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Contact analysis is very important in Multibody Dynamics.

Most of the mechanical systems include contact. In CAE, the contact algorithm occupies most of the calculations and affects the accuracy of the simulation. So it is very important to understand the basics of the contact algorithm and contact parameters.

Penalty Method is one of the most common contact algorithms and RecurDyn contact is based on this. (Even if the contact algorithm of CAE software is based on the Penalty Method, since the contact algorithm includes many other algorithms, the performance or the accuracy can vary greatly)

The important characteristic of Penalty Method is that it uses overlap to calculate the contact force.

Many RecurDyn beginners use RecurDyn contact without knowing this. But if you understand this basic algorithm, it will be very helpful in using RecurDyn contact and setting contact parameters.

Let's use the below bodies which contact each other as an example.

In reality, the bodies are not overlapped. But Penalty Method assumes that they can be overlapped and use the overlap to calculate the contact force as below.

And the amount of the overlap is called, 'penetration' or 'penetration depth'.

This is the important part.

(The explanation here is to help your understanding. So please refer to the papers about the accurate explanation or theoretical description about Penalty Method.)

Penetration

Penalty Method calculates the contact force as if there is a spring between the 'overlapped area' and the spring is compressed by the penetration. In other words, if the penetration is δ, the contact force f is calculated by f = kδ. (K is one of the contact parameters, Stiffness Coefficient.)

The accurate contact force formula is as below, but conceptually, just remember f = kδ.

(the explanation about each variable is omitted here.)

So, Stiffness/Damping Coefficient in the contact parameter dialog is conceptually the same as Stiffness/Damping Coefficient in the spring force dialog.

Examples

In the example below, the penetration increases until the external force and the contact force (f = kδ) reach equilibrium (To make it simple, Unit was ignored here.)

In case #1, the weight of the upper box applies force 30 but there is no contact force because δ=0. So the upper box moves downward.

In case #2 , There is penetration, δ=1. So contact force occurs, but since 30 > 10, the box still moves downward.

In case #3, Since   30 > 20, so the box still moves downward.

In case #4,   finally the force equilibrium is achieved. ( 30 = 30) (Here, to help your understanding, it was explained as if δ is quite big. But in reality, δ is very small.)

Since f = kδ, if you set K (stiffness coefficient) too small, δ must be very big to achieve the force equilibrium. In fact, penetration (δ) is an artificial value so very small δ is reasonable. Therefore, it is good to use big enough value for K. (For your information, the default K of RecurDyn Geo Surface Contact and Solid Contact is 100,000 N/mm.)

In the example below, a box whose mass is 1Kg is put on a bigger box. In this case, the contact force is calculated as 10N (gravitational acceleration is regarded as 10m/s^2) and the penetration is 0.0001 mm when K = 100,000 N/mm.

If K is too big, since f = kδ, small change of the penetration (δ) affects the magnitude of the contact force drastically. If the force changes a lot, it can make the solver unstable. Therefore, it is very important to use the appropriate K values under different situations. (If K is too small, too big penetration occurs and the result becomes inaccurate. But if K is too big, the affects the solver stability.)

So you need to tune K carefully. (Usually, when tuning K, use x10, x100 or x0.1,  x0.01)

This article is continued in  RecurDyn Contact - Becoming an Experienced User, 5th Episode: Basics of the contact algorithm #2 .

If you want to know more about RecurDyn Contact, please refer to the below articles

• RecurDyn Contact - Becoming an Experienced User, 1st Episode: 2D / 3D Contact Objects
• RecurDyn Contact - Becoming an Experienced User, 2nd Episode: Solid / Geo Contact Objects
  
• RecurDyn Contact - Becoming an Experienced User, 3rd Episode: Primitive 3D Contact Objects
• RecurDyn Contact - Becoming an Experienced User, 4th Episode: Basics of the contact algorithm
• RecurDyn Contact - Becoming an Experienced User, 5th Episode: Basics of the contact algorithm #2
  
• [Webinar] Easy guide to understand RecurDyn Contact