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Clearance and friction-induced dynamics of chain CVT drives

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Abstract

A continuously variable transmission (CVT) is an emerging automotive transmission technology that offers a continuum of gear ratios between desired limits. A chain CVT is a friction-limited drive as its performance and torque capacity rely significantly on the friction characteristic of the contact patch between the chain and the pulley. Moreover, such a CVT is susceptible to clearance formation due to assembly defects or extensive continual operation of the system, which further degrades its performance and leads to early wear and failure of the system. The present research focuses on developing models to understand the influence of clearance and different friction characteristics on the dynamic performance of a chain CVT drive. A detailed planar multibody model of a chain CVT is developed in order to accurately capture the dynamics characterized by the discrete structure of the chain, which causes polygonal excitations in the system. A suitable model for clearance between the chain links is embedded into this multibody model of the chain CVT. Friction between the chain link and the pulley sheaves is modeled using different mathematical models which account for different loading scenarios. The mathematical models, the computational scheme, and the results corresponding to different loading scenarios are discussed. The results discuss the influence of friction characteristics and clearance parameters on the dynamic performance, the axial force requirements, and the torque transmitting capacity of a chain CVT drive.

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Abbreviations

a :

Starting coefficient of friction between chain and pulley (∼0.003)

1/b,κ :

Rate of growth of friction coefficient, μ

(x c ,y c ):

Coordinates of the center of mass of a link

θ :

Rotational degree of freedom of a link

(ac x ,ac y ):

Linear acceleration of the center of mass of a link

m :

Mass of a chain link

I c :

Moment of inertia of a chain link about its center of mass

λ N ,N :

Normal force between a chain link and a pulley

λ T :

Force during the sticking phase of a contact

J p :

Pulley rotational inertia

φ :

Pulley rotational coordinate

β 0 :

Half-sheave angle of non-deformed pulley

β :

Half-sheave angle of deformed pulley

θ c :

Angular location of center of wedge-expansion

Δ :

Amplitude of the sheave angle sinusoid

τ :

Torque on the driver pulley

r,r′:

Link pitch radius on driver and driven pulleys

z :

Local distance between the pulley surfaces

u :

Axial width variation due to pulley flexibility

v rel :

Relative velocity between the contacting surfaces

ζ :

Angular location of a link over the pulley wrap

k,p :

Stiffness and damping parameters of the interconnecting force element

ε :

Clearance between the chain-links

μ :

Coefficient of friction between link and pulley

μ 0 :

Coefficient of kinetic friction between link and pulley

σ :

Parameter related to the ratio of the coefficients of static and kinetic friction

χ :

Stribeck-effect/lubrication parameter

γ :

Sliding angle

M :

Mass matrix (assembled)

h :

Forcing vector containing contributions from active forces/torques and other gyroscopic terms

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Authors and Affiliations

  1. Clemson University, 106 EIB, Flour Daniel Bldg., Clemson, SC, 29634, USA

    Nilabh Srivastava & Imtiaz Haque

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  1. Nilabh Srivastava
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  2. Imtiaz Haque
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Correspondence to Nilabh Srivastava.

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Srivastava, N., Haque, I. Clearance and friction-induced dynamics of chain CVT drives. Multibody Syst Dyn 19, 255–280 (2008). https://doi.org/10.1007/s11044-007-9057-3

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