Variable Translational Spring

Translational spring with variable spring stiffness

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• Simscape / Driveline / Couplings & Drives / Springs & Dampers

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Description

The Variable Translational Spring block represents a translational spring with variable stiffness. A physical signal input port provides the variable spring stiffness. The magnitude of the spring force is equal to the product of the physical signal input and the relative linear displacement between the two translational conserving ports. A minimum spring rate prevents nonphysical values.

The translational spring force satisfies the following expression:

$$F=\{\begin{array}{cc}K\cdot x,& K\ge K_{\min }\\ K_{\min }\cdot x,& K<K_{\min }\end{array}$$

where:

• F is the force transmitted through the spring between the two translational conserving ports.

• K is the spring rate coefficient.

• K_min is the minimum allowed spring rate.

• x is the relative displacement between the two translational conserving ports according to $$x=x_{init}+x_R-x_C$$.

• x_init is the initial spring deformation.

• x_R is the absolute displacement of the translational conserving port R.

• x_C is the absolute displacement of the translational conserving port C.

The block applies equal and opposite spring forces on the two translational conserving ports. The sign of the spring force acting on port R is equal to the sign of the relative linear displacement between the two ports. A positive linear velocity corresponds to a positive spring force acting on port R, and a negative spring force of equal magnitude acting on port C.

Assumptions and Limitations

The block limits the value of the variable spring stiffness to remain above zero.

Variables

Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

Ports

Input

K — Variable spring coefficient, N/m

physical signal

Physical signal input port associated with variable spring stiffness.

Conserving

C — Base port

mechanical translational

Mechanical translational conserving port associated with the negative spring end. The positive direction is from port R to port C.

R — Follower port

mechanical translational

Mechanical translational conserving port associated with the positive spring end. The positive direction is from port R to port C.

Parameters

Minimum spring rate — Spring rate limit value

1 N/m (default) | positive scalar

Minimum value allowed for the spring rate. The physical signal input saturates below the specified value.

Model Examples

Suspension System Comparison

A testbed containing three sets of springs and dampers excited by the same oscillating velocity source. The first uses the Shock Absorber block and includes linear stiffness and damping. Optional friction and hard stops are not used. The second shock absorber uses a Nonlinear Translational Spring and a Nonlinear Translational Damper specified by symmetric polynomials. The third uses a Variable Translational Spring and Variable Translational Damper. The spring constant is varied during the simulation using open loop control and the damping coefficient adjusts to ensure critical damping is achieved. Closed loop control can be added to simulate an adaptive suspension system.

Open Model

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2013a