Gear and gear train - Lecture notes 3 PDF

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MECHANICS OF MACHINES ME 224

Chapter 12, 13 Gears ((Tooth Tooth Wheels Wheels)) and Gear Trains oGears oGeometry and Terminology of Gears

Gears • Slipping in the belt drive, reduces the velocity ratio of the system • Gear of toothed wheel is a positive drive, used when distance between the driver and follower is very small

Gears

In precision machines, in which a definite velocity ratio is of importance (as in watch mechanism), the only positive drive is by means of gears or toothed wheels.

Gears

Wheel B will be rotated (by the wheel A) so long as the tangential force exerted by the wheel A does not exceed the maximum frictional resistance between the two wheels. But when the tangential force (P) exceeds the frictional resistance (F), slipping will take place between the two wheels.

Thus the friction drive is not a positive drive. Friction wheel running without slipping and toothed gearing are identical

Advantages & Disadvantages of Gear Drives

The following are the advantages an Disadvantages of Gear drives as compared to belt, rope and chain drives : Advantages 1. It transmits exact velocity ratio. 2. It may be used to transmit large power. 3. It has high efficiency. 4. It has reliable service. 5. It has compact layout. Disadvantages 1. The manufacture of gears require special tools and equipment. 2. The error in cutting teeth may cause vibrations and noise during operation.

Types of Gear

According to position of axis

Helical Spur

Double Helical

Types of Gear Bevel & Worm

Types of Gear

According to type of gearing a) External gearing b) Internal gearing c) Rack and pinion

Terminology of Gears

Pitch circle. It is an imaginary circle which by pure rolling action, would give the same motion as the actual gear. Pitch circle diameter. It is the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter.

Terminology of Gears

Pitch point. It is a common point of contact between two pitch circles. Addendum. It is radial distance of a tooth from pitch circle to top of tooth. Dedendum. It is radial distance of a tooth from pitch circle to bottom of tooth.

Terminology of Gears

Circular pitch. It is distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth denoted by pc

two gears will mesh together if two wheels have same Pc

Terminology of Gears

Diametral pitch. It is the ratio of number of teeth to the pitch circle diameter denoted by pd

Module. It is the ratio of the pitch circle diameter to the number of teeth denoted by m.

Total depth. It is the radial distance between the addendum and the dedendum circles of a gear. It is equal to the sum of the addendum and dedendum. Tooth thickness. It is width of tooth measured along pitch circle.

Terminology of Gears Tooth space . It is the width of space between the two adjacent teeth measured along the pitch circle. Backlash. It is the difference between the tooth space and the tooth thickness, as measured along the pitch circle. Theoretically, the backlash should be zero, but in actual practice some backlash must be allowed to prevent jamming of the teeth due to tooth errors and thermal expansion. Face of tooth. It is the surface of the gear tooth above the pitch surface. Flank of tooth. It is the surface of the gear tooth below the pitch surface. Top land. It is the surface of the top of the tooth. .

Gear Trains When two or more gears are made to mesh with each other to transmit power from one shaft to another. Such a combination is called gear train

Types

1.Simple gear train: one gear on each shaft

Gear Trains 1.Simple gear train: Motion of the driven gear is opposite to the motion of driving gear

Gear Trains 1.Simple gear train: When distance between the two gears is large. Either use large sized gear OR Use intermediate gears

Gear Trains 1.Simple gear train: Speed ratio and train value is independent of size and number of intermediate gears. These intermediate gears are called idle gears.

1. Idle gears are used where a large centre distance is required 2. To obtain the desired direction of motion of the driven gear

Gear Trains 2.Compound gear train: There are more than one gear on a shaft. Distance between the driver and the driven or follower has to be bridged over by intermediate gears and at the same time a great ( or much less ) speed ratio is required

Gear Trains 2.Compound gear train:

Gear Trains 2.Compound gear train: Gears 2 and 3 are mounted on one shaft B, therefore N2 = N3 Gears 4 and 5 are mounted on shaft C, therefore N4= N5

Gear Trains 2.Compound gear train:

Advantage of a compound train over a simple gear train: Much larger speed reduction can be obtained with small gears. If a simple gear train is used : the last gear has to be very large.

Problem

The gearing of a machine tool is shown in Fig. The motor shaft is connected to gear A and rotates at 975 r.p.m. The gear wheels B, C, D and E are fixed to parallel shafts rotating together. The final gear F is fixed on the output shaft. What is the speed of gear F ? The number of teeth on each gear are as given below :

Problem

Design of Spur Gears Spur gears (both driver and driven) are usually designed for given velocity ratio and distance between the centres of their shafts.

Two gears will mesh together if they have same Circular pitch Pc

Problem

Two parallel shafts, about 600 mm apart are to be connected by spur gears. One shaft is to run at 360 r.p.m. and the other at120 r.p.m. Design the gears, if the circular pitch is to be 25 mm.

Problem

Two parallel shafts, about 600 mm apart are to be connected by spur gears. One shaft is to run at 360 r.p.m. and the other at120 r.p.m. Design the gears, if the circular pitch is to be 25 mm.

Problem

1

Number of teeth on both the gears are to be in complete numbers, therefore let us make the number of teeth on the first gear as 38. Therefore for a speed ratio of 3, the number of teeth on the second gear should be 38 × 3 = 114.

Problem Exact pitch circle diameter of the first gear

Exact distance between the two shafts

Gear Trains 3.Reverted gear train: Shafts of the first gear and the last gear are co-axial. Direction of motion of the first gear and the last gear is same. •These have applications in automotive transmissions, lathe back gears and in clocks (where the minute and hour hand shafts are co-axial)

Gear Trains 3.Reverted gear train:

Gear Trains 3.Reverted gear train:

Gear Trains 4.Epicyclic Gear Train: Axes of the shafts, over which the gears are mounted, may move relative to a fixed axis

Gear Trains 4.Epicyclic Gear Train: useful for transmitting high velocity ratios with gears of moderate size in a comparatively lesser space •These have applications in differential gears, lathe back gears, wrist watches, Wankle engines.

Gear Trains 4.Epicyclic Gear Train: If arm is fixed, the gear train is simple and gear A can drive gear B or vice- versa, but if gear A is fixed and the arm is rotated about the axis of gear A (i.e. O1), then the gear B is forced to rotate upon and around gear A. Such a motion is called epicyclic Velocity Ratio 1. Tabular method 2. Algebraic method.

Gear Trains Velocity Ratio using Tabular method

Suppose arm is fixed When the gear A makes one revolution anticlockwise, the gear B will make Assuming the anticlockwise rotation as positive and clockwise as negative, when gear A makes + 1 revolution, then the gear B will make (– TA/ TB ) revolutions

Gear Trains Velocity Ratio using Tabular method A makes + x revolutions, then the gear B will make – x × TA / TB Revolutions (Row 2) Each element of an epicyclic train is given + y revolutions (Row 3)

Gear Trains Velocity Ratio using Tabular method Motion of each element of the gear train is added up from Row 2 to row 3 (Row 4)

Gear Trains Velocity Ratio using Algebraic method Let the arm C be fixed. Speed of the gear A relative to the arm C speed of the gear B relative to the arm C gears A and B are meshing directly, therefore they will revolve in opposite directions

Since the arm C is fixed, therefore its speed, NC = 0

Problems

Problems Tabular method

Problems Tabular method

Problems Algebric method

Problems...