This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive ...This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive and improve the loaded distribution of the tooth. Based on the constraint conditions of predesigned seventh-order polynomial function curve and the theory of linear algebra, the polynomial coefficients of the seventh-order polynomial function of transmission error can be obtained. By applying a method named reverse tooth contact analysis, the modified roll coefficients as well as parts of machine-tool settings for the face-milling of spiral bevel gears can be individually determined. Therefore, a predesigned seventh-order polynomial function of transmission error for spiral bevel gears can be obtained by the modified roll with high-order coef- ficients, and comparisons of the seventh-order polynomial and parabolic functions of transmission error are also performed. The achievement of spiral bevel gears with the seventh-order function of transmission error can be accomplished on a universal Cartesian-type hypoid gear generator or a numerically controlled cradle-style hypoid gear generator due to its simple generating motion of axes of the cradle and the work piece. The results of a numerical example show that the bending stresses of the tooth of seventh-order are less than those of a parabolic one, while the contact stresses remain almost eouivalent.展开更多
The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for e...The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.展开更多
基金the National Science Foundation of China (Nos.51205310 and 51175423)the Fundamental Research Funds for the Central Universities (Nos.2013G3252005 and 2013G2252027)
文摘This paper proposes a new approach to mial function of transmission error （TE） for spiral design and implement a seventh-order polyno- bevel gears with an aim to reduce the running vibration and noise of gear drive and improve the loaded distribution of the tooth. Based on the constraint conditions of predesigned seventh-order polynomial function curve and the theory of linear algebra, the polynomial coefficients of the seventh-order polynomial function of transmission error can be obtained. By applying a method named reverse tooth contact analysis, the modified roll coefficients as well as parts of machine-tool settings for the face-milling of spiral bevel gears can be individually determined. Therefore, a predesigned seventh-order polynomial function of transmission error for spiral bevel gears can be obtained by the modified roll with high-order coef- ficients, and comparisons of the seventh-order polynomial and parabolic functions of transmission error are also performed. The achievement of spiral bevel gears with the seventh-order function of transmission error can be accomplished on a universal Cartesian-type hypoid gear generator or a numerically controlled cradle-style hypoid gear generator due to its simple generating motion of axes of the cradle and the work piece. The results of a numerical example show that the bending stresses of the tooth of seventh-order are less than those of a parabolic one, while the contact stresses remain almost eouivalent.
基金supported by National Natural Science Foundation of China(Grant Nos. 50775190No.51275425)+2 种基金Spring Sunshine Plan of Ministry of Education of China(Grant No. 10202258)Talent Introduction of Xihua UniversityChina(Grant No. Z1220217)
文摘The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.
