11/23/2013. Chapter 13. Gear Trains. Dr. Mohammad Suliman Abuhiba, PE

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1 Chapter 13 Gear Trains 1

2 Types of Gear Trains 1. Simple gear train 2. Compound gear train 3. Reverted gear train 4. Epicyclic gear train: axes of shafts on which the gears are mounted may move relative to a fixed axis. In the first three types of gear trains, axes of shafts over which the gears are mounted are fixed relative to each other

3 Simple Gear Train Simple gear train: only one gear on each shaft Gears are represented by their pitch circles.

4 Simple Gear Train N 1 = Speed of gear 1(driver) in rpm N 2 = Speed of gear 2 (driven or follower) in rpm T 1 = Number of teeth on gear 1 T 2 = Number of teeth on gear 2

5 Simple Gear Train When the number of intermediate gears are odd, the driver & driven rotate in the same direction If number of intermediate gears are even, the motion of the driven will be in the opposite direction of the driver

6 Simple Gear Train Consider a simple train of gears with one intermediate gear N 1 = Speed of driver in rpm N 2 = Speed of intermediate gear in rpm N 3 = Speed of driven or follower in rpm T 1 = Number of teeth on driver, T 2 = Number of teeth on intermediate gear T 3 = Number of teeth on driven or follower

7 Simple Gear Train

8 Simple Gear Train Speed ratio & train value, in a simple train of gears, is independent of size & number of intermediate gears. Intermediate gears are called idle gears The idle gears are used to: 1. connect gears where a large center distance is required 2. obtain desired direction of motion of driven gear

9 Compound Gear Train Compound train of gears: more than one gear on a shaft, Fig Used Whenever distance between driver & driven has to be bridged over by intermediate gears and at the same time a great speed ratio is required Each intermediate shaft has two gears rigidly fixed to it

10 Compound Gear Train

11 Compound Gear Train

12 Compound Gear Train Usually for a speed reduction in excess of 7 to 1, a simple train is not used and a compound train or worm gearing is employed. Gears which mesh must have the same circular pitch or module

Example 13.1 13 The gearing of a machine tool is shown in Fig. 13.3. The motor shaft is connected to gear A & rotates at 975 rpm.

13 Example The gearing of a machine tool is shown in Fig The motor shaft is connected to gear A & rotates at 975 rpm. Gear wheels B, C, D and E are fixed to parallel shafts rotating together. The final gear F is fixed on output shaft. What is the speed of gear F? Gear A B C D E F No. of teeth

14 Design of Spur Gears x = Distance between centers of two shafts N 1 = Speed of the driver T 1 = Number of teeth on the driver d 1 = Pitch circle diameter of the driver N 2, T 2 & d 2 = Corresponding values for driven pc = Circular pitch Distance between centers of two shafts

15 Example Two parallel shafts, about 600 mm apart are to be connected by spur gears. One shaft is to run at 360 rpm and the other at 120 rpm. Design the gears, if the circular pitch is to be 25 mm.

16 Reverted Gear Train Reverted gear train: axes of 1 st driver & last driven are co-axial (Fig. 13.4) motion of 1 st gear & last gear is like

17 Reverted Gear Train T 1 = # of teeth on gear 1 r 1 = Pitch circle radius of gear 1 N 1 = Speed of gear 1 in rpm T 2, T 3, T 4 = Number of teeth on respective gears r 2, r 3, r 4 = Pitch circle radii of respective gears N 2, N 3, N 4 = Speed of respective gears in rpm

18 Reverted Gear Train Circular pitch or module of all gears is assumed to be same number of teeth on each gear is directly proportional to its circumference or radius.

19 Example 13.3 The speed ratio of the reverted gear train, Fig. 13.5, is to be 12. The module pitch of gears A & B is mm and of gears C & D is 2.5 mm. Calculate the suitable numbers of teeth for the gears. No gear is to have less than 24 teeth. 19

20 Epicyclic Gear Train Axes of the shafts, over which the gears are mounted, may move relative to a fixed axis. Epicyclic gear trains are useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space.

