TRANSLATOR

Description

Connection type TRANSLATOR.

Connection type TRANSLATOR imposes kinematic constraints and uses local orientation definitions equivalent to combining connection types SLOT and ALIGN.

The connector constraint forces and moments reported as connector output depend strongly on the order and location of the nodes in the connector (see Connector Behavior). Since the kinematic constraints are enforced at node b (the second node of the connector element), the reported forces and moments are the constraint forces and moments applied at node b to enforce the TRANSLATOR constraint. Thus, in most cases the connector output associated with a TRANSLATOR connection is best interpreted when node b is located at the center of the device enforcing the constraint. This choice is essential when moment-based friction is modeled in the connector since the contact forces are derived from the connector forces and moments, as illustrated below. Proper enforcement of the kinematic constraints is independent of the order or location of the nodes.

Friction

Predefined Coulomb-like friction in the TRANSLATOR connection relates the kinematic constraint forces and moments in the connector to the friction force (CSF1) in the translation along the slot.

The frictional effect is formally written as

where the potential $\mathrm{P}\left(\mathbf{f}\right)$ represents the magnitude of the frictional tangential traction in the connector in the local 1-direction, ${\mathrm{F}}_{\mathrm{N}}$ is the friction-producing normal (contact) force in the direction normal to the slot, and $\mu$ is the friction coefficient. Frictional stick occurs if $\mathrm{\Phi }<0$; and sliding occurs if $\mathrm{\Phi }=0$, in which case the friction force is $\mu {\mathrm{F}}_{\mathrm{N}}$.

The normal force ${\mathrm{F}}_{\mathrm{N}}$ is the sum of a magnitude measure of contact friction-producing connector forces, ${\mathrm{F}}_{\mathrm{C}}=g\left(\mathbf{f}\right)$, and a self-equilibrated internal contact force, ${\mathrm{F}}_{\mathrm{C}}^{\mathrm{int}}$:

The contact force magnitude ${\mathrm{F}}_{\mathrm{C}}$ is defined by summing the following three contributions:

• a force contribution from torque, $F_{torq}$, obtained by scaling the torque constraint moment about the 1-direction, $M_{torq}$, by a length factor, as follows:

  $$M_{torq}=\left|m_1\right|,$$
  $$F_{torq}=\frac{M_{torq}}{R_r},$$

  where $R_r$ represents the effective radius of the shaft cross-section in the local 2–3 plane (if $R_r$ is 0.0, $M_{torq}$ is ignored);

• a radial force contribution, $F_r$ (the magnitude of the constraint forces enforcing the SLOT constraint):

  $$F_r=\sqrt{f_2{}^2+f_3{}^2};$$

  and

• a force contribution from “bending,” $F_{bend}$, obtained by scaling the bending constraint moment, $M_{bend}$, by a length factor, as follows:

  $$M_{bend}=\sqrt{m_2{}^2+m_3{}^2},$$
  $$F_{bend}=2\frac{M_{bend}}{L},$$

  where L represents a characteristic overlapping length in the slot direction. If L is 0.0, $M_{bend}$ is ignored.

Thus,

where $\beta =\frac{2}{L}$.

The magnitude of the frictional tangential tractions, $\mathrm{P}\left(\mathbf{f}\right),$ is $\left|f_1\right|$.

Summary