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Research Papers

Helical Shift Mechanics of Rubber V-Belt Variators

[+] Author and Article Information
Francesco Sorge

Dipartimento di Ingegneria Industriale,  Università di Palermo, Viale delle Scienze, Palermo 90128, Italyfrancesco.sorge@unipa.it

Marco Cammalleri

Dipartimento di Ingegneria Industriale,  Università di Palermo, Viale delle Scienze, Palermo 90128, Italymarco.cammalleri@unipa.it

J. Mech. Des 133(4), 041006 (May 18, 2011) (8 pages) doi:10.1115/1.4003803 History: Received August 09, 2010; Revised February 25, 2011; Published May 18, 2011

A very common configuration of V-belt variators for motorcycles considers the correction of the belt tensioning depending on the resistant torque by means of suitable helical-shaped tracks allowing the driven half-pulleys to close/open. The theoretical model for belt-pulley coupling is rather complex for this configuration, where one half-pulley may run in advance and the other one behind with respect to the belt, and requires the repeated numerical solution of a strongly nonlinear differential system by a sort of shooting technique, until all the operating conditions are fulfilled (angular contact extent, torque, and axial force). After solving the full equations, the present study develops closed-form approximations, which are characterized by an excellent correspondence with the numerical plots, and suggests a simple and practical formulary for the axial thrust as a function of the torque and of the tension level. Then, the results of a theoretical–experimental comparison are also reported, and they indicate a fine agreement between the model and the real operation.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Scheme of the actuators on (a) the driver side and (b) the driven side

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Figure 2

Interaction between belt and pulley. C = center of belt element, ABf Bs  = pulley meridian plane, CDs Df  = plane of rotation, ABj Dj  = planes tangent to pulley walls, Bj CDj  = planes of sliding.

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Figure 3

Control volume. Triangles of velocities (projection on the plane of rotation).

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Figure 4

Driver solutions during opening phase. Dots: approximate solutions of Sec. 3. Data: α = 13°, k = 0.115, f = 0.4, ɛE  = 0.001, μvb2/Sl=0.0001, ρ= − 0.0002 Entries: γE = − 175°, χE = − 5.1980906°.

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Figure 5

Driver solutions during closing phase. Dots: approximate solutions of Sec. 3. Data: α = 13°, k = 0.115, f = 0.4, ɛE  = 0.001, μvb2/Sl=0.0001, ρ = + 0.0002. Entries: γE = − 174°, χE = − 6.3025879°.

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Figure 6

Driven solutions during opening phase. Dots: approximate solutions of Sec. 3. Data: α = 13°, k = 0.115, f = 0.4, ɛE  = 0.001, μvb2/Sl=0.0001, ρ = −0.0002. Entries: γf,E = − 177°, χE = − 4.9411456°.

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Figure 7

Driven solutions during closing phase. Dots: approximate solutions of Sec. 3. Data: α = 13°, k = 0.115, f = 0.4, ɛE  = 0.001, μvb2/Sl=0.0001, ρ = + 0.0002. Entries: γf,E = − 176.5°, χE = − 4.8080541°.

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Figure 8

Driven torque fraction on sliding half-pulley vs. axial-to-traction force ratio, for several values of the exit elongation and of the shift speed. Data: α = 13°, k = 0.115, f = 0.4, μvb2/Sl=0.0001.

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Figure 9

Experimental test bench

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Figure 10

Test 1. Shift up. Data: see Table 1

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Figure 11

Test 2. Shift up. Data: see Table 1

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Figure 12

Test 3. Shift down. Data: see Table 1

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Figure 13

Test 4. Shift down. Data: see Table 1

Tables

Errata

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