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SIMULIA India Regional Users Meeting ‘11 of 9

Prediction of tread geometry influence on Ply steer Residual Aligning Torque (PRAT) T.Muthu Siva Sankar*, P. Sankarganesh, S.K.P.Amarnath and Peter Becker

Apollo Tyres Ltd., Vadodara, India

Key words: Tyre, PRAT, Vehicle Pull, Tread Pattern

ABSTRACT:

Ply steer residual aligning torque (PRAT) is one of major parameters which influences vehicle pull. A

vehicle pull problem is directly related to safety and comfort. The value of PRAT is influenced by the

various constructional parameters and treads pattern designs. Experimental evaluation of PRAT is

time consuming and costly. This paper presents the numerical procedure for computation of PRAT

values of tyres and investigation is restricted to change in tread pattern design. This procedure

helps the tyre designers to meet/balance the Vehicle pull requirements at an early stage of product

development.

Introduction:

Among the problems related to vehicle stability, straight running of a vehicle is a relevant safety

feature of vehicle performance. Vehicle pull/drift can

Fig 1


be easily sensed by driver. Vehicle drifts to one particular side when there is an asymmetry present

either in steering system/suspension system, tyre uniformity, road crown or incompatible

interaction among them. Vehicle pull is affected by force and moment generated either by tyre or

suspension system.

Major parameters causing the pull problem are includes PRAT and conicity of tires, road crown, cross

camber, cross caster and other manufacturing non uniformity of the vehicle. Force and moment

behaviours are function of tyre body parameters (profile, belt angle, belt constructions etc) and

contact behaviour of tread pattern by the geometry of tread pattern.

To minimize vehicle drift VRAT should be counter balanced by PRAT. So co work between vehicle

and tyre industry is mandatory to optimize the vehicle pull. This paper describes the effect of pattern

in particular and influences of Shoulder lateral groove angle on ply residual aligning torque.

PRAT

A typical radial tyre structure is made with multiple layers of plies bonded together. The individual

plies have various prescribed orientations of carcass layer which are parallel to the meridonial

direction and anti symmetric belt package in the crown region. The classical lamination theory

assumes that the orthotropic layers are perfectly bonded together with an infinitely thin bond line

and the deformations across the bond line are continuous. Generally, the multi-ply systems twist

and bend when subjected to simple tensile load. The result is a combination of bending, shearing

and stretching of the laminate. Moreover If the tyre is free rolling, the toroidal shape of tyre (shown

in fig2) becomes flat at the contact patch, so lateral and longitudinal shear stresses are generated in

the contact area (tread blocks) and additional in plane shear also occurs due to change in belt

tension at contact patch. These shear stresses applied to the individual tread blocks cause coupled

reaction forces, resulting in an aligning torque. Thus radial tyres generate measurable lateral force

and self aligning moment under straight rolling condition. Ply steer side force is an inherent property

of a belted radial tyre which is the nonzero side force at zero slip angles.

Fig 2


PRAT is defined as the level of tyre aligning torque at the slip angle where the lateral force is zero. The phenomenon is governed by the structural parameters of both tire body and treads pattern as

Fig 3

Well as the frictional dynamics of rolling tire, which is mechanically complex? Conventionally, tyre PRAT is adjusted through the classical approach in which trial productions of tires by adjusting the construction and tread design parameters are too costly and time-consuming and there has been a demand for a new approach to address the above method. The mechanism of PRAT can be decomposed into two effects, i.e. the pattern effect and the body effect. The pattern effect is usually extracted by changing the signs of belt cord angle about a particular tread design. The pattern effect is can be calculated by below formula. The pattern effect = (PRAT1 + PRAT2)/2 PRAT1 – PRAT evaluated at Regular belt cord orientation PRAT1 – PRAT evaluated at Reverse belt cord orientation Tire engineers have to evaluate the sensitivity of the tread pattern design to PRAT on the occasion of accommodating the design to several markets of different PRAT requirements. Modelling Strategy: To investigate the effects of Tread Pattern, the tread pattern is modeled with longitudinal and lateral

grooves consisting of 50 numbers of pitches around the circumference. Tread and carcass is

modelled separately and later Tread region is tied with carcass model. Rubber components are

modeled with continuum 8 noded brick and 6 noded penta elements. Reinforcements which are

embedded in rubber elements are modeled with 4 noded membrane elements. Road and rim are

modelled as analytical rigid. Coulomb friction law is used between tyre/ rim as well as with Tyre/

road.


