Nonlinear Rotational Damper

Nonlinear damper in mechanical rotational systems.

blockType: Engee1DMechanical.Elements.Rotational.NonlinearDamper

Path in the library:

/Physical Modeling/1D Mechanical/Couplings & Drives/Springs & Dampers/Nonlinear Rotational Damper

Description

Block Nonlinear Rotational Damper It is a nonlinear rotational damper. The polynomial and tabular parameterizations determine the nonlinear relationship between the torque and the relative angular velocity. The torque can be symmetrical or asymmetrical relative to the zero velocity point. The unit applies equal opposite torques to two non-directional ports.

The symmetric polynomial parameterization determines the torque for positive and negative relative angular velocities according to the expression:

where

— the torque transmitted through the damper;
— damping coefficients;
— relative angular velocity between ports R and C:

where
- — absolute angular velocity of the port R;
- — the absolute angular velocity of the port C.

To avoid zero crossings that slow down the simulation, eliminate the sign function from the polynomial expression by specifying an odd polynomial ( ).

The two-way polynomial parameterization determines the torque for positive and negative relative velocities according to the expression:

where

— damping coefficients for positive relative speeds;
— damping coefficients for negative relative speeds.

Both polynomial parameterizations use a fifth-order polynomial. To use a lower-order polynomial, set the higher-order coefficients to zero. For polynomials of order greater than five, perform an approximation with a polynomial of order no higher than the fifth, or use parameterization based on tabular data.

Parameterization according to the search table determines the damping torque based on the specified angular velocity and torque vectors. If a point with zero angular velocity and zero moment is not included in the specified vectors, the block automatically adds it as a data point at the origin.

Assumptions and limitations

Viscous damping is assumed in this block. The torque depends only on the angular velocity.

Ports

Conserving

# R — stock
rotational mechanics

Details

Mechanical rotary port, corresponds to the damper rod.

Program usage name

rod_flange

# C — body
rotational mechanics

Details

Mechanical rotary port, corresponds to the damper body.

Program usage name

case_flange

Parameters

# Parameterization — parameterization of damping
By polynomial | By table lookup

Details

Choose the type of torque parameterization: a polynomial or a search table.

Values	`By polynomial` \| `By table lookup`
Default value	`By polynomial`
Program usage name	`parameterization`
Evaluatable	Yes

# Symmetry — symmetry of damping

Details

Select this option to use symmetric parameterization. If the box is not checked, the block uses two-way parameterization.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By polynomial.

Default value	`true (switched on)`
Program usage name	`symmetric_parameterization`
Evaluatable	Yes

# Vector of damping coefficients — damping coefficients for parameterization by a polynomial
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Damping coefficients for symmetric parametrization by a polynomial.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By polynomial and check the box Symmetry.

Units	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`[0.0001, 0.0, 1.0e-5, 0.0, 1.0e-6] N*m/(rad/s)`
Program usage name	`damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Vector of positive rotation damping coefficients — damping coefficients for positive angular velocities
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Damping coefficients for positive angular velocities.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By polynomial and uncheck the box Symmetry.

Units	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`[0.0001, 0.0, 1.0e-5, 0.0, 1.0e-6] N*m/(rad/s)`
Program usage name	`positive_damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Vector of negative rotation damping coefficients — damping coefficients for negative angular velocities
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Damping coefficients for negative angular velocities

Dependencies

To use this parameter, set for the parameter Parameterization meaning By polynomial and uncheck the box Symmetry.

Units	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`[0.001, -1.0e-5, 0.0001, 0.0, 0.0] N*m/(rad/s)`
Program usage name	`negative_damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Angular velocity vector — vector of angular velocities for tabular parameterization
rpm | deg/s | rad/s

Details

The vector of angular velocities. The minimum number of vector elements depends on the chosen interpolation method. If for the parameter Interpolation method the value is set:

Linear, then the minimum number of elements of the vector is two.
Smooth, then the minimum number of elements of the vector is three.

The elements of the vector must correspond to the elements of the vector Torque vector.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By table lookup.

Units	`rpm` \| `deg/s` \| `rad/s`
Default value	`[-1.0, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 1.0] rad/s`
Program usage name	`delta_w_vector`
Evaluatable	Yes

# Torque vector — The torque
N*m | mN*m | lbf*ft

Details

Damping torque for a given angular velocity. The minimum number of vector elements depends on the chosen interpolation method. If for the parameter Interpolation method the value is set:

Linear, then the minimum number of elements of the vector is two.
Smooth, then the minimum number of elements of the vector is three.

The elements of the vector must correspond to the elements of the vector Angular velocity vector.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By table lookup.

Units	`Nm` \| `mNm` \| `lbf*ft`
Default value	`[-0.0001, -4.0e-5, -2.0e-5, -5.0e-6, 5.0e-6, 2.0e-5, 4.0e-5, 0.0001] N*m`
Program usage name	`T_vector`
Evaluatable	Yes

# Interpolation method — the method of interpolation between the values of the reference points
Linear | Smooth

Details

The method used to interpolate between the reference points of the search table:

Linear — choose this value for the lowest computational cost;
Smooth — select this value to get a continuous curve with continuous first-order derivatives.

For more information about the search tables, see Methods for approximating function values.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By table lookup.

Values	`Linear` \| `Smooth`
Default value	`Linear`
Program usage name	`interpolation_method`
Evaluatable	Yes

# Extrapolation method — extrapolation method for points outside the range specified by the reference points
Linear | Nearest | Error

Details

The method used to extrapolate breakpoints in the search table. This method determines the output value when the input value is outside the range specified in the argument list.:

Linear — select this value to obtain a curve with continuous first-order derivatives in the extrapolation region and on the boundary with the interpolation region.
Nearest — Select this value to use an extrapolation that does not rise above the largest value in the data or fall below the smallest value in the data.
Error — select this value to avoid extrapolation when you want the data to be within the range of the table. If the input signal is outside the range of the table, the simulation stops and outputs an error.

Dependencies

To use this parameter, set for the parameter Parameterization meaning By table lookup.

Values	`Linear` \| `Nearest` \| `Error`
Default value	`Linear`
Program usage name	`extrapolation_method`
Evaluatable	Yes