SimDriveline™

Hard Stop - Model restriction on relative angular motion of two driveline axes to free gap with elastic upper and lower limits

Library

Dynamic Elements

Description

The Hard Stop block simulates a two-position rotational stop that restricts the relative angular displacement θ of the two connected driveline axes.

If the relative displacement falls in the gap between the stop's upper and lower limits, the stop applies no torque.
If the relative displacement becomes greater than the upper limit θ₊ or smaller than the lower limit θ_-, the stop applies a torque.

At each limit, the stop imposes a one-sided damped, linear torsional torque limiting the motion of θ.

The relative angular displacement is the difference of the follower and base driveline axis angles, θ = θ_F – θ_B, and the relative angular velocity ω = dθ/dt = ω_F – ω_B. If the angular displacement reaches beyond one of the stop limits, the torque applied is a sum of restoring and damping terms,

τ = –k·(θ – θ_±) – bω

where k is the contact stiffness, b the contact damping, and θ_± is the upper limit θ₊ or the lower limit θ_-. Both constants k and b must be nonnegative. The restoring torque depends only on the deformation angle θ – θ_±, measuring how far the displacement has penetrated beyond the upper or lower limit.

Relationship to Restitution

A restitution description of impact specifies the ratio of postimpact and preimpact velocities.

The effective inertias attached to the base and follower axes are I_B and I_F, respectively. The reduced inertia for the relative motion is

I = I_BI_F/( I_B + I_F)

Let the relative motion begin penetration of a one-sided stop limit at time t_i and complete its bounce at time t_f. The damped, linear springy torque reduces the final angular velocity, compared to the initial, by the ratio

Using Dynamic Element Blocks

Use the blocks of the Dynamic Elements library as a starting point for vehicle modeling. To see how a Dynamic Element block models a driveline component, look under the block mask. The blocks of this library serve as suggestions for developing variant or entirely new models to simulate the same components. Break the block's library link before modifying it and creating your own version.

Dialog Box and Parameters

Relative displacement upper limit: The largest relative displacement angle, in radians (rad), for which the stop does not apply a torque, measured relative to the initial relative angle. Must be larger than the relative displacement lower limit. The default is 0.15.
Relative displacement lower limit: The smallest relative displacement angle, in radians (rad), for which the stop does not apply a torque, measured relative to the initial relative angle. Must be smaller than the relative displacement upper limit. The default is -0.1.
Contact stiffness: The linear contact stiffness constant k, in newton-meters/radian (N·m/rad). Must be nonnegative. The default is 1e6.
Contact damping: The linear damping torque constant b, in newton-meter-seconds/radian (N·m·s/rad). Must be nonnegative. The default is 100.

Examples

The demo model drive_hard_stop simulates angular motion limited by a hard stop.