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MECHANICAL POWERTRANSMISSIONS (SPG8005)
NEWCASTLE UNIVERSITY
School of Mechanical & Systems Engineering
INTRODUCTION TO
TOLERANCES
1. INTRODUCTION TO SPECIFICATION OF DIMENSIONS AND FORM (SHAPE)
Much of the information in this document is derived from BS 308: Parts 1-3 (1990), from BS8888 (2000) and from other related documents, including PP7308, PP7309 and PP8888-2.However, the full British Standards should be consulted for complete explanation. BS8888: Parts1-3: 2000 have now superceded BS 308: Parts 1-3 but the concepts andsymbols remain.
1.1 Standards of measurement
Definition of the metreoriginal: 1/10 000 000 of distance from North Pole to Equator current: 1 650 763.73 wavelengths in vacuum of orange light from Krypton 86
Hierarchy of standardscomparison of international standards
national standardscalibration organisation
factory calibration standardsworkshop instruments
Typical Metrology systemcomparison of international “Master Gears”national collection of “Master Gears” (Newcastle Univ.)Newcastle testing machines checked with Master Gearsfactory testing machines checked with Master Gearsproduction gears checked on factory test machinesproduction machinery checked by checking output
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1.2 Measuring uncertainties
Reading errors
accuracy of using the instrument (if it can be done wrong.......)
ease of reading
interpolation errors
beware meaning of readouts
System / fundamental errors
mounting errors: of object to be measured
of measuring scales (etc.)
temperature differences object - equipment “reversal errors”
temperature changes during measurement Abbe Error dynamic errors during movement environment
friction, dirt, shocks calibration errors
control system feedback “error” signals software errors
ABILITY TO READ ABILITY TO RESOLVE
(the scale) (be repeatable)
Lots of digits are often “fluff”.
RESOLUTION ACCURACY
Even if can resolve does not mean that every
increments reliably, increment is identical or accurate.
ACCURACY REPEATABILITY
Correct indication does not imply correct
on one day, indication the next.
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2. FUNCTIONAL DIMENSIONING & TOLERANCING
Because the correct performance of any product is vital, the dimensions of eachcomponent clearly need to be controlled.
However, dimensions and their tolerances must always be related to the function of the component features they control.
Make sure that the features that control performance are dimensioned and toleranceddirectly and not by a “tolerance chain” of many toleranced dimensions. See the drawing for an example.
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3. DIMENSIONAL TOLERANCINGThe ISO system of dimensional tolerances is intended to control the limits of size of adimension: is does not control the shape of the component or its features, just the value of the dimensioned distances. Whilst the information often refers only to round components,the system can be applied to any drawn dimension.
2.1 Each dimension can be allocated any one of 18 different tolerance grades: the tolerancegrades specify the different between the maximum and minimum allowable values of thedimension. The tolerance grades are known as IT grades.
3.2 Components may be required to assemble freely with some slack (a clearance fit) or maybe required to need force to assemble (an interference fit). It is convenient to say that a20mm hole is needed for a M20 bolt: however, they need (usually) to assemble easily (a
clearance fit) and neither dimension should be exactly 20mm. See the diagram for atypical clearance fit and note that none of the specified dimensions are on the “zero” linewhich represents the nominal dimensions.
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3.3 Each tolerancerange (specified by the ITgrade table) can beallocated any one of 56different “fundamentaldeviations”: these specifythe value of the dimensionrelative to the nominal(drawn) dimension.
3.4 In practice, mostdimensions are specifiedfrom a much reduced set of IT grades and fundamental
deviations: see below.
These may be said to be“Hole Based” (used wherethe hole dimensions aremore difficult to vary: i.e.normally) or “Shaft Based”used where the shaftdimensions are moredifficult to control.
