5. Measurement of Gears
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Transcript of 5. Measurement of Gears
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Experiment 5 - Measurement of Gears
1. AIM
To measure various parameters of a spur gear
2. THEORY
Gears are used in a wide variety of machines (automobiles, machine tools, processing
machine for cement, sugar, etc., material handling equipment like cranes). The material and
the geometric features of the gears will influence the performance of those machines.
There are many types of gears. Spur gears are the simplest one very commonly used. Here
the teeth will be parallel to the axis of the gear. Both the driving and the driven gears are
mounted on the parallel shafts.
To measure its various features one has to be familiar with the gear tooth terminology. All
gears have generally involute profile for teeth. The generation of an involute curve is
shown in (Fig-1). (Fig-2) shows the terminology.
Figure 1
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Figure 2
The various errors that occur during manufacture are
1. Profile error of the teeth
2. Error in tooth thickness
3. Error in circular pitch
4. Eccentricity between axis of rotation and pitch circle diameter etc.
For practical applications, an assessment of total composite error will be adequate (Fig-3a)
and (Fig-3b) show the composite error in one revolution of gear when meshed with the
master gear (Fig-3a) shows the error as displacement along pitch circle, whereas (Fig-3b)
shows the errors as the displacement along centre line.
Figure 3(a): Typical single flank error chart
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Figure 3(b): Errors are shown as the displacement along center line
However, this cannot be separate out individual errors. It can be used as a quality test, but
not for analysis of the errors.
For analyzing, the individual errors are to be measured. The error on tooth can be
measured with a Vernier Caliper. Gear tooth Vernier Calipers (Fig-4), has a horizontal and
vertical scale so that one can set as reference and measure the variation in the other. Since
the tooth thickness varies throughout its height, it is measured at the pitch circle diameter.
Hence, the vertical scale can be set for addendum and horizontal scale can measure the
error in tooth thickness.
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Figure 4: Gear tooth Vernier Caliper
For measuring the error along pitch circle, tangent micrometer is used (Fig-5b). The
opposing involute on one or more teeth will have the same dimension if it is measured
across root of one and tip of the other and vice versa (Fig-5a). Hence if the dimension
across 2-3 teeth is measured, the corresponding theoretical value can be evaluated and the
difference fives the error. By repeating this process along the entire pitch circle, it is
possible to measure circular pitch errors at the different parts of the gear.
Figure 5(a)
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Figure 5(b): ‘David Brown’ Base Tangent Comparator
Where, S: No. of teeth covered during measurement
m: Module
N: No. of teeth
3. PROCEDURE
1. Measure the outer diameter of the gear and the number of teeth
2. Calculate the module and adjust it to standard value
3. Calculate all dimensions of the tooth, circular pitch and tooth clearance
4. Using gear tooth caliper, measure thickness of all teeth and tabulate
5. Using Flange Micrometer, measure circular pitch of the hear at different points of
the pitch circle, tabulate the results
(Please refer to Table-1 in the Appendix)
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
APPENDIX
Involute Curve
An involute curve is defined as the locus of a point on a straight line which rolls around a
circle without slipping. It could also be defined in another way as the locus on a piece of
string which is unwound from a stationary cylinder.
Thus it is obvious that in an involute curve the length of the generator (G1R1) will always be
equal to the arc length (GR1) of the base circle from the point of tangency to the origin of
involute at G. (Fig.15.1)
Similarly generator G2R2=arc GR2
It is also clear that the tangent to the involute at any point will be perpendicular to the
generator at that point. This condition fulfills the requirements of laws of gearing.
Further, will also be noticed that the shape of the involute curve is entirely dependent upon
the diameter of the base circle from which the involute is generated. The curvature of the
involute goes on decreasing as the base circle diameter goes on increasing and finally
involute become straight line when the circle diameter is infinity.
Terminology of Gear Tooth
A gear tooth is formed by portions of a pair of opposed involutes. Most of the terms used in
connection with gear teeth are explained in Fig. 15.2.
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Base Circle: It is the circle from which involute form is generated. Only the base circle on a
gear is fixed and unalterable.
Pitch Circle: It is an imaginary circle most useful in calculations. It may be noted that an
infinite number of pitch circles can be chosen, each associated with its own pressure angle.
Pitch Circle Diameter (P.C.D.): It is the diameter of a circle which by pure rolling action
would produce the same motion as the toothed gear wheel. This is the most important
diameter in gears.
Module: It is defined as the length of the pitch circle diameter per tooth. Thus if P.C.D. of
gear be D and number of teeth N, then module (m) = D∕N. It is generally expressed in mm.
