Ball Joint Rubber Boot

Chapter 13: Ball Joint Rubber Boot

13

Ball Joint Rubber Boot

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Summary

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Introduction

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Solution Requirements

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FEM Solution

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Results

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Modeling Tips

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Input File(s)

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Video

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CHAPTER 13 221 Ball Joint Rubber Boot

Summary Title

Chapter 13: Ball Joint Rubber Boot

Contact features

Load controlled rigid bodies and friction with viscoelastic relaxation +

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Geometry

r = 0.017557 m r=0m

Clamp 2

Knuckle

CL Original Shape of Boot Deformed Shape of Boot

Stud

R

Clamp 1 Housing

Material properties

Shear Modulus, G = 2.0 MPa - using time dependent and independent Mooney and Ogden elastomeric material models

Boundary conditions

Housing moves to seat clamp 1; stud and knuckle move to seat clamp 2.

Element types

Axisymmetric 4-node quad element

FE results

Verify the equivalence of the two elastomeric models and underscore the importance of time effects of material properties in elastomers. Verify the deformed shape with actual installation. CL

R

222 MD Demonstration Problems CHAPTER 13

Introduction In the design of ball joints for automotive applications, the major design concern is to prevent sealing boots from leaking. Because most ball joint failures occur as a result of corrosion, contamination or dirt ingress, causing excessive wear. Figure 13-1 shows some typical ball joint failure modes. In practice the stud of a ball joint is subjected to axial, oscillatory and rotational loads. Currently, most designs of sealing boots are based on design engineer's experience, experimental tests, and/or much more simplified FEA models. In this example, we will install the boot using a 2-D axisymmetric FEA model whereby the boot is fitted onto the housing under the large clamp, and then the stud and knuckle moved to fit the boot onto the shaft. The deformed profile of the boot is then compared to the actual boot. Contamination in the grease

Wear in labyrinth from corrosion on the pin

Contamination at the parting line.

Figure 13-1

Ball Joint Sealing Boot Failure: Excessive Wear in Labyrinth

Solution Requirements MD Nastran is used to model the assembly process of the boot onto the housing and stud. Since the stiffness of the housing, ball stud, knuckle and clamping rings is much higher than the rubber sealing boot, they are modeled with rigid bodies. The simulation is performed as three different cases as explained below: Cases A and B: The rubber-sealing boot material is modeled using Mooney-Rivlin (Case A) and Ogden (Case B) material models and equivalent performance of both is studied. Case C:

Viscoelastic Relaxation follows the installation with Mooney as the material mode. A time dependence of hyperelastic properties is taken into account where the viscoelasticity is represented as linear perturbations over hyperelastic material capable of representing large strains. The viscoelastic relaxation will drop the strain energy density by about 50% in a two hour time period.

CHAPTER 13 223 Ball Joint Rubber Boot

FEM Solution The numerical solution has been obtained with MD Nastran's solution sequence 400. The details of finite element models, contact simulations, material, load, boundary conditions, and solution procedure are discussed next.

Finite Element Models An axisymmetric model of the Ball Joint rubber boot is used in the simulation. The rubber boot is meshed with 845 lower-order axisymmetric solid elements. The bulk data file entries defining the axisymmetric properties of the CQUADX elements are as follows: PLPLANE 1 PSHLN2,1,1 ,C4,AXSOLID,L

1

Contact Models The model has six contact bodies. The rubber boot is the deformable contact body while the housing, ball stud, knuckle, ring small and ring large are represented as the rigid contact bodies. Each of the contact bodies is defined through the BCBODY bulk data entry. Each rigid body is defined to contact the deformable rubber boot, and hence, six contact pairs are defined through BCTABLE. In each contact pair, the contacting rigid body is defined as MASTER and the deformable rubber boot is defined as SLAVE. The contact tolerance is zero and the bias factor is globally defined for all contact pairs as 0.95. For simplicity, no friction has been included in the analysis. The BCPARA bulk data entry is used to define the global bias factor.