21 Velocity Ratios of Epicyclic Gear Train 1. Tabular method 2. Algebraic method

22 Velocity Ratios of Epicyclic Gear Train - Tabular method TA = Number of teeth on gear A TB = Number of teeth on gear B CCW = +ve CW = -ve

23 Velocity Ratios of Epicyclic Gear Train - Tabular method Step No. Conditions of motion Revolutions of elements Arm C Gear A Gear B 1 Arm fixed-gear A rotates through +1 rev T A / T B 2 Arm fixed-gear A rotates through +x rev 0 +x -x T A / T B 3 Add + y revolutions to all elements +y +y +y 4 Total motion +y x+y y -x T A / T B 2. Algebraic method

24 Example In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 rpm in the ccw direction about the center of gear A which is fixed, determine the speed of gear B. If gear A instead of being fixed, makes 300 rpm in the cw direction, what will be the speed of gear B?

25 Example In a reverted epicyclic gear train, arm A carries two gears B and C and a compound gear D - E. Gear B meshes with gear E and gear C meshes with gear D. The number of teeth on gears B, C and D are 75, 30 and 90 respectively. Find the speed and direction of gear C when gear B is fixed and arm A makes 100 rpm clockwise.

26 Example An epicyclic gear consists of three gears A, B and C. Gear A has 72 internal teeth and gear C has 32 external teeth. Gear B meshes with both A and C and is carried on an arm EF which rotates about the center of A at 18 rpm. If gear A is fixed, determine the speed of gears B & C.

Example 13.7 27 How many revolutions does the arm, to which the pinions B and C are attached, make: 1.

27 Example How many revolutions does the arm, to which the pinions B and C are attached, make: 1. when A makes one revolution cw and D makes half a revolution ccw 2. when A makes one revolution cw and D is stationary The number of teeth on gears A & D are 40 and 90 respectively.

Example 13.8 In an epicyclic gear train, the internal wheels A and B and compound wheels C and D rotate independently about axis O. The wheels E and F rotate on pins fixed to the arm G.

28 Example 13.8 In an epicyclic gear train, the internal wheels A and B and compound wheels C and D rotate independently about axis O. The wheels E and F rotate on pins fixed to the arm G. E gears with A & C and F gears with B & D. All the wheels have the same module and the number of teeth are: T C = 28; T D = 26; T E = T F = Find the number of teeth on A & B 2. If arm G makes 100 rpm cw and A is fixed, find the speed of B 3. If arm G makes 100 rpm. Cw and wheel A makes 10 rpm ccw; find the speed of wheel B. 28

Example 13.9 In an epicyclic gear of the sun and planet type shown, the pitch circle diameter of the internally toothed ring is to be 224 mm and the module 4 mm.

29 Example 13.9 In an epicyclic gear of the sun and planet type shown, the pitch circle diameter of the internally toothed ring is to be 224 mm and the module 4 mm. When the ring D is stationary, the spider A, which carries three planet wheels C of equal size, is to make one revolution in the same sense as the sun wheel B for every five revolutions of the driving spindle carrying the sun wheel B. Determine suitable numbers of teeth for all the wheels. 29

30 Example Two shafts A and B are co-axial. A gear C (50 teeth) is rigidly mounted on shaft A. A compound gear D-E gears with C and an internal gear G. D has 20 teeth and gears with C. E has 35 teeth and gears with an internal gear G. Gear G is fixed and is concentric with the shaft axis. The compound gear D-E is mounted on a pin which projects from an arm keyed to the shaft B. Find the number of teeth on internal gear G assuming that all gears have the same module. If shaft A rotates at 110 rpm, find the speed of shaft B. 30

31 Example

32 32 Evaluation Quiz Quiz will be held on Wednesday 20/11/2013

428 l Theory of Machines

428 l Theory of Machines 428 l heory of Machines 13 Fea eatur tures es 1. Introduction. 2. ypes of Gear rains. 3. Simple Gear rain. 4. ompound Gear rain. 5. Design of Spur Gears. 6. Reverted Gear rain. 7. picyclic Gear rain. 8.