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Planet Planet Gear

Planet Planet Gear component     

     

 

The Planet Planet Gear component models a set of carrier, inner planet, and outer planet gear wheels with a specified gear ratio without inertia, elasticity, or backlash. The inertia of the gears and carrier may be included by attaching Inertia components to the ‘inplanet,’ ‘outplanet’, or ‘carrier’ flanges respectively. The damping in the bearing connecting the planet(s) to carrier can be included via the component options. Bearing friction on the ‘inplanet’, ‘outplanet’, and ‘carrier’ shafts may be included by attaching Bearing Friction component(s) to these flanges.

Note 1: Since the outer planet’s mass is rotating at a distance from the Planet Planet gear axis, ensure that when adding inertia to the ‘outer planet', proper inertia is also added to the ‘carrier’.

Note 2: When attaching a bearing friction component to the outer planet shaft to represent outplanet/carrier bearing friction, the configuration shown in the figure below should be used to correctly account for the relative velocity of the outer planet with respect to the carrier.

 

Including Outer Planet/Carrier Bearing Friction

 

 

Kinematic Equation

 

1+rO/I ϕc = rO/I·ϕO  +ϕI 

 

 

Where rO/I  is the gear ratio and is defined as:

 rO/I=NONI 

Where   NO is the number of teeth of the outer planet gear and    NI  is the number of teeth of the inner planet gear.
  Also ϕC , ϕO  and ϕI are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively.

 

 

 

Torque Balance Equation (No Inertia)

 

npl ·rO  =   rO/I·τIτloss

τC +npl· τO  + τI=  0

 

Where τC , τO ,τI  are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively. npl is the number of identical outer planets meshing with the inner planet.

Also τloss is the loss torque and is defined as:

 

  τloss&equals;     nplrO&sol;I ·  d·&omega;0&sol;C &plus; &lpar;1&eta;2&lpar;&omega;I&sol;C&rpar;&rpar;· &tau;1       &tau;10  &lpar;11η1&lpar;ωI&sol;C&rpar; &rpar;·&tau;1    &tau;1<0        

 

 

Also

ωI&sol;C = ωI  - ωC

ωO&sol;C = ωO  - ωC

 

Where

&omega;x  &equals; &varphi;·x  ,      x  I&comma;O&comma;C

 

 

Power Loss

 

The power loss (Ploss) is calculated as:

 

Ploss &equals; 0        ideal&equals;true npl·d·ω0&sol;C 2&plus; 1η2τ1·ωI&sol;C        &tau;1· ωI&sol;C0 npl·d·ω0&sol;C 2&plus; 11η1τ1·ωI&sol;C        &tau;1· ωI&sol;C0 

 

 

 

Connections 

 

Name

Condition

Description

ID

Carrier

-

Carrier flange

carrier

Inner planet

-

Inner planet flange

inplanet

Outer planet        

-

Outer planet flange

outplanet

Loss Power

ideal&equals;false

Conditional real output port for power loss

lossPower

Meshing Loss Data

data source = input port

Conditional real input port for meshing 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

• 

1 input: &eta;&equals;&eta;1 &equals; η2

• 

2 inputs: &eta;1 &comma; &eta;2

inputNo

rO&sol;I

-

1

-

Gear ratio

ratio

npl

ideal&equals;false

1

Number of planet gears

numberofPlanets

ηωI&sol;C

ideal&equals;false

 

data source = GUI

  0&comma;1&comma;1 

rads&comma;&comma;

Defines Outer Planet/Inner Planet velocity dependant meshing efficiency as a function of ωI&sol;C .

The columns:

[ωI&sol;C     (η1 (ωI&sol;C )     η2 (ωI&sol;C )]

First column is angular velocity of inner gear w.r.t. carrier (ωI&sol;C)

Five options are available:

• 

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

η1 (ωI&sol;C ) = &eta;2 (ωI&sol;C ) = &eta;

• 

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

η1 (ωI&sol;C ) = &eta;1 &comma; &eta;2 (ωI&sol;C ) = 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: Second column is forward and backward efficiency

&eta; (ωI&sol;C ) = η1 (ωI&sol;C ) = η2(ωI&sol;C )

• 

n by 3 array:

Second column is forward efficiency

η1 (ωI&sol;C)

Third column is backward efficiency

η2 (ωI&sol;C )

meshinglossTable

ideal&equals;false

 

data source = attachment

   

 

 

Defines velocity dependant meshing efficiency

First column is angular velocity (ωI&sol;C )

(See col &eta; below)

 

data

ideal&equals;false

 

data source = file

   

 

fileName

col &eta;

ideal&equals;false

  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 efficiency (&eta;&equals;&eta;1 &equals; η2&rpar; 

• 

1 by 2 array:

Data column corresponding to the first column number is used for forward efficiency ( &eta;1&rpar; 

and data column corresponding to the second column number is used for backward efficiency ( &eta;2&rpar;

columns1

d

ideal&equals;false

0

N·mrads

Linear damping in planet/carrier bearing

d

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:  Gear ratio rO&sol;I  must be strictly greater than zero.

 

See Also

MapleSim Driveline Library Overview

MapleSim Library Overview

1-D Mechanical Overview

Basic Gear Sets

 

 

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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