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IS 7504 (1995): Gears - Cylindrical Gears - Accuracies -Methods of inspection [PGD 31: Bolts, Nuts and FastenersAccessories]

Indian Standard

GEARS-CYLINDRICA~L GEARS-ACCURACIES- MBTHODSOFINSPECTION

( First Revision )

UDC 621-833.1 : 620~111~1

Q BIS 1995

BUREAU OF INDIAN STANDARDS MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG

NEW DELHI 110002

December 1995 Price Group 9

Gears Sectional Committee, Lhl 13

FOREWORD

This Indian Standard ( First Revision ) was adopted by the Bureau of Indian Standards, after -the draft finalized by the Gears Sectional Committee had been approved by the Light Mechanical Engineer- ing Division Council.

This standard was originally published in 1974. The present revision incorporates the latest internation- ally accepted techniques for inspection of cylindrical gears which includes inspection of gear blanks of meshing gears, inspection of teeth forms of gears pairs and the inspection of gear pairs in assembled conditions. The gears are classified into 12 grades based on their accuracies. The revision also incor- porates the methods for determining individual errors,_schematic for electronic pitch testing equipment, schematic circuit for single flank testing and measurement of double flank total composite error

Assistance has been derived from the following standards while revising the standard:

i) DIN 3960 : 1987 Definitions parameters and equations for involute cylindrical gears and gear pairs, issued by DIN. Dxutsches Institut fiir Normung, Germanv.

ii) DIN 3961 : 1978 Tolerances for cylindrical gear teeth, issued by DIN. Deutsches Institut ftir Normung, Germany.

iii) DIN 3967 : 1978 System of gear fits, backiash tooth thickness allowances, tooth thickness tolerances, principles, issued by DIN. Deutsches Institut fiir Normung, Germany.

IS 3681 : 1994 Gears -- Cylindrical gears - Accuracies (Jivsi revision ) may be referred for definitions and notations.

In reporting the result of a test or analysis made in accordance with this standard, if the final value, observed or calculated, is to be rounded off, it shall be done in accordance with IS 2 : 1960 Rules for rounding off numerical values ( revised ).

IS 7504 : 1995

Indian Standard

GEARS - CYLINDRICAL GEARS -ACCURACIES METHODS OF INSPECTION

( First Revision )

1 SCOPE

1.1 This standard covers the general plan for cylindrical gears of involute, modified involute flank forms, comprising of gears with straight or inclined teeth for connecting parallel shafts.

I.2 This standard covers the inspection methods for gear teeth oncylindrical gears of module 1 to 70 and with reference circle diameter up to 10 000 mm graded in 12 gear tooth qualities.

2 REFERENCES

IS 3681 : 1994 Gears - Cylindrical gears - Ac- curacies (first revision)may be referred for definitions and notations.

3 SYMBOLS a _

6 -

d -

4 - db -

dM -

ff - 4 - fi _

fP -

fv -

fu -

fHa - h-v - fif - Ii -

& - In -

k -

m -

ma -

mt -

Pb -

s -

Radial pitch distance (double flank pitch distance)

Face width

Reference circle diameter

Top diameter, Blank diameter

Base circle diameter

Measuring circle diameter

Profile form error

Single flank tooth to tooth composite error

Double flank tooth to tooth composite error

Individual pitch error

Base pitch error

Tooth to tooth pitch error

Profile angle error

Flank line angle error

Longitudinal form error

Chordal height

Constant chordal height

Normal backlash

Number of teeth measured

Module

Normal plane module

Transverse module

Base pitch

Tooth thickness

SMax -

Win -

sb -

Fn -

SC - Y -

z -

zv - A -

Cl - c2 -

OM -

Ff -

Fi -

F; -

FP -

Fpk -

Fpz/a-

Fs -

Fr -

IT -

M -

Ml -

MR -

Rp -

Rs -

cl -

an -

at -

aw -

awt -

aR -

aRt -

B -

fib -

* -

Maximum tooth thickness

Minimum tooth thickness

Tooth thickness on base cylinder

Chordal tooth thickness

Constant chordal tooth thickness

Addendum modification co-efficient

Number of teeth

Virtual number of teeth

Factor (Table 7)

Factor (Table 8)

Factor (Table 9)

Measuring pin or ball diameter

Total profile error

Single flank total composite error

Double flank total composite error

Total cumulative pitch error

Cumulative pitch error over k pitches.

Cumulative pitch error over 1/8%of periphery

Total alignment error

Radial run-out error

Tolerance grade

Tooth width

Tooth width for module 1

Dimension over pins or balls

Range of pitch errors

Tooth thickness fluctuation

Pressure angle

Normal pressure angle

Transverse pressure angle

Working pressure angle

Transverse working pressure angle

Pressure angle, pin or ball

Transverse pressure angle, pin or ball

Helix angle

Base helix angle.

Tooth thickness semi-angle

t

1

IS 7504 : 1995

4 INSPECTION METHODS FOR CYLINDRICAL GEARS

4.1 The logical order of manufacture of a gear pair is:

a) Machining the blanks of the two gears, b) Cutting of the teeth of the hvo gears, and c) Assembling the toothed wheels in operating

condition.

