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Planet Ring Gear

Planet Ring Gear component

          

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

 

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

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

 

Including Planet/Carrier Bearing Friction

 

 

Kinematic Equation

 

 rR/P 1ϕc = rR/P·ϕR  +ϕP 

 

 

where   rR/P  is the gear ratio and is defined as:

 rR/P=NRNP 

where NR is the number of teeth of the outer planet gear and   NP  is the number of teeth of the inner planet gear.

Also ϕC , ϕR  and ϕP are defined as the rotation angles of the carrier, outer planet, and inner planet, respectively.

 

 

Torque Balance Equation (No Inertia)

 

rR/P·npl · τp =  τloss  τR 

 

τc+npl · τp + τR  = 0 

 

where τC , τR and τp are the torques applied to the carrier, ring, and planet, respectively and npl is the number of identical planets meshing with the ring.

Also τloss is the loss torque and is defined as:

 

  τloss=     npl · rR/P · d·ωP/C + (1η1(ωR/C))· τR       ωR/C · τR  >0  (11η2(ωR/C) )·τR    ωR/C · τR  0        

Also

ωP/C = ωP  - ωC

ωR/C = ωR  - ωC

 

where

ωx  = ϕ·x  ,      x  P,R,C

 

 

Power Loss:

The power loss (Ploss) is calculated as:

 

 

Ploss =  0       ideal=true npl·d·ωP/C 2+ 1η1τR·ωR/C         τR· ωR/C0npl·d·ωP/C 2+ 11η2τR·ωR/C        τR· ωR/C0

 

 

Connections 

Name

Condition

Description

ID

carrier

-

Carrier flange

carrier

planet

-

Planet flange

planet

ring

-

Ring flange

ring

Loss Power

ideal=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=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

ninput

data source = input port

1

-

Number of efficiency inputs

• 

1 input: η=η1 = η2

• 

2 inputs: η1 , η2

inputNo

rR/P

-

1

-

Gear ratio

ratio

npl

ideal=false

1

Number of planet gears

numberofPlanets

ηωR/C

ideal=false

 

data source = GUI

  0,1,1 

rads,,

Defines Ring/Planet velocity dependant meshing efficiency as a function of ωR/C .

The columns:

[ωR/C    (η1 (ωR/C )     η2 (ωR/C )]

First column is angular velocity of inner gear w.r.t. carrier (ωR/C)

Five options are available:

• 

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

η1 (ωR/C ) = η2 (ωR/C ) = η

• 

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

η1 (ωR/C ) = η1 , η2 (ωR/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

η (ωR/C) = η1 (ωR/C ) = η2(ωR/C )

• 

n by 3 array:

Second column is forward efficiency

η1 (ωR/C)

Third column is backward efficiency

η2 (ωR/C )

meshinglossTable

ideal=false

 

data source = attachment

   

-

 

 

Defines velocity dependant meshing efficiency

First column is angular velocity (ωR/C )

(See col η below)

 

data

ideal=false

 

data source = file

   

-

 

fileName

col η

ideal=false

 

data source = attachment or file

  2,3

 

-

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 (η=η1 = 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)

columns1

d

ideal=false

0

N · mrads

Linear damping in planet/carrier bearing

d

smoothness

ideal=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 rR/P  must be strictly greater than one.

 

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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