PLANETARY GEAR OPERATIONSM1759151
PLANETARY GEAR OPERATION

D6E051719540A03

• The planetary gear works as a transaxle when the sun gear and the internal gear are engaged.
• The sun gear, installed inside of the pinion gears, and the internal gear, installed outside of the pinion gears, are engaged with their respective gears.
The sun gear and the internal gear rotate on the center of the planetary gear.
B3E0517A006

1
Sun gear
2
Internal gear
3
Planetary carrier
4
Pinion gear

• The pinion gears turn in the following two ways:
- On their own centers (rotation)
- On the center of the planetary gear (revolution)
B3E0517A0072

1
Rotation
2
Revolution


Gear ratio of each range

• The relation between each element of the planetary gear set and the rotation speed is generally indicated in the formula below.
(Z R+Z S) N C=Z RN R+Z SN S: formula (1)
In this formula Z stands for the number of teeth, N stands for the rotation speed, and R, S, C stand for each gear element (refer to the table below).
B3E0517A0063

1
Sun gear
2
Internal gear
3
Planetary carrier
4
Pinion gear

Number of teeth and symbol of each gear

Planetary gear unit

Planetary gear element

Number of teeth

Unit identification symbol

Gear element

Unit

Front
Internal gear
89
R
F
Planetary carrier
(part of pinion gear)
20
C
F
Sun gear
49
S
F
Rear
Internal gear
98
R
R
Planetary carrier
(part of pinion gear)
30
C
R
Sun gear
37
S
R
Secondary
Internal gear
89
R
S
Planetary carrier
(part of pinion gear)
29
C
S
Sun gear
31
S
S


First gear

D6E517YA50044
　

1
Front planetary gear
2
Secondary planetary gear
3
Sun gear N SF (input)
4
Internal gear (fix)
5
Planetary carrier N CF (output)
6
Pinion gear
7
Sun gear (fix)
8
Internal gear N RS (input)
9
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear unit

Front

Secondary

Internal gear
0 (fix)
N RS (input)
Planetary carrier
N CF (output)
N CS (output)
Sun gear
N SF (input)
0 (fix)

• Suppose the reduction ratio on the main shifting side is i 1,
i 1=N SF/N CF.
• From the result N RF=0 in formula (1), the rotation speed of the front planetary gear unit can be calculated using the following formula:
(Z RF+Z SF)N CF=Z SFN SF
Therefore,
i 1=N SF/N CF=(Z RF+Z SF)/Z SF=(89+49)/49=2.8163.
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii 1,
ii 1=N RS/N CS.
• From the result N SS=0 in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=Z SSN RS
Therefore,
ii 1=N RS/N CS=(Z RS+Z SS)/Z RS=(89+31)/89=1.3483
And the reduction ratio of 1st gear= i 1 x A x ii 1=2.8163 x 0.9535 x 1.3483=3.620
As a result, the reduction ratio of 1st gear is 3.620.

Second gear

D6E517YA50055
　

1
Front planetary gear
2
Rear planetary gear
3
Secondary planetary gear
4
Sun gear N SF (input)
5
Internal gear N RF=N C
6
Planetary carrier N CF (output) =N R
7
Pinion gear
8
Sun gear (fix)
9
Internal gear N RR (output) =N R
10
Planetary carrier N CR=N C
11
Sun gear (fix)
12
Internal gear N RS (input)
13
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear

Front

Rear

Secondary

Internal gear
N RF=N C
N RR (output) =N R
N RS (input)
Planetary carrier
N CF (output) =N R
N CR=N C
N CS (output)
Sun gear
N SF (input)
0 (fix)
0 (fix)

Note
• The front internal gear and the rear planetary carrier are integrated.
• The front planetary carrier and the rear internal gear rotate at the same speed.
• Suppose the reduction ratio on the main shifting side is i 2,
i 2=N SF/N R.
• From formula (1), the relation between the gear ratio in second gear and the rotation speeds of the front and the rear planetary gar sets is indicated in formulas (2) and (3).
(Z RF+Z SF) N R=Z RFN C+Z SFN SF: (2) (Front planetary gear set)
(Z RR+Z SR) N C=Z RRN R+Z SRN SF: (3) (Rear planetary gear set)
• From the result N SR=0 in formula (3).
N C= (Z RR/ (Z RR+Z SR)) N R: (4)
• Here we substitute formula (4) in formula (2).
Z SRN SF= (((Z RR+Z SR) (Z RF+Z SF) -Z RFZ RR) / (Z RR+Z SR)) N R
Therefore,
i 2=N SF/N R= (((Z RR+Z SR) (Z RF+Z SF) -Z RFZ RR) / (Z SF (Z RR+Z SR))) N R
= ((98+37)(89+49) -89 x 98) / (49 (98+37)) =1.4978
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii 2,
ii 2=N RS/N CS.
• From the result N SS=0 in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=Z SSN RS
Therefore,
ii 2=N RS/N CS=(Z RS+Z SS)/Z RS=(89+31)/89=1.3483
And the reduction ratio of 2nd gear= i 2 x A x ii 2=1.4978 x 0.9535 x 1.3483=1.925
As a result, the reduction ratio of 2nd gear is 1.925.

