18. Time-Variation Functions#

Defines time-variation functions used by other settings.

Time-variation functions define currents and voltages in external electrical circuits. They also define the magnetization of permanent magnets, MAGNET(17.7), and the displacement of translational or rotational motion.

Settings#

18_Time_Function(18) JSON key: time-variation function object

TIME_ID(18) Source-term identifier

OPTION(18) Option that specifies how the time variation is defined

解析式(18.1)

C0/C1/C2/C3/C4/C5/C6 TEXP TCYCLE PHASE4(18.1) Parameters of the analytical expression for the time variation

時間テーブル(18.2) Parameters of the time table for the time variation

NO_TIME_POINTS(18.2) Number of time points

CYCLE(18.2) Repetition period (sec)

TIME(18.2) Time (sec)

VALUE(18.2) Value

交流表示(18.3) Parameters for the AC waveform

AMPLITUDE(18.3) Amplitude

TCYCLE(18.3) Period (sec)

PHASE(18.3) Phase (deg)

PSIM，MATLAB/Simulink 連成解析(18.4) Parameters for PSIM and MATLAB/Simulink input/output data

PSIM_IN(18.4) Input number for the voltage from PSIM

PSIM_OUT(18.4) Output number for the current to PSIM

数式入力(18.5) Formula input for the time-variation function f(t)

MATH_EQ(18.5) Input for the time-variation function f(t)

運動方程式入力(18.6) Parameters of the equation of motion

INITIAL_POSITION(18.6) Initial relative position from the reference position (m[deg])

INITIAL_VELOCITY(18.6) Initial velocity (m/sec[deg/sec])

POSITION_ERROR(18.6) Position calculation tolerance (m[deg])

LOWER_LIMIT(18.6) Lower displacement limit (m[deg])

UPPER_LIMIT(18.6) Upper displacement limit (m[deg])

LOWER_REFLECTION(18.6) Reflection coefficient at the lower displacement limit

UPPER_REFLECTION(18.6) Reflection coefficient at the upper displacement limit

MASS(18.6) Mass (kg) [moment of inertia (kg·m²)]

CONST_FORCE(18.6) External force independent of position and velocity (N) [torque (Nm)]

STATIC_FRICTION(18.6) Static friction force (N [Nm])

TIME_CONST_FORCE(18.6) Data number for the time-varying external force

MASS_ACCELERATION(18.6) Acceleration applied to the mass (m/s² [deg/s²])

CONST_DISPLACEMENT(18.6) Displacement per step (m[deg])

POSITION_DEPEND_MASS(18.6) Position-dependent mass

NO_SPRING(18.6) Number of spring definitions

NO_DAMPER(18.6) Number of damper definitions

MATH_EQ(18.6) Formula input for the applied force as a function of position and velocity

SPRING(18.6.1) Parameters of the spring definition

SPRING_TYPE(18.6.1) Spring definition type

LOWER_RANGE(18.6.1) Lower bound of the definition range (m[deg])

UPPER_RANGE(18.6.1) Upper bound of the definition range (m[deg])

SPRING_CONST(18.6.1) Spring constant (N/m [Nm/deg])

EQUIL_POSITION(18.6.1) Spring equilibrium position (m[deg])

POSITION(18.6.1) Relative position from the reference position (m[deg])

FORCE(18.6.1) Spring force at the position (N [torque (Nm)])

DAMPER(18.6.2) Parameters of the damper definition

DAMPER_TYPE(18.6.2) Damper definition type

C0(18.6.2) Kinetic friction force (N [Nm])

C1(18.6.2) Viscous coefficient (N/(m/sec) [Nm/(deg/sec)])

C2(18.6.2) Coefficient of the squared-velocity force (N/(m²/sec) [Nm/(deg²/sec)])

C3(18.6.2) Coefficient of the cubed-velocity force (N/(m³/sec) [Nm/(deg³/sec)])

VELOCITY(18.6.2) Velocity (m/sec [deg/sec])

MATH_EQ(18.6.3) Formula-input parameters

電磁力積算領域(18.6.4) Parameters of the electromagnetic-force integration region

MOTION_TYPE(18.6.4) Motion type

REGION_FACTOR(18.6.4) Ratio to the analysis region of the full model

NO_MAT_IDS(18.6.4) Number of material IDs in the nodal-force summation region

MAT_IDS(18.6.4) Material IDs in the nodal-force summation region

FORCE_TYPE(18.6.4) Type of electromagnetic force considered during motion

Input format#

Text-format section

Type:

Fixed parameter set 1

Number of rows:

2

Number of parameters:

1, 2

Text format#

* NO_DATA *
    I
* TIME_ID *     OPTION  *
    I         I

JSON format#

JSON format from 2024.11#

"18_Time_Function": [
    {
        "TIME_ID": I,
        "OPTION": I,
        "comment": "set time functions from here"
    }
]

Detailed description#

18_Time_Function(18)#

Sets a time-variation function. A time-variation function defines the time variation of a source term, 17_Field_Source(17) or SOURCE(17).

