Gears and Gearing Part 1 Types of Gears Types of Gears

Gears and Gearing Part 1 <ul style="display: flex;"><li style="flex:1">Types of Gears </li><li style="flex:1">Types of Gears </li></ul><ul style="display: flex;"><li style="flex:1">Spur </li><li style="flex:1">Helical </li></ul><ul style="display: flex;"><li style="flex:1">Bevel </li><li style="flex:1">Worm </li></ul>Nomenclature of Spur-Gear Teeth Fig. 13–5 Shigley’s Mechanical Engineering Design Rack  A rack is a spur gear with an pitch diameter of infinity.  The sides of the teeth are straight lines making an angle to the line of centers equal to the pressure angle. Fig. 13–13 Shigley’s Mechanical Engineering Design Tooth Size, Diameter, Number of Teeth Shigley’s Mechanical Engineering Design Tooth Sizes in General Industrial Use Table 13–2 Shigley’s Mechanical Engineering Design How an Involute Gear Profile is constructed A1B1=A1A0, A2B2=2 A1A0 , etc Pressure Angle Φ has the values of 20° or 25 ° 14.5 ° has also been used. Gear profile is constructed from the base circle. Then additional clearance are given. Relation of Base Circle to Pressure Angle Fig. 13–10 Shigley’s Mechanical Engineering Design Standardized Tooth Systems: AGMA Standard  Common pressure angles f : 20º and 25º  Older pressure angle: 14 ½º  Common face width: 3p  F  5p P p  3 P5 P  F  Shigley’s Mechanical Engineering Design Gear Sources • Boston Gear • Martin Sprocket • W. M. Berg • Stock Drive Products …. Numerous others Shigley’s Mechanical Engineering Design Conjugate Action  When surfaces roll/slide against each other and produce constant angular velocity ratio, they are said to have conjugate action.  Can be accomplished if instant center of velocity between the two bodies remains stationary between the grounded instant centers. Fig. 13–6 Shigley’s Mechanical Engineering Design Fundamental Law of Gearing: The common normal of the tooth profiles at all points within the mesh must always pass through a fixed point on the line of the centers called pitch point. Then the gearset’s velocity ratio will be constant through the mesh and be equal to the ratio of the gear radii. Shigley’s Mechanical Engineering Design Conjugate Action: Fundamental Law of Gearing  Forces are transmitted on line of action which is normal to the contacting surfaces.  Velocity. VP of both gears is the VP same at point P , the pitch point  Angular velocity ratio is inversely proportional to the radii to point P , the pitch point.  Circles drawn through P from each fixed pivot are pitch circles, each with a pitch radius. Fig. 13–6 Shigley’s Mechanical Engineering Design Gear Ratio VP of both gears is the same at point P , the pitch (circle contact) point 푉푃 = 휔1푟1=휔2푟2 Gear Ratio >1 ꢀꢀ<ul style="display: flex;"><li style="flex:1">ꢁ</li><li style="flex:1">푁</li></ul><ul style="display: flex;"><li style="flex:1">2</li><li style="flex:1">1</li><li style="flex:1">2</li></ul>= = ꢁ1푁<ul style="display: flex;"><li style="flex:1">1</li><li style="flex:1">2</li></ul>ω2 ω2 rotates opposite of ω1 r1 Pr2 ω1 Pitch Circle of Gears N2 N1 Nomenclature Smaller Gear is Pinion and Larger one is the gear In most application the pinion is the driver, This reduces speed but it increases torque. Simple Gear Trains  For a pinion 2 driving a gear 3, the speed of the driven gear is VP n3 =ω3 r2 Pr3 n2 =ω2 N3 N2 Shigley’s Mechanical Engineering Design Simple Gear Trains (Gear 2 to Gear 4) Fig. 13–27 Shigley’s Mechanical Engineering Design Compound Gear Train  A practical limit on train value for one pair of gears is 10 to 1  To obtain more, compound two gears onto the same shaft Fig. 13–28 Shigley’s Mechanical Engineering Design Compound Gear Trains <ul style="display: flex;"><li style="flex:1">n5 </li><li style="flex:1">N3 </li></ul> ( )( )( ) n1 N2 N4 N5 <ul style="display: flex;"><li style="flex:1">N1 </li><li style="flex:1">N4 </li></ul>Example 13–3 Shigley’s Mechanical Engineering Design Example 13–4 Shigley’s Mechanical Engineering Design Example 13–4 Shigley’s Mechanical Engineering Design Example 13–5 Shigley’s Mechanical Engineering Design Example 13–5 Shigley’s Mechanical Engineering Design Example 13–5 Shigley’s Mechanical Engineering Design Example 13–5 Shigley’s Mechanical Engineering Design Example 13–5 Shigley’s Mechanical Engineering Design

Gears and Gearing Part 1 Types of Gears Types of Gears

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