gear errors.docx

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what-when-howIn Depth Tutorials and Information

Sources ofErrorsin Manufacturing Gears (Metrology

)

15.4.

The gears (gear teeth) are generally made by one of thefollowing two methods :

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

forms the gear teeth profiles by reproducing the shape ofthe cutter itself. In this

method, each tooth space is cut independentlyofthe other tooth spaces. _

(ii) Generating method,in which the cutting tool (hob) forms the profiles ofseveral

teeth simultaneously during constant relative motion ofthe tool and blank.

The various sources oferrorsin 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 and (Hi) incorrect indexing ofthe blank.

The sources oferror when gears are made by generating method are :

(i) Errorsin the manufacture ofthe cutting tool (ii) errorsin positioning the

tool in relation to the work and (Hi) errorsin the relative motion ofthe tool and blank

during the generating operation.

15.4.1.

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.

The chief requirements, which an idle gearing must fulfil are : (i) The

maintenance ofa constant gearing ratio ; (ii) Provision ofcontact along the full

length ofthe tooth, and (Hi) Providing the proper backlash.

(The backlash or side playofa gear is clearance between teeth ofmeshing gears which

provides for a slight rotation ofone gear in reference to the mating gear.)

The important factor in case ofhigh speed gearsin a limitation ofvariations in the

gearing ratio. When gears are operating at very high speeds then considerable
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acceleration appears even for small gearing ratio variations. These accelerations cause

large dynamic loads which can damage the gear tooth.

High power gears are generally operated at low speeds but their teeth have to transmit

large force. Therefore the gear teeth for this purpose should specify fullest possible

contact along the tooth length.

The man requirement ofthe precision gears is the constant gearing ratio.

These gears are generally used for counting and timing purposes, or inthe

measuring instruments and indexing devices, and usually have small face width and

are ofsmall module.

From what has been said above for the gearing operationrequirements, it can be concluded thatgears can be gradedon the basis of the following accuracies :

(i) Kinematic accuracyofthe gear, (ii) Smoothness ofgear operation. (iii) Tooth

bearing contact.

We shall now discuss about these accuracies in more details :

15.4.2.

Kinematic Accuracy.

This is represented by the permissible accumulated error in gear rotation per

revolution ofthe gear.

The index ofkinematic accuracyofa gear is the maximum kinematic error, which is

defined as the maximum angular error in rotation ofa gear, when it meshes in single-profile engagement with a precise (master) gear. This error is evaluated by drawing the

kinematic error curve as shown inFig. 15.10. This error is caused when the gear is being

cut, due to errorsin positioning the tool in rela-

tion to the blank, as well as to kinematic errors (errorsin gear train) ofthe gear-

cutting machine.

Fig. 15.10. Kinematic Error Curve.

The kinematic error may also be evaluated by the maximum accumulated error in the
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circular pitch. This is the maximum error between like profilesofany two teeth

measured on a single gear.

Thus in Fig. 15.11 the maximum accumulated error in circular pitch = maximum plus

error + maximum minus error. Another index ofkinematic error may be the

variations in the base tangent length. This constitutes the difference between the

maximum base tangent and the minimum value on a single gear.

15.4.3.

Smoothness of gear operation.

Smoothness ofgear operation is ofvital importance to provide for noiseless engage-

Fig. 15.11

ment and longer service life ofgearing. It is represented by the value ofthe

components ofthe full error in the angle or rotation ofa gear, which are repeated many

times per revolution ofthe gear. The index ofsmoothness ofgear operation is the

cyclic error which in the kinematic error curve inFig. 15.12, is represented by Cyclic

error = (oi + a% + a3 + an)ln.

Thus the cyclic error may be defined as the mean value ofthe range ofvariation in the

kinematic error ofthe gear taken for all cycles during one revolution.

Smoothness ofgear operation is also ensured by limiting the maximum permissible

deviations in basic pitch and the involute profile tolerance.

15.4.4.

Tooth bearing contact.

The index oftooth bearing contact in gearing is the gear contact pattern, which is the

part ofthe surface on a gear tooth profile showing traces ofbearing contact with the

teeth ofthe mating gear after they have been run together with the

drive gear braked slightly.

Bearing contact for mating gears is represented by the relative size ofthe bearing

contact pattern in per cent.
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Along the tooth length it is denoted by the ratioofthe traces ofcontact, subtracting

gaps or skipped places large than the size ofthe module in mm, to the full length ofthe

tooth.

Fig. 15.12. Tooth bearing contact pattern.

Gear errors. Various possible types of error on spur,helical, bevel and worm gears are described below :

(i) Adjacent pitch error Actual pitchdesign pitch.

(ii) Cumulative pitch error Actual length between corresponding flanks ofteeth not

adjacent to each otherdesign length. (Hi) Profile error The maximum distance ofany

point on the tooth profile

form and normal to the design profile when the two coincide at the reference circle.

(iv) The tooth to tooth com- The range ofdifference between the displacement at the

posite errorsingle flanks pitch circle ofa gear and that ofa master gear meshed

with it at fixed centre when moved through a distance (Refer Fig. 15.13 a).

corresponding to one pitch with only the driving and

driven flanks in contact.

(v) The total composite The range ofdifference between the displacement at

the errorssingle flank pitch circle ofa gear and that ofa master gear meshed

with it at fixed centre distance when moved through one revolution with only the

driving and driven flanks in contact (Refer Fig. 15.3 a).

Fig. 15.13. (6) Composite ErrorsTypical double flank error chart.
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(vi) The tooth to tooth The range ofvariation in the minimum centre distance

composite error

doublebetween a gear and a master gear when rotated through

flank a distance corresponding to the pitch of the teeth (Refer Fig. 15.13 a).

(vii) The total composite The range ofvariation in the minimum centre distance

errordouble flankbetween a gear and a master gear when the gear is rotated throughone revolution (Refer Fig. 15.13 b).

(viii)The tooth thicknesserror

Actual tooth thickness measured along the surface ofthe referencecylinderdesign tooth thickness.

(ix) Cyclic errorAn error occurring during each revolution of the element underconsideration.

(x) Periodic errorAn error occurring at regularintervals not necessarily corresponding

to one revolution ofthe component.

(xi) Run outIt is the total range ofreading ofa fixed indicator with the contactpoint applied to a surface rotated, without axial movement about a

fixed axis.(xii) Radial run out

It is the run-out measured along a perpendicular to the

axis ofrotation.

(xiii) Eccentricity It is half the radial run-out.

(xiv)Axial run-out

(wobble)

It is the run-out measured parallel to the axis ofrotation, at a

specified distance from the axis.

(xv) UndulationA periodical departure ofthe actual tooth surface from the design

surface (Refer Fig. 15.13 b).

(xvi) Undulation heightThe normal distance between two surfaces that contain respectivelythe crests and the troughs of the tooth undulation (Refer Fig. 15.13 c).

(xvii) Wavelength ofan The distance between two adjacent crests ofan undula-

undulation tion (Refer Fig. 15.13 c).

(xviii)Tooth alignment

error

The distance ofany point on a tooth trace from the design tooth trace

passing through a selected reference point on that tooth (Refer Fig.15.13 c).

The presence ofthese errors caused interference in efficient operation ofgears.

These result in non-smooth and noisy operation which ultimately affect the working

life.

N E X T P O S T : Gear Measurement (Metrology)

P R E V I O U S P O S T : TerminologyofGear Tooth (Metrology)

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Indian Standard (IS 9191993) (Part I & Part II) (Metrology)

Data Presentation (Metrology)

Gauge Design (Metrology)

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