Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

Abstract

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to five are applied to conduct the variation of the cradle radial setting and of the cutting ratio in the process for pinion teeth generation. Two cases were investigated: in the first case the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface, in the second case the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation of the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation of the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase of transmission errors can be considerably reduced.

Design and analysis of modified cylindrical gears with a higher-order transmission error

“…(1), a series of Δθ 1 and θ 1 can be individually determined by solving TCA equation in Eqs. (17) and (18). Then, using a regression method, the rotation angle of the imaginary Δθ 1 can be represented by polynomials of θ 1 up to sixth order as…”

Spiral bevel gear true tooth surface precise modeling and experiments studies based on machining adjustment parameters

“…Wang et al used tensor analysis for spiral bevel gear design, 2,3 Yang studied the dynamic characteristics of spiral bevel gear, 4 Hong developed a new milling method for gear, 5 Wang and Hua established a dynamic model of high speed spiral bevel gear, 6 Yao et al carried out a contact analysis on spiral bevel gear, 7 Li conducted simulation on mesh of spiral bevel gear, 8 Zhang et al put forwarded a design method of low-noise face-milled spiral bevel gears, 9 Astoul et al used a new spiral bevel gear generation method for simple and robust design, 10 Litvin et al developed an integrated approach for spiral bevel gears design including multiple point of view, 11,12 Gonzalez-Perez et al studied the method for calculating the machining adjustment parameters, 13 Alves et al used CNC milling machines to study the design and manufacturing problems of spiral bevel gear, 14 Fan optimized design method for spiral bevel gear, 15 Zhang et al employed theory of spherical involute for the study on the generation of spiral bevel gears, 16 Lee et al investigated kinematic analysis of spiral bevel gear from the view of spherical involute, 17 Simon studied transmission error of spiral bevel gear, 18 20 Fang and coworkers proposed a function-oriented active tooth surface design method of spiral bevel gears, 21 Fong and coworkers deeply studied the correction method used in processing spiral bevel gears, [22][23][24] Simon systemically studied the influence of different errors on tooth contact in spiral bevel gears and developed an algorithm for execution of motions on CNC hypoid generating machine. [25][26][27] All these researches have important effects on the design and manufacture of spiral bevel gears and the main research methods for spiral bevel gear modeling can be concluded as the following four: (1) establish the equation of spherical involute based on the basic geometric parameters of spiral bevel gear via mathematical methods, get the spherical involute curve by inputting the equation into a CAD software or programming, and then scan or loft for the tooth surface; 4-6 (2) calculate a set of coordinates of discrete points of the standard tooth surface through programming numerical values, and import those points into a CAD software for the tooth surface; (3) make use o...…”

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

“…In order to reduce the transmission errors in mismatched face-milled spiral bevel gears, a method for the determination of the optimal polynomial function for the conduction of machine tool setting variation in pinion teeth finishing was developed in Ref. [38]. An algorithm for the execution of motions on the CNC hypoid generating machine using the relations on the cradle-type machine is developed for face-milled spiral bevel gears by Simon [39].…”

“…[27][28][29][30][31][32][33][34][35][36][37][38][39]. Procedure to obtain the correction values of machine settings for tooth surface modification in the case of face hobbing and the construction of the corresponding prototype gear cutting machine is presented in Ref.…”