Text-format section

NO_DATA(18)#

NO_DATA (text)

Fixed parameter set 1#

[row, col] = [1, 1]
Type=I

Number of time-variation data items.

TIME_ID#

TIME_ID(18)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Integer (I)
Description:: Source-term identifier. TIME_ID(18)

OPTION#

OPTION(18)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 2]

Type:: Integer (I)
Value:: 0, 1, 2, 3, 4, 11
Description:: Option that specifies how the time variation is defined

=0: analytical expression
=1: time table
=2: AC waveform
=3: solve the equation of motion to obtain the time variation
=4: PSIM, MATLAB/Simulink co-simulation
=11: enter the time variation of the function as a formula (Appendix 1).

Caution

For AC steady-state analysis, only OPTION =2 is supported.
The <DYNAMIC module> is required when the equation of motion is solved to obtain the time variation.
The <PSIM Coupler module> and <MATLAB/Simulink Coupler module> are required for PSIM or MATLAB/Simulink co-simulation.

18.1. Analytical expression#

解析式(18.1)#

Required when OPTION =0.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

2

Number of parameters:

6, 3

Text format#

* C0 * C1 * C2 * C3 * C4 * C5 * C6 *
   E    E   E    E    E    E    E
*  TEXP  *  TCYCLE      *    PHASE4   *
    E      E        E

JSON format from 2024.11#

        {
            "TIME_ID" : I,
            "OPTION" : 0,
            "C0" : E,
            "C1" : E
            "C2" : E,
            "C3" : E,
            "C4" : E,
            "C5" : E,
            "C6" : E,
            "TEXP" : E,
            "TCYCLE" : E,
            "PHASE4" : E
        }

C0/C1/C2/C3/C4/C5/C6 TEXP TCYCLE PHASE4#

C0/C1/C2/C3/C4/C5/C6 TEXP TCYCLE PHASE4(18.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1~6]

[row, col] = [2, 1~3]

Type:

Real number (E)

Description:

Parameters of the analytical expression for the time variation

The time variation is given by the following equation.

\[\begin{split}\begin{aligned} f(t) &= C_{0} \\ &\;+\; C_{1}\,t \\ &\;+\; C_{2}\,\exp\bigl(-t/T_{\mathrm{EXP}}\bigr) \\ &\;+\; C_{3}\,\sin\!\bigl(2\pi t/T_{\mathrm{CYCLE}}\bigr) \\ &\;+\; C_{4}\,\cos\!\Bigl(2\pi t/T_{\mathrm{CYCLE}} + \tfrac{\mathrm{PHASE4}\,\pi}{180}\Bigr) \\ &\;+\; C_{5}\,\exp\bigl(-t/T_{\mathrm{EXP}}\bigr)\, \sin\!\bigl(2\pi t/T_{\mathrm{CYCLE}}\bigr) \\ &\;+\; C_{6}\,\exp\bigl(-t/T_{\mathrm{EXP}}\bigr)\, \cos\!\bigl(2\pi t/T_{\mathrm{CYCLE}}\bigr) \end{aligned}\end{split}\]

The units are \(/sec\) for \(C_1\), \(sec\) for \(T_{\mathrm{EXP}}\) and \(T_{\mathrm{CYCLE}}\), and \(deg\) for \(\mathrm{PHASE4}\).

18.2. Time table#

時間テーブル(18.2)#

Required when OPTION =1.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1 + NO_TIME_POINTS

Number of parameters:

2, 2

Text format#

* NO_TIME_POINTS * CYCLE *
    I      E
*   TIME   *   VALUE    *
    E      E

JSON format from 2024.11#

        {
            "TIME_ID": I,
            "OPTION" : 1,
            "CYCLE" : E,
            "TIME" : [ E ],
            "VALUE" : [ E ]
        }

Text-format section

NO_TIME_POINTS(18.2)#

NO_TIME_POINTS (text)

Fixed parameter set 1#

[row, col] = [1, 1]
Type=I

Number of time points

CYCLE(18.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 2]

Type:: Real number (E)
Value:: 0, >0
Unit:: sec
Description:: Repetition period (sec)

If =0, CYCLE is ignored.
If >0, CYCLE specifies the repetition period (sec).

