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Basic Gear

Basic Gear component

        

The Basic Gear component models two meshing gears without inertia, elasticity or backlash. Gear and bearing friction inertia may be included by attaching the Inertia and Bearing Friction components to either ‘flange_a’ or ‘flange_b’, respectively.

 

Kinematic Equation

 

ϕa = rb/a·ϕb  

 

Where   rb/a  is the gear ratio and is defined as:

 rb/a=NbNa 

Where Na is the number of teeth of the a-side gear and Nb is the number of teeth of the b-side gear. Also, ϕa  and ϕb are defined as

 

ϕx = ϕfx  ϕsupport      use Support = true0otherwise  ,   x ∈ a,b

 

 

Where ϕfa and ϕfb are the absolute rotation angles of flange_a and flange_b, respectively.

 

 

 

 

 

Torque Balance Equation (No Inertia)

 

τb=rb/a·τaτloss

 

Where τa and τb are the torques applied to flange_a and flange_b, respectively.

 

Also   τloss is the meshing loss torque and is defined as:

τloss&equals;&lpar;1&eta;1&lpar;&omega;a&rpar;&rpar; · &tau;a        &omega;a·&tau;a0  &lpar;11η2&lpar;ωa&rpar; &rpar;·&tau;a     &omega;a·&tau;a<0        

Where

ωa = &DifferentialD;&DifferentialD; t ϕa &equals;&varphi;·a 

When useSupport = true, the following equation is added to calculate the support reaction torque:

 

τsupport  =   τa&plus;&tau;b

 

Power Loss:

The power loss (Ploss) is calculated as:

 

Ploss &equals; 0          ideal&equals;true1η1 · &tau;a· ωa          &tau;a· ωa0 11η2  · &tau;a· ωa        &tau;a· ωa<0

 

Connections 

Name

Condition

Description

ID

flangea

-

Flange to driver shaft

flange_a

flangeb

-

Flange to driven shaft

flange_b

support

use support&equals;true

Conditional Support Flange

support

Loss Power

ideal&equals;false

Conditional real output port for power loss

lossPower

Loss Data

data source = input port

Conditional real input port for loss data

lossdata

 

Parameters

Symbol

Condition

Default

Units

Description

ID

ideal

-

true

-

Defines whether the component is:

true - ideal or

false - non-ideal

ideal

data source

ideal&equals;false

GUI

-

Defines the source for the loss data:

• 

entered via GUI [data entered via GUI]

• 

by an attachment [data is attached to model]

• 

by an external file [data is stored in a file]

• 

an input port [input port]        

datasourcemode

ninputs

data source = input port

1

-

Number of inputs

• 

One input (ninputs=1): Forward and backward efficiencies are the same:&eta;&equals;&eta;1 &equals; η2

• 

Two inputs (ninputs=2): Forward and backward efficiencies are given independently: &eta;1 &comma; &eta;2

inputNo

use support        

-

false

-

Enables/disables the support flange        

useSupport

rb&sol;a

-

1

-

Gear ratio

ratio

&eta;&omega;a

data source = GUI

  0&comma;1&comma;1 

rads&comma;&comma;

Defines velocity dependant meshing efficiency

The columns:

[ωa     (η1 (ωa )     η2 (ωa )]

Five options are available:

• 

1 by 1 array: entered value is taken as the constant efficiency for forward and backward cases

η1 (ωa ) = η2 (ωa ) = η

• 

1 by 2 array: first entered value is taken as the constant efficiency for forward case and the second for backward cases

η1 (ωa ) = η1 &comma; &eta;2 (ωa ) = η2

• 

1 by 3 array: first column is ignored and the second and third values are taken as constant efficiencies for forward and backward cases, respectively

• 

n by 2 array: 2nd column is forward and backward efficiency

&eta; (ωa ) = η1 (ωa ) = η2(ωa )

• 

n by 3 array:

2nd column is forward efficiency

η1 (ωa )

3rd column is backward efficiency

η2 (ωa )

Note: The rows of the array are ordered according to ωa, with the first row having the smallest |ωa|

meshinglossTable

data source = attachment

   

Defines velocity dependant meshing efficiency

First column is angular velocity (ωa )

(See col &eta; below)

data

data source = file

   

Defines velocity dependant meshing efficiency

fileName

col &eta;

data source = attachment or file

  2&comma;3

 

-

Defines the corresponding data columns used for forward efficiency (η1) and backward efficiency (η2 )

Two options are available:

• 

1 by 1 array:

Data column corresponding to the column number is used for both forward and backward efficiencies (η&equals;η1 &equals; η2) 

• 

1 by 2 array:

Data column corresponding to the first column number is used for forward efficiency (η1)

and data column corresponding to the second column number is used for backward efficiency (η2)

columns

smoothness

ideal&equals;false

Table points are linearly interpolated

-

Defines the smoothness of table interpolation. There are two options:

• 

Table points are linearly interpolated

• 

Table points are interpolated such that the first derivative is continuous

smoothness

 

 

Note:  The ratio (rb&sol;a) must be non-zero. Negative values are permissible.  For (rb&sol;a) < 0, the Basic Gear component resembles the Ideal Gear (when ideal = true) and Lossy Gear (ideal = false).

 

See Also

MapleSim Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

Basic Gear Sets

Ideal Gear

Lossy Gear

 

 

References

Pelchen C., Schweiger C., and Otter M., “Modeling and Simulating the Efficiency of Gearboxes and Planetary Gearboxes,” 2nd International Modelica Conference, Proceedings, pp. 257-266.

 

 


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