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IPE 381Chapter:15

Measurement and Testing of GEARS

Abdullah-Al-Mamun

Lecturer, Dept. of IPE

Outline

• Common terms

• Involute Curve

• Line of Action and Pressure Angle

• Errors in Mfg Gears

• Measurement of Tooth Thickness

• Constant-Chord Method

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Gears

Involute Curve

• An involute curve is defined as the locus of a point on straight line which rolls, around a circle without slipping.

• G2 R2 = arc GR2.

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Involute Curve

Cycloidal Profile

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Line of Action and Pressure Angle

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.

Involute Functionit is the locus of the end of a thread (imaginary) unwound from the

base circle.

OA = base circle radius = Rb

OP = pitch circle radius = Rp

BP = involute profile of gear tooth

AP is tangent to base circle at A,

<AOC = φ= pressure angle

Now OA = OP cos φ , or Rb = Rp cos φ

<COB = Involute function of φ

By definition of involute, length AP = arc AB

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Helix and Lead angle

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

Two method of Mfg. Gears

(i) Reproducing method, in which the cutting tool is

form cutter, which forms the gear teeth profiles by reproducing the shape of the cutter itself. In this method, each tooth space is cut independently of the other tooth spaces. (ii) Generating method, in which the cutting tool (hob) forms the profiles of several teeth simultaneously during constant relative motion of the tool and blank.

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Reproducing method

Generating method

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Errors in Mfg. GearsThe various sources of errors in the gear made by reproducing method

be due to

(i) incorrect profile on the cutting tool,

(ii) incorrect positioning the tool in relation to the work

(iii) incorrect indexing of the blank.

The sources of error when gears are made by generating method are :

(i) Errors in the manufacture of the cutting tool

(ii) errors in positioning the tool in relation to the work.

(iii) errors in the relative motion of the tool and blank during the generating operation.

Gearing Operation Requirements

• The gears can be classified into three categories according to the operation requirements as follows :

(i) High speed gears,

(ii) High power gears,

(iii) Precision gears.

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Basis of the Accuracies

• gears can be graded on the basis of the following accuracies

(i) Kinematic accuracy of the gear,

(ii) Smoothness of gear operation.

(iii) Tooth bearing contact.

Kinematic Accuracy

• Kinematic Accuracy

This is represented by the permissible

accumulated error in gear rotation

per revolution of the gear.

• Smoothness of gear operation.

Smoothness of gear operation is of vital importance to provide for noiseless engage ment and longer service life of gearing. The index of smoothness of gear operation is represented by Cyclic error = (a1 + a2 + a3 + … an)/n

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• Tooth bearing contact

The index of tooth bearing contact in gearing is the gear contact pattern.

(L-L1)/B x100%

Gear Measurement

• Concentricity of Teeth: Fluctuationg velocity will be noticed otherwise

• Good alignment of each teeth:Load will not be distributed evenly otherwise

• Hardness

• Accuracy of measurement

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Gear Inspection

• Analytical

– Profile.

– Spacing.

– Pitch.

– Runout or eccentricity or concentricity.

– Thickness of tooth.

– Lead.

– Backlash.

• Functional

Running test with control

gear or Master gear to determine:

Composite vibration

Noise level

Variation in action

Rolling test

This test reveals any errors in tooth form, pitch and concentricity of pitch line. When two gears are in mesh with each other, then any of the above errors will cause the variation of centre distance

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15.8.1 Parkinson Gear Tester

Measurement of tooth thickness

• tooth thickness is defined as the length of an arc, which is difficult to measure directly.

• it is sufficient to measure the chordal thickness i.e., the chord joining the intersection of the tooth profile with the pitch circle.

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Constant Chord Method

• If an involute tooth is considered symmetrically in close mesh with a basic rack form, then it will be observed that regardless of the number of teeth for a given size of tooth (same module), the contact always occurs at two fixed point A and B. AB is known as constant chord.

Effect of eccentricity on Pitch Error

• Runout

• Lead

• Backlash

• Lead Measurement

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Thank You