MBD simulation of 3D contact modelling of a Ball Bearing

Introduction:

Contact Forces in MotionSolve

MotionSolve contains a very sophisticated contact modelling capability that can handle complex contact scenarios between rigid bodies. Creating contact is rather simple:

1. The user can identify geometries on one body that can contact a different set of geometries on a second body.
2. The user can also specify the contact material properties such as the coefficient of restitution and friction.

`to` MotionSolve monitors the proximity of the specified geometries to each other. When any penetration between the two sets of geometries occurs, a force based on the defined contact properties is generated. This represents the contact force. Both normal, as well as frictional forces, are modelled.

`to` When the bodies separate, the force becomes zero.

There are four key features to the contact capability in MotionSolve:

• Modelling the geometry of the bodies that are in contact.
• Detecting the onset of contact.
• Applying the contact force.
• Detecting the end of a contact "incident" and removing the contact force.

Geometry for Contacts

• Geometries for contacts are represented through meshed surfaces. The mesh consists of interconnected triangular elements. There are several options for defining the geometry of the bodies in contact.
• There are certain criteria for the mesh geometry to be acceptable in a contact simulation:

a)The meshed surface must enclose a volume and not contain and T-connections. An enclosed volume means all elements share an edge with an adjacent element. ”T-connections” occur when more than two elements share an edge.

b) The mesh size should be relatively uniform. e there should not be large variations in the length of the element edges.

c) The element normal must point in the direction of the expected contact. The element normal is a vector which is normal to the element’s plane and along the side of the element determined by the sequence of node connection following the right-hand rule as depicted.

`to`MotionView’s Import CAD or FE tool has the ability to import the geometry that meets the above criteria

Detecting Point of Contact

When the onset of a collision is detected at a certain time-step, the collision detection algorithm

returns the set of interfering polygons.

From those, MotionSolve computes the following:

• The point of contact and surface normal vector
• Relative tangential slip velocity
• The magnitude and direction of the normal and friction forces.

Applying the Contact Force

Once the point of contact and surface-normal vectors are known, the normal force magnitudes are computed. For the Ball-bearing problem, Impact method will be used

Contact Force

• Normal Force has two components and each of the predefined method has its own way of computing these components.

`F_(Contact)=F_(spri_ng)+F_(damp_i_ng)`

Where,

• `F_(Contact)` = Contact force
• `F_(spri_ng)` = Elastic spring force
• `F_(damp_i_ng)` = Dissipative damping force

• The Friction Force is calculated using the Coulomb friction model.

Impact method

The Impact model can be thought of as a non-linear spring-damper introduced when there is penetration.

The following four parameters define the Impact Contact Model:

Stiffness: Non-negative stiffness of the contact

Stiffness Exponent: Exponent of the force deformation characteristic

value > 1 `to` Stiffening characteristic

value < 1 `to` Softening characteristic

Maximum Damping: The maximum damping coefficient

Penetration at maximum Damping: The contact penetration at which maximum damping is applied

Besides this, there are parameters which are needed to be defined under Friction Force:

MU Static: The static coefficient of friction, which has to be overcome by a body before it can move

MU Dynamic: The coefficient of friction, which the body experiences while in motion

Stiction transition velocity: The velocity limit below which the coefficient of friction becomes MU Static

Friction transition velocity: The velocity above which the coefficient of friction becomes MU Dynamic.

When the slip velocity is in between Stiction transition velocity and Friction transition velocity then the coefficient of friction is in transition between the two.

When the collision detection algorithm detects contact, the penetration depth, rate of penetration, and the above four parameters are sent to the MotionSolve's IMPACT function where the normal force is calculated for each node.

Model-Building Process:

Step 1) Import the Parasolid file containing mass and inertia properties. Also, set the control mesh coarseness value to 5. With this step, MotionView invokes Hypermesh in the background and applies mesh on the solid surfaces, calculates the volume, centre of mass and the mass of Inertia.

2) The model contains a Ground body (default), Rim, Inner Race, Outer Race, and 6 balls numbering from Ball_1 to Ball_6 as shown in the figure below.

3) Created a Fixed joint between the Outer race and Ground Body at the Outer Race CG position. Revolute Joint between the Rim and Ground Body at the Rim CG position and oriented/aligned about global X-axis.

4) Next, it is necessary to create contact between these 6 balls with Rim, Outer race and Inner race. So the total number of contacts will be 6*3 = 18 contacts. For all the 18 contacts 18 Output requests will be automatically created which can be seen in the figure below.

5) As mentioned before in order to find out the Normal force and Friction force Impact method is used. and the following values were assigned.

Stiffness `to` 1000 N/mm

Stiffness Exponent `to` 2.1

Maximum Damping `to`0.1

Penetration depth `to` 0.1

Similarly for Friction force

MU Static `to` 0.2

Stiction transition velocity `to` 1.0 mm/sec

MU Dynamic `to` 0.1

Friction transition velocity `to` 1.5 mm/sec

6) Assigned motion to the Inner race and defined motion using Markers. Markers were defined about the CG.

7) Motion is defined as an expression of 360D*TIME.

8) Before running the simulation it is necessary to change the following simulation settings in order to avoid convergence failures.

Results:

Force reaction

Contact penetration Animation

Session files can be found here

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