Operation

Operation
^ The planetary gear works as a transmission 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.





^ The pinion gears turn in the following two ways:
- On their own centers ("rotation")
- On the center of the planetary gear ("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: (1)

Meaning of symbol
Z: Number of teeth
N: Rotation speed
R: Internal gear
S: Sun gear
C: Planetary carrier (pinion gear)
?: Unit symbol





Number of teeth and symbol of each gear





First gear





Gear rotation speed





Suppose gear ratio in first gear is i1
i1=Rear planetary gear ratio (i1') x Reduction planetary gear ratio (iRD)
^ From the result NRR=O in formula (1), the relation between the gear ratio in first gear and the rotation speed of the planetary gear set is indicated in the formula below.
(ZRR+ZRS)NRC=ZRSxNRS
i1'=NRS/NRC=(ZRR+ZRS)/ZRS

Next iRD
^ From the result NDS=0 in formula (1), the relation between the gear ratio in first gear and the rotation speed of the planetary gear set is indicated in the formula below/
(ZDR+ZDS)NDC=ZDRxNDR
iRD=NDR/NDC=(ZDR+ZDS)/ZDR
Therefore,
i1=i1'xiRD=(ZRR+ZRS)/ZRSx(ZDR+ZDS)/ZDR =(75+42)/42x(85+31)/85=3.802

Second gear





Gear rotation speed





Suppose gear ratio in second gear is i2,
i2=front and rear planetary gear ratio (i2')x reduction planetary gear ratio (iRD)
i2'=NRS/NRR
NRC=NFR, NRR=NFC: condition A
^ From formula (1), the relation between the gear ratio in second gear and the rotation speeds of the front and the rear planetary gear sets is indicated in formulas (2) and (3).
(ZFR+ZFS)xNFC=ZFRxNFR+ZFSxNFS: (2)
(ZRR+ZRS)xNRC=ZRRxNRR+ZRSxNRS: (3)
^ From the result NFS=0 in formula (2)
NFC=ZFR/(ZFR+ZFS)xNFR: (4)
^ According to condition A
NFC=NRR=ZFR/(ZFR+ZFS)xNRC
^ Here we substitute condition A in formula (3)
(ZRR+ZRS)xNRC=ZRRxZFR/(ZFR+ZFS)xNRC+ZRSxNRS
i2'=NRS/NRC=((ZRR+ZRS)-ZRRxZFR/(ZFR+ZFS))/ZRS
i2=i2'xiRD=((ZRR+ZRS)-ZRRxZFS/(ZFR+ZFS))/ZRSx(ZDR+ZDS)/ZDR
=((75+42)-75x74/(74+34))/42x(85+31)/85
=2.132

Third gear





Gear rotation speed





i3=i3'xiRD
i3'=NRR/NRC
NRR=NRS: condition B
^ Here we substitute condition B in formula (1)
(ZRR+ZRS)xNRC=ZRRxNRS+ZRSxNRS
(ZRR+ZRS)xNRC=(ZRR+ZRS)xNRS
i3'=NRS/NRC=(ZRR+ZRS)/(ZRR+ZRS)=1.000
i3=(ZRR+ZRS)/(ZRR+ZRS)x(ZDR+ZDS)/ZDR
=(75+42)/(75+42)x(85+31)/85
=1.365

Fourth gear





Gear rotation speed





i4=i4'xiRD
i4'=NFC/NFR
^ From the result of NFS=0 in formula (1), the relation between the gear ratio in fourth gear and the rotation speed of the planetary gear set indicated in the formula below.
(ZFR+ZFS)xNFC=ZFRxNFR
i4'=NFC/NFR=ZFR/(ZFR+ZFS)
i4=ZFR/(ZFR+ZFS)x(ZDR+ZDS)/ZDR
=74/(74+34)x(85+31)/85
=0.935

Fifth gear





Gear rotation speed





i5=i4'xiRD
i4'=See forth gear
^ From the result of NDC=NDS in formula (1), the relation between the gear ratio in fifth gear and the rotation speed of the planetary gear set is indicated in the formula below.
(ZDR+ZDS)xNDC=ZDRxNDR+ZDSxNDC
iRD=NDR/NDC=(ZDR+ZDS)/(ZDR+ZDS)=1.000
i5=i4'xiRD=ZFR/(ZFR+ZFS)x(ZDR+ZDS)/(ZDR+ZDS)
=0.685

Reverse








iR=iR'xiRD
iR'=NFS/NFR
^ From the result of NFC=0 in formula (1), the relation between the gear ratio in reverse gear and the rotation speed of the planetary gear set is indicated in the formula below.
0=ZFRxNFR+ZFSxNFS
iR'=NFS/NFR=ZFR/ZFS
iR=-ZFR/ZFSx(ZDR+ZDS)/ZDR
=-74/34x(85+31)/85
=-2.970