Modelica.Mechanics.Rotational.Sources

Information

This package contains ideal sources to drive 1D mechanical rotational drive trains.

Extends from Modelica.Icons.SourcesPackage (Icon for packages containing sources).

Package Content

Name	Description
Position	Forced movement of a flange according to a reference angle signal
Speed	Forced movement of a flange according to a reference angular velocity signal
Accelerate	Forced movement of a flange according to an acceleration signal
Move	Forced movement of a flange according to an angle, speed and angular acceleration signal
Torque	Input signal acting as external torque on a flange
Torque2	Input signal acting as torque on two flanges
LinearSpeedDependentTorque	Linear dependency of torque versus speed
QuadraticSpeedDependentTorque	Quadratic dependency of torque versus speed
ConstantTorque	Constant torque, not dependent on speed
ConstantSpeed	Constant speed, not dependent on torque
TorqueStep	Constant torque, not dependent on speed

Modelica.Mechanics.Rotational.Sources.Position

Information

The input signal phi_ref defines the reference angle in [rad]. Flange flange is forced to move according to this reference motion relative to flange support. According to parameter exact (default = false), this is done in the following way:

1. exact=true
   The reference angle is treated exactly. This is only possible, if the input signal is defined by an analytical function which can be differentiated at least twice. If this prerequisite is fulfilled, the Modelica translator will differentiate the input signal twice in order to compute the reference acceleration of the flange.
2. exact=false
   The reference angle is filtered and the second derivative of the filtered curve is used to compute the reference acceleration of the flange. This second derivative is not computed by numerical differentiation but by an appropriate realization of the filter. For filtering, a second order Bessel filter is used. The critical frequency (also called cut-off frequency) of the filter is defined via parameter f_crit in [Hz]. This value should be selected in such a way that it is higher as the essential low frequencies in the signal.

The input signal can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2 (Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Boolean	exact	false	true/false exact treatment/filtering the input signal
Frequency	f_crit	50	if exact=false, critical frequency of filter to filter input signal [Hz]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component
input RealInput	phi_ref	Reference angle of flange with respect to support as input signal [rad]

Modelica definition

model Position 
  "Forced movement of a flange according to a reference angle signal"
  import SI = Modelica.SIunits;
  extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2;
  parameter Boolean exact=false 
    "true/false exact treatment/filtering the input signal";
  parameter SI.Frequency f_crit=50 
    "if exact=false, critical frequency of filter to filter input signal";
  SI.Angle phi(stateSelect=if exact then StateSelect.default else StateSelect.prefer) 
    "Rotation angle of flange with respect to support";
  SI.AngularVelocity w(start=0,stateSelect=if exact then StateSelect.default else StateSelect.prefer) 
    "If exact=false, Angular velocity of flange with respect to support else dummy";
  SI.AngularAcceleration a(start=0) 
    "If exact=false, Angular acceleration of flange with respect to support else dummy";
  Modelica.Blocks.Interfaces.RealInput phi_ref(final quantity="Angle", final unit="rad", displayUnit="deg") 
    "Reference angle of flange with respect to support as input signal";

protected 
  parameter Modelica.SIunits.AngularFrequency w_crit=2*Modelica.Constants.pi*f_crit 
    "Critical frequency";
  constant Real af=1.3617 "s coefficient of Bessel filter";
  constant Real bf=0.6180 "s*s coefficient of Bessel filter";
initial equation 
  if not exact then
    phi = phi_ref;
  end if;
equation 
  phi = flange.phi - phi_support;
  if exact then
    phi = phi_ref;
    w = 0;
    a = 0;
  else
    // Filter: a = phi_ref*s^2/(1 + (af/w_crit)*s + (bf/w_crit^2)*s^2)
    w = der(phi);
    a = der(w);
    a = ((phi_ref - phi)*w_crit - af*w)*(w_crit/bf);
  end if;
end Position;

Modelica.Mechanics.Rotational.Sources.Speed

Information

The input signal w_ref defines the reference speed in [rad/s]. Flange flange is forced to move relative to flange support according to this reference motion. According to parameter exact (default = false), this is done in the following way:

1. exact=true
   The reference speed is treated exactly. This is only possible, if the input signal is defined by an analytical function which can be differentiated at least once. If this prerequisite is fulfilled, the Modelica translator will differentiate the input signal once in order to compute the reference acceleration of the flange.
2. exact=false
   The reference angle is filtered and the second derivative of the filtered curve is used to compute the reference acceleration of the flange. This second derivative is not computed by numerical differentiation but by an appropriate realization of the filter. For filtering, a first order filter is used. The critical frequency (also called cut-off frequency) of the filter is defined via parameter f_crit in [Hz]. This value should be selected in such a way that it is higher as the essential low frequencies in the signal.

