Kinematics of machinesMechanical-1

Babaria Institute of Technology

Prepared by Burhani Burhan A : (011)Bhimani Vipul S : (010)

Kinematics of machines

Gears and Gear train

Content:

• Types Of Gears (Bevel and Worm gear)• Applications Of Gears• Gear Trains (simple and compound gear train)• Velocity Ratio• Examples

Types of gears

According to the position of axes of the shafts. a. Parallel shaft

1.Spur Gear 2.Helical Gear 3.Rack and Pinion

b. Intersecting shaft Bevel Gear

c. Non-intersecting and Non-parallel shaft worm and worm gears

Intersecting shafts

• Kinematically, the motion between two intersecting shafts is equivalent to the rolling of two cones, assuming no slipping.

• These gears are known as bevel gears.

Bevel gears • When power is required to be transmitted from

one shaft to another shaft which are interesting to each other then bevel gears are used.

• Bevel gears are useful when the direction of a shaft's rotation needs to be changed .

• The angle between two shafts is 90 degrees.

Bevel gears

• Standard bevel gears have teeth that are cut straight. The teeth point toward the apex of the cone on which they are machined.

• The teeth of these gears are formed on a conical surface.

Apex of the cone

Bevel gears • Application locomotives, marine applications, automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection machines.

Bevel gears

The bevel gears are of three types:- 1. straight bevel gears 2. spiral bevel gears 3. zerol (hypoid) bevel gears

Straight bevel gears

• In straight bevel gears the teeth are formed straight on the cone.

• They are parallel to the axis of the gear.• They are used for transmitting power between

intersecting shafts.• They can operate under high speeds and high load.• They are suitable for higher velocity ratio.• Application-automotive differential gear box,

right angle drives of blenders

Straight bevel gears

•Standard bevel gears are mainly used in low speed (less than 500 rpm) applications. At high speeds they become noisy. They are typically used in applications such as hand drills.

Spiral bevel gears

• In spiral bevel gear the teeth are formed at an angle with respect to its axis .

• The contact between two meshing teeth is gradual and smooth from start to end ,as in case of helical gears.

• Because of spiral tooth, the contact length is more & contact ratio is more. They operate smoother than straight bevel gears and have higher load capacity.

• But ,their efficiency is lower then straight bevel gears .

Spiral bevel gears

Spiral bevel gears are typically used for high speed (greater than 500 rpm) and performance applications, where low noise and vibration levels are important. They are typically used in transmission systems.

Zerol (Hypoid) bevel gears

• These gears are also used for right angle drive in which the axes do not intersect .

• These drives requires good lubrication to reduce the friction and wear.

• Their efficiency is lower then other two types of bevel gears.

• Application :- in current day automobile drive line power transmission system.

Bevel gear

Worm and worm gears

• Worm and worm gears are used to transmit power from one shaft to another shaft which are non intersecting and their axis are normally right angles to each other.

• Worm and worm gears is special case of spiral gear in which shaft angle is 90 degree.

• Worm is threaded screw while worm gear is toothed gear.

• Generally worm have 1 to 8 teeth.

Worm and worm gear

• Worm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater

• Worm gears are used widely in material handling and transportation machinery, machine tools, automobiles etc

Worm and worm gears

Gear trains• Gear train is combination of gear which is used to

transmit motion and power from one shaft to another.

• a Gear train is also called as train of toothed wheels.

• A gear train is two or more gear working together by meshing their teeth and turning each other in a system to generate power and speed

• It reduces speed and increases torque• Gear train may use spur, bevel, or spiral gears

Gear trains

Application • Gear trains are used to either speed up or

stopped down the speed of the driven shaft .• Gear trains are widely used in modern machines

like, in automobile ,ships, clocks, watches, lathes, milling and planning machines etc.

Gear trains

Types of gear trains are following , 1. Simple gear train 2. Compound gear train 3. Reverted gear train 4. Epicyclic gear train

Simple gear train

• A series of gears capable to receiving and transmitting motion from one shaft to another shaft is called simple gear trains.

• The most common of the gear train is the gear pair connecting parallel shafts. Gear axes are fixed to frame.

• Two end gears always moves in opposite direction s.• All odd number gears move in one direction and

even number gears moves in opposite direction.

Simple gear train

A simple gear train is one in which each shaft carries only one gear. The velocity ratio (sometimes called train ratio) of this gear-set is found by expanding equation: Consider a simple gear train with four gears in series. The expression for this simple train's velocity ratio is:

mv = (-N1/N2) (-N2/N3) (-N3/N4) = -N1/N4

“Simple Gear Trains are limited to a ratio of about10: 1”.Gear ratio = Number of Driver Gear Teeth

Number of Driven Gear Teeth

Simple gear train

Compound gear train

• A series of gears are connected in such way that two or more gears rotate about an axis with same angular velocity, it is known as compound gear trains.

• In compound gear trains intermediate shaft carries two gears.

• For large velocities, compound arrangement is preferred

• Compound gear trains are used in headstock of lathe machine.

Compound gear train

When there are more than one gear on a shaft, it is called a compound train of gear. Since the idle gears, in a simple train of gears do not effect the speed ratio of the system. But these gears are useful in bridging over the space between the driver and the driven.To get a train ratio of greater than about 10:1 with spur, helical, or bevel gears (or any combination thereof) it is necessary to compound the train.

Gear ratio = Number of Driver Gear TeethNumber of Driven Gear Teeth

mv = (-N1/N2)x(-N3/N4)x(-N5/N6) “The advantage of a compound train over a simple gear train is that a much larger speed

reduction from the first shaft to the last shaft can be obtained with small gears.”

Compound gear train

exampleThe gearing of a machine tool is shown in Figure. 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 :No. of teeth on each Gear, TA = 20, TB = 50, TC = 25, TD = 75, TE = 26, TF = 65

Solution-NA = 975 r.p.m. ;NF = ?mv = NA /NB x NC /ND x NE /NF = NA /NF

Or NA /NF = TB /TA x TD /TC x TF /TE

So, NA /NF = 50 /20 x 75 /25 x 65 /26

NF = NA /(18.75)

NF = 975 /(18.75) NF = 52 r.p.m. Ans

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