Cam-Follower Connection Force Computation
The cam-follower connection constraints can be imposed in several forms:
•
Pointwise constraint
•
Weak constraint
•
Penalty method
The connection constraint enforces a continuous contact between the cam and follower; however, in order to find out whether the follower actually remains continuously in contact with the cam, the connection force can be computed. A negative value of the connection force throughout the rotation of cam indicates the continuous contact between the cam and follower.
The pointwise constraint is the default form of the cam-follower connection constraints. In this form of constraint, the reaction forces representing the connection forces are not computed. In order to find connection forces, weak constraints or a penalty method can be used.
Using Weak Constraints
When using weak constraints, the connection constraints are applied in a weak form, and the values of the Lagrange multipliers give the connection forces (
F
w
). The use of Lagrange multipliers can, however, have an effect on the structure of the equation system, which limits the solvers that can be used.
Using Penalty Formulation
When using penalty method, the connection constraints are applied using penalty formulation, and the values of the penalty forces (
F
p
) give the connection forces.
Since the value of penalty factor directly affects the connection constraints, it should be chosen judiciously. The penalty factor value should be large enough to ensure that the connection constraints are not violated beyond a permissible limit. At the same time the penalty factor should not be too high, because that will make the system of equations numerically ill-conditioned.
The penalty forces (
F
p
) are computed as
where
p
c
is the penalty factor input having a default value,
0.1
dE
equ
. In this expression,
E
equ
is an effective Young’s modulus, and
d
is the geometric diagonal of the bounding box of the geometry.
