Translational damper based on polynomial or lookup table parameterizations

Couplings & Drives/Springs & Dampers

The block represents a nonlinear translational damper. Polynomial and lookup table parameterizations define the nonlinear relationship between damping force and relative linear velocity. The damping force can be symmetric or asymmetric about the zero velocity point. The block applies equal and opposite damping forces on the two translational conserving ports.

The symmetric polynomial parameterization defines the damping force for both positive and negative relative velocities according to the expression:

$$F={b}_{1}v+sign(v)\cdot {b}_{2}{v}^{2}+{b}_{3}{v}^{3}+sign(v)\cdot {b}_{4}{v}^{4}+{b}_{5}{v}^{5},$$

where:

*F*— Damping force*b*_{1},*b*_{2}, ...,*b*_{5}— Damping coefficients*v*— Relative linear velocity between ports R and C, $$v={v}_{R}-{v}_{C}$$*v*_{R}— Absolute linear velocity associated with port R*v*_{C}— Absolute linear velocity associated with port C

Using an odd polynomial (*b*_{2},*b*_{4} =
0), eliminates the sign function from the polynomial
expression, avoiding zero-crossings that slow down simulation.

The two-sided polynomial parameterization defines the damping force for both positive and negative relative velocities according to the expression:

$$F=\{\begin{array}{cc}{b}_{1e}v+{b}_{2e}{v}^{2}+{b}_{3e}{v}^{3}+{b}_{4e}{v}^{4}+{b}_{5e}{v}^{5},& v\ge 0\\ {b}_{1c}v-{b}_{2c}{v}^{2}+{b}_{3c}{v}^{3}-{b}_{4c}{v}^{4}+{b}_{5c}{v}^{5},& v<0\end{array},$$

where:

*b*_{1e},*b*_{2e}, ...,*b*_{5e}— Damping coefficients for positive relative velocities*b*_{1c},*b*_{2c}, ...,*b*_{5c}— Damping coefficients for negative relative velocities

Positive relative velocities correspond to damper extension (ports R and C moving away from each other). Negative relative velocities correspond to damper contraction (ports R and C moving towards each other).

Both polynomial parameterizations use a fifth-order polynomial expression. To use a lower-order polynomial, set the unneeded higher-order coefficients to zero. For polynomials of order greater than five, fit to a polynomial of order smaller than or equal to five, or use the lookup table parameterization.

The lookup table parameterization defines damping force based on a set of velocity and force vectors. If not included in the vectors, the block automatically adds a data point at the origin (zero velocity and zero force).

The block assumes viscous damping. The damping force depends only on velocity.

**Parameterization**Select damping parameterization. Options are

`By polynomial`

and`By lookup table`

.

Port | Description |
---|---|

C | Rotational conserving port |

R | Rotational conserving port |

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