OPTIONS
homework on the calculation of tolerance fields in the discipline "Metrology, Qualimetry and
Standardization" for students of the academic groups BGBi-19-01, BGRi-19-01, BGBi-18-01 and
BGRi-18-01
1 Homework Terms
For the homework option specified in table 1:
1) draw out graphically the disposition of tolerance fields of coupling according to the original
dates presented in table 1;
2) determine in which system (hole-basis fit system or shaft-basis fit system) the original
coupling of machined workpieces is performed;
3) determine the mode of coupling  clearance fit, interference fit or transition fit;
4) by international or interstate standard select the standard fit and indicate its designation;
5) determine the standard values of the upper and lower limits of size deviations of the shaft and
hole, the standard limits of size tolerances of the shaft and hole, the maximum dimensions of the shaft and
hole, the minimum and maximum values of the clearance or interference in the coupling;
6) check in the correct choice of the fit;
7) draw up a layout diagram of tolerance fields containing standard deviations, graphically
selected by calculation.
8) indicate the value of the roughness of the machined surfaces of the shaft and the hole.
Table 1  Homework options for calculating of tolerance fields
Size deviations
No.
Nominal size
A method of workpiece machining
size, m
option
of coupling
hole
shaft
1
40
+19
-16
Finishing turning
2
45
-25
-15
Fine cylindrical grinding
3
28
+52
-13
Semi-finishing turning
4
280
+48
+45
Finishing face milling
5
20
+41
-40
Semi-finishing reaming
+41
-40
6
20
Fine face milling
-20
-62
+48
7
20
+21
Fine planning
+35
+21
8
20
+16
Finishing reaming
+20
+98
9
25
-45
Finishing grinding
+65
10
32
+63
Semi-finishing grinding
23
+23
11
60
Finishing broaching
45
+16
-65
12
25
Drilling on the jig
35
-98
13
32
-62
+45
Drilling
14
14
+55
-55
Semi-finishing reaming
15
28
+13
+10
Finishing countersinking
16
42
+42
+26
Polishing
17
55
+30
+49
Honing
18
90
-28
+28
Finishing plane milling
19
70
+32
Rough slotting
25
No.
option
Nominal size
of coupling
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
10
100
16
20
35
68
90
140
190
270
350
450
630
720
900
500
160
100
38
125
39
63
40
320
41
42
80
280
43
560
44
630
45
2000
46
1400
47
80
48
100
49
125
50
160
Size deviations
size, m
hole
shaft
+45
-25
+120
- 100
-16
-12
+18
-80
+10
+15
+23
+12
+48
+35
+85
+60
+50
+20
-190
-400
-62
-96
-230
-400
-450
-151
+265
-480
+300
+185
+155
+145
-12
+27
-14
+58
+180
-270
+120
-700
-40
+50
+44
128
+38
-230
+46
+81
28
+220
+70
+125
-76
+110
-146
+500
-400
+450
-500
-150
+195
-110
+438
-305
-25
+23
-80
-44
-54
+110
-40
31
-110
A method of workpiece machining
Drilling on the jig
Finishing reaming
Planning finishing
Drilling
Fine turning
Semi-finishing turning
Finishing turning
Rough turning
Flat thin grinding
Cutting off with a power saw
End thin milling
Turning semi-finishing
End milling, semi-finishing
End thin milling
Finishing chiseling
Planning finishing
Drilling on the jig
Finishing turning
Fine turning
Round fine grinding
Flat grinding, semi-finishing
Thin scraping
Countersinking semi-finishing
End milling finishing
Rough milling with cylindrical cutter
Rough milling, semi-finishing
Face thin milling
Finishing broaching
End finishing broaching
Finishing broaching
Round fine grinding
2 Example homework on the calculations for selection the tolerance fields of the coupling
Original dates for computations:
+0,016
D = 20+0,021
; Type of workpiece machining  finished reaming
+0,002 ; d = 20
Define the values of the nominal size of the coupling and limits of size of the shaft and the hole.
The nominal size of the coupling is D = 20 mm.
Upper limit of deviation and lower deviation of the hole:
ES = +210 μm = 0,021 mm; EI = 20 μm
(1)
Upper limit of deviation and lower limit deviation of the haft:
es = 0,016 mm = 160 μm; ei = 0 μm
(2)
Upper limit of sizes and lower limit of sizes of the hole and shaft:
D max = 20,000 + 0,021 = 20,021 мм, Dmin = 20,000 + 0,002 = 20,002 мм,
d max = 20,000 + 0,016=20,016 мм, dmin= 20,000 – 0 = 20,000 мм
(3)
(4)
Define the values of interference and clearance of the coupling.
