Nonlinear rotary spring

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in the palette on the schematic

The block is designed to simulate a nonlinear rotary spring with a constant spring constant.

The deformation of the spring φ in rad is determined by the formula:

where:
  • φ0 – initial spring extension, rad
  • φC and φR – turn angles at the ports "C" and "R", respectively, rad

The dependence of the torque on the turn angle can be defined using a polynomial or a table.

Symmetric polynomial

This method allows you to define the dependence of the torque on the turn angle by a polynomial which is symmetric relative to zero:



where:
  • TC and TR – torques applied to ports "C" and "R", respectively, Nm
  • Bi – i-th element of the vector of spring constants, N·m/rad
  • N – number of elements in the vector of spring constants

Asymmetric polynomial

This method allows you to define the dependence of the torque on the turn angle separately for extension and compression. The polynomial Bp defines the dependence at a positive deformation value (extension) and the polynomial Bn defines the dependence at a negative deformation value (compression):



where:
  • TC and TR – torques applied to ports "C" and "R", respectively, Nm
  • Bpi – i-th element of the vector of spring constants Bp, N·m/rad
  • Bni – i-th element of the vector of spring constants Bn, N·m/rad
  • Np – number of elements in the vector of spring constants Bp
  • Nn – number of elements in the vector of constants Bn

Table

This method makes it possible to calculate the spring torque depending on the turn angle by interpolating a given table. If the deformation value exceeds the specified vector of the deformation values, extrapolation is not carried out.

Inputs

Name Description Connection line type
C Port for connecting a conditionally fixed case (case) Rotary mechanics
R Port for connecting a conditionally moving shaft (rotor) Rotary mechanics

Outputs

None.

Properties

Name Parameter Description By default Data type
Parameterization type par_type Allows you to specify the type of dependence of the torque on the turn angle. The possible values are: "Polynomial", "Table" Polynomial Перечисление
Symmetry sym_type Allows you to define a polynomial that is symmetric with respect to zero. The property is available when you select the "Polynomial" parameterization type. The possible values are: "Yes", "No" Yes Двоичное
Vector of spring constants, Nm/rad B Vector of spring constants. The property is available when the "Polynomial" parameterization type is selected and the "Symmetry" property is enabled [0 , 1 , 0 , 0.1 , 0 , 0.01] Массив
Vector of spring constants for Fi ≥ 0, Nm/rad Bp Vector of spring constants at positive deformation (extension). The property is available when the "Polynomial" parameterization type is selected and the "Symmetry" property is disabled [0 , 1 , 0 , 0.1 , 0 , 0.01] Массив
Vector of spring constants for Fi < 0, Nm/rad Bn Vector of spring constants at negative deformation (compression). The property is available when the "Polynomial" parameterization type is selected and the "Symmetry" property is disabled [0 , 10 , -0.1 , 1] Массив
Vector of deformation values, rad Fx Vector of deformation values. The property is available when you select the "Polynomial" parameterization type. [-1 , -0.5 , -0.3 , -0.1 , 0.1 , 0.3 , 0.5 , 1] Массив
Vector of spring torques, Nm Ty Vector of spring torques. The property is available when you select the "Polynomial" parameterization type. [-10 , -4 , -2 , -0.5 , 0.5 , 2 , 4 , 10] Массив
Initial extension (Fir - Fic), rad Fi0 Initial spring extension at zero angles of rotation at the block ports. A negative value sets the pre-compression 0 Вещественное

Parameters

Name Parameter Description Data type
Spring deformation, rad Fi Spring extension. Negative values mean compression Вещественное
Elastic torque, Nm T Torque transmitted to port "R" Вещественное

Examples

Examples of block application: