15 - 1 Chapter 15 Spur Gears 15.1 Introduction Gears are...

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Unformatted text preview: 1 Chapter 15 Spur Gears 15.1 Introduction Gears are defined as toothed members transmitting rotary motion from one shaft to another, and are among the oldest devices and inventions of man. In about 2600 B.C. the Chinese used a chariot incorporating a complex series of gears, see Fig. 15.1. Function: To transmit power, motion and position. Advantage: High power transmission efficiency, 98%, compact, high speed, precise timing. Disadvantage: Gears are more costly than belts and chains. Gear manufacturing costs increase sharply with increased precision including high speeds, heavy loads, and low noise. Spur gears, see Fig. 15.2, are the simplest and most common type of gears with teeth parallel to the shaft axes and transmitting motion between parallel shafts. Figure 15.1 (p. 591) Primitive gears. 2 15.2 Geometry and Nomenclature The basic requirement of gear-tooth geometry is the ability to transmit motion in a constant angular velocity ratio at all times. For example, the angular velocity ratio between a 20-tooth and a 40-tooth gear must be precisely 2 in every position. The action of a pair of gear teeth satisfying this requirement is termed conjugate gear tooth action, see fig. 15.3. The basic law of conjugate gear-tooth action is: As the gear rotate, the common normal to the surfaces at the point of contact must always intersect the line of centers at the same point P, called the pitch point. The law of conjugate gear-tooth action can be satisfied by various tooth shapes, but the most important one is the involute of the circle. An involute of the circle is the curve generated by any point on a taut thread as it unwinds from a circle, see Fig. Figure 15.2 (p. 592) Spur gears. Figure 15.3 (p. 593) Conjugate gear-tooth action. 3 15.4. Correspondingly, involutes generated by unwinding a thread wrapped counterclockwise around the base circle would form the outer portion of the left sides of the teeth. Note that at every point, the involute is perpendicular to the taut thread. An involute cannot exist inside its base circle. Fig. 15.5 shows two pitch circles. If there is no slippage, rotation of one cylinder will cause rotation of the other at an angular velocity ratio inversely proportional to their diameters. The smaller is called pinion and the larger one the gear. We have, ω p / ω g = - d p /d g ( 1 5 . 1 ) Where w is the angular velocity, d is the pitch diameter, and the minus sign indicates that the two cylinders rotate in opposite directions. The center distance is c = (d p + d g )/2 = r p + r g ( 1 5 . 1 a ) where r is the pitch circle radius. Figure 15.4 (p. 593) Generation of an involute from its base circle. 4 As in Fig. 15.6, in gear parlance, angle φ is called the pressure angle. Neglecting sliding friction, the force of one involute tooth pushing against the other is always at an angle equal to the pressure angle....
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This note was uploaded on 12/01/2010 for the course MEM MEM 431 taught by Professor Jackzhou during the Fall '10 term at Drexel.

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15 - 1 Chapter 15 Spur Gears 15.1 Introduction Gears are...

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