The block represents a nonlinear rotational damper. Polynomial
and lookup-table parameterizations define the nonlinear relationship
between damping torque and relative angular velocity. The damping
torque can be symmetric or asymmetric about the zero velocity point.
The block applies equal and opposite damping torques on the two rotational
conserving ports.

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

where:

T — Damping torque

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

ω — Relative angular
velocity between ports R and C,

ω_{R} —
Absolute angular velocity associated with port R

ω_{C} —
Absolute angular 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
torque for both positive and negative relative velocities according
to the expression:

Both polynomial parameterizations use a fifth-order polynomial
expression. To use a lower-order polynomial, set the unneeded higher-order
coefficients to zero. To use a higher-order polynomial, fit to a lower
order polynomial or use the lookup table parameterization.

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

Assumptions and Limitations

Damping is of the viscous type. It depends only on
velocity.

Dialog Box and Parameters

Parameterization

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

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 [1e-4 0 1e-5 0 1e-6].
The default unit is N*m/(rad/s).

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

Vector of positive rotation 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 [1e-4 0 1e-5 0 1e-6].
The default unit is N*m/(rad/s).

Vector of negative rotation damping
coefficients

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

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 torque vector.

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

Torque vector

Enter vector with damping torque 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 [-0.001 -4e-4 -2e-4 -5e-5 5e-5
2e-4 4e-4 0.001]. The unit is N*m.

Interpolation Method

Select method used to find velocity–torque values between
specified 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 between the last two data
points.

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