The input signal can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2 (Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Boolean	exact	false	true/false exact treatment/filtering the input signal
Frequency	f_crit	50	if exact=false, critical frequency of filter to filter input signal [Hz]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component
input RealInput	w_ref	Reference angular velocity of flange with respect to support as input signal

Modelica definition

model Speed 
  "Forced movement of a flange according to a reference angular velocity signal"
  import SI = Modelica.SIunits;
  extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2;
  parameter Boolean exact=false 
    "true/false exact treatment/filtering the input signal";
  parameter SI.Frequency f_crit=50 
    "if exact=false, critical frequency of filter to filter input signal";
  SI.Angle phi(start=0, fixed=true, stateSelect=StateSelect.prefer) 
    "Rotation angle of flange with respect to support";
  SI.AngularVelocity w(stateSelect=if exact then StateSelect.default else StateSelect.prefer) 
    "Angular velocity of flange with respect to support";
  SI.AngularAcceleration a 
    "If exact=false, angular acceleration of flange with respect to support else dummy";
  Modelica.Blocks.Interfaces.RealInput w_ref 
    "Reference angular velocity of flange with respect to support as input signal";

protected 
  parameter Modelica.SIunits.AngularFrequency w_crit=2*Modelica.Constants.pi*f_crit 
    "Critical frequency";
initial equation 
  if not exact then
    w = w_ref;
  end if;
equation 
  phi = flange.phi - phi_support;
  w = der(phi);
  if exact then
    w = w_ref;
    a = 0;
  else
    // Filter: a = w_ref/(1 + (1/w_crit)*s)
    a = der(w);
    a = (w_ref - w)*w_crit;
  end if;
end Speed;

Modelica.Mechanics.Rotational.Sources.Accelerate

Information

The input signal a defines an angular acceleration in [rad/s2]. Flange flange is forced to move relative to flange support with this acceleration. The angular velocity w and the rotation angle phi of the flange are automatically determined by integration of the acceleration.

The input signal can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2 (Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component
input RealInput	a_ref	Absolute angular acceleration of flange with respect to support as input signal

Modelica definition

model Accelerate 
  "Forced movement of a flange according to an acceleration signal"
  import SI = Modelica.SIunits;
  extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2;
  SI.Angle phi(start=0, fixed=true, stateSelect=StateSelect.prefer) 
    "Rotation angle of flange with respect to support";
  SI.AngularVelocity w(start=0, fixed=true, stateSelect=StateSelect.prefer) 
    "Angular velocity of flange with respect to support";
  SI.AngularAcceleration a 
    "Angular acceleration of flange with respect to support";

  Modelica.Blocks.Interfaces.RealInput a_ref 
    "Absolute angular acceleration of flange with respect to support as input signal";

equation 
  phi = flange.phi - phi_support;
  w = der(phi);
  a = der(w);
  a = a_ref;
end Accelerate;

Modelica.Mechanics.Rotational.Sources.Move

Information

Flange flange is forced to move relative to flange support with a predefined motion according to the input signals:

    u[1]: angle of flange
    u[2]: angular velocity of flange
    u[3]: angular acceleration of flange

The user has to guarantee that the input signals are consistent to each other, i.e., that u[2] is the derivative of u[1] and that u[3] is the derivative of u[2]. There are, however, also applications where by purpose these conditions do not hold. For example, if only the position dependent terms of a mechanical system shall be calculated, one may provide angle = angle(t) and set the angular velocity and the angular acceleration to zero.

The input signals can be provided from one of the signal generator blocks of the block library Modelica.Blocks.Sources.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2 (Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component
input RealInput	u[3]	Angle, angular velocity and angular acceleration of flange with respect to support as input signals

Modelica definition

model Move 
  "Forced movement of a flange according to an angle, speed and angular acceleration signal"
  import SI = Modelica.SIunits;
  extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2;

  Modelica.SIunits.Angle phi "Rotation angle of flange with respect to support";
  Modelica.Blocks.Interfaces.RealInput u[3] 
    "Angle, angular velocity and angular acceleration of flange with respect to support as input signals";
    
protected 
  function position
  annotation(derivative=position_der);
     input Real q_qd_qdd[3] "Required values for position, speed, acceleration";
     input Real dummy 
      "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)";
     output Real q;
  algorithm 
    q :=q_qd_qdd[1];
  end position;

  function position_der
  annotation(derivative=position_der2);
     input Real q_qd_qdd[3] "Required values for position, speed, acceleration";
     input Real dummy 
      "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)";
     input Real dummy_der;
     output Real qd;
  algorithm 
    qd :=q_qd_qdd[2];
  end position_der;

  function position_der2
     input Real q_qd_qdd[3] "Required values for position, speed, acceleration";
     input Real dummy 
      "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)";
     input Real dummy_der;
     input Real dummy_der2;
     output Real qdd;
  algorithm 
    qdd :=q_qd_qdd[3];
  end position_der2;
equation 
  phi = flange.phi - phi_support;
  phi = position(u,time);
end Move;

Modelica.Mechanics.Rotational.Sources.Torque

Information

The input signal tau defines an external torque in [Nm] which acts (with negative sign) at a flange connector, i.e., the component connected to this flange is driven by torque tau.