3.5 The “Hole Basis”simplified table is shown onthe next sheet.
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Extracted from BS 4500 BRITISH STANDARD SELECTED ISO FITS - HOLE BASIS (from) Data Sheet 4500A
Larger than
nominal sizeNOMINAL SIZE
Smaller thannominal size
Clearance Fits Transition Fits Interference Fits
Nominal sizes Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Tolerance (0.001mm) Nominal sizes
Over (mm)
to(mm)
H11 c11 H9 d10 H9 e9 H8 f7 H7 g6 H7 h6 H7 k6 H7 n6 H7 p6 H7 s6 Over (mm)
To(mm)
- 3 +60
0
-60
-120
+25
0
-20
-60
+25
0
-14
-39
+14
0
-6
-16
+10
0
-2
-8
+10
0
0
-6
+10
0
+6
+0
+10
0
+10
+4
+10
0
+12
+6
+10
0
34 - 3
3 6 +750
-70-145
+300
-30-78
+300
-20-50
+180
-10-22
+120
-4-12
+120
0-8
+120
+9+1
+120
+16+8
+120
+20+12
+120
+27+19
3 6
6 10 +900
-80-170
+360
-40-98
+360
-25-61
+220
-13-28
+150
-5-14
+150
0-9
+150
+10+1
+150
+19+10
+150
+24+15
+150
+32+23
6 10
10 18 +1100
-95-205
+430
-50-120
+430
-32-75
+270
-1634
+180
-6-17
+180
0-11
+180
+12+1
+180
+23 +12
+180
+29+18
+180
+39+28
10 18
18 30 +1300
-110-240
+520
-65-149
+520
-40-92
+330
-20-41
+210
-7-20
+210
0-13
+210
+15+2
+210
+28+15
+210
+35+22
+210
+48+35
18 30
30 40 +1600
-120-280 +62
0-80-180
+620
-50-112
+390
-25-50
+250
-9-25
+250
0-16
+250
+18+2
+250
+33+17
+250
+42+26
+250
+59+43
30 40
40 50 +160
0
-130
-29040 50
50 65 +190
0
-140
-330 +740
-100-220
+740
-60-134
+460
-30-60
+300
-10-29
+300
0-19
+300
+21+2
+300
+39+20
+300
+51+32
+30
0
+72
+5350 65
65 80 +1900
-150-340
+300
+78+59
65 80
80 100 +2200
-170-390 +87
0-120-260
+870
-72-159
+540
-36-71
+350
-12-34
+350
0-22
+350
+25+3
+350
+45+23
+350
+59+37
+350
+93+71
80 100
100 120 +220
0
-180
-400
+35
0
+101
+79100 120
120 140 +250
0
-200
-450+100
0-145-305
+1000
-84-185
+630
-43-83
+400
-14-39
+400
0-25
+400
+28+3
+400
+52+27
+400
+68+43
+40
0
+117
+92120 140
140 160 +2500
-210-460
+400
+125+100
140 160
160 180 +2500
-230-480
+400
+133+108
160 180
180 200 +2900
-240-530
+1150
-170-355
+1150
-100-215
+720
-50-96
+460
-15-44
+460
0-29
+460
+33+4
+460
+60+31
+460
+79+50
+460
+151+122
180 200
200 225 +2900
-260-550
+460
+159+130
200 225
225 250 +2900
-280-570
+460
+169+140
225 250
250 280 +320
0
-300
-620 +1300
-190-400
+1300
-110-240
+810
-56-108
+520
-17-49
+520
0-32
+520
+36+4
+520
+66+34
+520
+88+56
+52
0
+190
+158250 280
280 315 +3200
-330-650
+520
+202+170
280 315
315 355 +3600
-360-720 +140
0
-210
-440
+140
0
-125
-265
+89
0
-62
-119
+57
0
-18
-54
+57
0
0
-36
+57
0
+40
+4
+57
0
+73
+37
+57
0
+98
+62
+570
+226+190
315 355
355 400 +3600
-400-760
+570
+244+208
355 400
400 450 +4000
-440-840 +155
0-230-480
+1550
-135-290
+970
-68-131
+630
-20-60
+630
0-40
+630
+45+5
+630
+80+40
+630
+108+68
+630
+272+232
400 450
450 500 +400
0
-480
-880
+63
0
+292
+252450 500
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Refers to the axis Refers to the generatingor the median plane line or the surface
4. GEOMETRICAL TOLERANCING
Geometrical tolerancing can be used to specify:-# the size & shape of each component feature &# the relative position of component features.