It is, therefore, normal to carryout the successive inspection in corresponding order:

1. Inspection of the blanks of the two gears. 2. Inspection of the teeth of the two gearqand 3. Inspection of the assembly conditions of the two

gears.

5 INSPECTION OF THE GEAR BLARES

5.1 Reference Axis

In the case of pinions or wheels with bores, the axis of the bore is adopted as the reference axis.

In the case of pinions on shafts, the reference axis shall be the bearing axis of the bearings.

In order to facilitate the operations of machining, inspection and assembly of toothed wheels, it is recommended that radial and axial auxiliary reference surfaces should be indicated clearly on the working drawings ( see Fig. 1).

FIG. 1 REFERENCE SURFACES \\

5.2 Tip Cylinder

5.2.1 Tip Dimne~er

The value of the tip diameter is not of essential impor- tance. In cases where the apparatus for inspecting the tooth thickness rests on the tip cylinder, allowance should be made for the tip diameter error.

5.2.2 Radial Run-Out

This is the total range of movement of an indicator stylus which is in contact with the tip cylinder during a complete revolution of the gear (seeFig. 1). This check is important only in the case where certain tooth inspec- tion instruments rest on the cylinder.

5.3 Reference Surfaces

53.1 Radial Run-Out

This is the total range of movement of an indicator stylus which is in contact with the radial cylindrical reference surface during a complete revolution of the gear.

53.2 Axial Run-Out (wobble)

This is the total range of movement of an indtcator stylus which .is in contact with the axial reference surface during a complete revolution of the gear.

5.4 Tolerauces on Gear Blanks

The tolerances on gear blanks shall be as given in Table 1.

6 INSPECTION OF GEAR TEETH FOR INDIVIDUALERRORS

6.1 Circular Pitch Errurs

Circular pitch errors called as pitch errors in short, ilre measured on thereference circle or any other circle as close to it as possible and concentric with respect to the gear axis. The difference between the measuring circle diameter & and the reference circle diameter d in- fluences the measurement of the error by the factor d&d and these errors aregenerally negligible.

The measured values are also affected by eccentricity of the teeth with respect to reference axis and also by profile error.

Inspection of the pitch by measuring the deviation from the design value is normally performed only on high precision gears where exact angular transmission is indispensable, A tooth flank is butted against a fixed anvil in the region of the reference circle while a movable measuring feeler senses the corresponding flank of the adjacent tooth. The differences between the adjacent pitches csn be read from a dial indicator ( see Fig. -2 ).

Eccentricity of the teeth with reference to the gear axis gives rise to an error curve of overall sinusoidal form.

When pitch measurement is carried out using a hand operated comparator, the computation of the individual pitch error, tooth to tooth pitch and total cumulative pitch error is carried out as given in Table 2 and the graph of the errors can be drawn from the values thus computed.

The difference between the consecutive measured values gives tooth to tooth pitch error, fU. Then the algebraic mean value is calculated from all the measured values. The difference between the measured values and the mean valuegives individual ptich error, ft The algebraic addition of individual pitch error fp gives the cumulative pitch error. The total cumulative pitch error Fp is given by the difference between maximum and minimum values of cumulative pitch error.

The circular pitch errors can also be measured by using electronic pitch testers. Individual pitch errors are

2

I Quality

Table 1 Tolerances on Gear Blanks (pm)

( Clause 5.4 )

Bore error of form

Shaft error of form

Xp diameter

) Radial b-out of Xp cylinder

Radial run-out of the reference surface

Axial run-out of the reference surface

1

ITl

In

IT6

2

In

In

IT6

2.5

3 4

IT3 IT4 T IT3 IT4 IT7 IT7 0.014 + 5

5

IT4

IT4

IT7

w

NOTE-& - Blank diameter, mm.

) When the tip cylinder is used as a datum surface for a checking instrument.

6

IT6

IT5

IT7

7

IT6

ITS

IT7

0.0&f, + 10

8

IT6

IT5

IT8

9

IT7

IT6

Il?3

Usd, + 15

10

ITa

In

n-9

IT8 IT8

F IT11 IT11

O.O4d, + 25

i

G SUPPORT

FIG. 2 INS~YXX~ON OF GEAR Tmm POR INDMDUAL ERRORS

measured Lvith an attachment for involute and helix testers, which operates on the comparison pitch measuring principle and at the same time defines a mean value. Figure 3 shows a schematic of an electronic pitch testing equipment. The attachment compares the initial comparison pitch value 0 of any one pitch of the gear with all subsequent pitches. This is achieved with the electric tracer K which, with its pair of styli M switched to difference measurements, measures values in relation to the initial datum value 0. When the last measured value has been recorded, electronic unit R automatically evaluates the mean value which k then drawn automatically as a straight line through the previously recorded pitch diagram. The actually recorded individual pitch errors are then read Hoff along the line.