Figure 13-2

Original Axisymmetric Model

224 MD Demonstration Problems CHAPTER 13

Material Cases A and B: The experimental data is fitted with a one term Mooney (commonly known as neo-Hookean) model. To demonstrate the equivalence and accuracy of the implemented elastomer models in sol 400, both Mooney (Case A) and Ogden (Case B) models have been used for the rubber boot. The models are made equivalent by ensuring that the bulk modulus is the same for both models and taking care of the following: µ1 = 2C10 and 1 = 2 and µ2 = 2C01 and 2 = -2 It is important to note that this equivalence relation holds only one way i.e. any neo-Hookean or Mooney model can be represented by the Ogden model in general but not vice-versa. The bulk data entry used to define the material properties in Case A is MATHE for both Mooney and Ogden models. The properties of Mooney and Ogden materials have been input as follows: MATHE

MATHE

1 1. 0. 0. 1 2. 0.

Mooney 0. 0.

0.

Ogden 2. -2.

1.

1.

0.

0.

0.

Case C: In this case, along with the Mooney properties of Case A, a MATVE bulk data file entry is used to define the viscoelastic properties. Here, Wdi (multiplier or scale factor for deviatoric behavior in Prony series) and Tdi (time constant for deviatoric behavior in Prony series) need to be entered in the MATVE entry. They have been included in the input file as follows: MATHE

1 Mooney 0. 1. 1. 0. 0. 0. 0. MATVE,1,Mooney,,,0.111188,0.205057,, ,0.130683,1.71947,0.0967089,23.7532,0.0822848,273.121,0.0965449,3107.79

Loading and Boundary Conditions All the rigid bodies are load controlled and are assembled using displacement boundary conditions. Cases A and B: The control node 977 of the housing is given an x-displacement of 0.00273451 in the first load case. The control node 976 of the stud is held fixed in the y-direction in the first load case and given a y-displacement of 0.0031074 in the second load case. The control node 978 of knuckle is held stationary in the first load case and given a displacement 0.0105098 in the second load case. The clamping rings, ring large with control node 974, ring small with control node 975 are held stationary in the y-direction throughout the analysis but are allowed to translate in the x-direction.

CHAPTER 13 225 Ball Joint Rubber Boot

Case C: All the control node displacements are applied together in the first load step (as explained in the above case) which is followed by a step of visco-elastic relaxation.

Solution Procedure The assembly process for the different cases has been done as follows: Cases A and B: • In the first step, the housing is brought into place with the ball stud and knuckle held unassembled. A fixed time stepping procedure using NLSTEP with 50 increments is used to assemble the knuckle. UPV residual checking is used with KSTEP = -1 and the solution algorithm utilizes the full Newton-Raphson (PFNT) with convergence check using the infinity norm (as opposed to the L-2 norm): NLSTEP

1 1.0 general 25 fixed 50 mech UPV

1 0 .01

10 .01

NLSTEP

2 1.0 general 25 1 10 fixed 50 0 mech UPV .01 .01 • In the second step, both the stud and the knuckle are brought into position with the housing held in place. Again, a fixed time stepping procedure using NLSTEP with 50 increments is used to assemble the Knuckle. UPV convergence checking is used with KSTEP = -1. • Large displacement (PARAM, LGDISP, 2) • Large Strain analysis with updated Lagrangian approach with multiplicative decomposition of deformation gradient (NLMOPTS,LRGS,2) Case C: In this case, all three housing, knuckle, and stud are brought into place in the first load step. Here, the entire analysis is done in real time. The first load step is of 2 seconds.Again, a fixed time stepping is used with 100 increments with each increment representing a real time of 0.02 seconds. Again the convergence technique is PFNT and UPV convergence checking is used with KSTEP = -1. The NLSTEP entry is as follows NLSTEP

1 2.0 general 25 fixed 100 mech UPV

1 0 .01

10 .01

In the second load step, there are no additional loads or boundary conditions applied and the system is held in place through the contact conditions. The assembled system thus relaxes for the next 7200 seconds. This is easily accomplished with the adaptive time stepping scheme activated using the NLSTEP entry. The ADAPT field is employed