The input signal can be provided from one of the signal generator blocks of Modelica.Blocks.Sources.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2 (Partial model for a component with one rotational 1-dim. shaft flange and a support used for textual modeling, i.e., for elementary models).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component
input RealInput	tau	Accelerating torque acting at flange (= -flange.tau)

Modelica definition

model Torque "Input signal acting as external torque on a flange"
  extends Modelica.Mechanics.Rotational.Interfaces.PartialElementaryOneFlangeAndSupport2;
  Modelica.Blocks.Interfaces.RealInput tau 
    "Accelerating torque acting at flange (= -flange.tau)";

equation 
  flange.tau = -tau;
end Torque;

Modelica.Mechanics.Rotational.Sources.Torque2

Information

The input signal tau defines an external torque in [Nm] which acts at both flange connectors, i.e., the components connected to these flanges are driven by torque tau.

The input signal can be provided from one of the signal generator blocks of Modelica.Blocks.Sources.

Extends from Rotational.Interfaces.PartialTwoFlanges (Partial model for a component with two rotational 1-dim. shaft flanges).

Connectors

Type	Name	Description
Flange_a	flange_a	Flange of left shaft
Flange_b	flange_b	Flange of right shaft
input RealInput	tau	Torque driving the two flanges (a positive value accelerates the flange)

Modelica definition

model Torque2 "Input signal acting as torque on two flanges"
  extends Rotational.Interfaces.PartialTwoFlanges;

  Modelica.Blocks.Interfaces.RealInput tau 
    "Torque driving the two flanges (a positive value accelerates the flange)";

equation 
  flange_a.tau =  tau;
  flange_b.tau = -tau;
end Torque2;

Modelica.Mechanics.Rotational.Sources.LinearSpeedDependentTorque

Information

Model of torque, linearly dependent on angular velocity of flange.
Parameter TorqueDirection chooses whether direction of torque is the same in both directions of rotation or not.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialTorque (Partial model of a torque acting at the flange (accelerates the flange)).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Torque	tau_nominal		Nominal torque (if negative, torque is acting as load) [N.m]
Boolean	TorqueDirection	true	Same direction of torque in both directions of rotation
AngularVelocity	w_nominal		Nominal speed [rad/s]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component

Modelica definition

model LinearSpeedDependentTorque 
  "Linear dependency of torque versus speed"
  extends Modelica.Mechanics.Rotational.Interfaces.PartialTorque;
  parameter Modelica.SIunits.Torque tau_nominal 
    "Nominal torque (if negative, torque is acting as load)";
  parameter Boolean TorqueDirection=true 
    "Same direction of torque in both directions of rotation";
  parameter Modelica.SIunits.AngularVelocity w_nominal(min=Modelica.Constants.eps) 
    "Nominal speed";
  Modelica.SIunits.AngularVelocity w 
    "Angular velocity of flange with respect to support (= der(phi))";
  Modelica.SIunits.Torque tau 
    "Accelerating torque acting at flange (= -flange.tau)";
equation 
  w = der(phi);
  tau = -flange.tau;
  if TorqueDirection then
    tau = tau_nominal*abs(w/w_nominal);
  else
    tau = tau_nominal*(w/w_nominal);
  end if;
end LinearSpeedDependentTorque;

Modelica.Mechanics.Rotational.Sources.QuadraticSpeedDependentTorque

Information

Model of torque, quadratic dependent on angular velocity of flange.
Parameter TorqueDirection chooses whether direction of torque is the same in both directions of rotation or not.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialTorque (Partial model of a torque acting at the flange (accelerates the flange)).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Torque	tau_nominal		Nominal torque (if negative, torque is acting as load) [N.m]
Boolean	TorqueDirection	true	Same direction of torque in both directions of rotation
AngularVelocity	w_nominal		Nominal speed [rad/s]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component

Modelica definition

model QuadraticSpeedDependentTorque 
  "Quadratic dependency of torque versus speed"
  extends Modelica.Mechanics.Rotational.Interfaces.PartialTorque;
  parameter Modelica.SIunits.Torque tau_nominal 
    "Nominal torque (if negative, torque is acting as load)";
  parameter Boolean TorqueDirection=true 
    "Same direction of torque in both directions of rotation";
  parameter Modelica.SIunits.AngularVelocity w_nominal(min=Modelica.Constants.eps) 
    "Nominal speed";
  Modelica.SIunits.AngularVelocity w 
    "Angular velocity of flange with respect to support (= der(phi))";
  Modelica.SIunits.Torque tau 
    "Accelerating torque acting at flange (= -flange.tau)";
equation 
  w = der(phi);
  tau = -flange.tau;
  if TorqueDirection then
    tau = tau_nominal*(w/w_nominal)^2;
  else
    tau = tau_nominal*smooth(1,if w >= 0 then (w/w_nominal)^2 else -(w/w_nominal)^2);
  end if;
end QuadraticSpeedDependentTorque;

Modelica.Mechanics.Rotational.Sources.ConstantTorque

Information

Model of constant torque, not dependent on angular velocity of flange.
Positive torque acts accelerating.

