me 222: kinematics of machines and...

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Suril V. Shah

ME 222: Kinematics of Machines and Mechanisms

[L35] Gears and Gear Train: Introduction

4/20/19 1IIT Jodhpur

Suril V. Shah

History: goes back to 100 BCPrevalent: in all kinds of mechanisms and machines, from can openers to aircraft carriers. Function : change in the speed or torque of a rotating device Objective: theory of gear tooth action and the design of these ubiquitous devices for motion control. Kinematic design: selection of appropriate ratios, gear diameters stages of reduction. Considerations of strength of materials and the complicated stress analysis will be beyond the scope of studyGears of various sizes and styles are readily available from many manufacturers.

Gears and Gears Train


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Linkage: Angular Velocity Ratio

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Two Bodies


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I24

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Rolling Cylinder


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I24

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Low torque capability Possibility of slip

Rolling Cylinder


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Equivalent Linkage


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Gears – A closer look


I41

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The common normal to the tooth profiles at the point of contact must always pass through a fixed point (the pitch point) on the line of centersThe two profiles which satisfy this requirement are called conjugate profiles.

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The gear tooth contours on mating teeth must be conjugates of one another. Infinite number of possible conjugate pairs but only a few curves have seen practical application as gear teeth. The cycloid still is used as a tooth form in watches and clocks, but Most other gears use the involute curve for their shape.

Gear Profile


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Cycloidal vs Involute


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S.No Involute Tooth Profile Cycloidal Tooth Profile

1 The pressure angle remains constant throughout the engagement. This ensures smooth running

Pressure angle varies continuously causes continuous variation in power. The running is less smooth.

2 Involute tooth profile consists of a single (involute) curve and the method of manufacture is simpler.

The cycloidal tooth profile consists of two curves (epicyloid and hypocycloid). The method of manufacture is more involved and costly

3 Small variation in centre distance does not change the velocity ratio.

Exact centre distance is necessary to transmit constant velocity ratio.

4 Interference is always possible if base circle radius is larger than dedendum circle radius.

Cycloidal curve can exist everywhere on tooth profile and no interference exists.

5The radius of curvature of involute curve, near the base circle, is quite small and contact stresses are likely to be very high..

Cycloidal curve (hypocycloidal in particular) produces a spreading flank and, for this reason, cycloidal tooth is stronger .

6In involute tooth profile gears, convex surface of pinion tooth comes in contact with convex portion of gear tooth leading to more wear.

In cycloidal tooth profile epicycloidal face of gear tooth comes in contact with hypocloidal flank portion of pinion tooth. Thus a convex flank has a contact with concave face and lesser wear.

Cycloidal vs Involute


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The angular velocity ratio between the gears of a gearset remains constant throughout the mesh.

Fundamental Law of gearing


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I24+ for internal, - for external

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Spur gearThe most common type of gear. Teeth run perpendicular to the face of the gear.Problem of noise and vibration at high speedEfficiency: 98 – 99%

IIT Jodhpur 13

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Teeth are at an angle to the faceTeeth engage gradually causing them to run more smoothly and quietlyUsed on non-parallel shafts to transmit motion.Disadvantage: resultant thrust along the axis of the gearEfficiency: 96 – 98%, 50 – 90% (crossed)

Helical Gear

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Herringbone

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Worm gears are used to transmit power at 90° and where high reductions are required. Single tooth rapped on a cylinderHigh gear ratio and non back drivableHigh sliding and thrustEfficiency: 40 – 85%

Worm and worm wheel

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Bevel GearBased on principle of rolling conesWhen power to be transmitted at right angles.Can have different angles of application but tend to be 90°.Efficiency: 40 – 85%

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Straight Spiral

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Apices must be coincident for Constant ratio

Bevel Gear


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If the axes between the gears are nonparallel and also nonintersecting, bevel gears cannot be used. Hypoid gears are based on rolling hyperboloids of revolution as shown in Figure

HYPOID GEARS


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Rack and pinionStraight gear used to transmit power and motion in a linear movement.Automobile Steering

IIT Jodhpur 19

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Based on rolling centrodes of a double-crank fourbar linkageVelocity ratio is not constant

Non Circular Gears


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Applications

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To create larger gear ratios, gears are often connected in gear trainsSimple

Compound

Gear Trains


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Compound Gear Trains

Each gear turns at twice the speed of the one to its left, which means that the red gear turns at 2 x 2 x 2 = 8 times the speed of the blue gear.

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Automobile gear box

IIT Jodhpur 24

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Epicyclic gearing or planetary gearingPlanetary gear trains allow the output shaft to

be along the same axis as the input shaft:

Such a gearing system would be used in a device such as an electric screwdriver.

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Epicyclic gear train

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Used by James Watt on his early steam Reciprocating motion into rotary motionSun is yellow, the planet red, the reciprocating arm is blue, the flywheel is green and the driveshaft is grey.

Sun and planet

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Automobile differential gearIt is used to help cars turn corners. It allows wheels to turn at different speeds while providing same torque to both wheels.

IIT Jodhpur 28

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Automobile differential gear

IIT Jodhpur 29

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Belt driveReplacement for gears as power transmission device.

Suited for applications where the center distance between rotating shafts are large.

In contrast to other system that friction is no good, here we rely on the friction to transmit power

Efficiency: 95 – 98 % (V-belt), 93%

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Belt drive

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Toothed belt

Timing belt

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AdvantagesThey are simple and economical and highly efficient .Economical when shafts are separated by large distances. Parallel shafts are not required can tolerate small misalignmentProlonged life due to cushioning of noise and vibration They are lubrication-free requiring low maintenance.

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The torque capacity is limited by the coefficient of friction and pressure between belt and pulleyBecause of slip and/or creep, the angular velocity ratio will not remain constantLow speed reduction ratio, up to 3:1.Belt tension needs to be adjusted periodically.Idler pulley for wear and stretch compensation.

Disadvantages

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Chain driveChain drive is a way of transmitting mechanical power from one place to another. It is often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles. It is also used in a wide variety of machines besides vehicles.

Suril V. Shah

AdvantagesNo slip hence perfect velocity ratio is obtained.Occupy less space in width than a belt drive.Suitable for both long as well as short distances.It transmits more power than belts.It permits high speed ratio of 8 to 10 in one step.Works under adverse temperature and atmospheric conditions.

IIT Jodhpur 36

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DisadvantagesProduction cost of chains is relatively high.Accurate mounting and careful maintenance, particularly lubrication and slack adjustment.Velocity fluctuations when unduly stretched.Use is limited to slower speed than belt drive

IIT Jodhpur 37

Thank youNext Class: Involute Gear Set

4/20/19 IIT Jodhpur 38

me 222: kinematics of machines and...

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