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Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

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Chinese Journal of Mechanical Engineering 2013年第5期26卷 948-956页

作者： DENG Xingqiao WANG Jinge HORSTEMEYER Mark F School of Mechanical Engineering and Automation Xihua University Center for Advanced Vehicular Systems Mississippi State University

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 *** 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 ***,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 *** 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 *** results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment *** modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

关键词： worm gears tooth contact analysis machining and misalignment errors tooth profile errors modification method

Pinion tooth Surface Generation Strategy of Spiral Bevel Gears

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Chinese Journal of Mechanical Engineering 2012年第4期25卷 753-759页

作者： LIU Guanglei FAN Hongwei School of Mechatronics Northwestern Polytechnical University Xi'an 710072 China

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll *** this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact *** the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of *** digitized machine,four tooth surface generation styles of pinion are *** every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error *** the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are *** weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error *** computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth *** four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear *** study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.

关键词： spiral bevel gears tooth surface generation strategy local synthesis tooth contact analysis transmission error optimization

Design and analysis of spiral bevel gears with seventh-order function of transmission error

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Chinese Journal of Aeronautics 2013年第5期26卷 1310-1316页

作者： Su Jinzhan Fang Zongde Cai Xiangwei Key Laboratory of Road Construction Technology and Equipment Ministry of EducationChang’an University School of Mechanical Engineering Northwestern Polytechnical University

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.

关键词： Loaded tooth Modified roll Spiral bevel gear tooth contact analysis Transmissions

Mesh stiffness calculation of cycloid-pin gear pair with tooth profile modification and eccentricity error

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Journal of Central South University 2018年第7期25卷 1717-1731页

作者： LI Xuan CHEN Bing-kui WANG Ya-wen LIM Teik Chin School of Mechanical and Electric Engineering Soochow UniversitySuzhou 215021China State Key Laboratory of Mechanical Transmission Chongqing UniversityChongqing 400030China Department of Mechanical and Aerospace Engineering University of Texas at ArlingtonArlingtonTX76019USA

Cycloid speed reducers are widely used in many industrial areas due to the advantages of compact size, high reduction ratio and high stiffness. However, currently, there are not many analytical models for the mesh stiffness calculation, which is a crucial parameter for the high-fidelity gear dynamic model. This is partially due to the difficulty of backlash determination and the complexity of multi-tooth contact deformation during the meshing process. In this paper, a new method to calculate the mesh stiffness is proposed including the effects of tooth profile modification and eccentricity error. The time-varying mesh parameters and load distribution of cycloid-pin gear pair are determined based on the unloaded tooth contact analysis （TCA） and the nonlinear Hertzian contact theory, allowing accurate calculations of the contact stiffness of single tooth pair and the torsional stiffness of multi-tooth pairs. A detailed parametric study is presented to demonstrate the influences of tooth profile modification, applied torque and eccentricity error on the torsional mesh stiffness, loaded transmission error, Hertzian contact stiffness and load sharing factor. This model can be applied to further study the lost motion and dynamic characteristics of cycloid speed reducer and assist the optimization of its precision, vibration and noise levels.

关键词： cycloid speed reducer mesh stiffness tooth contact analysis load distribution modification

Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling contact Path and Transmission Errors

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Chinese Journal of Aeronautics 2008年第2期21卷 179-186页

作者：曹雪梅方宗德许浩苏进展西北工业大学机电工程学院陕西西安710072 中南传动机械厂湖南长沙410200

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

关键词： spiral bevel gear contact path transmission error blank offset tooth contact analysis

Valuable Impulses and Successful Models of Gearbox Development from Practice

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Journal of Mechanics Engineering and Automation 2016年第8期6卷 408-418页

作者： Tobias Schulze DriveConcepts GmbH Dresden 01067 Germany

Gears play an important role in mechanical engineering because of their moment and speed transmission possibilities. Design and optimization of a complete gearbox provide many requirements to the designer. The complex gearbox model consists of many machine elements （shafts, gears, bearings, housing, seals, and shaft-hub connections）. The gearbox must be understood as a system with interactive parts. Next to the calculation of kinematics, load capacities and life times of single elements, aspects of load distribution and efficiency and noise excitation of gearboxes become important. The wide range of knowhow needed mostly cannot be covered by a small number of engineers. The development of automated calculation routines with understandable and comprehensive results is the goal for these research projects that lead to sottware-realizing solutions for engineers to efficiently design, calculate, optimize and verify gearboxes with minimal resources in terms of calculation experts and time.

关键词： tooth contact analysis gearbox design and verification finite element gearbox calculation gear modifications/optimization planetary gearboxes automated calculation process.

contact analysis and load distribution of double-envelop hourglass worm gearing affected by errors and load

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Journal of Chongqing University 2003年第2期2卷 1-5页

作者：徐戊矫 The State key Lab of Mechanical transmission Chongqing University Chongqing 400044 P.R.China

An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.

关键词： double-envelop hourglass worm gearing tooth contact analysis errors load