4.1 Toleranced feature and datum feature indications
A
geometricaltoleranceapplies tothe wholeextent of atolerancedfeatureunlessotherwisespecified, as for example 0.02/50 which indicates that a tolerance of 0.02 is permitted for an extent of 50 at any place on the toleranced feature.
4.2 Identification of toleranced features and datums
When ageometricaltoleranceapplies to anaxis or a medianplane, thearrowhead of
the leader lineterminates at the dimension line as onthe left.
When ageometricaltolerance appliesto a surface or lineon a surface, theleader line with itsarrowhead
terminating on thecontour of the feature has to be clearlyseparated from the dimension line as on theright.
4.3 Symbols, indications and interpretations
Form tolerances limit the deviations of an individual feature from its ideal geometricalform.
Orientation, location and run-out tolerances limit the deviations of the mutual orientationand/or location of two or more features.
For functional reasons one or more features may be indicated as a datum. If necessary, ageometrical tolerance is applied to the datum feature in order to ensure that the datumfeature is sufficiently exact for its purpose.
Toleranced Datum Area Line Area PointFeature Feature --------- Datum Target Indications -------
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Symbol Indication on Drawing Tolerance Zone Interpretation
for single features only:-
Straight -ness
The axis of the cylinder, to whichthe tolerance frame isconnected, is to be containedwithin a cylindrical zone of diameter 0.08.
Flatness
The surface is to be contained
betweentwo parallel planes 0.08 apart.
Circularity
The circumference of eachcross-sectionis to be contained between twoco-planar concentric circles 0.1 apart.
Cylindricity
The considered surface is to becontained between two coaxial
cylinders 0.1 apart.
for single or related features:-
Profileof any
line
(bilateral)
In each section parallel to theplane of projection, theconsidered profile is to becontained between linesenveloping circles of diameter 0.04, the centres of which are
situated on a line of theoreticallyexact geometrical profile.
Profileof any
surface
(bilateral)
The considered surface is to becontained between two surfacesenveloping spheres of diameter 0.02, the centres of which aresituated on a surface of theoretically exact geometricalform.
for related features only:-
Parallelismof a line (axis)
with reference
to a datum line
The toleranced axis is to becontained within a cylindricalzone of diameter 0.03, parallel tothe datum axis A (datumline).
Perpendic -ularityof a line (axis)
with reference
to a datumsurface
The axis of the cylinder is to becontained between two parallelplanes 0.1 apart, perpendicular to the datum surface.
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Angularityof a line (axis)
with reference
to a datum
surface
The axis of the hole is to becontained between two parallelplanes 0.08 apartwhich are inclined at 60 todatum surface A.
Positionof a line
The axis of the hole is to becontained within a cylindrical
zone of diameter 0.08, the axisof which is in the theoreticallyexact position of the consideredline, with reference to thedatum surfaces A and B.
Coaxialityof an axis
The axis of the cylinder is to becontained within a cylindricalzone of diameter 0.08 coaxialwith the datum axis A-B.
Symmetryof a median
plane
The median plane of the slot isto be contained between twoparallel planes, which are 0.08apart and symmetricallydisposed about the medianplane with respect to the datumfeature A.
Circular run-out
radial
The radial run-out is to be notgreater than 0.1 in any plane of measurement during onerevolution about the datum axis
A-B.
Total run-outradial
The total radial run-out is to benot greater than 0.1 at any pointon the specified surface whilstrevolving about the datum axis A-B, and with relative axialmovement between workpieceand measuringinstrument. With relativemovement the measuringinstrument or the workpiece is tobe guided along a line having thetheoretically exact form of thecontour and being in its correctposition relative to the datumaxis.
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TheoreticallyExact Dimension32mm
Used to specify theoretical (ideal)positions of features, etc.
Theoretically Exact Dimensionshave zero tolerance.
ProjectedTolerance Zone
Means of specifyingwhere adjoiningcomponents needparticular dimensions.
Important whenassembling:consequences areoften very great.
Maximum MaterialConditionqualification
Least MaterialConditionqualification
Means of specifyingmaximum sizeof a feature,combiningdimensionalandgeometricaltolerances.
EnvelopeRequirement
Means of specifyingoverall sizeof afeature.
R I Davidson r.i.davidson@ncl.ac.uk
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