TIME#

TIME(18.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

NO_TIME_POINTS 組入力。

Type:: Real number (E)
Unit:: sec
Description:: Time. In JSON format, specify this as an array.

VALUE#

VALUE(18.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 2]

NO_TIME_POINTS 組入力。

Type:: Real number (E)
Description:: Value. In JSON format, specify this as an array.

Note

When CYCLE is specified, enter a time table from TIME =0 to TIME = CYCLE.

When this time table represents a voltage, a step change can be specified by assigning the same time to two consecutive TIME values and entering different VALUE values.

18.3. AC waveform#

交流表示(18.3)#

Required when OPTION =2.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1

Number of parameters:

3

Text format#

* AMPLITUDE * TCYCLE * PHASE *
      E      E      E

JSON format from 2024.11#

        {
            "TIME_ID": I,
            "OPTION": 2,
            "AMPLITUDE": E,
            "TCYCLE": E,
            "PHASE": E
        }

AMPLITUDE#

AMPLITUDE(18.3)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1]

Type:: Real number (E)
Description:: Amplitude.

TCYCLE#

TCYCLE(18.3)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 2]

Type:: Real number (E)
Unit:: sec
Description:: Period.

PHASE#

PHASE(18.3)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 3]

Type:: Real number (E)
Unit:: deg
Description:: Phase.

Hint

The time variation is

\[f(t) = \text{AMPLITUDE} \cdot \cos\left(\frac{2\pi t}{\text{TCYCLE}} + \frac{\text{PHASE} \cdot \pi}{180}\right)\]

is used. For AC analysis, only this form is supported, and TCYCLE must be the same for all data in this set. Make it consistent with FREQUENCY(8.2) under 8.2 Calculation Step and Frequency, 8_2_Calculation_Frequency. This form can also be used to represent time variation in analyses other than AC analysis.

18.4. PSIM, MATLAB/Simulink co-simulation#

PSIM，MATLAB/Simulink 連成解析(18.4)#

Required when PSIM or MATLAB/Simulink input/output data (00) are provided and OPTION =4.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1

Number of parameters:

2

Text format#

* PSIM_IN * PSIM_OUT *
    I      I

JSON format from 2024.11#

        {
            "TIME_ID": I,
            "OPTION": 4,
            "PSIM_IN": I,
            "PSIM_OUT": I,
        }

PSIM_IN#

PSIM_IN(18.4)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1]

Type:: Integer (I)
Description:: Input number for the voltage from PSIM in the PSIM or MATLAB/Simulink input/output data (00). The default is 0 (not set).

PSIM_OUT#

PSIM_OUT(18.4)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 2]

Type:: Integer (I)
Description:: Output number for the current to PSIM in the PSIM or MATLAB/Simulink input/output data (00).

18.5. Formula input#

数式入力(18.5)#

MATH_EQ(18.5)#

When OPTION =11, enter the time-variation function as a formula.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1

Number of parameters:

1

Text format#

* FUNCTION *
    S

JSON format from 2024.11#

        {
            "TIME_ID": I,
            "OPTION": 11,
            "FUNCTION": S
        }

Type:: String (S)
Description:: Formula-input string. Enter the time-variation function f(t). The unit of T is sec.

The following is equivalent to 18.1 Analytical expression represented using this input.

Text format#

f(t) = C0 + C1 * t + C2 * exp(-t/TEXP)
     + C3 * sin(2*PI*t/TCYCLE)
     + C4 * cos(2*PI*t/TCYCLE)
     + C5 * exp(-t/TEXP) * sin(2*PI*t/TCYCLE)
     + C6 * exp(-t/TEXP) * cos(2*PI*t/TCYCLE);;

Also, 18.3. AC waveform is equivalent to the following.

Text format#

f(t) = AMPLITUDE * cos(2*PI*t/TCYCLE + PHASE*PI/180 );;

18.6. Equation-of-motion input#

運動方程式入力(18.6)#

Required when OPTION =3.