6.1.1 Individual Pitch Error, fp

Individual pitch error, fp is the difference between the

actual value of a single transverse pitch and nominal transverse pitch.

In a gear with z teeth there are z individual pitch errors of the right flank and as many of the left flanks. The errors, fP are obtained as the difference between the individual measured value and the mean of all z measured values.

6.12 Cumulative Pitch Error, Fpk

This is the deviation of the actual dimension of a pitch interval over k individual pitches from the correspond- ing nominal value. The cumulative pitch error is obtained as the algebraic sum of the k individual pitch errors contained in the interval, provided the error of measurement is sufficiently small.

k F pk-Zf

OP

Table 2 Pitch Errors on Gears ( Clause 6.1 )

pitch No. %x? izil%%f Individual Pitch Emu- ;;IuhtAa4a; w fu, Irm fp. CM Fp7 w

1 0 1 +l +l

2 +3 3 +4 +5

3 +5 2 +6 +I1

4 +l 4 +2 +13

5 -1 2 0 +13

6 -3 2 -2 +I1

7 -5 2 -4 +7

8 -3 2 -2 +.5

9 -6 3 -5 0

10 -3 3 -2 -2

11 -1 2 0 -2

12 +l 2 +2 0

- NOTE - Mean value - +lO 22 - -

12 1 (Mean value to be rounded off to the nearest micrometer).

4

N

0

P

Q

2 R S T iJ V W

Base or guide- body for H and J Ckria side for eleck tracer K Gvrier side for electric tracer L I!kctric tracer for pitch tests, etc F%ztric tracer for true nmning tests

Pair of tracer styli of K switched to different measurements.

Selector switch for separate tracer pressure direction setting for M

Fine setting screw for adjusting the distance betwken tracer styli of M

Supporting ball pin or ball/type stylus of L for true running teats Measuring head adjustment swivelling and locking members

Counting mechanism

Computer for mean value evaluation Measured Glue store Stroke mechanism

Stroke restriction

Indicator instrument

Ekctric tracer for involute tests, etc

FIG. 3 ELECRCNW PITQI TEWNG E~JIPMENT

If the errors of all the pitch intervals are measured from a particular reference tooth profile or calculated from the individual errors& according to the above equation and then plotted against the corresponding teeth num- bers, then the cumulative pitch errors are obtained as per Fig. 4.

6.13 Cumulative Pitch Ermr Over 118 of Periphery, Fpzf8

This is the Amulative pitch error over-an iuterval of l/8 circumference of the gear (k = z/8).

i.lA T&al Cumulative Pdch Errs, Fp

The maximum cumulative pitch error in agear is called the total cumulative pitch error. It is indicatedwithout sign and is obtained from the cumulative pitch ermrs as the difference belweeu the algebraic maximum value and the algebraic minimum value. 6.1.5 Range ofPitch Errors, Rp This is the difference between maximum and minimum actual values of the transverse pitches of the right or left flanks of a gear.

6.I.6 Tooth to Tooth P&h Errol fi

The tooth to tooth pitch error is the difference between the actual values of two successive right or left tmnsverse pitches.

Tooth to-tooth pitch errors are directly obtained from ciradar pitch measurements as the difference of measurements offleighbouring pitches.

65.7 Base Pitch Error, fp

Base pitch error is the difference between the ac-1 and nominal values of the base pitch. Deviations measured in the transverse plane are denoted by fpt and in the normal plane by fpea.

Insped~on is performed by means of a base pitch measuting instrument which is pie-adjusted to setting gauges. Either portable or bench instruments can be

. employed. In both cases, measurement is independent of the gear axis with no influence of radial run-out on the base pitch. -Se2 Fii. 5.

The absolute value of the base pitch on the line of action ksn idicative of the pressure angle. Error in the base piti Implies an error ln the pressure angle. For spur gears, error in the pressure angle can be - determined by means of the equation:

For helical gears, the measured error of the base pitch may be due to an error in the pressure angle or in the helix angle or both. Measurement of the base pitch on the line of action is particularly important for the gears produced by si@e tooth cutters.

5

Is 7504 : 1995

FLANK F(O. 21 1 2 3 4 5 6 7 8 9101-l 12131415161718192021

r 1 fu II PjTCH NO. r-

b

C

r

a - Individual pitch em+ marked as vertical blocks between the flnak numbers.

R, - Range of pitch exror, fU - Tooth to tooth pitch error

b-Total cumulative pitch error referred to flank 21.

Fp - Total cumulative pitch error.

c -Cumulative pitch error over intervals of every three teeth,&3 (k = 3) shown a5 vertical blocks in the middle of the flanks.

FIG. 4 DEIERMNKIION OF Prm ERROR (Eg : 21)

MEASURING F

ER SUPPORT

BASE

FIG. 5 Mars UREMENTOF BASE Pm ERROR

6

l

Is 7504 : 1995

4.2 FlankDeviations

6.2.1 Inspection of the involute Profile

tester, flank test graph as shown in Fig. 7 can be obtained.

This inspection, together with the pitch measurement is of foremogt importance in the schedule of individual error tests, since for the correct meshing and the measurement ofgears it is essential that the tooth flanks are really involutes.

