Curvature Interference Characteristic of ZC1 Worm Gear

Author(s):  
Qingxiang Meng ◽  
Yaping Zhao
2011 ◽  
Vol 86 ◽  
pp. 352-356 ◽  
Author(s):  
Ya Ping Zhao ◽  
Tian Chao Wu

The double-point downhill secant method (the DPDS method) is proposed to solve the nonlinear equations to determine the curvature interference limit points for modified hourglass worm drives. Thereupon, the whole curvature interference limit line can be obtained by interpolation. Based on this, the undercutting feature of the corrected worm gear can be investigated. The DPDS method has two main merits in principle. The first is the avoidance of the computation of the Jacobi matrix of the system of nonlinear equations. The second is that the sensitivity to the guess value can be decreased evidently owing to adopt the technique of the norm reduction. The effectiveness of the DPDS method is inspected and verified by a numerical example.


2019 ◽  
Vol 83 (3) ◽  
pp. 759-773
Author(s):  
Qingxiang Meng ◽  
Yaping Zhao ◽  
Zaiyou Yang

Author(s):  
Yaping Zhao

Abstract The toroidal enveloping cylindrical worm drive, also called the ZC1 worm drive, is grinded by the toroidal grinding wheel. In this paper, the meshing theory for this worm drive is systematically established. According to this meshing theory, the meshing function, the meshing limit function, the equations of the worm helicoid and the worm gear tooth surface are obtained. A method for computing the normal vector of the instantaneous line of the ZC1 worm pair is proposed. Due to this method, the curvature interference limit function and the meshing quality parameters can be more simply and clearly obtained. Based on above results, the methods of the numerical calculation of the instantaneous lines and the conjugate zone are proposed. The initial values of the nonlinear equation systems, computed the conjugate zone and the contact lines, are detected and solved by the method based on the elimination method and geometric construction. The results of numerical example clearly reflect that the conjugate zone can almost cover the whole tooth surface of the worm gear and the effective working length of the worm cannot nearly exceed the half of its thread length. The values of the induced principle curvature and the sliding angle show that the lubrication performance is poor and the stress level is higher, near the meshing limit line and at the dedendum of the worm gear.


1955 ◽  
Vol 34 (12) ◽  
pp. 789
Author(s):  
J.E. Hill ◽  
I.C. Hopkinson ◽  
Everest ◽  
J. Blakiston ◽  
Ward ◽  
...  
Keyword(s):  

Author(s):  
Yang Jie ◽  
Li Haitao ◽  
Rui Chengjie ◽  
Wei Wenjun ◽  
Dong Xuezhu

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are usually adopted. But for the hob with multiple threads, the absolute values of the negative rake angles at one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are usually adopted to solve the problem. However, no method of determination of the spiral flute of the hourglass worm gear hob has been put forward till now. Based on the curved surface generating theory and the hourglass worm forming principle, a generating method for the spiral flute of the planar double enveloping worm gear hob is put forward in this paper. A mathematical model is built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth of four hobs with different threads from one to four threads are analyzed when straight flutes and spiral flutes are adopted respectively. The laws between the value of the negative rake angles of the hob with four threads and the milling transmission ratio are studied. The most appropriate milling transmission ratio for generating the spiral flute is obtained. The machining of the spiral flutes is simulated by a virtual manufacturing system and the results verify the correctness of the method.


2020 ◽  
Vol 103 (4) ◽  
pp. 003685042098122
Author(s):  
Jingzi Zhang ◽  
Jin’ge Wang ◽  
Kai Wang

Although a significant amount of research on robot joint reducer was conducted, there are few systematic investigations on a novel joint reducer adopting inner worm-gear plane enveloping drum worm drive. To satisfy the development of modular robot joint, the primary objective of this paper was to systematically investigate the drum worm drive adopted in the novel joint reducer with integrated structure of drive, transmission, and support in the following aspects: meshing theory, design, analysis, and manufacture. According to the gear meshing theory, mechanical design method, classical mechanics, finite element method, and machining principle of virtual center distance, the systematic investigations around the drum worm pair applied in the novel joint reducer were conducted including the macro and micro meshing theory, structure design, mechanical and contact properties analyses, and manufacturing method. The novel joint reducer’s integrated structure was designed, and the drum worm pair’s mechanical and contact properties analyses were conducted, which showed: (1) the worm’s bending stress and deflection, worm-gear teeth’s shear stress and bending stress as well as the maximum contact stresses were all below their corresponding allowable values; (2) the maximum contact stresses appeared at the engage-in position of the worm pair opposing to the engaging-out position where the largest contact areas appeared. Then the manufacturing of drum worm’s spiral tooth was conducted via the modified 4-axis linkage CNC grinder according to the conjugate motion. Finally the novel joint reducer’s industrial prototype was assembled. The novel joint reducer with integrated structure of drive, transmission and support was designed and manufactured for the first time. The flowchart of design and manufacture of the reducer’s drum worm pair in this process was formulated, which provides a new insight on the research of joint reducers as well as other fields.


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