# Kinematic model of a gear set dp

 Date 06.02.2017 Size 130 Kb.

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## Problem #M8:

A pair of straight-tooth bevel gears (as shown in the figure above) are in mesh transmitting 35 hp at 1000 rpm (pinion speed). The gear rotates at 400 rpm. The gear system has a pitch of 6 and a 20-degree pressure angle. The face width is 2 inches and the pinion has 36 teeth. Determine the tangential, radial, and axial forces acting on the pinion. Answers (839 lbs, 283 lbs, 113 lbs).

## The geometric relation for finding worm lead angle

Problem #M9: A worm gear reducer is driven by a 1200 rpm motor. The worm has 3 threads and the gear has 45 teeth. The circular pitch of the gear is p=0.5”, the center distance is 4.5 inches, the normal pressure angle is 20 degrees, and face-width of the gear is b=1 inch. Use a coefficient of sliding friction of 0.029. Determine:

1. Gear and worm diameters, and worm Lead. (7.16, 1.84, 1.5 in)

2. The worm gear efficiency (88.6%)

3. Is the unit self-locking – show work? (No)

Driver

F1

F2

Tight side

## Slack side

Transmitted Hp is

Where F1 and F2 are in lbs and V is in ft/min.

## Initial Tension

Belts are tensioned to a specified value of Fi. When the belt is not transmitting torque:

F1=F2=Fi

As the belt start transmitting power,

F1 = Fi + F and F2 = Fi - F

The force imbalance continues until the slippage limit is reached.
Problem M #10: A 10”-wide flat belt is used with a driving pulley of diameter 16” and a driven pulley of rim diameter 36” in an open configuration. The center distance between the two pulleys is 15 feet. The friction coefficient between the belt and the pulley is 0.80. The belt speed is required to be 3600 ft/min. The belts are initially tensioned to 544 lbs. Determine the following. (answers are in parentheses)
Belt engagement angle on the smaller pulley (3.03 radians).

Force in belt in the tight side just before slippage. (1000 lbs).

Maximum transmitted Hp. (99.4 hp)