The formof the profile can be opticallyenlarged and compared with the drawing of an involute, especially in case of fme pitches. The diftkulty lies in determining the position of the proftie in relation to the base circle.

Usually the test is made by means of an apparatus which generates the true involute by roiling a straight edge on a base circle disc and records the deviations of the actual tooth profile to an enlarged scale on graph paper. See Fig. 6. The diameter of the base circle disc follows from the equations:

For spur gears: db = z.m cosa

For helical gears:

d,=z.m= cos&

By plotting the flank deviations with the help of a flank

\ EDGE STRAIGHT

FE. 6 IXSPECXON OF TCIOIX PROFILE

Profile

Total profile error, Ff

Profile angle errorha -

0 3 Profile form error,fi BB Intermediate actual profile AA,AA Nominal profile RB, BB Actual profile

Cc, CC Nominal profile

Flank Line

Total alignment error, Fp

Flank line angle error&

Longitudinal form error faf

Intermediate actual flank line Nominal-flank lines which envelop the actual flank Actual helical lines which envelop the actual flank Nominal flank lines which cut the actual flank lines at the beginning and end point of the teat range

FIG. 7 FLANK DIZVIATONS AND TEST GRAPH

7

IS 7504 : 1995

6.2.1.1 Totalprofile err06 Ff

In a test graph, as shown in Fig. 7, the total profile error, Ff is the measurement made perpendicular to the paper feed direction between the parallel lines AA and A' A', drawn in the direction of the paper feed within the profile test region through tbe extreme point of the test graph. Tbe desired modifications from the involute form are taken into consideration by corresponding deviations of the lines AA and AA from tbe straight line.

6.2.1.2 Pnzjile form error, ff In a test graph as shown in Fig. 7, the profile form error ff is the measurement taken perpendicular to the paper feed direction between the lines BB and BB which am parallel to the actual involute BB. Line BB is drawn to average the involute curve which touches tbe test curve within the profile test region.

62.13 Profile angle err03 fia

In a test graph as shown in Fig. 7, the profile angle error, fHa, is the measurement taken perpendicular to the direction of paper feed between the lines CC and CC parallel to AA, which cut the line BB at the start and end point of the profile test region respectively.

6.2.2 Inspection of Tooth Alignment Errors

623.1 Total alignment error Fp

For measuring the tooth alignment errors, Fig. 8 shows an apparatus that imparts the gear, a rotation cor- responding to the helix angle set on the apparatus. This rotation, combined with the movement of tbe feeler parallel to tbe gear axis, results in a vertical straight line diagram, if tbe acutal helix angle coincides with the design value.

In a test graph as per Fig. 7, the total alignment error Fg is the distance, measured perpendicular to the paper feed direction, between the parallel lines AA and AA which are drawn iu the direction of paper feed within the flank line test region through the extreme points of the test graph. The intended deviations from tbe helix line form are taken into account by corresponding deviations of the lines AA and AA from the straight line.

62.2.2 Longitudinal form error, fpf

The longitudinal form error, fbf of a tooth flank is the distance between the two helix lines with the actual lead, which touch and envelop the actual flank line within the flank line t&t region taking into account the intended deviations from the helix line form.

6.2.2.3 Flank line angle error, fHp

For all the defiirritions and calculations concerning the gear pair, 3 flank line angle for an external gear is considered a:, pcsitive when it is right banded with respect to a helix line witb the nominal lead and it is considered negative wbcn it is left handed with respect to a helix line with the nominal lead. In case of an iuternal gear, the signs are opposite. Thus in case of a spur ge;lr mating, equal errors with opposite signs csn- ccl each other out.

FIG. 8 A~PARKIUS FOR MENSWUNG TOOTH ,~GNMENT ERROR

Hence, there are two different definitions for tbe sign of the Eat& line angle error. In all production docu- ments, test reports, etc, the direction of the effect of the errors should be clearly indicated.

In a test graph, as shown in Fig. 7, the flank line angle error,fHg is the distance measured perpendicular to the direction of the paper feed, between the lines CC and CC which are parallel to the 1ineAA and cut the line BB at the end of the Eank line test region.

6.3 Radial Run-Out-Error, Fr

Radial run-out error, Fr of a gear is tbe radial positional difference of a measuring piece (Ball, cylinder or wedge), placed successively in all the tooth spaces, which touches the tooth flanks near the reference circle, while tbe gear is mounted on its guide axis, free to rotate. Fr is used to designate the maximum difference between the measurements at the gear peripbery.

The simple method to measure the radial run-out error of small and medium diameter gears consists of succes- sively introducing a ball or roller into all the tooth spaces, whilst the-gear is supported between centres. The relative depths attained by tbe ball iu the tooth spaces are mad from a dial indicator. See Fig. 9.

