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Modelling and measuring the axial force generated by tripod joint of automotive drive-shaft

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Abstract

The present paper deals with measurements and models of axial force produced by a tripod joint of an automotive drive-shaft. An automotive drive-shaft consists of a plunging tripod joint close to the gearbox and a fixed ball joint close to the wheel. Both joints are connected by an intermediate shaft.

The measurements of axial force are derived from a gauge extensometry sensor placed on an industrial test bench. The ball joint is modeled as a true and perfect spherical link. For the tripod joint, the rollers between the tripod and the tulip ramps are introduced in such a way that their orientation is taken in account. Then, two inverse models are proposed with a constant input velocity and a constant output torque. To start with, an analytical model is proposed; then a more sophisticated model using Adams software is introduced. It is shown that both models are coherent and in good agreement with experimental measurements of axial forces. Since axial forces generate nuisance vibration harshness with shudder in particular, models are used to predict shudder excitation dependence on tulip radius, input torque, shaft rotation speed and Coulomb friction. Finally, the Coulomb friction coefficient is identified in the models.

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Abbreviations

CVJ:

Constant Velocity Joint

NVH:

Noise and Vibration Harshness

RX:

X fold frequency vibration (X times that of input velocity)

i A j :

Orientation matrix of base b j with respect to base b i

Ω :

Tulip center

I :

Tripod center

C i :

Roller i center

r :

Tulip radius

r i :

Roller i to tripod center I distance

r r :

Roller radius

r a :

Gothic arch radius

r n :

Needles inscribed circle radius

l i :

Roller i to ramp i distance

L :

length of the intermediate shaft

α i :

Roller i roll angle

χ i :

Roller i yaw angle

φ :

Input angle

T o :

Constant output torque

φ i :

Ramp i input angle (gearbox) φ 1=φ

θ :

Output angle

δ :

Joint bending angle

β :

Angle of roller ramp force transmission

e :

Tripod center offset expressed in the tripod plane

d :

Interpenetration of parts in contact

μ s :

Static friction coefficient

μ d :

Dynamic friction coefficient

μ g :

Roller to ramp friction coefficient

μ f :

Roller to trunnion slipping friction coefficient

μ r :

Roller to trunnion rolling friction coefficient (rotation)

P i :

Contact point between roller i and ramp i

N i :

Normal effort at contact point P i

T i :

Tangential effort at contact point P i

F i :

Friction effort generated by the roller i projected along the tulip shaft

Q :

Total axial effort generated by the three rollers (sum of the F i )

F G :

Roller to trunnion friction effort (translation)

C R :

Roller to trunnion friction torque (rotation)

K :

Stiffness at contact point

D :

Damping at contact point

s :

Exponent of the force-deformation law

P needles :

Needles load

References

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Authors and Affiliations

  1. Laboratoire des Activités Physiques et Sportives, Université du Maine, Avenue Olivier Messiaen, 72085, Le Mans, Cedex 9, France

    S. Serveto & J.-P. Mariot

  2. NTN Transmissions Europe, ZA Les Trémellières, 72704, Allonnes, Cedex, France

    S. Serveto & M. Diaby

Authors
  1. S. Serveto
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  2. J.-P. Mariot
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  3. M. Diaby
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Correspondence to S. Serveto.

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Serveto, S., Mariot, JP. & Diaby, M. Modelling and measuring the axial force generated by tripod joint of automotive drive-shaft. Multibody Syst Dyn 19, 209–226 (2008). https://doi.org/10.1007/s11044-007-9091-1

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  • DOI: https://doi.org/10.1007/s11044-007-9091-1

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