Text-format section

Type:

Fixed parameter set 1

Number of rows:

6

Number of parameters:

3

Text format#

* INITIAL_POSITION * INITIAL_VELOCITY * POSITION_ERROR * PSIM_IN * PSIM_FORCE_OUT * PSIM_POS_OUT * PSIM_V_OUT * PSIM_CONST_F_IN *
          E                  E                  E     I             I               I     I              I
* LOWER_LIMIT * UPPER_LIMIT * LOWER_REFLECTION * UPPER_REFLECTION *
       E              E                 E                 E
* MASS * CONST_FORCE * STATIC_FRICTION * CONST_FORCE_ID * MASS_ACCELERATION *
     E          E              E         I                  E
* NO_DATA * OPTION *
     I         I
* POSITION * MASS *
     E         E

JSON format from 2024.11#

    {
        "TIME_ID": I,
        "OPTION": 3,
        "INITIAL_POSITION": E,
        "INITIAL_VELOCITY": E,
        "POSITION_ERROR": E,
        "PSIM_IN": I,
        "PSIM_FORCE_OUT": I,
        "PSIM_POS_OUT": I,
        "PSIM_V_OUT": I,
        "PSIM_CONST_F_IN": I,
        "LOWER_LIMIT": E,
        "UPPER_LIMIT": E,
        "LOWER_REFLECTION": E,
        "UPPER_REFLECTION": E,
        "MASS": E,
        "CONST_FORCE": E,
        "STATIC_FRICTION": E,
        "CONST_FORCE_ID": I,
        "MASS_ACCELERATION": E,
        "CONST_DISPLACEMENT" : E,
        "POSITION_DEPEND_MASS": {
            "OPTION" : I,
            "POSITION": [ E ],
            "MASS": [ E ]
        }
    }

INITIAL_POSITION#

INITIAL_POSITION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Initial relative position from the reference position.

INITIAL_VELOCITY#

INITIAL_VELOCITY(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 2]

Type:: Real number (E)
Unit:: m/sec[deg/sec]
Description:: Initial velocity.

POSITION_ERROR#

POSITION_ERROR(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 3]

Type:: Real number (E)
Unit:: m[deg]
Description:: Position calculation tolerance. When =0.0, no convergence calculation is performed.

The following data are required when PSIM or MATLAB/Simulink input data (00) are used.

MATLAB/PSIM input data#

Required when MATLAB/PSIM input/output data (00) are provided and OPTION =4.

PSIM_IN#

PSIM_IN(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 4]

Type:

Integer (I)

Description:

Input number for the voltage from PSIM in the PSIM input/output data (00). The default is 0 (not set).

When =0, EMSolution calculates the equation of motion.
When ≠0, PSIM performs the calculation. In this case, PSIM_IN is the input number for position (Position(m[deg])) or angle (Angle(deg)) in the PSIM input/output data (00).

PSIM_FORCE_OUT#

PSIM_FORCE_OUT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 5]

Type:: Integer (I)
Description:: Output number for the electromagnetic force (Force(N)) or torque (Torque(Nm)) from PSIM in the PSIM input/output data (00). Required when PSIM_IN ≠0; it may also be specified when PSIM_IN =0.

PSIM_POS_OUT#

PSIM_POS_OUT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 6]

Type:: Integer (I)
Description:: Output number for position (Position(m)) or angle (Angle(deg)) to PSIM in the PSIM input/output data (00). It may be specified when PSIM_IN =0. When PSIM_IN ≠0, it is not required (set it to zero).

PSIM_V_OUT#

PSIM_V_OUT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 7]

Type:: Integer (I)
Description:: Output number for velocity ((m/s) or angular velocity (deg/sec)) to PSIM in the PSIM input/output data (00). It may be specified when PSIM_IN =0. When PSIM_IN ≠0, it is not required (set it to zero).

PSIM_CONST_F_IN#

PSIM_CONST_F_IN(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 8]

Type:: Integer (I)

Description: Input number for the external force (Force(N)) or torque (Torque(Nm)) from PSIM in the PSIM input/output data (00).: It may be specified when PSIM_IN =0. When PSIM_IN ≠0, it is not required (set it to zero).

LOWER_LIMIT#

LOWER_LIMIT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Lower displacement limit. When =-999., no lower limit is applied.

UPPER_LIMIT#

UPPER_LIMIT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 2]

Type:: Real number (E)
Unit:: m[deg]
Description:: Upper displacement limit. When =999., no upper limit is applied.

LOWER_REFLECTION#

LOWER_REFLECTION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 3]

Type:: Real number (E)
Description:: Reflection coefficient at the lower displacement limit. (0.≦ LOWER_REFLECTION ≦1.)

UPPER_REFLECTION#

UPPER_REFLECTION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 4]

Type:: Real number (E)
Description:: Reflection coefficient at the upper displacement limit. (0.≦ UPPER_REFLECTION ≦1.)

Caution

The condition LOWER_LIMIT ≦ INITIAL_POSITION ≦ UPPER_LIMIT must be satisfied.