Fig 3

Under the assumption of cyclic symmetry inflation and rim mounting was performed in single pitch.

Using symmetric model generation and symmetric result transfer, full tyre model was generated.

Vertical loading was performed in the subsequent step.

Steady State Rolling Analysis

The steady state dynamic interaction between tyre and road is investigated using the steady state

transport analysis capability available in Abaqus. Steady state transport is carried out by using mixed

Langrangian/Eulerean formulation. This option uses a reference frame attached to the wheel axle,

which does not rotate with the tire. The tire then rotates through this frame. Stream lines are

defined through axis of rotation in symmetric model generation and the path through which

material will flow. This kinematic description that converts the steady-state moving contact

problem into a purely spatially dependent simulation in which rigid body rotation is described in a

spatial or Eulerian manner, and deformation, which is now measured relative to the rotating rigid

body, is described in a Lagrangian manner.

This approach represents a huge saving in computational overhead when compared with a transient

analysis, with fine mesh defined along the entire surface of the deformable tire. Restarting from the

solution of the static deflection analysis, the steady state transport option is first used to obtain the

straight line steady state rolling conditions while varying the tire angular spinning velocities at the

desired constant road speed (30 km/hr was used in this study). With the straight line free rolling

solution obtained, the steady state simulation of the tire when subjected to a prescribed slip angle is

then implemented and the tire’s dynamic response in terms of the lateral forces and aligning

moments is obtained.


Variants:

Three variants have been studied which are in 3 groups. In group I, belt lay is changed from regular

orientation to reverse orientation. In group II, shoulder lateral groove angle is varied from 0 to 40

degrees. In Group III, orientation of pattern is reversed. Refer below fig 4

Fig 4

Influence of belt lay:

When reversing the belt lay the sign of the lateral force generated reverses from the reference belt

lay and there by PRAT also reverses.


Fig 5a

Influence of shoulder Lateral groove angle:

The value of PRAT increases with increasing groove angle up to 30 degree and any further angle

increase reduces the PRAT values.

Fig 5b

Influence of Pattern Reverse:

When reversing the pattern orientation the PRAT value decreases in magnitude by half.


Fig 5c

Validation:

2 tyres were hand carved, one with regular pattern orientation and the other with reverse tread

pattern orientation. PRAT values were evaluated in indoor pulley wheel.

Fig 6a

Fig 6b


Fig 6c

Fig 6c, compares the experimental footprint pressure distribution against the simulated foot print

and both are comparable. Both simulated and experimental footprint pressure values in the

shoulder region shows relatively higher pressure intensity. The experimental and simulated PRAT

values are shown in the table below.

Result and Discussion:

Based on the investigation, highest influence is

observed when we reverse the belt lay orientation

and followed by reversing the pattern orientation and

then shoulder lateral angle change. The differences

between experimental values against simulated

values can be improved by incorporating the viscous

parameters. The experimental and simulated prat

values are in good agreement behaviourally.

Item PRAT ( Nmm)

Abaqus

Simulation

Experimental

Regular

Pattern

1246 1643

Reverse

Pattern

623 380


Conclusions:

Abaqus evaluation of PRAT results are very well in agreement with experimental results. With this

approach Pattern PRAT setting, tuning can be done at tyre design stage and leaves an opportunity to

cooperate with Vehicle manufacturers at the design stage itself. PRAT evaluation through Abaqus

simulation saves a lot of time and cost.

Acknowledgement

The authors wish to express their appreciation to the Apollo tyres management for permitting to share the presentation. And special thanks to both Product Development and Design & Development teams of R&D Apollo Tyres Ltd for their constant support.

References

1. Abaqus/Standard User’s Manual, Version 6.10

2. Okonieski, R. E., Moseley, D. J., Cai, K. Y., "Simplified Approach to Calculating Geometric

Stiffness Properties of Tread Pattern Elements," Tire Science and Technology, TSTCA, Vol.

31, No. 3, 2003

3. K. Ohishi, H. Suita, and K. Ishihara, " The Finite Element Approach to Predict the Plysteer Residual Cornering Force of Tires ," Tire Science and Technology, TSTCA, Vol. 30,

No. 2, 2002

4. Kabe, K. and Morikawa, T., "A New Tire Construction Which Reduces Ply Steer," Tire Science and Technology, TSTCA, Vol. 19, No. 1, 1991.

5. Gent, A. N., The Pneumatic Tire, NHTSA US DOT, Washington, D.C., August, 2005

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