Engee documentation

Nonlinear Translational Damper

Nonlinear damper in mechanical translational systems.

blockType: Engee1DMechanical.Elements.Translational.NonlinearDamper

nonlinear translational damper

Path in the library:

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

Description

Block Nonlinear Translational Damper It is a translational nonlinear damper. The polynomial and tabular parameterizations determine the nonlinear relationship between the damping force and the relative velocity of translational motion. The damping force can be symmetrical or asymmetrical relative to the zero velocity point. The unit applies equal opposite damping forces to two non-directional ports.

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

where

  • — damping force;

  • — damping coefficients;

  • — relative translational velocity between ports R and C:

    where

    • — the absolute speed of translational movement of the port R;

    • — the absolute forward 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 damping force for positive and negative relative velocities according to the expression:

where

  • — damping coefficients for positive relative speeds;

  • — damping coefficients for negative relative speeds.

The positive relative speeds correspond to the stretching of the damper when ports R and C move away from each other. The negative relative speeds correspond to the compression of the damper when ports R and C come closer.

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 based on tabular data determines the damping force based on the specified velocity and force vectors. If a point with zero velocity and zero force 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 damping force depends only on the speed.

Ports

Conserving

# R — stem
translational mechanics

Details

Mechanical progressive port, corresponds to the damper rod.

Program usage name

rod_flange

# C — hull
translational mechanics

Details

Mechanical progressive port, corresponds to the damper housing.

Program usage name

case_flange

Parameters

Parameters

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

Details

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

Values

By polynomial | By table lookup
Default value

By polynomial
Program usage name

parameterization
Evaluatable

No

# 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

No

# Vector of damping coefficients — coefficients of polynomial damping
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

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

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

[10.0, 0.0, 1.0, 0.0, 0.1] N*s/m
Program usage name

damping_polinomial_coefficients_vector
Evaluatable

Yes

# Vector of extension damping coefficients — coefficients of polynomial damping under tension
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Coefficients of tension damping.

Dependencies

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

Units

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

[10.0, 0.0, 1.0, 0.0, 0.1] N*s/m
Program usage name

extension_damping_polinomial_coefficients_vector
Evaluatable

Yes

# Vector of contraction damping coefficients — coefficients of polynomial damping during compression
N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in

Details

Compression damping coefficients.

Dependencies

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

Units

N*s/m | kgf*s/m | lbf*s/ft | lbf*s/in
Default value

[100.0, -1.0, 10.0, 0.0, 0.0] N*s/m
Program usage name

contraction_damping_polinomial_coefficients_vector
Evaluatable

Yes

# Velocity vector — velocity vector for tabular parameterization
m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn

Details

Vector of translational motion 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 Force vector.

Dependencies

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

Units

m/s | mm/s | cm/s | km/s | m/hr | km/hr | in/s | ft/s | mi/s | ft/min | mi/hr | kn
Default value

[-1.0, -0.5, -0.3, -0.1, 0.1, 0.3, 0.5, 1.0] m/s
Program usage name

delta_v_vector
Evaluatable

Yes

# Force vector — damping force for tabular parameterization
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

Details

Damping force for a given translational 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 Velocity vector.

Dependencies

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

Units

N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf
Default value

[-100.0, -40.0, -20.0, -5.0, 5.0, 20.0, 40.0, 100.0] N
Program usage name

F_vector
Evaluatable

Yes

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

Details

The method used for interpolation between data table reference points:

  • 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_type
Evaluatable

No

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

Details

The method used to extrapolate the reference points in the data 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_type
Evaluatable

No