6.4 Tooth Thkkness Measurement

The measurement of tooth thickness is to guarantee the observance of a specified backlash for a given cenire distance taking into account, tbe inevitable tooth errors:

a) Measurement independent of the axis is applied mainly for setting up the gear production machine. It should be noted that tbe specifying of the tooth thickness consistent with a likewise specified backlash at the theoretical centre dis- tance postulates that all mother errors are withirr their respective limits, particularly the radial and axial run-out. Thus the measurement of

8

b)

cl

tooth thickness, independent of the axis can be regarded as a form of acceptance test only on condition that other errors (radial run-out in particular) are also inspected and remain within the limits specified. The measurement of tooth thickness with refer- ence to the axis, usually-included in the accep- tance test schedule,supplies the most important information for the determination of the effec- tive tooth thickness, namely, the tooth thickness of an imaginary gear concentric with the axis, which encloses all the errors of the gear. The theoretical tooth thickness measured on the reference cylinder is:

The tooth thickness fluctuation, R, is the difference between the maximum and minimum tooth thickness s of a gear:

4 = %,- &I

6.4.1 Measurement tif the Tooth Thickness by Means of

FIG. 9 MFASJREMENTOF RADLAL RUN-OUT ERROR

Gear Tooth Calipers

a) Meizsurement on the reference cylinder

Refer Fig. 10. Measurement on the reference cylinder is given b-y:

IS 7504 : 1995

b)

For spurgears: zv = z

inv at For helical gears : zv = z -

inv a

For backlash allowance $ the dimension S is

to be reduced by &

For corrected gears the dimension & must be reduced by the appropriate amount. Inspection by constant chord method

Refer Fig. 11, in this case, the measurement is not taken on the reference cylinder, but a little ~higher, which has a detrimental effect when the ~pressure angle is large and/ or the number of teeth is low.

YC-m. cos2a[t*Zr.tana]

EC-m 1 [

- Ic sina cosa f x . 4

cos2a I

For module = 1 and a - 20, & - 1.387 05

and & = 0.747 58.

BASE ClRCLf

6.4.2 Tooth Width Measurement with the Aid of M-Test Dimension

The tooth width M is the distance betweeri two parallel planes each touching a right and left flank in the vicinity of the pitch circle, measured over k teeth. See Fig. 12. Its particular advantage is that it permits measurement of the tooth width independent of the outside diameter. Since the variations in the pitch also come into the measurement, it is necessary to measure at several

points of the periphery. All individually measured tooth widths must lie within the tolerances in accordance with tooth thickness fluctuation, R,

Measurement is possible in case of both spur and helical gears. In case of helical gears, measurement has to be made~in the normal plane.

NOTE - * sign used in the formulae given in the text means plus sign forpositive correction and minus sign for negative correction and the absolute value of xis to be substituted in the formulae.

6.43.1 General formulae

The general formida for nominal dimension A4 of tooth width is:

M=mncc6 a,[(k-05)x+z. inv at] + 2r.mn.sina.. . . . . . (1)

To ensure the contact between the measuringjaws and tooth flanks is made near half the tooth depth, k must be calculated from:

k_f tmw 1 --2Etanan- II cos2Bb inv at + 0.5 1 . . ...(2) k must always be rounded off to a whole number. The transversti working pressure angle awt on the cylinder with the diameter (d + 2x.mn) can be calculated from:

Z cosawt-cosat

z+2r.cosp . . ...(3)

The helix angle on the base cylinder is computed from:

tanfib - tar+ cosat . . ...(4)

The transverse pressure angle is calculated from:

tana, tanat = -

cosS . . . .

6.4.2.2 Gears wtihoutprofile correction

a) Spur gears The odoth width M in case of a spur gear is calculated from: M - m cosa [(k - 0,0.5) n + z&v a] . . ...(a) The number of teeth measured is computed from the formula:

k=z ao - + 0,OS (rounded off to whole 180

number) . . . ...(7) In case of spur gears, without profile correc- tion with module = 1; the value of k and the width ikft for the pressure angles a = 14.9, lS, 2@ and 30 can be obtained from the Tables 3 to 6. With any given module, the tooth width is computed from: M = M1.m. . . . ...(8)

10

Is 7504 : 19YJ Tabk3 Tooth Width of Gears Without Profile Correction, Module = 1, Pressure Angle = 14.F

( Clause 6.4.2.2 )

z = number of teeth in gear blank, k = number of teetb measured, MI = tooth width for module 1

p, - m.n cos 14.5 = 3.041527. m

a = 14.50

IS 7504 : 1995 Table 4 Tooth Width of Gears Without Profile Correction, Module = 1, Pmssure Angle = 15

( Chse 6.4.2.2 )

z = ,number of teeth in gear blank, R = number of teeth measured, Ml = tooth width for module 1

pe = m.3c. cosW = 3.034 546.m

a = 15O

t i i

/~/~!~757 1 )l159! 14 ! 41.9109 !!209! 18 ! 54.3461

112 ) 10 ) 29.4935 11 162 1 14 1 41.9287

115 1 10 1 29.5113 11 165 1 14 1 41.9465 /+j+%%j~! 17.0821 ] ll116! 10 ! 29.5173 !!~166! 14 ! 41.9525

