Simple and Planetary gear trains(3)

Assembly of Planetary gear trains Reverted Gear Train

Compound Epicyclic Gear Train—Sun and Planet Gear

A compound epicyclic gear train is shown in fig. It consists of two co-axial shafts S₁ and S₂, an annulus gear A which is fixed, the compound gear or planet gear B-C, sun gear D and the arm H. The annulus gear has internal teeth and the compound gear which is carried by an arm and that revolves freely on the pin of the arm H. The sun gear is co-axial with the annulus gear and the arm but independent of them.

The annulus type gear A meshes with the gear B and the sun gear D meshes with the gear C. It is noted that when the annulus gear is fixed then the sun gear provides drive and when the sun gear is fixed then the annulus gear provides that drive. In both cases the arm acts as a follower. The gear which is at the centre is called sun gear and the gears whose axes move are called the planet gears.

Fig: Compound epicyclic gear train.

Let ,

Suppose T_A , T_B , T_C and T_D be the teeth and N_A, N_B, N_C and N_D be the speeds for the gears A, B, C and D respectively. A little supposition will shows that when the arm is fixed and that sun gear D is turned anticlockwise then the compound gear B-C and the annulus gear A will be rotate in the clockwise direction.

The motion of rotations of the various elements are shown in the table below.

Table: Table of motions.

If the annulus gear A is rotated through one revolution anticlockwise with the arm fixed then the compound gear rotates through with T_A / T_B revolutions in the same sense and the sun gear D rotates through with T_A / T_B × T_C / T_D revolutions in given clockwise direction.

Epicyclic Gear Train with the Bevel type Gears

This type ofbevel gears are also used to make a more than compact epicyclic gear system and they allow a very high speed reduction with the only few gears. The mostly useful application of epicyclic gear train with bevel gears which is found in Humpage’s speed reduction gear also in differential gear of an automobile as we studied below.

a) Humpage’s speed reduction gear

The Humpage’s speed reduction gear was inatially designed as a substitute for back gearing of the lathe but its used in now considerably extended to all the types of workshop machines and also in the electrical machinery parts. In the Humpage’s speed reduction gear which is shown in fig. The driving shaft X and driven shaft Y are co-axial. Then the driving shaft carries a bevel gear A and the driven shaft carries a bevel gear is E. The bevel gear then B meshes with gear A which also known as pinion and a fixed gear C. The gear E meshes with gear D that is compound with gear the B.

This type of compound gear B-D is mounted on the arm or spindle F which is rigidly joined with a hollow sleeve G. The sleeve then revolves freely loose on the axes of the driving and driven shafts.

Fig: Humpage’s speed reduction gear

b) Differential gear of the automobile

The differential gear is used in the rear drive of an automobile is shown in fig. Its function is given below

(a) To transmit the motion from the engine shaft to the back driving wheels and

(b) To rotate the rear wheels at various speeds when the automobile is taking a turn

As long the automobile is running on a straight path then the rear wheels are driven directly by the engine and the speed of both wheels is same. But when the automobile is taking a turn then the outer wheel will run much faster than the inner wheel because at that time the outer rear wheel has to cover more distance than inner rear wheel. This is gained by epicyclic gear train with bevel gears as shown in fig.

Fig: Differential gear of an automobile

The bevel gear is known as pinion is keyed to the propeller shaft which driven from the engine shaft with universal coupling. This gear A drives with gear B which is known as crown gear that rotates freely on the axle P. Two equal gears C and D are mounted on two main separate parts of P and Q of the rear axles axis respectively. These gears which in turn and mesh with equal pinions E and F which can rotate freely on spindle which provided on the arm which is attached to gear B.

When the automobile run on a straight path then the gears C and D must be rotate same together. These gears are rotated through the spindle axis on the gear B. The gears E and F do not rotate on spindle. But when an automobile is taking a turn then the inner rear wheel should have lesser speed than the outer rear wheel due to the relative speed of the inner with outer gears D and C, the gears E and F start to rotating about the spindle axis and at same instant of time revolve about the axle axis.

Due to this epicyclic effect the speed of the inner rear wheel decreases by the fixed amount and the speed of the outer rear wheel increases by the same that amount. This is well known by drawing the table of motions as follows. From the table we see that when the gear B which takes motion from engine shaft rotates at y revolutions then the speed of inner gear D or the rear axle Q is less than y by amount x revolutions and the speed of the outer gear C or the rear axle P is greater than y by x amount revolutions. In is said that the two parts of the rear axle and thus the two wheels rotate at two different speeds. It is also see from the table that the speed of the gear B is the mean of speeds of the gears C and D.

References:
1. H.H. Mabie and C. F. Reinholtz, “Mechanism and Dynamics of Machinery”, Wiley.
2. J.S. Rao & R.V. Dukkipati Mechanisms and Machine Theory, New Age International (P) Limited..
3. J.E. Shigley and J.J. Uicker, Jr., “ Theory of Machines and Mechanisms”, McGraw Hill.
4. B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice Hall.
5. C. E. Wilson, J.P. Sadler and W.J. Michels, “Kinematics and Dynamics of Machinery”, Harper Row.