Epicyclic or Planetary Gear Train (Automobile)

25.11.

Epicyclic or Planetary Gear Train

Epicyclic gear trains are generally used for automatic transmission, overdrives, and final drives. The most commonly used gear trains in automatic transmission system are three-speed Simpson gear train and two-speed Ravingeau gear train. The layout of a simple single-stage epicyclic gear train is shown in Fig. 25.24. Epicyclic gears are very widely used in automatic transmission because,
(a) they are always in constant-mesh
(fc) engagement of these gears may be obtained smoothly and quietly by the application of brake bands, and
(c) considerable variation in gear ratios both forward and reverse can be obtained through epicyclic gear trains.
25.11.1.

Simple Epicyclic Gear Train

An epicyclic single-stage gear train consists of an internally toothed annular (ring) A (Fig. 25.24) with a band brake encircling it. In the centre of this gear is sun gear S, which forms part
Positive baulk pin synchromesh unit A. Sectioned view. B. Disengaged position. C. Synchronization position. D. Engaged position.
Fig. 25.23. Positive baulk pin synchromesh unit
A. Sectioned view. B. Disengaged position.
C. Synchronization position. D. Engaged position.
of the input shaft. The sun gear and the annular gear are connected by a number of planet (pinion) gears P which are mounted on a carrier C and is integral with the output shaft. For transmission of torque, either the sun gear, the carrier, or the annular gear must be held stationary.
The situation is considered when only the annular gear is stationary. When the input sun gear shaft is driven keeping the annular gear band brake fixed, the planet gears simultaneously rotate around their axes and revolve around the input sun gear axis along the inner circum­ference of the annular gear. Consequently, the carrier and the output shaft, which support the planet-gear axes, also rotate, but slower than the input shaft.
Let, Ta = number of teeth on annular, internal or ring gear
Ts = number of teeth on sun or centre gear Tp = number of teeth on planet gear Tc = number of effective teeth on arm or planet carrier
Also Ta = Ts + 2Tp and Tc = Ts + Ta


First Gear Ratio.

The annular gear is held stationary and the planet carrier is driven by the power supplied to the sun gear.
clip_image002

Second Gear Ratio.

The sun gear is held stationary. The planet carrier is the driven member and the annular gear is the driving member.
clip_image003
 Simple epicyclic gear train
Fig. 25.24. Simple epicyclic gear train.

Reverse Gear

Here the planed carrier is held stationary. The annular gear is driven by the sun gear to which the power is applied.
clip_image005
25.11.2.

