Research Papers: Design of Direct Contact Systems

A Zero-Spin Design Methodology for Transmission Components Generatrix in Traction Drive Continuously Variable Transmissions

[+] Author and Article Information
Qingtao Li

School of Mechanical Engineering,
Xihua University,
Chengdu 610039, Sichuan, China
e-mail: tsingtau.lee@gmail.com

Min Liao

School of Mechanical Engineering,
Xihua University,
No. 999 Jinzhou Road,
Chengdu 610039, Sichuan, China
e-mail: liaominxhu@163.com

Shuang Wang

School of Mechanical Engineering,
Xihua University,
No. 999 Jinzhou Road,
Chengdu 610039, Sichuan, China
e-mail: wsh@mail.xhu.edu.cn

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 8, 2017; final manuscript received November 23, 2017; published online December 15, 2017. Assoc. Editor: Massimo Callegari.

J. Mech. Des 140(3), 033301 (Dec 15, 2017) (9 pages) Paper No: MD-17-1547; doi: 10.1115/1.4038646 History: Received August 08, 2017; Revised November 23, 2017

With the advantages of high torque and low noise, traction drive continuously variable transmissions (TDCVTs) have a promising application in future vehicles. However, their efficiency is limited by spin losses caused by the different speed distributions between the contact areas of the traction. To overcome this shortcoming, this paper proposes a novel zero-spin design methodology applicable to any type of TDCVTs. The methodology analyzes the features of TDCVTs in terms of the variation of contact position and the shifting motion of traction components. It also establishes a mathematical model resulting in differential equations, whose general solution is the substitute for the equation of traction components generatrix. After applications of the methodology to two original TDCVTs, two zero-spin TDCVTs are proposed. A computational method of spin ratios, which are in direct proportion to spin losses, of four TDCVTs is introduced. The results of comparisons demonstrate that the proposed methodology can dramatically reduce the spin losses.