MASS#

MASS(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 1]

Normally >0. When <0, enter the position-dependent mass table in rows 4 and 5.

Type:

Real number (E)

Unit:

kg[kg·m²]

Description:

Mass

Mass need not be entered when a position-dependent mass table is provided.

CONST_FORCE#

CONST_FORCE(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 2]

Type:

Real number (E)

Unit:

N[Nm]

Description:

External force independent of position and velocity.

Gravity should preferably be specified using MASS_ACCELERATION(18.6).

STATIC_FRICTION#

STATIC_FRICTION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 3]

Type:

Real number (E)

Unit:

N[Nm]

Description:

Static friction force.

Motion starts when a force [torque] equal to or greater than this value is applied while stationary.

TIME_CONST_FORCE#

TIME_CONST_FORCE(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 4]

Type:: Integer (I)
Description:: Data number TIME_ID(18) for the time-varying external force (N) [torque (Nm)].

MASS_ACCELERATION#

MASS_ACCELERATION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 5]

Type:

Real number (E)

Unit:

m/s²[deg/s²]

Description:

Acceleration applied to the mass

Suitable for specifying gravitational acceleration.

CONST_DISPLACEMENT#

CONST_DISPLACEMENT(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 6]

Type:

Real number (E)

Unit:

m[deg]

Description:

Specifies the displacement per step.

During coupled analysis of sliding motion and the equation of motion, an accelerated motion with a constant time step can cause the travel distance to increase as the calculation advances. The resulting increase in the sliding distance may reduce calculation accuracy. In that case, set this value to the sliding-motion travel distance, that is, the mesh width, to keep the travel distance fixed and improve calculation accuracy.

POSITION_DEPEND_MASS (JSON)#

… paramdef:: POSITION_DEPEND_MASS(18.6)

Required when specifying a position-dependent mass in JSON format.

Text-format section

NO_DATA

Fixed parameter set 1#

[row, col] = [4, 1]
Type=I

Number of points in the position-dependent mass table. The next row must contain this number of data items.

OPTION#

OPTION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [4, 2]

Type:

Integer (I)

Value:

0, 1

Description:

Whether to account for velocity changes caused by mass changes.

If =0, velocity changes caused by mass changes are not considered.
If =1, velocity changes caused by mass changes are considered.

POSITION#

POSITION(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [5, 1]

Type:

Real number (E)

Unit:

m[deg]

Description:

Relative position from the reference position.

In JSON format, specify this as an array.

MASS#

MASS(18.6)#

Text-format section

Fixed parameter set 1#

[row, col] = [5, 2]

Type:

Real number (E)

Unit:

kg[kg·m²]

Description:

Mass at the relative position from the reference position. Normally >0.

In JSON format, specify this as an array.

Text-format section

NO_SPRING(18.6)#

NO_SPRING

Fixed parameter set 1#

[row, col] = [6, 1]
Type=I

Number of spring definitions (position-dependent mechanical forces). >=0.

NO_DAMPER(18.6)#

NO_DAMPER

Fixed parameter set 1#

[row, col] = [6, 2]
Type=I

Number of damper definitions (velocity-dependent mechanical forces). >=0.

MATH_EQ(18.6)#

MATH_EQ

Fixed parameter set 1#

[row, col] = [6, 3]
Type=I

=0: no formula input (Appendix 1).
=1: enter the applied force as a formula of position and velocity.

Note

When PSIM_IN ≠0, INITIAL_VELOCITY and POSITION_ERROR have no effect.
Enter the same value as the initial position in PSIM for INITIAL_POSITION.

Hint

The position, velocity, and electromagnetic force at each time are output in tabular form to the motion file.

Caution

PSIM, MATLAB/Simulink co-simulation

When PSIM_IN ≠0, INITIAL_VELOCITY and POSITION_ERROR have no effect.
Enter the same value as the initial position in PSIM for INITIAL_POSITION.
When PSIM_IN ≠0, the other data in 運動方程式入力(18.6) must still be entered in the same format as for operation without PSIM coupling. These data do not affect the calculation except for the data in 電磁力積算領域(18.6.4).