Over Drive

Propulsive power of a vehicle is a measure of the amount of work being developed by the engine in unit time. At higher vehicle speed, more power has to be developed by the engine in a shorter time. The characteristic power curve over a speed range for a petrol engine (Fig. 25.25) initially increases linearly and fairly rapidly. Towards mid-speed the gradient of the power curve decreases until the curve reaches a peak. With further speed increase, due to the difficulties experienced in breathing at very high engine speeds, the curve bends over and drops. Usually a petrol engine car is so geared that in its normal direct top gear on a level road the engine speed exceeds the peak power speed by about 10 to 20%. As a result, the falling engine power curve intersects the road resistance power curve. The point of intersecting fixed the road speed at which all the surplus power has been used and this is the maximum possible vehicle speed.
If a 20% overdrive top gear is selected, the transmission gear ratio can be so chosen that the engine and road resistance power curves coincide at peak engine power (Fig. 25.25). The under-gearing has thus caused the whole of the engine power curve to be shifted nearer the opposing road resistance power curve due to which slightly more engine power is being used. Consequently, a marginally higher maximum vehicle speed is achieved. If the amount of overdrive for top gear is increased to 40%, the engine power curve shifts to such a large extent that it intersects the road resistance power curve before peak engine power has been obtained (Fig. 25.25). Consequently, in this case the maximum possible vehicle speed cannot be reached.
Comparing the direct drive 20% and 40% overdrive with direct drive top gear power curves with respect to the road resistance power curve at 70 km/h, as an example, it can be seen (Fig. 25.25) that the power is 59%, 47% and 38% respectively. This surplus of engine power over the power utilised in overcoming road resistance is a measure of the relative acceleration ability for a particular transmission overall gear ratio setting. Also the area in the loop made between the developed and opposing power curves for direct drive top gear is the largest and therefore the engine has greatest flexibility to respond to the changing driving conditions.
In direct drive 20% over drive, the maximum engine power is developed at maximum vehicle speed. Although this provides tjie highest possible theoretical speed, but the amount of reserve power over the road resistance power is less, so that acceleration response is not rapid as with the direct drive top gear. Therefore, under these conditions, the engine speed can never exceed the peak power speed and so the engine cannot ‘over-run’, so that engine wears and noise is reduced. Fuel consumption is also less (Fig. 25.25) and the lowest specific fuel consumption is shifted to a higher cruising speed, which is desirable on motorway journeys.
At direct drive 40% o”erdrive, the engine ever reaches peak power so that not only the maximum vehicle speed is reduced compared to the 20% overdrive gearing, but the much smaller difference between power developed and power dissipated curves severelly reduce the flexibility of driving in this gear. This, therefore, necessitates for more frequent down changes of the gears with the slightest fall-off in road speed. An additional disadvantage with excessive overdrives
is that the minimum specific fuel consumption is theoretically shifted to the engine upper speed range, which is an impractical situation.
Effect of over and under gearing on vehicle performance
Fig. 25.25. Effect of over and under gearing on vehicle performance.
Thus, with a good choice of under gearing in top gear for motorway cruising conditions, benefits of prolonged engine life, reduced noise, better fuel economy and reduced driver fatigue are achieved. Another major consideration is the unladen and laden operation of the vehicle, particularly if it is to haul heavy loads. Therefore, a compromise has to be made in arriving at an optimum top gear overdrive ratio.
For obtaining overdrive gear ratio, the sun gear is held stationary (Fig. 25.24). The planet carrier becomes the driving member and the annular gear the driven one. Therefore, the input shaft drives the planet carrier and the output shaft is driven by the annular gear.
clip_image007
Example 25.4. An overdrive simple epicyclic gear train has sun and annulus gears with 21 and 75 teeth respectively. If the input speed from the engine drives the planet carrier at 3000 rpm, determine,
(a) the overdrive gear ratio, (b) the number of planet gear teeth,
(c) the annulus ring and output shaft speed, and id) the percentage of overdrive.
clip_image008
25.11.3.

Algebraic Method of obtaining Gear Ratios for Epicyclic Gear Train

Algebraic method of determining velocity ratios is most suitable in the case of simple and compound epicyclic gear trains. To apply this method to the simple gear train it is convenient to consider the velocity of gear relative to that of the arm or planet carrier as the arm can be imagined fixed. Refer Fig. 25.24.
Thus, the speed of sun relative to arm = Ns – Nc.
The speed of planet wheel relative to arm = Np – Nc
and the speed of annular or internal gear relative arm = Na – Nc
clip_image009
clip_image010
For Over-drive: Ns = 0 and drive is from Nc to Na-
Thus,
clip_image011
In the c’gse* of compound epicyclic gear trains also, the above algebraic method can be applied directly. It is only the algebra that becomes complex in these cases.
25.11.4.

Tabular Method for Obtaining Gear Ratios for Epicyclic Gear Train

When slin “gear makes one revolution anit-clockwise, the planet carrier makes (Ts/Tc) clockwise. If anticlockwise rotation’is considered positive, then clockwise rotation becomes negative (i.e. – Ts/Tc). The annujar gear makes ( – Ts/Tc) (Tc/Ta) = ( – Ts/Ta) rotation in clockwise direction. This statement il entered in the first column of the Table 5.1.

If the sun gear makes x revolution, then planet carrier makes ( – x Ts/Tc) revolution and annular makes ( – x Ts/Ta) revolution. In other words multiply the each motion (entered in the first low) by x. These statements are entered in the second row of the table.
Each element of an epicyclic gear is given y revolution and entered in the third row of the table. Finally the motion of each element of the gear train is added up and entered in the fourth row of the table.
Table 25.1.

Step No. Condition of Motion Revolution of Elements
1. Sun gear rotates +1 revolution +1 Ts Tc Ts TA
2. Sun gear rotates through x revolution + x Ts XTc Ts XTA
3. Add + y revolution to all elements +y +y +y
4. Total motion x+y Ts
y-XT-c
Ts
y-XTl

25.11.5.

Torque and Tooth Loads in Epicyclic Gear Trains

Let, ti = input torque or driving torque having wheel speed, col
t0 = output torque or resisting torque having wheel speed, co0
th = holding torque or braking torque which makes the
corresponding wheel speed, coh zero.
Assuming the different gears in the epicyclic gear train to move with uniform speed (i.e. accelerations are zero), then sum total of the torques must be zero, i.e.
clip_image012
clip_image013
25.11.6.