Diametral Pitch: It is expressed as the number of teeth per inch of the P.C.D.
Circular Pitch (C.P.): It is the arc distance measured around the pitch circle from the flank
of one tooth to a similar flank in the next tooth.
.’. C.P. =πD∕N=πm
Addendum: This is the radial distance from the pitch circle to the tip of the tooth. Its value
is equal to one module.
Clearance: This is the radial distance from the tip of a tooth to the bottom of a mating
tooth space when the teeth are symmetrically engaged. Its standard value is 0.157 m.
Dedendum: This is the radial distance from the pitch circle to the bottom of the tooth
space.
Dedendum=Addendum + Clearance
=m+0.157 m=l.157 m.
Blank Diameter: This is the diameter of the blank from which gear is a t. It is equal to
P.C.D. plus twice the addenda.
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Blank diameter =P.C.D + 2m.
=mN+2m = m (N+2).
Tooth Thickness: This is the arc distance measured along the pitch circle from its
intercept with one flank to its intercept with t le other flank of the same tooth.
Normally tooth thickness=½ C.P. =πm∕2
But thickness is usually reduced by certain amount to allow for some amount of backlash
and also owing to addendum correction.
Face of Tooth: It is that part of the tooth surface which is above the pitch surface.
Flank of the Tooth: It is that part of the tooth surface which is lying below the pitch
surface.
Line of Action and Pressure Angle: The teeth of a pair of gears in mesh, contact each
other along the common tangent to their base circles as shown in Fig. 15.3. This path is
referred to as line of action. As this is the common generator to both the involutes, the load
or pressure between the gears is transmitted along this line. The angle between the line of
action and the common tangent to the pitch circles is therefore known as pressure angle ø.
The standard values of ø are 14½ 0 and 20°.
In Fig. 15.3
𝑂𝐴
𝑂𝑃= 𝑐𝑜𝑠𝜙 =
𝑅𝑏𝑅𝑝
=𝐷𝑏𝐷
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
.’. Dia. Of base circle 𝐷𝑏 = 𝑃.𝐶.𝐷.𝑋 𝑐𝑜𝑠𝜙
Base Pitch: It is the distance measured around the base circle from the origin of the
involute on the tooth to the origin of a similar involute on the next tooth.
Base Pitch=Base Circumference/ No. of teeth= π × Dia. of base circle/N
=π × D cosø /N= πmcosø.
Involute Function: It is found from the fundamental principle of the involute, which it is
the locus of the end of a thread (imaginary) unwound from the base circle.
Mathematically its value is Involute function δ=tan ø—ø, where ø is the pressure angle.
The relationship between the involute function and the pressure angle can be derived as
follows:
In Fig. 15.4,
OA=base circle radius=Rb
OP=Pitch circle radius=Rp, and
BP=involute profile of gear tooth.
AP is tangent to base circle at A,
AOC=ø=Pressure angle
Now OA=OP cosø, or Rb=Rp cosø
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
COB=Involute function of ø.
By definition of involute, length=AP=arc Ab
and tan ø=AP/OA=AP/Rb=arc AB/Rb, Also ø+δ=arc AB/Rb
.’. ø+δ=tan ø or δ=tanø−ø.
Helix Angle: It is the acute angle between the tangent to the helix and axis of the cylinder
on which teeth are cut.
Lead Angle: It is the acute angle between the tangent to the helix and plane perpendicular
to the axis of cylinder (Refer Fig. 15.5).
Back Lash: It is the distance through which a gear can be rotated to bring its non-working
flank in contact with the teeth of mating gear (Ref. Fig 15.6).
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IIT Gandhinagar, Discipline of Mechanical Engineering ME 352 Mechanical Engineering Laboratory II HPM Jan/Feb 2014
Table 1: Basic tooth Proportions for Involute Spur Gears
Pressure Angles
20° 14½° Addendum
Dedendum
Teeth Depth
Circular teeth thickness
Fillet radius
Clearance
m
1.25 m
2.25 m
πm/2
0.3 m
0.25 m
m
1.157 m
2.157 m
πm/2
0.157 m
0.157m
Table 2: Some Important Relationships between Various Elements of Gears
To find Having Formula (a) Spur Gears Module (m) Module Outside diameter (Do) Base circular diameter (Db)
No. of teeth (N) and pitch diameter (D) Circular pitch (p) Pitch diameter and Module Pitch diameter and pressure angle
𝑚 = 𝐷 𝑁 𝑚 = 𝑝 𝜋 𝐷𝑜 = 𝐷 + 2𝑚 𝐷𝑏 = 𝐷𝑐𝑜𝑠𝜙