Engee documentation

Unbalanced Load

Unbalanced load with moment of inertia depending on the angle of rotation.

unbalanced load

Description

The Unbalanced Load unit is an unbalanced load whose moment of inertia varies with the angle of rotation.

Examples are the oscillation of a rotating shaft and the shaking of a machine with misaligned rotation. You can specify the inertia of a load by specifying the characteristics of its rotation path or as an angle-inertia correspondence table.

The trajectory of the load rotation is specified by two directions of motion - circular or elliptical. In each case, the distance between the unbalanced load and the principal axis of rotation varies with the angle of rotation. The varying distance causes the moment of inertia, defined by the parallel axis theorem, to change during rotation:

where

  • - is the moment of inertia about the main axis of rotation;

  • - moment of inertia about its own axis;

  • - mass of the unbalanced load;

  • - distance between the unbalanced load and the main axis of rotation.

The angular dependence of the moment of inertia leads to the angular dependence of the inertial moment acting on the unbalanced load:

where

  • - moment of inertia;

  • - angular velocity of the load.

If the load moves along a circular trajectory, its distance to the main axis of rotation is defined as:

where

  • - is the distance between the principal axis of rotation and the offset axis of rotation;

  • - is the radius of the circular trajectory.

Circular trajectory of rotation

unbalanced load 1 en

If the load moves along an elliptical trajectory, its distance to the principal axis of rotation is defined as:

where

  • - is the radius of the elliptical trajectory located at a distance from the main axis of rotation;

  • - is the radius of the elliptical trajectory perpendicular to the distance from the main axis of rotation.

Elliptical trajectory of rotation

unbalanced load 2 en

Ports

Conserving

# Port_1 — shaft connection
`rotational mechanics

Details

A mechanical rotational port associated with connecting a shaft to an unbalanced load.

Program usage name

flange

Parameters

Inertia

# Parameterization — method of modelling the moment of inertia
Circular rotation | Elliptical rotation | By table lookup

Details

Selects the method of modelling the moment of inertia of an unbalanced load. Defined as:

  • Circular rotation or Elliptical rotation to specify the inertia of the load along its rotation path;

  • By table lookup to set the load inertia using a table.

Values

Circular rotation | Elliptical rotation | By table lookup
Default value

Circular rotation
Program usage name

inertia_moment_parameterization
Evaluatable

No

# Moment of inertia about own axis — moment of inertia
g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2

Details

Constant moment of inertia about the natural axis of rotation of an unbalanced load.

Dependencies

To use this parameter, set the Parameterization parameter to Circular rotation or Elliptical rotation.

Units

g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2
Default value

1.0 kg*m^2
Program usage name

I
Evaluatable

Yes

# Mass — load weight
g | t | kg | mg | oz | lbm | slug

Details

The mass of the unbalanced load.

Dependencies

To use this parameter, set the Parameterization parameter to Circular rotation or Elliptical rotation.

Units

g | t | kg | mg | oz | lbm | slug
Default value

1.0 kg
Program usage name

mass
Evaluatable

Yes

# Distance from axis to center of rotation — displacement radius
m | cm | ft | in | km | mi | mm | um | yd

Details

Distance between the principal axis of rotation and the centre of the rotation path.

Dependencies

To use this parameter, set the Parameterization parameter to Circular rotation or Elliptical rotation.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.01 m
Program usage name

offset_radius
Evaluatable

Yes

# Radius of rotation — radius of rotation
m | cm | ft | in | km | mi | mm | um | yd

Details

The radius of the circular path of rotation travelled by the unbalanced load.

Dependencies

To use this parameter, set the Parameterization parameter to Circular rotation.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.01 m
Program usage name

radius
Evaluatable

Yes

# Radius of rotation inline with distance from axis — radius of the major semi-major axis of the ellipse
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the major semi-axis of an elliptical path of rotation travelled by an unbalanced load. The semi-major axis is in line with the segment connecting the main axis of rotation and the centre of the ellipse.

Dependencies

To use this parameter, set the Parameterization parameter to Elliptical rotation.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.01 m
Program usage name

semimajor_radius
Evaluatable

Yes

# Radius of rotation perpendicular to distance from axis — radius of the minor semi-axis of the ellipse
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the minor semi-axis of the elliptical trajectory of rotation traversed by an unbalanced load. The semi-major axis is perpendicular to the line segment connecting the main axis of rotation and the centre of the ellipse.

Dependencies

To use this parameter, set the Parameterization parameter to Elliptical rotation.

Units

m | cm | ft | in | km | mi | mm | um | yd
Default value

0.005 m
Program usage name

semiminor_radius
Evaluatable

Yes

# Angle vector — vector of rotation angle values
deg | rad | rev | mrad

Details

A vector of angular positions at which the load inertia is to be specified. The block calculates the load inertia between the specified angles using linear interpolation.

Dependencies

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

Units

deg | rad | rev | mrad
Default value

[0.0, π, 3π/2] rad
Program usage name

angle_vector
Evaluatable

Yes

# Inertia vector — vector of values of moments of inertia
g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2

Details

Vector of moments of inertia with respect to the load’s own axis of rotation. Each value corresponds to the angle specified in the Angle vector parameter.

Dependencies

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

Units

g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2
Default value

[1.0, 10.0, 1.0] kg*m^2
Program usage name

I_vector
Evaluatable

Yes

Initial Conditions

# Initialization — kinetic momentum at the initial moment of time
Specify angular momentum | Specify angular velocity

Details

Parameterization of the kinetic momentum at the initial instant of time. Defined as:

  • Specify angular momentum - initial value of kinetic momentum;

  • Specify angular velocity - initial value of angular velocity.

Values

Specify angular momentum | Specify angular velocity
Default value

Specify angular momentum
Program usage name

initial_angular_momentum_parameterization
Evaluatable

No

# Initial angular momentum — initial value of kinetic momentum
kg*m^2/s

Details

Setting the initial value of the kinetic moment.

Dependencies

To use this parameter, set the Initialisation parameter to Specify angular momentum.

Units

kg*m^2/s
Default value

0.0 kg*m^2/s
Program usage name

L_start
Evaluatable

Yes

# Initial angular velocity — initial value of angular velocity
rpm | deg/s | rad/s

Details

Sets the initial value of the angular velocity.

Dependencies

To use this parameter, set the Initialisation parameter to Specify angular velocity.

Units

rpm | deg/s | rad/s
Default value

0.0 rad/s
Program usage name

w_start
Evaluatable

Yes

# Initial angle — initial value of rotation angle
deg | rad | rev | mrad

Details

Sets the initial value of the rotation angle.

Units

deg | rad | rev | mrad
Default value

0.0 rad
Program usage name

phi_start
Evaluatable

Yes

See also

  1. Variable Inertia

  2. Variable Mass