Compound Epicyclic Gear Train

A simple epicyclic gear train presented above can not provide adequate velocity ratios. Therefore a compound epicyclic gear train (Fig. 25.26) is used in a gearbox to give higher velocity ratios and to allow several ratios to be obtained. A compound epicyclic gear train is obtained by joining together all the arms of simple gear train ; of course the compounding can be made by different methods. In these trains the members, which become fixed when the trains are is use, are arranged to be free. The brakes are provided to bring any of these members to rest as and when required. The train to which that member belongs then come into operation and if that member is released the train becomes non-operational. Generally some of the wheels are common to all the epicyclic trains. «*
For only small degrees of overdrive (under-gearing), for example 0.82 : 1 (22%), the simple epicyclic gearing requires a relatively large diameter annulus ring gear, about 175 mm, to provide sufficiently large gear teeth for adequate strength. To reduce the diameter of the annulus ring gear for a similar degree of overdrive, a compound epicyclic gear train can be used which incorporates double pinion gears on each carrier pin. This reduces the annulus diameter to about 100 mm and the number of annulus teeth to 60 only as compared to the 96 annulus teeth in the simple epicyclic gear train.

Overdrive Gear Train.

To transmit power in overdrive gear train, the sun gear is held stationary, and the input shaft and planet carrier are rotated. This forces are large planet gear to roll around the stationary sun gear as well as each pair of combined pinion gears to revolve about their carrier pin axis. As a result, the small pinion gear imparts both the pinion carrier orbiting motiom and the spinning pinion gear motion to the annulus ring gear and the output shaft is driven at a higher speed than that of the input shaft. Thus from Fig. 25.26,
Compound epicyclic gear train
Fig. 25.26. Compound epicyclic gear train.
clip_image015
The amount of overdrive (under-gearing) used in cars, vans, coaches and commercial vehicles varies from as little as 15% to as much as 45%. This corresponds to under gearing ratios of 0.87:1 and 0.69:1 respectively. Typical overdrive ratios which are frequently used are 0.82:1 (22%), 0.78:1(28%) and 0.75:1 (37%).
Example 25.5. A compound epicyclic gear train overdrive has sun, small planet and large planet gears with 21, 15 and 24 teeth respectively. Determine the following if the engine drives the input planet carrier at 4000 rpm.
(a) The overdrive gear ratio.
(b) The number of annulus ring gear teeth.
(c) The annulus ring and output shaft speed.
(d) The percentage of overdrive. Solution.
clip_image016
clip_image017
Example 25.6. An arrangement of the Wilson epicyclic gearbox giving four forward and one reverse speed of shaft D for an input speed of shaft E is shown in Fig. 25.27. In 1st gear Ii is fixed.
In 2 gear I2 is fixed. In 3 gear S3 is fixed. Top gear F is locked to Gi. Reverse gear I\ is connected to S4 and h is fixed. The numbers of teeth on the gears are : Si = 20, S2 = 20, S3 = 17, Sa=26, h = 70, h = 70, h = 61 and 74 = 70. Calculate all the gear ratios. If 22.1 kW is
transmitted in 1st gear at an engine speed of 3000 rpm, find the required fixing torque on the annulus I\.
Wilson epicyclic gear train
Fig. 25.27. Wilson epicyclic gear train.
Solution. The Wilson gear box giving four forward and a reverse ratio, contains four sun wheels Si, S2, S3 and S4, four internal gears I\, I2, h and I4. Each sun is geared to the corresponding annulus by means of three planet wheels and thus there are four sets of planet wheels, Pi, P2, P3 and P4. Bi, B2, B3, and2?4 are four contracting brake bands to bring the brake drums to rest. Only one of the brake bands is contacted for each gear ratio, all others remaining free. The action of the gearbox is as follows :
clip_image019
clip_image020
clip_image021
The above input torque acts in the same direction as the engine speed.
The output torque = 4.5 x 70.38 = 316.72 Nm where 4.5 is the first gear ratio. This torque acts on whatever the gear is driving in the direction of the output speed Nd- Therefore, the reaction of this torque that acts on the gearbox is in the opposite direction to the above output torque.
The fixing torque = 316.72 – 70.38 = 246.34 N. The fixing torque is required to keep the gearbox in equilibrium and acts in this case in the same direction as input torque. Ans.

Next post:

Previous post: