gear fundamentals

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Page 1: Gear fundamentals
Page 2: Gear fundamentals

M.WAQAR AHSANBSME 01093069

GROUP NO #2

Page 3: Gear fundamentals

TOPIC:

GEAR FUNDAMENTALS

Page 4: Gear fundamentals

Among other things, it is necessary that you actually be able to draw the teeth on a pair of meshing gears .

You should understand, however, that you are not doing this for manufacturing or shop purposes.

Rather, we make drawings of gear teeth to obtain an understanding of the problems involved in the meshing of the mating teeth.

Page 5: Gear fundamentals

1st it is necessary to learn how to construct an involutes curve. Divide the base circle into a number of equal parts, and construct radial lines OA0, OA1, OA2, etc.

Beginning at A1, construct perpendiculars A1B1, A2B2, A3B3,etc. Then along A1B1 lay off the distance A1A0, along ay off twice the distance A1A0, etc., producing points through which the involute curve can be constructed.

Page 6: Gear fundamentals

O

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When two gears are in mesh, their pitch circles roll on one another without slip-ping.

Designate the pitch radii as r1andr2and the angular velocities as ω1andω2,respectively. Then the pitch-line velocity isV=|r1ω1| =|r2ω2|

Thus the relation between the radii on the angular velocities is ω1ω2=r2r1

Page 8: Gear fundamentals

VELOCITY RATIO OF GEAR DRIVE

d= Diamter of the wheel

N =Speed of the wheel

ω= Angular speed

velocity ratio (n) =

2

1

1

2

1

2

d

d

N

N

Page 9: Gear fundamentals

Suppose now we wish to design a speed reducer such that the input speed is 1800rev/min and the output speed is 1200 rev/min. This is a ratio of 3:2; the gear pitch diameters would be in the same ratio,For example, a 4-in pinion driving a 6-in gear. The various dimensions found in gearing are always based on the pitch circles.

Page 10: Gear fundamentals

Suppose we specify that an 18-tooth pinion is to mesh with a 30-tooth gear and that the diametral pitch of the gear-set is to be 2 teeth per inch. The pitch diameters of the pinion and gear are, respectively,

d1 =N1\P=18\2=9 in d2 =N2\P=30\2=15 in

Page 11: Gear fundamentals

The first step in drawing teeth on a pair of mating gears the center distance is the sum of the pitch radii, in this case 12 in. So locate the pinion and gearcentersO1andO2, 12 in apart . Then construct the pitch circles of radii r1andr2.These are tangent at P, the pitch point. Next draw line ab, the common tangent, through the pitch point. We now designate gear 1 as the driver, and since it is rotating counter-clockwise, we draw a line cd through point P at an angle φ to the common tangent ab.

Page 12: Gear fundamentals

The line cd has three names, all of which are in general use. It is called the pressureline.The generating line , and the line of action. It represents the direction in which theresultant force acts between the gears.The angle φ is called the pressure angle,and it usually has values of 20 or 25◦, though 14*1\2 was once used.

Page 13: Gear fundamentals
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Next, on each gear draw a circle tangent to the pressure line. These circles are thebase circles. Since they are tangent to the pressure line, the pressure angle determinestheir size.The radius of the base circle isrb =rcosφwherer is the pitch radius.The addendum and dedendum distances for standard interchangeable teeth are, aswe shall learn later, 1/P and 1.25/P respectively. Therefore, for the pair of gears we are constructing,

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a=1\p =>1\2=>.500inb=1.25\p =>1.25\2 =>0.625Next, using heavy drawing paper, or preferably, a sheet of 0.015- to 0.020-in clear plastic, cut a template for each involute, being careful to locate the gear centers prop-erly with respect to each involute. A reproduction of the template used to create some of the illustrations for this book. Note that only one side of the tooth pro-file is formed on the template. To get the other side, turn the template over. For some problems you might wish to construct a template for the entire tooth.

Page 16: Gear fundamentals
Page 17: Gear fundamentals

To draw a tooth, we must know the tooth thickness and the circular pitch p=π\Pp=π\2=1.57 in

t =p\2t=1.57\2=0.785 in The portion of the tooth between the clearance circle and the dedendum circleincludes the fillet. In this instance the clearance is c=b−a =0.625−0.500 =0.125 in

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Referring again to Fig. the pinion with center at O1 is the driver and turnscounterclockwise. The pressure, or generating, line is the same as the cord used in to generate the involute, and contact occurs along this line. The initial con-tact will take place when the flank of the driver comes into contact with the tip of thedriven tooth. This occurs at point where the addendum circle of the dri-ven gear crosses the pressure line. If we now construct tooth profiles through point aand draw radial lines from the intersections of these profiles with the pitch circles to thegear centers, we obtain the angle of approachfor each gear.

Page 19: Gear fundamentals

As the teeth go into mesh, the point of contact will slide up the side of the drivingtooth so that the tip of the driver will be in contact just before contact ends. The finalpoint of contact will therefore be where the addendum circle of the driver crosses thepressure line. This is point bin Fig. 13–12. By drawing another set of tooth profilesthroughb, we obtain the angle of recess.

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Page 21: Gear fundamentals

The sum of the angle of approach and the angle of recess for either gear is called the angle of action.The line ab is called the line of action.

Page 22: Gear fundamentals

The base pitch is related to the circu-lar pitch by the equation pb =pccosφwhere pb is the base pitch.Figure shows a pinion in mesh with an internal,orring, gear.Note that bothof the gears now have their centers of rotation on the same side of the pitch point. Thus the positions of the addendum and dedendum circles with respect to the pitch circle are reversed;

Page 23: Gear fundamentals

the addendum circle of the internal gear lies inside the pitch circle. Note, too,from Fig. that the base circle of the internal gear lies inside the pitch circle near the addendum circle.

Page 24: Gear fundamentals

Thus the pitch circles of gears really do not come into existence until a pair of gears arebrought into mesh.Changing the center distance has no effect on the base circles, because these wereused to generate the tooth profiles. Thus the base circle is basic to a gear. Increasing thecenter distance increases the pressure angle and decreases the length of the line of action, but the teeth are still conjugate, the requirement for uniform motion transmis-sion is still satisfied, and the angular-velocity ratio has not changed.

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