12012 4.6706 117016

12312 4.6884 117317

35 13 / 7.7943 1185 18 1 23.2640 ll1351~12 1 35.6992 111851 16 1 48.1344 11235)20 j 60.5697

/ 42 1 4 1 10.8704 IL

45 ( 4 1 10.8882 11 95 1 8 1 233234 jj145( 13 ) 38.7932 11195) 17 1 51.2284 I1245 1 21 1 6

IS 7504 : 1995

Table 5 Tooth Width of Gears Without Profile Correction, Module = 1, Pressure Angle = 20 ( Clause 6.4.2.2 )

z = number of teeth in gear blank, k = number of teeth measured, MI = tooth width for module 1 pe = m.n ws20 - 2.952 133.m

a-20"

t-,mf$$ 38.5262 /1166! 19 ! 1 56.9393 !!216! 2.5 ! 75.3524

t-\-j@ ! 47.6768 lj187! 21 1, 63.1377 1)237! 27 ! 81

141 1 5 1 13.8588 11 91 Ill 1 32.2719 IL

I!S7504:1995 hble 6 Tooth Width of Gears Without Profile Cormction, Module = 1, Pressurp Angle = 30

( Cluuse 6.4.2.2 ) z = number of teeth in gear blank, k = number of teeth measured, MI = tooth width for module 1

p,-m.ncos300= 2.720 698.m

a-300

73931

795930 11211 I36 I 106.4068

5465 11 186 1 32 1 94360 2 ii236 1 40 1 118.453 3 1

187 1 32 1 94.406 8 237 1 40 1 118.4998

138 17 1 19.4534 43.5466 11138b41 703603 ljl88l 32 ( 94.45331rUign

46.4068 11411241 70.4999 11191)32 1 94.59301241

/+!-%%j#%%ii&42!24! 705465 !!192!33! 97.3602 jl242141 l-:21.4533 1 ,l 1 121.4067 1

145 ] 8 1 225000 1195 116 ] 465930 )]145)25 1 73.4068 )I195133 1.97.4

33 1 97.5464 11 246 ( 42 1 124.360 2 j

150 1 9 1 25.4534 \\100\ 17 1 49.5465 Ill50126 1 76.3602 j1200) 34 \ 100.4533 1[12itjy .2 1 124.5464 1

14

kOOT CIRCLE I!3 7504 : 1995

b)

M

FIG. 12 MEASUREMFN OF Tocrrn WIDTH

Helical gears In case of helical gears the tooth width is com- puted from: j%f I ma.cosaa [(k - 0,O.S) rt + z.inv at] . . . . . (9)

and the number of teeth is measured from:

t.mattan2 Bb R;

. . . . ..(lO)

for &-- 200, k can be obtained from Fig. 13. By introducing, constants that can be tabulated, formula 4 can be simplified as follows:

M-ma(A+z.Cl) . . ...(n)

where A = (k - 0.5)~. cosas Cl Anv at. cosan

The values of A for various values of k are given in Table 7. The values of Cl for various helix angles p and various pressure angles an can be obtained from Tabb 8. The minimum face width 6 required for M-measurement is calculated from formula 19.

6.433 Gears withprofile correction

a) Spur gears The nominal dimension M of the tooth width of a spur gear with profile correction factor n over k teeth is: .

All dimensions in millimetres. FIG. 13 NUMBER OFTEEIH MEASUREMENT FOR g, I u)O

15

Table 7 FactorA

( Clause 6.4.2.2 )

M - mcosa[ (k - 0,5) x + zinva] + 2xmsina . . . . . . . (12)

Number of teeth measured, k is computed from:

tana,,,-2Ztsna-inva I +OS . . . ..(13) By introducing constant C2, the formula 12 can be simplified as:

M-m.(Mt +C2) . . . ..(14) Value of C2 can be obtained from Table 9.

Value of Ml can be obtained from Tables 3 to 6.

0) EVEN NUMBER OF TEETH b) ODD NUMBER OF TEETH

The effective pressure angle aw on the diameter (d + 2xm) is computed from:

z cosaw =eosa-

2+2X . . . ..(15)

b) Helical gears The nominal dimension M~of the tooth width of a helical gear with profile correction over k teeth according to formula 1 is:

M = mn cosa [(k~- 0,s) x + z.inv at]

+ 2xmn sin an . . . ..(16)

FIG. 14 DLMENSION OVER BAUD OR PINS FOR E-AL GEARS

16

IS 7504 : 1995

Table 8 Factor C, ( Chse 6.4.2.2 )