18.6.1. Spring data#

SPRING(18.6.1)#

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1 + NO_SPRING

Number of parameters:

2, 3, 4, 5

Text format#

* SPRING_TYPE * LOWER_RANGE * UPPER_RANGE *
    0           E             E
* SPRING_CONST * EQUIL_POSITION *
    E           E

* SPRING_TYPE * LOWER_RANGE * UPPER_RANGE *
    1           E             E
* NO_POINTS * POSITION * FORCE *
    I           E           E

JSON format from 2024.11#

        "SPRING": [
            {
                "LOWER_RANGE": E,
                "UPPER_RANGE": E,
                "LinearSpring": {
                    "SPRING_CONST": E,
                    "EQUIL_POSITION": E
                }
            },
            {
                "LOWER_RANGE": E,
                "UPPER_RANGE": E,
                "NonlinearSpring": {
                    "POSITION": E,
                    "FORCE": E
                }
            }
        ]

Text-format section

SPRING_TYPE(18.6.1)#

SPRING_TYPE

Fixed parameter set 1#

[row, col] = [1, 1]
Type=I

Spring definition type

=0: linear spring
=1: nonlinear spring; enter a table.

LOWER_RANGE#

LOWER_RANGE(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Lower bound of the definition range. When =999., no lower bound is applied.

UPPER_RANGE#

UPPER_RANGE(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Upper bound of the definition range. When =999., no upper bound is applied.

LinearSpring (JSON)#

LinearSpring(18.6.1)#

Represents a linear spring.

For text input, used when SPRING_TYPE =0.

SPRING_CONST#

SPRING_CONST(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Real number (E)
Unit:: N/m[Nm/deg]
Description:: Spring constant. Normally a positive value.

EQUIL_POSITION#

EQUIL_POSITION(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 2]

Type:

Real number (E)

Unit:

m[deg]

Description:

Spring equilibrium position.

When the position is x, the spring force is

SPRING_CONST * (x- EQUIL_POSITION ).

NonlinearSpring(18.6.1)#

Represents a nonlinear spring. For text input, used when SPRING_TYPE =1.

POSITION#

POSITION(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Relative position from the reference position. Enter values in ascending order.

FORCE#

FORCE(18.6.1)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 2]

Type:: Real number (E)
Unit:: N[Nm]
Description:: Spring force at the relative position from the reference position.

18.6.2. Damper data#

DAMPER(18.6.2)#

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1 + NO_DAMPER

Number of parameters:

2, 3, 4, 5

Text format#

* DAMPER_TYPE * LOWER_RANGE * UPPER_RANGE *
    I             E             E
* C0 * C1 * C2 * C3 *
    E    E    E    E

* DAMPER_TYPE * LOWER_RANGE * UPPER_RANGE *
    I             E             E
* NO_POINTS * POSITION * C1 *
    I           E         E

* DAMPER_TYPE * LOWER_RANGE * UPPER_RANGE *
    I             E             E
* NO_POINTS * VELOCITY * FORCE *
    I           E         E

JSON format from 2024.11#

        "DAMPER": [
            {
                "LOWER_RANGE": E,
                "UPPER_RANGE": E,
                "AnalysisInput": {
                    "C0": E,
                    "C1": E,
                    "C2": E,
                    "C3": E
                }
            },
            {
                "LOWER_RANGE": E,
                "UPPER_RANGE": E,
                "PositionFunction": {
                    "POSITION": [ E ],
                    "C1": [ E ]
                }
            },
            {
                "LOWER_RANGE": E,
                "UPPER_RANGE": E,
                "VelocityFunction": {
                    "VELOCITY": [ E ],
                    "FORCE": [ E ]
                }
            }
        ]

Text-format section

DAMPER_TYPE(18.6.2)#

DAMPER_TYPE

Fixed parameter set 1#

[row, col] = [1, 1]
Type=I

Damper definition type

=0: polynomial representation
=1: enter the viscous coefficient as a function of position in a table
=2: enter a table as a function of velocity

LOWER_RANGE#

LOWER_RANGE(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 2]

Type:: Real number (E)
Unit:: m[deg]
Description:: Lower displacement limit. When =-999., no lower limit is applied.

UPPER_RANGE#

UPPER_RANGE(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 3]

Type:: Real number (E)
Unit:: m[deg]
Description:: Upper bound of the definition range. When =999., no upper bound is applied.

PolynomialInput (JSON)#

PolynomialInput(18.6.2)#

Represents a damper using a polynomial representation.

For text input, used when DAMPER_TYPE =0.

C0#

C0(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Real number (E)
Unit:: \(\mathrm{N/(m/sec)}[\mathrm{Nm/(deg/sec)}]\)
Description:: Constant friction force. A force independent of velocity and opposite to the velocity direction. Normally a positive value.

C1#

C1(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 2]

Type:: Real number (E)
Unit:: \(\mathrm{N/(m/sec)}[\mathrm{Nm/(deg/sec)}]\)
Description:: Viscous (friction) coefficient. Normally a positive value.

