AGMA-05FTM05-2005.pdf
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1、05FTM05 Computerized Design of Face Hobbed Hypoid Gears: Tooth Surfaces Generation, Contact Analysis and Stress Calculation by: M. Vimercati, Politecnico di Milano and A. Piazza, Centro Ricerche FIAT - - ScpA TECHNICAL PAPER American Gear Manufacturers Association Copyright American Gear Manufacture
2、rs Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:26:53 MDTNo reproduction or networking permitted without license from IHS -,-,- Computerized Design of Face Hobbed Hypoid Gears: Tooth Surface Generation, Contact
3、 Analysis and Stress Calculation Martino Vimercati, Politecnico di Milano and Andrea Piazza, Centro Ricerche FIAT - - ScpA The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association.
4、 Abstract Whilefacemilledhypoidgearshavebeenwidelystudied,aboutfacehobbedonesonlyveryfewstudieshave beendeveloped.Aimofthispaperisjusttoproposeanaccuratetoolforcomputerizeddesignoffacehobbed hypoidgears.Firstly,amathematicalmodelabletocomputedetailedgeartoothsurfacerepresentationwillbe derived; then
5、, the obtained surfaces will be employed as input for an advanced contact solver that, using a hybridmethodcombiningfiniteelementtechniquewithsemianalyticalsolutions,isabletoefficientlycarryout contact analysis under light and heavy loads and stress calculation of these gears. Copyright 2005 America
6、n Gear Manufacturers Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2005 ISBN: 1-55589-853-X Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11
7、:26:53 MDTNo reproduction or networking permitted without license from IHS -,-,- 1 Computerized Design of Face Hobbed Hypoid Gears: Tooth Surfaces Generation, Contact Analysis and Stress Calculation M. Vimercati a, A. Piazza b a Politecnico di Milano Dipartimento di Meccanica, Italy, e-mail: martino
8、.vimercatipolimi.it b Centro Ricerche FIAT ScpA, Italy, e-mail: andrea.piazzacrf.it Nomenclature Nb Number of blade groups Rb Ratio between Nb and the number of being generated gear teeth rb Blade Radius b Eccentric Angle b Hook Angle hf Blade Height e Rake Angle e Blade Angle re Edge Radius LT Leng
9、th of Toprem Angle of Toprem t Blade radius of curvature i Tilt Angle j Swivel Angle Sr Radial Setting q Cradle Angle Em Blank Offset m Machine Root Angle Xp Machine Center to Back Xb Sliding Base Ra Ratio of Roll 1. Introduction In the geared transmission design it is very useful to have a numerica
10、l tool able to simulate the real behavior of the gear drive, searching for proper contact pattern, low level of transmission error and acceptable fillet stress. In this paper a set of numerical procedure for performance analysis of face hobbed hypoid gear will be proposed. As well known, this kind o
11、f gear is largely applied when it is needed to transfer power and motion between intersecting and crossing axles 1. Hypoid pairs are mainly manufactured by face hobbing (FH) or face milling (FM) cutting process 2; while this latter uses a single indexing cutting method, in FH process the being gener
12、ated gear has continuous rotation and rotates in a timed relationship with the cutter. As the gear is being cut, successive cutter blades groups engage successive tooth slots guaranteeing a continuous indexing. This process is now spreading in automotive industry because of its fast manufacturing ti
13、me. Since many decades, a lot of studies about tooth surface representation, contact and stress analysis of FM gears have been carried out 3-6. On the contrary, about FH process, which is considerably more complex, only a small number of papers have been published. Regarding tooth geometry, Litvin e
14、t al. derived a mathematical model able to describe tooth surfaces only of a non-generated Oerlikon gear member 7; Fong proposed a computerized universal generator able to simulate virtually all primary spiral bevel and hypoid cutting methods without providing a detailed description of the FH case 8
15、. Referring to performance analysis, the state of art is even worse: in the open literature any work has been found. Consequently, nowadays, it is possible to study this kind of gears only by using, basically as a “black box”, proprietary software which has been developed by manufacturing machine an
16、d tools suppliers. Goal of this paper is just to propose an integrated tool for computerized design of FH hypoid gears. The first step in order to build a reliable numerical model is to get a fine geometrical representation of gear tooth surfaces. With this aim, a series of algorithms able to comput
17、e tooth surfaces of FH gears starting from cutting process will be described 9. The geometry of real FH head cutter (Gleason Tri-Ac) will be firstly analyzed; many kinds of blade configuration (straight and curve blades, with or without Toprem) will be considered. Then, according to the theory of ge
18、aring, FH cutting process (with and without generation motion) will be simulated and gear tooth surfaces equations will be computed. The proposed mathematical model is able to provide an accurate description of the whole tooth, including fillet region; it will also take into account undercutting occ
19、urrence, which is very common in FH gears due to uniform depth tooth 4. By means of this model, tooth surfaces of a real gear drive, which is mounted in a truck differential system, will be computed and the results will be validated by comparing them with the ones calculated by a reference proprieta
20、ry software and with the real surfaces. Copyright American Gear Manufacturers Association Provided by IHS under license with AGMA Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/18/2007 11:26:53 MDTNo reproduction or networking permitted without license from IHS -,-,- 2 Then,
21、 the obtained tooth surfaces will be used as fundamental input for a powerful contact solver which is based on a unique semianalytical finite element formulation 10-11. Firstly, the gear drive it will study under light load by monitoring, for drive and coast side, the contact pattern and transmissio
22、n error (Tooth Contact Analysis - TCA). After that, with the aim to find out gear drive performance in the real service conditions, a set of torque values will be applied and the influence of the load on contact pattern, on transmission error and on load sharing will be accurately analyzed (Loaded T
23、ooth Contact Analysis - LTCA). Contact pressure and stress distribution will be also evaluated. The obtained results will be compared with the ones calculated by a reference software. 2. Theoretical Background of Face Hobbing Method As known 2, FH head cutter is provided with a proper number of blad
24、e groups Nb, each of them consists in an outer and an inner blade. As reported in Figure 1, in order to accomplish continuous indexing, the head cutter and the being generated gear are rotating in opposite directions and the next group of blades will start to cut the next gear tooth after that the c
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