, B

0

a, 14.50 - an 1.5 -

0.0053 68 0.005 940

lo 0.005 370 0.005 943

2 0.005 378 0.005 950

3O 0.005 390 0.005 967

4 0.005 407 0.005 982

5O 0.005 428 0.006 007

6 0.005 455 0.006 036

7 0.005 486 0.006 071

7 lo 51 0.005 493 0.006 078

8 0.005 522 o.cKl6 112

9O 0.005 564 0.006 155

lo 0.005 614 0.006 212

104825 0.005 657 0.006 259

1402840 0.005 899 0.006 527 38O 0.015 355 1 1 1 0.010721 1 0.011849 0.027 431

181236 0.006 238 0.006 900

190 0.006 323 0.006 994

24O 0.006 988 0.007 723 0.018 113

25O 0.007 153 0.007 914 0.018526

0.014 103 1 1 25O5640 1 0.007 317 1 0.008092 1 0.018 942

26 0.007 327 0.008 102 0.018 968

27 0.007 515 0.008 310 0.019 440

1 0.014 307 1 1 a0 ! 0.0~7716 0.008 531 0.019 944

k the number of teeth measured, computed horn formula 2 is:

z cosa, = cosa,

z+2xcos~ . . . ..(18)

2 bna, k=- Jc cos2p,

[ - - 2:tatq -_inv a,

1

+ 0.5 . . . ..(17)

k, for a, = 20 can be obtained from Fig. 13.

The transverse working pressure angle awr~on the

diameter (d + 2xmn) follows from:

By using tactors A, Cl, Cz the following formula is obtained:

M=m,(A+z.Cl+Cz) . . . ..(19) where

A = (k - 0.5)x cosa,, according to Table 7, Ct = cosa,,.invat according to Table 8, and

C;? = &.sina, acwrdingto Table 9.

17

Table 9 Factor C,

( Clause 6.4.2.3 )

In the case of negative profile correction a minus sign (-) must be placed before the values cz.

18

IS 7504 : 1995

7 INSPECTION OF GEAB TEETH IN ASSEMBLY CONDITIONS

7.1 Single Flank Total Composite Error Testing

In this test two gears are meshed and rotated at the prescribed centre distance with either the right or left flanks in constant contact. See Fig. 16. The single flank composite errors of the right flank are generally different from those of left flank of the same gear. The deviations of the rotating positions of the gear with respect to nominal positions given by the positions of the mating gear and by the ratio of the number of teeth are measured starting lrorn a start position. For this, a comparative measuring device is required where the error free rotating angle positions are obtained. The errors are generally indicated as paths along with circumference of a measuring circle, for example, the reference circle or base circle. The errors can also be given in angles.

7.1.1 Single Flank Total Composite Errol; Fi

In a circular test graph as shown in Fig. 17, the single flank total composite error, Fi is the difference between the maximum and minimum distance of the recorded test graph from the axis of rotation of the test chart, namely, F, is the difference between the maximum and minimum Y-axis of the test graph.

7.12 Single Flank Tooth to Tooth Composite Error, fi

The single flank tooth to tooth composite error,j is the maximum difference that occurs in the rotating posi- tions deviations within a rotating angle corresponding to the period of a tooth contact.

To ensure that two parallel planes touch the flanks, the face width must be:

b 2 iti sin& + b co@, . . . ..(20)

tat& = tang. cosar where !q,.t = Constant line overlap or width of the measuring surface in tooth width measurement. For gears without chamfering

&f z 1.2 + 0.018M

bkj > 2.0 + 0.03M

Summary of the important formulae~for the tooth width measurement with the aid of M-test dimension for spur and helical gears are furnished in Table IO. 6.4.3 Tolerance on M-Test Dimension The upper allowance and tolerance on M-test dimension can be obtained by multiplying the upper tooth thickness allowance (A,,) and tooth thickness tolerance (7,, values from Tables 7and 8 of IS 3681 : 1995, respectively by cosa,.

6.4.4 Tooth Thickness Measurement Over Pins or Balls Tooth thickness can be determined by taking the meas- urement over pins or balls placed in diametrically opposite tooth spaces as shownin Fig. 14 and Fig. 15. This method is suitable for both external and internal spur and helical gears. The size of the balls or pins should be selected in such a way that they touch the tooth flanks on or approximately near the reference circle. The theoretical dimension,Mu over the pins or balls can be calculated from Table 11. The selection of pin orball diameter and the calculation procedure for other parameters are given in Table 12. The tolerance on dimension, MR over pins or balls can be obtained by multiplying the upper tooth thickness allowance (A,,) and tooth thickness tolerance. (Ta values loom Tables 7 and 8 of IS 3@31 : 1995, respec-

tively by a factor given by --- * sinaRt . wsf3

6.5 Blue Bearing Test (TR4) Due to various gear errors and inIluence of working conditions..a near flank will not have full bearinn on the mating flank & a gear mesh. The blue bearing t&t indi- cates the bearing zone of one flank with its mating flank.

a) EVEN NUMBER OF TEETH

7.2 Double Flank Total Composite Error Testing

In this test two gears are meshed with each other and rotated with a left and right flank of thegears always in contact at the same time (two Sank contact) under the inlIuence of a force acting in the direction of the centre distance. See Fig. 18. In this process, the changes of the centre distance arc measured. The centre distance found in the double flankcomposite error testing is designated as a.

b) ODD NUMBER OF TEETH

FIG. 15 DIMENSION OVER BALLS OR PINS FOR INERNAL GEARS

19

Table 10 Summary of Important Formulae for the Tbotb Width Measurement

(Clause 6.4.2.3)

Gear Prome Tooth Width, M Number of Teeth Measured, t

spur gears M=m.M1 According to Gears without profile Tables 3 to 6

correction Helical gears M-m.(A +r.Cl) Aaxrding to Fig. 13

Gears with profile crorrecGon

spur gears

Helical gears

Ml = according to Tables 3 to 6 A = according to Table 7

Cl = according to Table 8

C2 = according to Table 9

) check whether the value of k read from Tables 3 to 6 and also from Fig. 13 are tbe same. If the value is not same, use the fomitiae 12 and 13 of 642.3 to evaluate M and k.

