Worm-gear Plane Enveloping Drum Worm Drive

A novel joint reducer with high integrated structure,the inner worm-gear plane enveloping drum worm drive reducer(IDW reducer),was proposed and investigated under the competition between various countries for developing robot technology and under the development trend of robot joints' modularization.With the integrated structure of drive,transmission and support,the IDW reducer is characteristic with advantages of compact structure,large single-stage transmission ratio,high transmission accuracy,adjustable backlash,wear compensation,etc.Therefore,the IDW reducer is suitable for space-limited precision transmission and conforms the development trend of robot joints' modularization.The paper took the target of manufacture of the IDW reducer to conduct systematic research around its transmission(IDW transmission),including meshing theory,meshing performance analysis,parameters optimization,elastohydrodynamic lubrication analysis,structure design,mechanical analysis,prototype manufacturing,and bench test.The specific content is as follows:1.The study of meshing theory of the IDW transmission was conducted according to gear meshing theory,which provided theoretical basis for the design,analysis,optimization and machining.The coordinate frame systems of the IDW transmission during forward and reverse rotations were established separately by the moving coordinate method.Base on that,equations of contact-lines,boundary curves,sliding angles,entrainment-speeds,induced normal curvatures,etc.on both A and B sides of the transmission were deduced.Therefore,the meshing theory system of the IDW transmission was established.2.According to the IDW transmission's meshing theory and with utilization of method of control variates,the macro-micro meshing performances parameters on both A and B sides were analyzed by Matlab on its data visualizing environment,including contact-lines,sliding angles,entrainment-speeds,induced normal curvatures,etc.,which provided basis to optimization design.The study found:(1)the IDW transmission was characteristic with good meshing performance in theory due to multi-tooth meshing,big sliding angles and small induced normal curvatures;(2)with the change of modulus,base circle radius and generating plane inclination angle,contact-lines' distribution parameters and meshing parameters(sliding angles,entrainment-speeds,induced normal curvatures)displayed different variation rules on between A and B sides;(3)A side was suggested to be designed as the main working side because its macro-micro meshing performance was better than B side's in theory.3.According to the theory of optimization design,the nonlinear multi-objective optimization model of the IDW transmission was studied to improve its macro-micro meshing performance,which offered theoretical guidance for the IDW transmission's design and manufacture.In the optimization model,modulus,base circle radius and generating plane inclination angle were taken as optimization variables,and constraints were built combining with the theory of worm drive design.The optimization model was solved by Matlab's fmincon toolbox with SQP algorithm,the result showed: the optimized variables improved the IDW transmission's macro-micro meshing performances in theory.4.According to Hertz elastic contact theory and elastohydrodynamic lubrication theory,the elastohydrodynamic lubrication analysis of the IDW transmission was conducted to supply theoretical basis for its prototype's manufacture and test.Referring to the induced normal curvature along the tangent of contact-line,the isothermal line-contact elastohydrodynamic lubrication model was established in several segments.Meanwhile,load sharing ratio between the meshing teeth and load distribution along the contact-line were comprehensively taken into consideration.Base on that,the formula of minimum film thickness evaluating the IDW transmission's lubrication performance was deduced.The influence of each corresponding parameter on the lubrication performance was observed on Matlab's data visualization environment according to control variates method,which showed:(1)the lubrication performance of the IDW transmission at the meshing exit side was better than that at the meshing entrance side,as well as which on worm-gear's addendum was better than that on worm's addendum;(2)A side's minimum film thickness' s maximum values were larger while its minimum values were smaller than B side's,and parameters according to their influence on lubrication performance from big to small were modulus,worm's rotation speed,output torque,base circle radius and generating plane inclination angle;(3)increasing modulus and worm's rotation speed,and decreasing output torque and base circle radius,could be dedicated to the improvement of the IDW transmission's lubrication performance.5.According to the mechanical design method,the IDW reducer with integrated structure of drive,transmission and support was proposed,which is characteristic with advances of large transmission ratio,high integration and compact structure,etc.So the IDW reducer is in accord with the development trend of modularization of robot joints.The drive was realized by an external rotor motor installed inside the hollow worm.And the novel orthogonal internal meshing worm transmission was adopted to make most parts such as worm and motor locate inside the worm-gear.In addition,there was no need for the box with complicated structure,so parts of the IDW reducer were easy to process due to their simple structure.Therefore,the IDW reducer's characteristics are shown as follows:(1)the reducer is characteristic with advantages of compact structure,small volume and large internal space utilization rate;(2)the worm's tooth-surface is easy to be ground to guarantee high processing accuracy;(3)functions of adjustable backlash and wear compensation dedicate to the IDW reducer's high transmission accuracy and long service life.6.According to the theory of mechanical strength,the mechanics analysis of the IDW transmission was conducted to guarantee the mechanical property satisfy the working requirements,including the bending stress and stiffness of the worm,the shear stress and bending stress of the worm-gear teeth.And the contact stress analysis of the worm-gear tooth-surfaces and the contact analysis of the transmission were performed through Workbench in the light of finite element method.The study found:(1)the worm's bending stress and stiffness,worm-gear tooth's shear stress and bending stress,and worm-gear tooth-surface's maximum contact stress were within the allowable value range,which indicated that the IDW transmission's mechanical property met the design requirement;(2)the contact area map was consistent with the theoretical contact-line's distribution,which verified the correctness of the IDW transmission's meshing theory.7.According to mechanical machining principle,the manufacture of the IDW reducer was conducted for the first time,and the bench test was also carried out,which provided a model for the novel reducer's production.The worm spiral tooth-surface was ground by the 4-axis 4-link CNC grinding machine with function of virtual center distance in the light of the IDW transmission's generating machining principle.Base on that,the processing procedure of the worm was formulated.Procurement and processing of parts were conducted,and then the IDW reducer's industrial prototype was assembled.Finally,bench test was carried out to test the IDW reducer's vibration,noise,temperature and efficiency.Opening the prototype and checking after the test,the wear region on worm-gear tooth-surface was consistent with the theoretical contact-line's distribution,which indicated that the correctness of the IDW transmission's meshing theory was proved.