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:

where:

F — Damping force

b_{1}, b_{2},
..., b_{5} — Damping
coefficients

v — Relative linear velocity
between ports R and 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:

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).

Assumptions and Limitations

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

Dialog Box and Parameters

Parameterization

Select damping parameterization. Options are By
polynomial and By lookup table.

Specify coefficients of polynomial damping function.

Symmetry

Choose between symmetric and two-sided polynomial parameterizations.

Symmetric — Specify
a single set of polynomial coefficients governing damping for both
positive and negative relative velocities.

Vector of damping coefficients

Enter five-element vector with polynomial damping coefficients.
Physical units are for the first coefficient.

The default vector is [10 0 1 0 0.1].
The default unit is N/(m/s).

Two-sided — Specify
two sets of polynomial coefficients governing damping, one for positive
relative velocities, the other for negative relative velocities.

Vector of extension damping coefficients

Enter five-element vector with polynomial damping coefficients
for positive relative velocities. Physical units are for the first
coefficient.

The default vector is [10 0 1 0 0.1].
The default unit is N/(m/s).

Vector of contraction damping coefficients

Enter five-element vector with polynomial damping coefficients
for negative relative velocities. Physical units are for the first
coefficient.

The default vector is [10 0 1 0 0.1].
The default unit is N/(m/s).

Enter vector with relative velocity values. The vector requires
a minimum number of elements, based on the selected interpolation
method — two for Linear, and three
for Cubic or Spline.
The number of elements must match the force vector.

The default vector is [-1 -0.5 -0.3 -0.1 0.1 0.3 0.5
1]. The default unit is m/s.

Force vector

Enter vector with damping force values corresponding to velocity
vector. The vector requires a minimum number of elements, based on
the selected interpolation method — two for Linear,
three for Cubic or Spline.
The number of elements must match the velocity vector.

The default vector is [-100 -40 -20 -5 5 20 40 100].
The default unit is N.

Interpolation Method

Select method used to find intermediate velocity–force
values between lookup-table data points.

Linear — Interpolate
between two points using a first-order polynomial function.

Cubic — Interpolate
between two points using a third-order polynomial function.

Spline — Interpolate
between two points using a piecewise polynomial function.

Extrapolation Method

Select method used to calculate values outside the lookup-table
data range.

From last two points —
Extrapolate by extending the straight line connecting the last two
lookup-table data points.

From last point —
Extrapolate by extending the horizontal straight light passing through
the last lookup-table data point.