Third gear

D6E517YA50066
　

1
Front planetary gear
2
Secondary planetary gear
3
Sun gear N SF (input)
4
Internal gear N RF (input)
5
Planetary carrier N CF (output)
6
Pinion gear
7
Sun gear (fix)
8
Internal gear N RS (input)
9
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear

Front

Secondary

Internal gear
N RF (input)
N RS (input)
Planetary carrier
N CF (output)
N CS (output)
Sun gear
N SF (input)
0 (fix)

• Here we have the result on N RF=N SF.
• Suppose the reduction ratio on the main shifting side is i 3,
i 3=N SF/N CF.
• From the result of N RF=N SF in formula (1), the relation between the gear ratio in 3rd gear and the rotation speed of the front planetary gar set is indicated in the following formula:
(N RF+Z SF) N CF= (Z RF+Z SF) N RF
Therefore,
i 3=N RF/N CF= (Z RF+Z SF) / (Z RF+Z SF) = (89+49) / (89+49) =1.000
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii 3,
ii 3=N RS/N CS.
• From the result N SS=0 in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=Z SSN RS
Therefore,
ii 3=N RS/N CS=(Z RS+Z SS)/Z RS=(89+31)/89=1.3483
And the reduction ratio of 3rd gear= i 3 x A x ii 3=1.000 x 0.9535 x 1.3483=1.285
As a result, the reduction ratio of 3rd gear is 1.285.

Fourth gear

D6E517YA50077
　

1
Rear planetary gear
2
Secondary planetary gear
3
Sun gear (fix)
4
Internal gear N RR (output)
5
Planetary carrier N CR (input)
6
Pinion gear
7
Sun gear (fix)
8
Internal gear N RS (input)
9
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear

Rear

Secondary

Internal gear
N RR (output)
N RS (input)
Planetary carrier
N CR (input)
N CS (output)
Sun gear
0 (fix)
0 (fix)

• Suppose gear ratio in fourth gear is i 4,
i 4=N CR/N RR
• From the result of N SR=0 in formula (2), the relation between the gear ratio in fourth gear and the rotation speed of the rear planetary gear set is indicated in the following formula:
(Z RR+Z SR) N CR=Z RRN RR
Therefore,
i 4=N CR/N RR=Z RR/ (Z RR+Z SR) =98/ (98+37) =0.7259
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii 4,
ii 4=N RS/N CS.
• From the result N SS=0 in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=Z SSN RS
Therefore,
ii 4=N RS/N CS=(Z RS+Z SS)/Z RS=(89+31)/89=1.3483
And the reduction ratio of 4th gear= i 4 x A x ii 4=0.7259 x 0.9535 x 1.3483=0.933
As a result, the reduction ratio of 4th gear is 0.933.

Fifth gear

D6E517YA50088
　

1
Rear planetary gear
2
Secondary planetary gear
3
Sun gear (fix)
4
Internal gear N RR (output)
5
Planetary carrier N CR (input)
6
Pinion gear
7
Sun gear N SS (input)
8
Internal gear N RS (input)
9
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear

Rear

Secondary

Internal gear
N RR (output)
N RS (input)
Planetary carrier
N CR (input)
N CS (output)
Sun gear
0 (fix)
N SS (input)

• Suppose gear ratio in fifth gear is i 5,
i 5=N CR/N RR
• From the result of N SR=0 in formula (2), the relation between the gear ratio in fourth gear and the rotation speed of the rear planetary gear set is indicated in the following formula:
(Z RR+Z SR) N CR=Z RRN RR
Therefore,
i 5=N CR/N RR=Z RR/ (Z RR+Z SR) =98/ (98+37) =0.7259
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii 5,
ii 5=N RS/N CS.
• From the result N RS=N SS in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=(Z RSZ SS)N RS
Therefore,
ii 5=N RS/N CS=(Z RS+Z SS)/(Z RS+Z SS)=(89+31)/(89+31)=1.000
And the reduction ratio of 5th gear= i 5 x A x ii 5=0.7259 x 0.9535 x 1.000=0.692
As a result, the reduction ratio of 5th gear is 0.692.

Reverse

D6E517YA50099
　

1
Rear planetary gear
2
Secondary planetary gear
3
Sun gear N SR (input)
4
Internal gear N RR (output)
5
Planetary carrier (fix)
6
Pinion gear
7
Sun gear (fix)
8
Internal gear N RS (input)
9
Planetary carrier N CS (output)

Gear rotation speed

Planetary gear

Rear

Secondary

Internal gear
N RR (output)
N RS (input)
Planetary carrier
0 (fix)
N CS (output)
Sun gear
N SR (input)
0 (fix)

• Suppose gear ratio in reverse gear is i REV,
i REV=N SR/N RR
• From the result of N CR=0 in formula (2), the relation between the gear ratio during reverse movement and the rotation speed of the planetary gar set is indicated in the formula below.
(Z RR+Z SR) 0=Z RRN RR+Z SRN SR
Therefore,
i REV=N SR/N RR=Z RR/Z SR=-98/37=-2.6486
• Because the reduction ratio on the main shifting side is transmitted from the primary gear to the secondary gear, it can be calculated using the following formula:
The reduction ratio of the primary/secondary gear A = the number of primary gear teeth/the number of secondary gear teeth
Therefore,
A=82/86=0.9535
• Suppose the reduction ratio on the sub-shifting side is ii REV,
ii REV=N RS/N CS.
• From the result N SS=0 in formula (1), the rotation speed of the secondary planetary gear unit can be calculated using the following formula.
(Z RS+Z SS)N CS=Z SSN RS
Therefore,
ii REV=N RS/N CS=(Z RS+Z SS)/Z RS=(89+31)/89=1.3483
And the reduction ratio of reverse gear= i REV x A x ii REV=-2.6486 x 0.9535 x 1.3483=-3.405
As a result, the reduction ratio of reverse gear is -3.405.