226 MD Demonstration Problems CHAPTER 13

in the NLSTEP entry to achieve this. While options like PV convergence test method and PFNT technique with KSTEP=-1 and convergence tolerance of 0.100 are specified in the MECH option of the NLSTEP entry, the ADAPT option is used which specifies the following: • Initial time step (=1.0e-3) • Minimum time step as a fraction of total load step time (=1.0E-5) • Maximum time step as a fraction of total load step time (=.10) • Desired number of iterations (=10) • Factor for increasing the time steps (=1.20) • Output flag (=-1) • Maximum number of increments in the current load case (=999999) • Flag for damping (=0) • Damping co-efficient (=.100E-03) The NLSTEP entry is as follows: NLSTEP

2 72000.0 GENERAL 25 0 ADAPT 1.0E-03 1.0E-5 .10 0 .100E-03 MECH PV 0.00 .100

10 0 0.00

10 1.20 0 1 PFNT

-1 .100

999999 1.2

-1

Results The installation of the boot onto the housing and stud is shown in Figure 13-3. The deformed shape is overlaid onto the actual deformed boot geometry to validate the modeling techniques. CL

Undeformed

Deformed R

Figure 13-3

Undeformed and Deformed Rubber Boot

CHAPTER 13 227 Ball Joint Rubber Boot

As expected, the knuckle force is identical for both the models as shown in Figure 13-4. In addition, the results agree with Marc's results which have been taken as reference. Figure 13-5 shows the fall of the knuckle force due to the subsequent relaxation associated with the viscoelastic effects. The fall is quite dramatic and consistent with the material data. Also, it can be noticed that the SOL 400 solution is very close to the Marc reference results. Axial Force (N)

80 70 60 50 40

Ogden (MD Sol 400)

30 Mooney (MD Sol 400) 20 Mooney (Marc) 10 0 0.000

0.002

Figure 13-4

0.004

0.006

0.008 0.010 Axial Displacement (m)

Comparison of Knuckle Force during Assembly

Axial Force (N) 80 Install

70

Mooney (MD Sol 400)

60 Mooney (Marc) 50 40 30 Relax

20 10 Time (sec) 0

0

Figure 13-5

2000

4000

6000

Insertion Force History

8000

10000

228 MD Demonstration Problems CHAPTER 13

Modeling Tips Use of NLMOPTS,LRGS,2 and PARAM,LGDISP,2 must be included in the analysis. The KSTEP field in the NLSTEP entry should be set to -1,especially for these kind of problems. Finally, for an efficient solution using the adaptive time stepping scheme, the ADAPT option is used in the NLSTEP entry. It must be noticed that additional laboratory tests (and corresponding curve fitting to get the Prony coefficients) would need to be carried out to get the time dependence of the material properties. The need for the addition of time dependent effects in an analysis requires judgment. In analyses involving both rolling resistance (important for designing for fuel efficiency) or standing waves (tire blowout) in tires, viscous effects are important,; however, a simple static loading to capture load-deflection curves does not require modeling of any time dependent effects. This can save time and money to do the additional tests. In general, adaptive load stepping is recommended to provide robust automatic control of the applied load even in the presence of strong nonlinearities. In this case, however, the large amount of contact throughout loadcase one together with the time-dependent aspects of loadcase two made fixed stepping the better option.

Input File(s) File

Description

nug_13a.dat

Mooney model

nug_13b.dat

Ogden model

nug_13c.dat

Mooney model with viscoelastic properties

CHAPTER 13 229 Ball Joint Rubber Boot

Video

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Click on the image or caption below to view a streaming video of this problem; it lasts approximately 30 minutes and explains how the steps are performed. r = 0.017557 m r=0m

Clamp 2

Knuckle

CL Original Shape of Boot Deformed Shape of Boot

Stud

R

Clamp 1 Housing

Figure 13-6

Video of the Above Steps