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Research Papers

# The Lubrication Regime at Pin-Pulley Interface in Chain CVTs

[+] Author and Article Information
G. Carbone

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Viale Japigia 182, 70126 Bari, Italycarbone@poliba.it

M. Scaraggi

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Viale Japigia 182, 70126 Bari, Italym.scaraggi@poliba.it

L. Soria

Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Viale Japigia 182, 70126 Bari, Italysoria@poliba.it

J. Mech. Des 131(1), 011003 (Dec 11, 2008) (9 pages) doi:10.1115/1.3013320 History: Received February 14, 2008; Revised August 07, 2008; Published December 11, 2008

## Abstract

This paper deals with the strongly nonstationary squeeze of an oil film at the interface between the chain pin and pulley in chain belt continuously variable transmission. We concentrate on the squeeze motion as it occurs as soon as the pin enters the pulley groove. The duration time to complete the squeeze process compared with the running time the pin takes to cover the entire arc of contact is fundamental to understand whether direct asperity-asperity contact occurs between the two approaching surfaces to clarify what actually is the lubrication regime (elastohydrodynamic lubrication (EHL), mixed, or boundary) and to verify if the Hertzian pressure distribution at the interface can properly describe the actual normal stress distribution. The Hertzian pressure solution is usually taken as a starting point to design the geometry of the pin surface; therefore, it is of utmost importance for the designers to know whether their hypothesis is correct or not. Taking into account that the traveling time, the pin spends in contact with the pulley groove, is of about 0.01 s, we show that rms surface roughness less than $0.1 μm$, corresponding to values adopted in such systems, guarantees a fully lubricated EHL regime at the interface. Therefore, direct asperity-asperity contact between the two approaching surfaces is avoided. We also show that the Hertzian solution does not properly represent the actual pressure distribution at the pin-pulley interface. Indeed, after few microseconds a noncentral annular pressure peak is formed, which moves toward the center of the pin with rapidly decreasing speed. The pressure peak can grow up to values of several gigapascals. Such very high pressures may cause local overloads and high fatigue stresses that must be taken into account to correctly estimate the durability of the system.

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## Figures

Figure 1

A schematic of the GCI chain made of pins, strip, and links properly connected. Only the pins touch the surface of the pulley sheaves and transmit normal and frictional force.

Figure 2

The gear chain industrial b.v. chain with the pins entering the pulley groove

Figure 3

The squeeze geometry for the system under consideration

Figure 4

The dimensionless film thickness h̃ as a function of the dimensionless radial position r̃ at different times. Observe the flat central hole-shaped region. Only after a period of time of order seconds (see the dashed line) the elastic deformation and therefore the shape of the deformed bodies converge to that of the classical Hertz solution.

Figure 5

The dimensionless pressure distribution as a function of the dimensionless radial coordinate r/(2R) in a linear-log diagram. The calculations have been performed for F0=1500 N. Observe the characteristic noncentral pressure peak, which occurs as soon as the lubrication regime becomes of the EHL type.

Figure 6

The calculated pressure distribution (solid line) and the pressure distribution (dashed line) given by Eq. 32. The agreement between the two distributions for r<rp is relatively good, thus supporting the conclusion that the oil behaves as a rigid punch in the high pressure central region.

Figure 7

The oil viscosity distribution as a function of the radial coordinate r in a linear-log diagram. Observe the very large increase (of several orders of magnitude) of μ in the central high pressure region. The calculations have been carried out for F0=1500 N.

Figure 8

The central dimensionless pressure ζp0=p̃(r̃=0) as a function of time t in a log-log diagram for different load conditions (F0=500,1000,1500 N). The lines parallel to the time axis represent the corresponding Hertzian solution. The spikes correspond to time values t at which the annular peak of the pressure reaches the center of the contact. Also note that reducing the load F0 reduces the time at which the spike occurs.

Figure 9

The dimensionless position of the pressure peak rp/(2R) as a function of t for different load conditions (F0=500,1000,1500 N)

Figure 10

The minimum dimensionless film thickness h̃min and the central film thickness h̃0 as a function of time t in a log-log diagram for different load conditions (F0=500,1000,1500 N). Note that increasing the load slows down the squeeze process. Also observe that the central thickness of the oil film is almost constant until the time at which the pressure peak reaches the center of the pin. Also the influence of the load on the central thickness is nonsignificant.

Figure 11

The fraction of the load supported by a circular area of radius r as a function of the dimensionless radial coordinate r̃=r/(2R) for t=0.42 μs (i.e., just at the beginning of the squeeze—solid line) and t=15 ms (i.e., when the pin is about to leave the contact with the pulley—dashed line). For convenience the oil film thickness profile is also plotted for the same two values of t.

Figure 12

The radial position rhmin of the minimum film thickness as a function of time for different load conditions (F0=500,1000,1500 N). The lines parallel to the time axis represent the corresponding Hertzian solutions. Observe that rhmin is always smaller than the Hertzian radius and approaches it only asymptotically.

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