Nonlinear Translational Damper

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Nonlinear damping in mechanical translational systems.

blockType: Engee1DMechanical.Elements.Translational.NonlinearDamper

Path in the library:

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

Description

The block Nonlinear Translational Damper is a progressive nonlinear dampener. Polynomial and tabular parameterizations define the non-linear relationship between the damping force and the relative velocity of the translational motion. The damping force can be symmetrical or asymmetrical with respect to the zero velocity point. The unit applies equal opposite damping forces to the two non-directional ports.

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

where

- damping force;
- damping coefficients;
- relative velocity of translational motion between ports R and C:

where
- - is the absolute velocity of translational motion of the port R;
- - is the absolute velocity of translational motion of the port C.

To avoid zero crossings that slow down the simulation, exclude 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

- are damping coefficients for positive relative velocities;
- damping coefficients for negative relative velocities.

Positive relative velocities correspond to damper stretching when the R and C ports move away from each other. Negative relative velocities correspond to damper compression when the R and C ports move closer together.

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, approximate with a polynomial of order no higher than five, or use parameterization from tabular data.

The tabular parameterization determines the damping force based on the given 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 velocity.

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

Main

# Parameterization — damping parameterization
By polynomial | By table lookup

Details

Select the type of damping force parameterization: polynomial or look-up table.

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

# Symmetry — damping symmetry

Details

Select this check box to use symmetrical parameterization. If the check box is not selected, the block uses bilateral parameterization.

Dependencies

To use this parameter, set the parameters Parameterization to . By polynomial.

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

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

Details

Damping coefficients for symmetric polynomial parameterization.

Dependencies

To use this parameter, set the parameters Parameterization to . By polynomial and select the check box Symmetry.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`[10.0, 0.0, 1.0, 0.0, 0.1] N/(m/s)`
Program usage name	`damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Vector of extension damping coefficients — polynomial tensile damping coefficients
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Tensile damping coefficients.

Dependencies

To use this parameter, set the Parameterization parameters to . By polynomial and uncheck Symmetry.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`[10.0, 0.0, 1.0, 0.0, 0.1] N/(m/s)`
Program usage name	`extension_damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Vector of contraction damping coefficients — polynomial compression damping coefficients
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Compression damping coefficients.

Dependencies

To use this parameter, set the Parameterization parameters to the value of By polynomial and uncheck Symmetry.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`[100.0, -1.0, 10.0, 0.0, 0.0] N/(m/s)`
Program usage name	`contraction_damping_polinomial_coefficients_vector`
Evaluatable	Yes

# Velocity vector — velocity vector for tabular parameterization
fpm | fps | kph | mph | m/s | cm/s | ft/s | in/s | km/s | mi/s | mm/s

Details

The velocity vector for translational motion. The minimum number of elements of the vector depends on the selected interpolation method. If the parameter Interpolation method is set to:

Linear, then the minimum number of vector elements is two.
`Smooth`If the parameter is set to: , 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 the Parameterization parameters to By table lookup.

Units	`fpm` \| `fps` \| `kph` \| `mph` \| `m/s` \| `cm/s` \| `ft/s` \| `in/s` \| `km/s` \| `mi/s` \| `mm/s`
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 | kN | lb | mN | dyn | lbf

Details

Damping force for a given translational velocity. The minimum number of vector elements depends on the selected interpolation method. If the parameter Interpolation method is set to:

Linear, then the minimum number of vector elements is two.
`Smooth`If the parameter is set to: , 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 the Parameterization parameters to By table lookup.

Units	`N` \| `kN` \| `lb` \| `mN` \| `dyn` \| `lbf`
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 — method of interpolation between the values of reference points
Linear | Smooth

Details

A method used to interpolate between the anchor points of a data table:

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

For more information on lookup tables, see Methods of approximation of function values.

Dependencies

To use this parameter, set the Parameterization parameters to . 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 defined by the reference points
Linear | Nearest | Error

Details

A method used to extrapolate reference points in a data table. This method determines the output value when the input value falls 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 at the boundary with the interpolation region.
Nearest - select this value to use 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 table range, the simulation stops and displays an error.

Dependencies

To use this parameter, set the Parameterization parameters to By table lookup.

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