Static ride analysis of flexible lower control arm on SLA Suspension to compute stress,strain and displacement using Altair Hyper works MotionView/MotionSolve and OptiStruct.

Published _Journal_on_Flexible_Body_Simulation

https://drive.google.com/file/d/18AACyt91o3EUfaZ3ctlrk5r5FuP4nnAg/view

Introduction to Flexible bodies.

It is a well-known fact that FEA models contain a higher number of degrees of freedom. Hence it is difficult for the MBD solvers to handle these models. This is one of the reason for the MBD to converge faster as compared to the FEA solvers. It is necessary to condense the FEA models to create flex bodies. A flex body is a modal representation of the FE model, an approximation of a deformable structure for CAE analysis. It can be used in conjunction with various CAE solvers to capture aspects associated with structures such as deformation, stress & strain. This data is used in various domains such as design, durability, etc. A flex body is based on the concept of modal superposition and is therefore very efficient for solvers that need to model structures as non-rigid. The MBD solver will calculate the coefficients for the various deflection modes calculated in the CMS method which when added together produce the deformed shape. Flex bodies connect to the MBD system through the interface nodes. Any constraint/force will be termed as an interface node. 

 Component Mode Synthesis Method (CMS): 

There are three CMS methods supported in Optistruct that will reduce the Finite-Element model to a set of orthogonal mode shapes:

Craig-Bampton method – In this method, two sets of modes are computed:

• The fixed interface constraint static modes are calculated by applying a unit displacement at each interface node in each degree of freedom individually while leaving all the other constraints active.
• The fixed interface eigenmodes are calculated with all the interface nodes constrained (Number of modes will be specified)

Finally, both sets of modes are orthogonalized producing the modal matrix of modes shapes that represent the flexible body.

Craig-Chang method – In this method, two sets of modes are also computed:

• The inertia-relief attachment static modes are computed by applying a unit displacement on each interface node in each degree of freedom individually while all the other interface nodes are free. When calculating the static modes the model is “mathematically” constrained by inertia, hence inertia-relief, to produce structural deformations required for calculating the mode shapes.
• The free-free eigenmodes are computed (i.e., without any constraints on the body). Again, both sets of modes are orthogonalized producing the modal matrix of modes shapes that represent the flexible body.  

Craig-Bampton Geometric - Stiffness method – best when analysing slender structures that have considerable influence of geometric stiffness effects especially during spinning. 

When to choose which CMS Method?

• Craig-Bampton - best when most of the degrees of freedom of the interface node are constrained by the MBD model.
• Craig-Chang - best when most of the degrees of freedom of the interface nodes are not constrained in many degrees of freedom by the MBD model.
• Craig-Bampton Geometric –Stiffness – best when analyzing slender structures that have considerable influence of geometric stiffening effects especially during the spinning

A common requirement of the CMS method is that the exterior grid points must be able to move independently of the interior nodes of the flexible body. A common case that causes CMS failures is when the centre point of a rigid spider which is defined as a flexible body is dependent on the displacement of the outer nodes. To avoid this configuration of the RBE3, the element must be changed to RBE2 element. To understand what this means one needs to understand what an RBE2/RBE3 element is.

  RBE are basically rigid body elements. RBE2 elements rigidly connect an independent FEA node to one or mode dependent nodes. Most often for MBD flexible bodies, the RBE2 elements are "rigid spiders" that have the independent node at the centre of a hole and the dependent nodes along with the circumference modelling bolts or other connection hardware. The independent node of the rigid spider becomes an interface node of the flexible body that allows the body to connect to other elements like joints or forces in the MBD model. RBE3 elements, on the other hand, the dependent node is in the centre and the independent nodes are along the circumference.

 Model -Building Process:

 The model building process is involved in two stages. Flex body Generation and Replacement of flex-body with the rigid lower control arm.

Stage I:  MotionView GUI is opened and then under "FlexTools" Flex Prep is selected. This opens a dialogue box where the flex-body will be created. The Finite Element model of the lower-control arm is imported into Hyperworks.