C2#

C2(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 3]

Type:: Real number (E)
Unit:: \(\mathrm{N/(m^2/sec)}[\mathrm{Nm/(deg^2/sec)}]\)
Description:: Coefficient of the squared-velocity force.

C3#

C3(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 4]

Type:: Real number (E)
Unit:: \(\mathrm{N/(m^3/sec)}[\mathrm{Nm/(deg^3/sec)}]\)
Description:: Coefficient of the cubed-velocity force.

The force for velocity v is expressed as follows.

\[F = -\text{sign}(v) \cdot (C_0 + C_1 \cdot |v| + C_2 \cdot v^2 + C_3 \cdot |v|^3)\]

PositionDependent (JSON)#

PositionDependent(18.6.2)#

Represents a position-dependent viscous coefficient.

For text input, used when DAMPER_TYPE =1.

POSITION#

POSITION(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 1]

Type:: Real number (E)
Unit:: m[deg]
Description:: Relative position from the reference position. Enter values in ascending order.

C1#

C1(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 2]

Type:: Real number (E)
Unit:: \(\mathrm{N/(m/sec)}[\mathrm{Nm/(deg/sec)}]\)
Description:: Viscous coefficient at the position. Normally a positive value.

The force for velocity v is expressed as follows.

\[F = -\text{sign}(v) \cdot C_1 \cdot |v|\]

VelocityDependent (JSON)#

VelocityDependent(18.6.2)#

Represents a velocity-dependent viscous force.

For text input, used when DAMPER_TYPE =2.

VELOCITY#

VELOCITY(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 1]

Type:: Real number (E)
Unit:: \(\mathrm{m/sec}[\mathrm{deg/sec}]\)
Description:: Velocity. Enter values in ascending order.

FORCE#

FORCE(18.6.2)#

Text-format section

Fixed parameter set 1#

[row, col] = [3, 2]

Type:: Real number (E)
Unit:: N[Nm]
Description:: Viscous (friction) force at the velocity.

If the velocity can be negative, values for negative velocities must also be entered.

18.6.3. Applied-force formula input#

MATH_EQ(18.6.3)#

Text-format section

Type:

Fixed parameter set 1

Number of rows:

N

Number of parameters:

N

Text format#

* MATH_EQ *
    S

JSON format from 2024.11#

    "MATH_EQ": S

Type:: String (S)
Description:: Applied-force formula input

When MATH_EQ =1, enter the applied external force as a formula of position x and velocity v.

Define F(x,v). The units are x (m[deg]), v (m/s [deg/sec]), and F (N [Nm]).

Note

The following is equivalent to 18.6.1 Spring data with SPRING_TYPE =0.

Text format#

[LOWER_RANGE<=x<UPPER_RANGE]F(x,v) = -SPRING_CONST*(x-EQUIL_POSITION);;

The following is also equivalent to 18.6.2 Damper data with DAMPER_TYPE =0.

Text format#

[v<0]F(x,v) = (C0 - C1*v + C2*v**2 - C3*v**3);;
[0.<=v]F(x,v) = -(C0 + C1*v + C2*v**2 + C3*v**3);;
F(x,v) = F1(x,v) + F2(x,v);;

18.6.4. Electromagnetic-force integration region#

電磁力積算領域(18.6.4)#

Text-format section

Type:

Fixed parameter set 1

Number of rows:

1 + NO_MAT_IDS

Number of parameters:

2, 3, 4, 5

Text format#

* MOTION_TYPE * REGION_FACTOR *
    I             E
* NO_MAT_IDS * MAT_IDS * FORCE_TYPE *
    I           I*NO_MAT_IDS   I

JSON format from 2024.11#

        "FORCE_INTEGRATION_REGION": {
            "MOTION_TYPE": I,
            "REGION_FACTOR": E,
            "FORCE_TYPE": I
        }

Defines the electromagnetic-force integration region.

Required when TIME_ID(18) =3.

MOTION_TYPE#

MOTION_TYPE(18.6.4)#

Text-format section

Fixed parameter set 1#

[row, col] = [1, 1]

Type:

Integer (I)

Value:

0, 1

Description:

Motion type.

=0: mesh deformation and the source-current magnetic field of COIL(17.1).
=1: sliding motion.

REGION_FACTOR#

REGION_FACTOR(18.6.4)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 1]

Type:: Real number (E)
Description:: Ratio to the analysis region of the full model. As with REGION_FACTOR(17.8) in CIRCUIT(17.8) and REGION_FACTOR(17.9) in NETWORK(17.9).