Maximum interference:
N max = d max – Dmin= 20,016 – 20,002 =-0,014 мм = 140 мкм
(5)
Maximum clearance:
Smax = Dmax – dmin = 20,021 – 20,000 = 0,021 мм = 210 мкм
(6)
Determine the mode of coupling and system in which the initial coupling of machined workpieces
is performed.
The mode of coupling is transition fit because there are both an interference and clearance:
Nmax = 140 μm, Smax = 210 μm.
The fit is non-standard, since in a standard fit one of the values of the deviations of the hole or
the shaft must correspond to the value of the fundamental deviation of the basic hole (H) or the
fundamental deviation of the basic shaft (h).
Define the tolerances of the hole and the shaft, span of a fit.
Hole tolerance
TD = Dmax - Dmin = 20,021 - 20,002 = 190 μm
(7)
Shaft tolerance
Td = dmax – dmin = 20,016 - 20,000 = 160 μm
(8)
Span of a clearance fit
TS = Smax - Smin = 20,021 – 20,002 = 190 μm
(9)
Span of an inteference fit
ТN = dmax – Dmin = 2,016 – 20, 002 = 140 μm
(10)
Span of a transition fit
TI = Smax + Nmax = 210 +140 = 350 μm
(11)
Based on the calculation results, draw a diagram (figure 1) of the tolerance fields of the coupling.
e s = 160
E I = 20
Е S = 210
Figure 1  Diagram of tolerance fields according with original dates
The values of the standard fit parameters for the nominal size D = 20 mm should be as close as
possible to the values of the basic parameters of the original dates.
According to the international (ISO) or interstate standard (GOST), the parameters of the standard
fit will be chosen in the hole-basis fit system:
- tolerance class of a hole  Ø20H10 = Ø 20+0,070;
- tolerance class of a shaft  Ø20js13 = Ø20± 0,0165;
- fit designation  Ø20H10 / js13.
Evaluate the correctness of the choice of the fit:
Maximum interference fit:
Nmax = dmax - Dmin = 20,0165 – 20,000 = -0,0165 mm = 165 μm
(12)
Maximum clearance fit:
Smax = Dmax - dmin = 20,0070 - (-20,0165) = 0,0235 mm = 235 μm
(13)
e i = 165 e s = 165
E S = 70
Conclusion:
The standard fit is chosen correctly, since the limit deviation values of the fit are as close as
possible to the values specified by international and interstate standards (the interference and clearance
values differ by 25 μm).
The span of a fits diagram corresponding to a standard fit are presented in figure 2.
For a given method of workpiece machining determine the roughness parameters of the shaft and
which equal to Ra 3.2 μm according to the corresponding reference books.
Figure 2  Diagram of standard tolerance fields
REFERENCES
1
2
3
4
5
6
7
Балабанов, А.Н. Технологичность конструкций машин / А.Н. Балабанов. – Москва :
Машиностроение, 1987.  336 с.
Гжиров, Р.И. Краткий справочник конструктора : Справочник / Р.И. Гжиров. – Ленинград :
Машиностроение, 1983. – 464 с.
ГОСТ 25346-2013 (ISO 286-1:2010) Основные нормы взаимозаменяемости. Характеристики
изделий геометрические. Система допусков на линейные размеры. Основные положения,
допуски, отклонения и посадки = Basic norms of interchangeability. Geometrical product
specifications. Code system for tolerances on linear sizes. General provisions, tolerances, deviations
and fits.
Допуски и посадки: Справочник / В.Д. Мягков, М.А. Палей, А.Б. Романов и др. – В 2-х ч. – 6-е
изд. – Ленинград : Машиностроение, 1982.
Мягков, В.Д. Допуски и посадки: Справочник / В.Д. Мягков. – 4-е изд., перераб. и доп.
Москва : Машиностроение, 1966. – 772 с.
Общетехнический справочник / Под ред. Е.А. Скороходова. – 4-е изд. – Москва :
Машиностроение, 1990. – 496 с.
Якушев, А.И. Взаимозаменяемость, стандартизация и технические измерения. – 6-е изд.,
перераб. и доп. / А.И. Якушев. – Москва : Машиностроение, 1987. – 352 с.
Professor
25.12.2021
Ferdinand Sh. Zabirov