73.1 Double Flank To& Composite Errq fi

Refer Fig. 19. The double flank total composite error, Fi is the diEerence between the maximum and mini- mum working centre distance within one test rotation.

7.22 Radial Run-Ou Fr

The radial run-& error& is the longwave component of the test diagram. This component can be obtained by drawing zm averaging line thereby suppressing the short-wave components. The radial run-out error, Fr is

21 = DRIVING GEAR

the distance between the highest and lowest points of an averaging line.

7.2.3 Double Flank Tooth to Tmth Composite Err04 X

The double flank tooth to tooth composite error, fi is the difference between the maximum and mini- mum working centre distance that occurs within a turning angle corresponding to the period of a tooth contact.

22 = DRIVEN GEAR

23 = f,(-12) puuu/s 22 -

FIG. 16 BLOCKDIAGRAM OF CIR~JKFDX SINGLE FLANKTFS~ING

Table 11 Calculation of Theoretical Dimension Over Pins or Balis, MR

( Clause 6.4.4 )

Dimension Spur Gears

External Geam Internal Gears

Helical Gears Spur Gears kklical Gears

With even No. of

MR-ms =+DM COSci,

a=R Mtt-q.z-

co% +DM

MR-mzz-DM a=% R

bfRm$-- *=Rt

hi

teeth Dimension over pins With or balls odd No.

of teeth MR-mz +DM

MR-ms -D, MR'T.Z -DM CosuR +44

MR-m,s waRt

wsaR axaRt

w

Table 12 Calculation of dR, aR, aRt and q~

( Chzuse 6.4.4 )

Gears Exterual Gears Internal Geals

Spur gears DM - 1.728m D, - 1.44m 1)

Pin or ball touching the tooth flanks above the reference circle

aR n 2rtanat) kaRinva+~COSQ--f-

22 2 invaR - inva _2!L+_*

sc 2x tana 1)

(without correction) mzcosa 22 z

--

Helical gears DM - 1.72&n,, D, - 1.44%

Inv a,, - inv% + dR _7C, bin% 1) dR L aanq, 1)

mnzoxa, 22 Z invaRt - invat +----f-

m,zccsa, 25 Z

spur gears DM - mz sinq/cxw$t D, - mz sinv/waR Pin or ball touching the tooth flanks on the reference circle

aR+a-3

Helical gears DM-

m, z sin *cosa, mn z sim+xosq,

cosaRt . co=t D,-

cDsaRt . *=I

%-a,+* Rt%-q .

spur gears DM=nm.cbsa

Pin or ball touching the tooth invaR=inta*+

flanks below the reference circle Helical gears

DM

2r tAna, 1) inva& = inva, f -

Z

) Use + sign for positive correction and - sign for negative correction. Substitute the apolute value of x in the equations.

IS 7504 : 1995

1 ROTATION OF THE GEAR UNDER TESt

40

so 20

10 . . . . . . . . . . . . . . . . . . . . . .

0 llIllIllllllllIllll111111 125242322212019181716151413121110 9 6 7 6 5 4 3 2 125

-c-- DIRECTION OF CHART FEED

FIG. 17 SINGLE FLANK TOTAL QMP~SIIEERROR DMGRAM

8 INSPECTION OF XNVOLUTE RACKS - Double flank composite error, and

8.1 Corresponding to the measurement of external - Profile. gears, the racks are checked.for following values:

- Tooth thickness, For the inspection of tooth thickness, the measurement

- Penetrating depth of a pin or ball (corresponding with balls or pins is the most accurate procedure. Refer

to runout of a gear), Fig. 20.

I I

FIG. 18 TIWING ON DOUBLE FLANK TOTAL COMFYBITE ERROL

23

IS 7504 : 1995

U) ) fl fr

b)

FIG. 19 DOUBLJZ FLANK TOTAL COMWSITE ERROR DIAGRAM

The dimension MR, over pins or balls is given by the formula: DM = $&- (Round off to a standard pin or~ball

diameter)

For double flank composite error testing of racks of limited length, double flank checking machines with suitable attachments are employed.

The pin or ball diameter, &+.t can be calculated from Measuring microscopes and profile projectors are suitable for profile and pitch inspection of racks.

T b

FIG. 20 INSPECXJON OF TOOTH THKKNFSS

24

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This Indian Standard has been developed from Dot: No. LM 13 (4280).

Amendments Issued Since Publicatioo

Amend No. Date of Issue Text Affected

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