Text-format section

NO_MAT_IDS(18.6.4)#

NO_MAT_IDS

Fixed parameter set 1#

[row, col] = [2, 2]
Type=I

Number of material IDs in the nodal-force summation region when FORCE_TYPE =0.

MAT_IDS(18.6.4)#

MAT_IDS

Fixed parameter set 1#

[row, col] = [3, 1]
Type=I*NO_MAT_IDS

Required when FORCE_TYPE =0. Enter the material IDs (16) of the nodal-force summation region.

add_FORCE_for_DYNAMIC_MOTION#

add_FORCE_for_DYNAMIC_MOTION(16.1) Specifies the electromagnetic-force integration region (16.1).

A total-potential region must be defined for this region and through one element layer outside it.

FORCE_TYPE#

FORCE_TYPE(18.6.4)#

Text-format section

Fixed parameter set 1#

[row, col] = [2, 3]

Type:

Integer (I)

Value:

0, 1

Description:

Specifies the type of electromagnetic force considered during motion. The default is 0.

=0: electromagnetic force by the nodal-force method, FORCE_NODAL(10.3)
=1: electromagnetic force by the Lorentz-force method, FORCE_J_B(10.3)

Note

Equation of motion

\[m \ddot{x} = F_0 + F_{\text{spring}} + F_{\text{damper}} + F_{\text{math_eq}} + F_{\text{magnetic}}\]

is solved. Here, \(x\) is the relative position from the mesh data (pre_geom), with units of \((m)\) for translational motion and \((deg)\) for rotational motion. \(m\) is the mass; \(F_0\) (\(\text{CONST_FORCE}\)) is the external force independent of position and velocity; \(F_{\text{spring}}\) is the position-dependent spring force; and \(F_{\text{damper}}\) is the velocity-dependent damper force.

\(F_{\text{math_eq}}\) is a function of position and velocity when a formula is entered. \(F_{\text{magnetic}}\) is the electromagnetic force. It is a force \((N)\) for translational motion and a torque \((Nm)\) for rotational motion.

The direction of motion and whether the motion is translational or rotational are determined by referencing this data’s TIME_ID in 19. Motion Definition, 19_Motoin(19).

Caution

Position-related data are relative to the reference position (an appropriately defined position; no input is required).

For rotational motion, use the relative angle.

The same applies to POSITION0(19.3) and POSITION1(19.3) of 19.3 Motion of the Deformed Mesh, MOTION(19).

18. Time-Variation Functions

Contents

18. Time-Variation Functions#

Settings#

Input format#

JSON format#

Detailed description#

TIME_ID#

OPTION#

18.1. Analytical expression#

C0/C1/C2/C3/C4/C5/C6 TEXP TCYCLE PHASE4#

18.2. Time table#

TIME#

VALUE#

18.3. AC waveform#

AMPLITUDE#

TCYCLE#

PHASE#

18.4. PSIM, MATLAB/Simulink co-simulation#

PSIM_IN#

PSIM_OUT#

18.5. Formula input#

18.6. Equation-of-motion input#

INITIAL_POSITION#

INITIAL_VELOCITY#

POSITION_ERROR#

MATLAB/PSIM input data#

PSIM_IN#

PSIM_FORCE_OUT#

PSIM_POS_OUT#

PSIM_V_OUT#

PSIM_CONST_F_IN#

LOWER_LIMIT#

UPPER_LIMIT#

LOWER_REFLECTION#

UPPER_REFLECTION#

MASS#

CONST_FORCE#

STATIC_FRICTION#

TIME_CONST_FORCE#

MASS_ACCELERATION#

CONST_DISPLACEMENT#

POSITION_DEPEND_MASS (JSON)#

OPTION#

POSITION#

MASS#

18.6.1. Spring data#

LOWER_RANGE#

UPPER_RANGE#

LinearSpring (JSON)#

SPRING_CONST#

EQUIL_POSITION#

POSITION#

FORCE#

18.6.2. Damper data#

LOWER_RANGE#

UPPER_RANGE#

PolynomialInput (JSON)#

C0#

C1#

C2#

C3#

PositionDependent (JSON)#

POSITION#

C1#

VelocityDependent (JSON)#

VELOCITY#

FORCE#

18.6.3. Applied-force formula input#

18.6.4. Electromagnetic-force integration region#

MOTION_TYPE#

REGION_FACTOR#

add_FORCE_for_DYNAMIC_MOTION#

FORCE_TYPE#