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Hewko, L. O. , 1986, “Automotive Traction Drive CVTs—An Overview,” SAE Technical Paper No. 861355.
Youqiang, Z. , 2001, Mechanical Continuously Variable Transmission, China Machine Press, Beijing, China (in Chinese).
Heilich, F. W. , and Shube, E. E. , 1983, Traction Drives: Selection and Application, Marcel Dekker, New York.
Akehurst, S. , Parker, D. A. , and Schaaf, S. , 2006, “ CVT Rolling Traction Drives—A Review of Research Into Their Design, Functionality, and Modeling,” ASME J. Mech. Des., 128(5), pp. 1165–1176. [CrossRef]
Riszczuk, D. , and Glovnea, R. , 2014, “Modelling and Testing of a Toroidal CVT,” ASME Paper No. ESDA2014-20371.
Ghariblu, H. , Behroozirad, A. , and Madandar, A. , 2014, “ Traction and Efficiency Performance of Ball Type CVTs,” Int. J. Automot. Eng., 4(2), pp. 738–748. http://www.iust.ac.ir/ijae/browse.php?a_id=268&sid=1&slc_lang=en
Machida, H. , Itoh, H. , Imanishi, T. , and Tanaka, H. , 1995, “ Design Principle of High Power Traction Drive CVT,” SAE Paper No. 950675.
Nabil, A. A. , 2004, “Performance Investigations of Half Toroidal Continuously Variable Transmissions (CVTs),” Ph.D. thesis, Chongqing University, Chongqing, China. https://www.dissertationtopic.net/doc/1584719
Zhang, Y. , Zhang, X. , and Tobler, W. , 2000, “ A Systematic Model for the Analysis of Contact, Side Slip and Traction of Toroidal Drives,” ASME J. Mech. Des., 122(4), pp. 523–528. [CrossRef]
Li, X. M. , Guo, F. , Fan, B. , and Yang, P. , 2010, “ Influence of Spinning on the Rolling EHL Films,” Tribol. Int., 43(11), pp. 2020–2028. [CrossRef]
Newall, J. P. , Cowperthwaite, S. , Hough, M. , and Lee, A. P. , 2005, “ Efficiency Modelling in the Full Toroidal Variator: Investigation Into Optimisation of EHL Contact Conditions to Maximize Contact Efficiency,” Tribol. Interface Eng. Ser., 48, pp. 245–255. [CrossRef]
Newall, J. , and Lee, A. , 2003, “ Measurement and Prediction of Spin Losses in the EHL Point Contacts of the Full Toroidal Variator,” Tribol. Ser., 43, pp. 769–779. [CrossRef]
Tanaka, H. , Machida, H. , Hata, H. , and Nakano, M. , 1995, “ Half-Toroidal Traction Drive Continuously Variable Power Transmission for Automobiles: Traction Drive Materials, Transmission Design and Efficiency,” JSME Int. J. Ser. C, 38(4), pp. 772–777.
Yan, X. L. , Wang, X. L. , and Zhang, Y. Y. , 2014, “ A Numerical Study of Fatigue Life in Non-Newtonian Thermal EHL Rolling–Sliding Contacts With Spinning,” Tribol. Int., 80, pp. 156–165. [CrossRef]
Akbarzadeh, S. , and Zohoor, H. , 2006, Sensitivity Analysis of Torque Transmission Efficiency of a Half-Toroidal CVT,” SAE Paper No. 2006-01-1304.
Yamamoto, T. , Matsuda, K. , and Hibi, T. , 2001, “ Analysis of the Efficiency of a Half-Toroidal CVT,” JSAE Rev., 22(4), pp. 565–570. [CrossRef]
Delkhosh, M. , and Foumani, M. S. , 2013, “ Multi-Objective Geometrical Optimization of Full Toroidal CVT,” Int. J. Automot. Technol., 14(5), pp. 707–715. [CrossRef]
Delkhosh, M. , and Foumani, M. S. , 2015, “ Introduction and Optimization of a Power Split Continuously Variable Transmission Including Several Fixed Ratio Mechanisms,” Sci. Iran. Trans. B, 22(1), pp. 226–234. http://scientiairanica.sharif.edu/article_3649.html
Delkhosh, M. , Foumani, M. S. , and Boroushaki, M. , 2014, “ Geometrical Optimization of Parallel Infinitely Variable Transmission to Decrease Vehicle Fuel Consumption,” Mech. Based Des. Struct. Mach., 42(4), pp. 483–501. [CrossRef]
Bell, C. A. , Mares, C. , and Glovnea, R. , 2014, “ Multi–Criteria Optimisation of a Continuously Variable Transmission,” Int. J. Des. Eng., 5(3), pp. 232–255.
Bell, C. A. , Mares, C. , and Glovnea, R. P. , 2011, “ Concept Design Optimisation for Continuously Variable Transmissions,” Int. J. Mechatronics Manuf. Syst., 4(1), pp. 19–34.
Bell, C. A. , and Glovnea, R. , 2011, “ Tribological Optimization of a Toroidal-Type Continuously Variable Transmission,” Proc. Inst. Mech. Eng., Part J, 225(6), pp. 407–417. [CrossRef]
Carbone, G. , Mangialardi, L. , and Mantriota, G. , 2004, “ A Comparison of the Performances of Full and Half Toroidal Traction Drives,” Mech. Mach. Theory, 39(9), pp. 921–942. [CrossRef]
Cretu, O. S. , and Glovnea, R. P. , 2003, “ Traction Drive With Reduced Spin Losses,” ASME J. Tribol., 125(3), pp. 507–512. [CrossRef]
Ai, X. , 2002, “ Development of Zero-Spin Planetary Traction Drive Transmission—Part 1: Design and Principles of Performance Calculation,” ASME J. Tribol., 124(2), pp. 386–391. [CrossRef]
Ai, X. , 2002, “ Development of Zero-Spin Planetary Traction Drive Transmission—Part 2: Performance Testing and Evaluation,” ASME J. Tribol., 124(2), pp. 392–397. [CrossRef]
De Novellis, L. , Carbone, G. , and Mangialardi, L. , 2012, “ Traction and Efficiency Performance of the Double Roller Full-Toroidal Variator: A Comparison With Half- and Full-Toroidal Drives,” ASME J. Mech. Des., 134(7), p. 071005. [CrossRef]
Li, Q. , Li, H. , Yu, D. , and Yao, J. , 2015, “ A Novel Continuously Variable Transmission With Logarithmic Disc Generatrix,” Mech. Mach. Theory, 93, pp. 147–162. [CrossRef]
Li, Q. , Wu, J. , Li, H. , and Yao, J. , 2015, “ A Mathematical Method for Eliminating Spin Losses in Toroidal Traction Drives,” Math. Probl. Eng., 2015, p. 501878.
Corless, R. M. , Gonnet, G. H. , Hare, D. E. G. , Jeffrey, D. J. , and Knuth, D. E. , 1996, “ On the LambertW Function,” Adv. Comput. Math., 5(1), pp. 329–359. [CrossRef]
Verbelen, F. , Druant, J. , Derammelaere, S. , Vansompel, H. , De Belie, F. , Stockman, K. , and Sergeant, P. , 2017, “ Benchmarking the Permanent Magnet Electrical Variable Transmission Against the Half Toroidal Continuously Variable Transmission,” Mech. Mach. Theory, 113, pp. 141–157. [CrossRef]
Verbelen, F. , Derammelaere, S. , Sergeant, P. , and Stockman, K. , 2017, “ Half Toroidal Continuously Variable Transmission: Trade-Off Between Dynamics of Ratio Variation and Efficiency,” Mech. Mach. Theory, 107, pp. 183–196. [CrossRef]


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Fig. 4

Simplified example of traction drive

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Fig. 3

The flowchart of the design methodology

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Fig. 2

The two zero-spin conditions

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Fig. 1

Structural diagrams for traction drive CVTs: (a) full-toroidal CVT, (b) half-toroidal CVT, (c) ball-type CVT, (d) flat-plate CVT, (e) spherical-rotor CVT, (f) Kopp CVT, (g) FU-type CVT, and (h) tapered-roller and ring-disk CVT

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Fig. 5

The structural schematic of FU-type CVT

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Fig. 6

The structural schematic of integral CVT

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Fig. 7

The structural schematic of TRCVT

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Fig. 8

The structural schematic of Lambert CVT

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Fig. 10

The spin ratios σspin of TRCVT and Lambert CVT as functions of the slip coefficient Cr

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Fig. 11

The spin ratios σspin of integral CVT and Lambert CVT as functions of the transmission ratio i

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Fig. 9

The spin ratios σspin of Fu-type CVT and integral CVT as functions of the slip coefficient Cr



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