A suitable file name is chosen to save it as a .h3d file. Craig-Bampton is selected as the component mode synthesis method since most of the degrees of freedom of the interface node are constrained by the MBD model.

The interface nodes are selected as 4887+4888+4890. The ID's of the RBE2/RBE3 central nodes will be the interface nodes. The node IDs are read from HyperMesh while creating the flex-body.

The next step is to choose the highest mode number which specifies the cut-off value and type. The default value of 15 is selected as the highest mode #. As the highest mode number increases, the accuracy of the solution increases until convergence is reached. However, with increase in the number of the highest mode number, the computational time and power also increase significantly. So, basically there is always a trade-off.

The solver mode is chosen as Lanczos which is the default algorithm in Optistruct. Under the additional options 'Perform Strain Recovery needs to be checked'.

 In order to avoid CMS failures, the RBE3 spiders need to be converted to RBE2 spiders. BY clicking on 'Create RBE2 spider' launches HyperMesh. Once Hypermesh is launched, Optistust needs to be selected under USER-Profiles. The lower-control arm appears on the screen.

RBE2 spider needs to be created on the outer part of the lower control arm which would attach to the knuckle. This is done by clicking on utility-user-step 2 super spider. This prompts the user to select an element on the hole following which an RBE2 spider is created. There are 3 more RBE spiders located on the LCA. One which would attach to the spring and the rest two would attach to the bushing

Stage II: Since only the left LCA flex-body was created, it is necessary to create the right LCA aswell. This can be done easily using 'Translation of FlexBody Files' and then selecting Mirror existing h3d body option. The original h3d file is imported and its corresponding mirrored h3d is specified.

Using Assembly wizard option in Model, the front end of the vehicle is selected as shown in the figure below.

Next, the driveline configuration is set to 'No driveline'. The suspension system is set to ' Front SLA susp (1pc LCA). Rest all options are set to default.

Next, under analysis, task wizard is selected to create a test rig for the vehicle model which would be used to run Static Ride Analysis.

Parameters that are to be considered:

1) Vehicle CG

2) Axle Ratio

3) Vehicle weight

4) Front Brake Ratio

5) Wheel Base

By default, the LCA of the vehicle is rigid which needs to be replaced with the generated flex-body. To do this, Lower Control Arm is selected under Front SLA suspension from the project column. Symmetric properties need to be unchecked and Flex Body CMS is checked. The .h3d file for both left and right LCA is then imported.

After importing the LCA flex-body it is observed that they are misaligned from the knuckle and bushing. This misalignment is corrected by clicking on nodes-Find All- Align All. One also needs to verify that the rigid body modes are unchecked. This model- completes the model-building process.

Simulation and Results

Quasi-Static Simulation means that the system is driven extremely slowly so as not to engage any transient dynamics into simulation results. This is the simulation that is performed to find the displacement, stress and strain on the lower control arm. The end time is chosen as 4 seconds and the print interval is set to 0.01 for the quasi-static simulation.

Displacement Contour: As the suspension moves into jounce it is observed that the outer side of the lower control arm which is attached to the knuckle gets displaced by the most. As the jounce motion progresses the displacement is echoed to the rest of the control arm. The area where compression of the spring happens also displaces the lower control arm by a significant amount. The max displacement observed is 1.13E+02 mm

Stress Contour: Stress is force/unit area. The maximum stress occurs at the spring and knuckle attachment of the lower control arm. Max stress is 8.126E+03 N/mm`^2` and minimum stress is 1.246E-11 N/mm`^2`

Strain Contour: Strain is the change in length divided by the original length and is a dimensionless quantity. The maximum strain is 2.16E-02 and the minimum strain is 4.119E-11

Session files and Model files can be found here:

 https://drive.google.com/open?id=1eGIiZq0m7-n524kKG6hkiWNCF59wmnYl