Study On Strength Analysis And Experiment Of Planar Double Enveloping Hourglass Worm Gears

The planar double enveloping hourglass worm drive has the virtue of high bearing capacity, low wear extent, silent running and longevity of service, and has obtained extensive application in the national defense and civil industry, but until now yet see the related strong test and calculation method vended. The design carrys on mostly refered other national standards, or refered the GB16444, both are conservation and roughness, and the development of worm gears have been restrictived. Thereby, how to establish the more effective strength calculation formulas is urgently needs to solution.Based on the spatial meshing principle, elasticity mechanics and finite element method, theoretical analysis proceededed, combined with simulation test of tooth stress state and bearing capacity experiment, consequently, the strength analysis method of planar double enveloping hourglass worm gears was put forward. the prime content of the paper may summarized as follows:The meshing equation, boundary equation and the micro-engagement parameters have been deduced, based on the theory of engagement; the distribution regularities of induction normal curvature radius, lubricating angle and the relative entrainment speed on tooth face have been studied, the influence of key parameters on the meshing parameters have been analyzed.The worm gear's geometry characteristic was analyzed, combined with practicable project, the mathematic model of tooth boundary have been established, and the running clearance has been considered; taking the secondary contact zone of wormgears in typical design as an example, reconfiguration methods of curved surface composed of unequally distribute data points were researched. On UG-GRIP platform, three dimensional model building system of planar enveloping hourglass worm drives has been developed, The accuracy of the solid model is validated by example.The finite element contact stress analysis model suitable for the worm gears was established. The influence of load and tooth face parameters on the contact stress distribution status and coefficient of load sharing among meshing teeth has been researched; The relationship between the number of teeth in the meshing and the maximum coefficient of load sharing among teeth under different load was calculated; the tooth root bending stress distribution rule along the gear tooth width has been analyzed, the influence of load and tooth face parameters on the bending stress distribution status was researched.The coefficient of conduction normal curve radius was obtained through regression analysis and interpolation method, and the variable is the coefficient of worm diameter, the formulas of contact instant statistical length and the smallest length have been established, the calculation formula of load distribution coefficient among the teeth was obtained by the regression analysis on the base of the finite element analysis. Based on the Hertz model, contact stress analysis formula of the tooth which carries the maximum load and the average contact stress were deduced; the bending stress formula has been deduced based on the projecting beam theory; the bending strength calculation formula of general cylindrical worm gears and Niemann worm gear have been improved by taking the load distribution coefficient among the meshing teeth into the consideration, which can get advisable result, too. At last, the foumulas have been applied on several sets worm gears that have been proved by the application, and the accuracy and feasibility of the methods have been approved.Several photoelastic materials with different ingredient proportion of firming agent were made up according to the elastic modular ratio of steel and copper, suitable materials for worm gears photoelastic model were selected; in order to ensure the rigidity and realize the multi-teeth in the meshing, the manufacture method of photoelastic model was studied and the models were made successly; Worm gears photoelastic models was assembled in the reduction box, stress freezing has been finished in the oven. Stress-difference line distribution property of sections of wormgear were observed and analyzed. At last, the result of photoelastic method and the result of the finite element method(FEM) were compared, that plays the role which verified mutually.In order to deeply understand the carrying capacity and transmission characteristic, the study on the character of planar double enveloping hourglass worm gears reducer prototype different rotative velocity was progressed. The reducer's performance was estimated by the record of torque at different levels of load, transmission efficiency, temperature rise and so on. The limit bearing capacity of the prototype has been tested at different rotational speed, and the maximum bearing capacity have been determined by the experiment.