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transmission

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transmission

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Iconic Diagrams\Mechanical\Rotation\Gears

Implementations

Ideal

Lossy

Use

Domains: Continuous. Size: 1-D. Kind: Iconic Diagrams (Rotation).

Description - Ideal

This models represents any type of gearbox with two shafts rotating in the same direction. The gear is ideal, i.e., it does not have inertia or friction. The gear has one fast moving shaft and one slow moving shaft. The gearbox has a reduction of i : 1 and thus a transmission ratio of 1/i.

 

The causality of this model is always mixed: one port has a torque out causality while the other has an angular velocity out causality:

 

p_in.T = 1/i * p_out.T

p_out.omega = 1/i * p_in.omega

 

or:

 

p_out.T = i * p_in.T

p_in.omega = i * p_out.omega

 

Interface - Ideal

Ports

Description

p_in

p_out

Input port

Output port

Causality

 

p_in not equal p_out

 

Parameters

 

i

gearbox reduction, i > 1

Description - Efficiency

This models represents any type of gearbox with two shafts rotating in the same direction. The gearbox has a reduction of i : 1 and thus a transmission ratio of 1/i.

 

p_in.omega = i * p_out.omega

 

Unlike the model of an ideal gearbox, this model includes power loss. The power loss is represented by the efficiency, where the efficiency is defined as the output power divided by the input power:

 

eff = Pout / Pin

 

The efficiency is a value between zero and one and given by the gearbox manufacturer. If you do no know the value, a good guess is a power loss of 3% per stage (eff = 0.97). If your gearbox for example contains three stages, you can set the efficiency as:

 

eff = 0.97*0.97*0.97 = 0.91

 

Interface - Efficiency

Ports

Description

p_in

p_out

Input port

Output port

Causality

 

p_in not equal p_out

 

Parameters

 

i

eff

gearbox reduction [-], i > 1

gearbox efficiency [-]

Description - Lossy

This models represents any type of gearbox with two shafts rotating in the same direction. The gearbox has a reduction of i : 1 and thus a transmission ratio of 1/i.

 

p_in.omega = i * p_out.omega

 

Unlike the model of an ideal gearbox, this model includes rotational inertia and power loss. The inertia is defined at the input axis. If the gearbox manufacturer gives the inertia at the output axis you can calculate the inertia at input axis as:

 

Jinput = Joutput/i^2

 

The power loss is represented by the efficiency, where the efficiency is defined as the output power divided by the input power:

 

eff = Pout / Pin

 

The efficiency is a value between zero and one and given by the gearbox manufacturer. If you do no know the value, a good guess is a power loss of 3% per stage (eff = 0.98). If your gearbox for example contains three stages, you can set the efficiency as:

 

eff = 0.97*0.97*0.97 = 0.91

Interface - Lossy

Ports

Description

p_in

p_out

Input port

Output port

Causality

 

preferred angular velocity out p_in

preferred angular velocity out p_out

 

Parameters

 

i

J

eff

gearbox reduction [-], i > 1

moment of inertia [kgm^2]

gearbox efficiency [-]