Extends from Rotational.Interfaces.PartialTorque (Partial model of a torque acting at the flange (accelerates the flange)).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Torque	tau_constant		Constant torque (if negative, torque is acting as load) [N.m]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component

Modelica definition

model ConstantTorque "Constant torque, not dependent on speed"
  extends Rotational.Interfaces.PartialTorque;
  parameter Modelica.SIunits.Torque tau_constant 
    "Constant torque (if negative, torque is acting as load)";
  Modelica.SIunits.Torque tau 
    "Accelerating torque acting at flange (= -flange.tau)";
equation 
  tau = -flange.tau;
  tau = tau_constant;
end ConstantTorque;

Modelica.Mechanics.Rotational.Sources.ConstantSpeed

Information

Model of fixed angular verlocity of flange, not dependent on torque.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialTorque (Partial model of a torque acting at the flange (accelerates the flange)).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
AngularVelocity	w_fixed		Fixed speed [rad/s]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component

Modelica definition

model ConstantSpeed "Constant speed, not dependent on torque"
  extends Modelica.Mechanics.Rotational.Interfaces.PartialTorque;
  Modelica.SIunits.AngularVelocity w 
    "Angular velocity of flange with respect to support (= der(phi))";
  parameter Modelica.SIunits.AngularVelocity w_fixed "Fixed speed";
equation 
  w = der(phi);
  w = w_fixed;
end ConstantSpeed;

Modelica.Mechanics.Rotational.Sources.TorqueStep

Information

Model of a torque step at time .
Positive torque acts accelerating.

Extends from Modelica.Mechanics.Rotational.Interfaces.PartialTorque (Partial model of a torque acting at the flange (accelerates the flange)).

Parameters

Type	Name	Default	Description
Boolean	useSupport	false	= true, if support flange enabled, otherwise implicitly grounded
Torque	stepTorque		Height of torque step (if negative, torque is acting as load) [N.m]
Torque	offsetTorque		Offset of torque [N.m]
Time	startTime	0	Torque = offset for time < startTime [s]

Connectors

Type	Name	Description
Flange_b	flange	Flange of shaft
Support	support	Support/housing of component

Modelica definition

model TorqueStep "Constant torque, not dependent on speed"
  extends Modelica.Mechanics.Rotational.Interfaces.PartialTorque;
  parameter Modelica.SIunits.Torque stepTorque(start=1) 
    "Height of torque step (if negative, torque is acting as load)";
  parameter Modelica.SIunits.Torque offsetTorque(start=0) "Offset of torque";
  parameter Modelica.SIunits.Time startTime=0 
    "Torque = offset for time < startTime";
  Modelica.SIunits.Torque tau 
    "Accelerating torque acting at flange (= -flange.tau)";

equation 
  tau = -flange.tau;
  tau = offsetTorque + (if time < startTime then 0 else stepTorque);
end TorqueStep;

Modelica.Mechanics.Rotational.Sources.Move.position_der

Inputs

Type	Name	Default	Description
Real	q_qd_qdd[3]		Required values for position, speed, acceleration
Real	dummy		Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)
Real	dummy_der

Outputs

Type	Name	Description
Real	qd

Modelica definition

function position_der
  annotation(derivative=position_der2);
   input Real q_qd_qdd[3] "Required values for position, speed, acceleration";
   input Real dummy 
    "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)";
   input Real dummy_der;
   output Real qd;
algorithm 
  qd :=q_qd_qdd[2];
end position_der;

Modelica.Mechanics.Rotational.Sources.Move.position_der2

Inputs

Type	Name	Default	Description
Real	q_qd_qdd[3]		Required values for position, speed, acceleration
Real	dummy		Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)
Real	dummy_der
Real	dummy_der2

Outputs

Type	Name	Description
Real	qdd

Modelica definition

function position_der2
   input Real q_qd_qdd[3] "Required values for position, speed, acceleration";
   input Real dummy 
    "Just to have one input signal that should be differentiated to avoid possible problems in the Modelica tool (is not used)";
   input Real dummy_der;
   input Real dummy_der2;
   output Real qdd;
algorithm 
  qdd :=q_qd_qdd[3];
end position_der2;