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Lossy Gear

Gear with mesh efficiency and bearing friction (stuck/rolling possible)

 

Description

Variables

Connections

Parameters

Constants

Modelica Standard Library

Description

The Lossy Gear component models the gear ratio and the losses of a standard gear box in a realistic way, including the stuck phases that may occur at zero speed. The gear boxes that can be handled are fixed in the ground or on a moving support, have one input and one output shaft, and are essentially described by the equations

φa=rφb

τb=rηmfτaτbf

where r is constant gear ratio, ηmf is the efficiency due to mesh friction, and τbf is the bearing friction torque.

Loss Table

The Loss Table parameter is five-column table that defines the loss terms ηmf and τbf in terms of the absolute value of the input shaft speed, wa, and of the energy flow direction. Its columns are |wa|,ηmf1,ηmf2,τbf1,τbf2 with

wa

rads

Angular speed of flangea

ηmf1

1

Mesh efficiency when input shaft is driving

ηmf2

1

Mesh efficiency when output shaft is driving

τbf1

Nm

Absolute bearing friction torque when input shaft is driving

τbf2

Nm

Absolute bearing friction torque when output shaft is driving

The rows of the Loss Table are ordered according to ωa, with the first row having the smallest ωa. The values for ηmf1, ηmf2, τbf1, and τbf2 at a particular shaft speed are interpolated from the values in the table.

To add rows to the table, right-click on the value and select Edit Matrix Dimension.

With these variables, the mesh efficiency and the bearing friction are formally defined as

{ηmf&equals;ηmf1&comma;τbf&equals;τbf1τaτbfawa&gt;0τa&equals;τbfawa&gt;0ηmf&equals;ηmf2&comma;τbf&equals;τbf2τaτbfawa<0τa&equals;τbfawa<0w&period;a&equals;0otherwise

Losses are modeled in a physically meaningful way taking into account that at zero speed the movement may be locked due to the friction in the gear teeth and/or in the bearings.

Variables

Name

Units

Description

Modelica ID

φx

rad

Absolute angle of flangex&comma;xa&comma;b

flange_x.phi

φsupport

rad

Absolute angle of support flange

support.phi

τx

Nm

Torque applied to flangex&comma;xa&comma;b

flange_x.tau

Connections

Name

Description

Modelica ID

flangea

Flange of left shaft

flange_a

flangeb

Flange of right shaft

flange_b

support

Conditional Support Flange

support

heatPort

Optional heat port

heatPort

Parameters

Name

Default

Units

Description

Modelica ID

r

1

1

Transmission ratio (φaφb)

ratio

Loss Table

0.&comma;1.&comma;1.&comma;0.&comma;0.

 

Matrix for mesh efficiencies and bearing friction depending on speed

lossTable

Use Heat Port

false

 

True (checked) means heat port is enabled

useHeatPort

Use Support Flange

false

 

True (checked) enables the support flange

useSupport

Constants

Name

Value

Units

Description

Modelica ID

Unknown

3

 

Value of mode is not known

Unknown

Free

2

 

Element is not active

Free

Forward

1

 

w_a > 0 (forward rolling)

Forward

Stuck

0

 

w_a = 0 (forward rolling, locked or backward rolling)

Stuck

Backward

−1

 

w_a < 0 (backward rolling)

Backward

unitAngularAcceleration

1

rads2

 

unitAngularAcceleration

unitTorque

1

Nm

 

unitTorque

Modelica Standard Library

The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here.

See Also

1-D Mechanical Overview

Rotational Bearings and Gears