Fase Final

It is the ratio of the gear diameter to the pinion diameter or the ratio of the pinion speed to the gear speed or ratio of number of teeth on gear to that on pinion.

G = D/d = n/N = T/t

Measurement of individual elements Measurement of tooth thickness

The permissible error or the tolerance on thickness of tooth is the variation of actual thickness of tooth from its theoretical value the tooth thickness is generally measured at pitch circle and is therefore, the pitch line thickness of the tooth. It may be mentioned that the tooth thickness is defined as the length of an arc, which is difficult to measure directly. In most of the cases, it is sufficient to measure the chordal thickness that is the cord joining the intersection of the tooth profile with the pitch circle. Also the difference between chordal tooth thickness and circular tooth thickness is very small for gear of small pitch. The thickness measurement is the most important measurement because most of the gears manufactured may not undergo checking of all other parameters, but thickness measurement is a must for all gears. There are various methods of measuring the gear tooth thickness:

Measurement of tooth thickness by Gear tooth vernier caliper.

Constant chord method.

Base tangent method.

Measurement by dimension over pins

The tooth thickness can be very conveniently measured by a gear tooth vernier.

Since the tooth thickness varies from the tip of the base circle of the tooth, the instrument must be capable of measuring the tooth thickness at a specified position on the tooth. Further this is possible only when there is some arrangement to fix that position where the measurement is to be taken. The tooth thickness is generally measured at pitch circle & is, therefore, referred to as pitch line thickness of tooth. The gear tooth in the vernier has two vernier scales &

they are set for the width ‘w’ of the tooth & the depth ‘d’ from the top, at which w occurs.

FIG- 5.8

Considering one gear tooth, the theoretical values of w & d can be found out which may be verified by the instrument. In the fig it may be noted that w is a

chord ADB, but tooth thickness specified as an arc distance AEB. Also the distance d adjusted on instrument is slightly greater than the addendum CE, w is therefore called chordal thickness & d is called the chordal addendum.

From the fig, w=AB=2AD, Now angle AOD = θ = 360⁰/4N Where N is the number of teeth, w=2AD=2*AO*sinθ

= 2R sin (360/4N) (R=PITCH CIRCLE RADIUS) Module, m= P.C.D/number of teeth = 2R/N R=N*m/2

w=(N*m)*sin(360/4N) Also from fig, d= OC-OD OC = OE+ addendum = R+m

= (N*m/2)+m OD = R * cosθ

= N*m/2 cos(90/N)

d = (N*m/2)+m-(N*m/2) cos(90/N)

Any error in the outside diameter of the gear must be allowed for when measuring tooth thickness.

In case of helical gears the above expressions must have to be modified to take into account the change in curvature along the pitch line. These formulae apply when backlash is ignored.

Gear tooth Caliper

FIG-5.9

It is used to measure the thickness of gear teeth at the pitch line or chordal thickness of teeth & the distance from the top of a tooth to the chord. An adjustable tongue, each of which is adjusted independently by adjusting the screw on graduated bars, measures the thickness of the tooth at pitch line & the addendum. The effect of zero errors should be taken into consideration.

This method is simple & inexpensive. However it needs different setting for a variation in number of teeth for a given pitch & accuracy is limited by the least count of instrument. Since the wear during use is concentrated on the two jaws, caliper has to be calibrated at regular intervals to maintain the accuracy of measurement.

Gear tooth Vernier

Most of the times a gear Vernier is used to measure the tooth thickness. As the tooth thickness varies from top to the bottom, any instrument for measuring on a single tooth must.

Fig 5.10

A gear tooth Vernier, figure is provided with two mutually perpendicular scales 1 and 5; the first is used in adjusting for a chordal height and the second, to measure the chordal tooth thickness. Before measurement, the adjustable tongue 3 is set by means of Vernier 2 to the height at which the chordal thickness is to be measured and locked in position. The measuring jaws are moved apart, and after testing the instrument with the tongue on the tip circle of gear being measured, the jaws are drawn closer together and brought into contact with the tooth flanks.

The values of the measured chordal thickness are directly read from Vernier 4.

Measurement at the constant- chord tooth thickness is preferable (the constant chord is the chord between the points of contact of the basic rack profile with the

tooth flanks at a normal section). The nominal values of the constant chord height and tooth thickness are selected from the corresponding tables compiled or are calculated by the corresponding formulae.

For standard spur gears with a normal pressure angle of 20⁰< the constant-chord height h equal to h=0.7476m.

And the constant chord tooth thickness is S=1.387m.

Where m is module, mm.

Base pitch

The base pitch is the circular pitch of the teeth measures on the base circle. The tooth span micrometer is used to check the mean value and variation in the base tangent length. It varies from the standard micrometers only with respect to the measuring anvils. Here disk type measuring anvils are used. The disk anvil frame may be partly cut away. These micrometers are often used to determine an unknown gear module. To this end the base tangent length is measured first over n teeth then over n-1 teeth. The difference in measurement gives the base pitch t0 which is used for module by the formula m=t0/π cosφ where φ is the pressure angle.

FIG:5.11