1. UNIT STRUCTURE
22
21
20
A5
3
d1
4
A4
A
1
2
d2
5
6
7
A
d3
A
d11
d4
d5
8
A-A
h
9
A3
A1
b
d6
l
10
11
12
13
14
15
16
17
19
d7
d12
d9
d10
18
100
Fig 1. Gear box
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A2
d8
Gear box is made out of driving shaft 5, driven shaft 14 and intermediate – 20. Motion from
driving shaft to driven shaft is submitted directly when claw coupling is connected with claw hub
19. When claw coupling is connected with gear 12, motion from driving shaft 5 to driven is
submitted by gears 4 – 22 and 20 – 12. The gear 5 is pressed on the shaft, 22 is connected with
shaft by prismatic key, and gear 12 is connected with driven shaft through claw coupling 11 and
straight splines. Selected radial ball bearings: 1 – No. 200, 6 – No. 205, and the rest No. 204.
Dimension A= 0,5 – 2 mm closes the dimension chain A and guarantees that the shaft 20
doesn‘t touch cover 2.
Bearing 6 is fixed in axial dirction by excentric ring GOST 13942, and bearing 16 by end
cover GOST 11641 (see Fig. 2 , a and b).
¨ 47
¨ 23,1
0
1,2 -0.12
a)
Fig 2. Standard parts: a –excentric fixing ring; b – end cover
b)
2. BASIC DIMENSIONS
Basic dimensions are selected according to the sizes pointed out in the assignment and the
dimensions in Fig. 1. The dimensions must be matched to preferred numbers raw. Dimensions of
bearings, keys and other standard parts are taken from appropriate literature [2] and [3].
Data of basic dimensions are put in the table 1.
Basic dimensions, mm
Dimension
Numeric value
marking
A1
150
A2
14
A3
145
A4
1
A5
20
A
2-1,5
d1
10
d2
30
d3
16
d4
18
d5
8
d6
6*16*20
d7
d8
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20
28
Table 1
Preferred numbers
raw
Ra40
Ra20
Extra dimension
Ra5
Ra10
Ra10
Ra5
Ra40
Ra5
Ra20
Ra10
-
Ra10
Ra20
2/12
Note
Measured in drawing
Bearing No. 204 width
Measured in drawing
Measured in drawing
Measured in drawing
Submitted in assignment
Bearing No. 200 inner diameter
Bearing No. 200 outer diameter
Measured in drawing
Straight splains teeth number, inner and
outer diameters. Submitted in assignment
Measured in drawing
Measured in drawing
Table 1, continued
Dimension
marking
d9
d10
d11
d12
b
h
l
Numeric value
Preferred numbers
raw
Note
47
16
20
20
6
6
20
Ra5
Ra10
Ra10
Ra40
Ra40
Ra10
Bearing No. 204 outer diameter
Measured in drawing
Measured in drawing
Bearing No. 204 inner diameter
Prismatic key height
Prismatic key width
Submitted in assignment
3. PLAIN CYLINDRIC CONNECTIONS CALCULATION
3.1. Connection of housing 7 and cover 18. Diameter d9
Fit is to be selected with clearance, as cover sometimes is taken off and alignment doesn‘t
have high requirements. According literature [3] the recommended tolerance zone for cover
diameter d9 is h9 – h11. The tolerance zone h10 is selected. Hole could be of the same accuracy,
but because of mounted bearing the tolerance zone H7 is selected.Hole and shaft tolerance zone
scheme is shown in Fig.3.
Fit parameters:
+ mm
+25
Basic dimension d9=47 mm;
shaft limit deviations:
es=0, ei= - 100 m;
maximum shaft limit of dimen-
H7
0
Dmax
0
sion:
dmax
dmax=d9+es=47+0=47,000 mm;
minimum shaft limit of dimension:
dmin=d9+ei=47+(-0,100)=
=46,900 mm;
Dmin
h10
hole limit deviations:
ES=+0,025m, EI= 0;
maximum hole limit of dimen-
- mm
-100
dmin
sion:
Dmax=d9+ES=47+0,025 =
= 47,025 mm;
the least hole limit of dimension:
Dmin=d9+EI=47+0=47,000 mm;
Fig 3. Tolerance zones scheme of fit 47 H7/h10
maximum clearance Smax=ES – ei=0,025 – (– 0,100) = 0,125 mm;
minimum clearance Smin=EI – es=0 – 0 = 0,000 mm;
3.2.. Connection of gear 22 and shaft 20. Diameter d11
We choose the fit H7/js6. The fit centers gear on shaft well. To submit the torsion moment
the prismatic key is used.
Basic fit parameters:
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Basic dimension d11=20 mm;
Shaft limit deviations:
es=6,5 m ei= - 6,5 m;
Maximum limit of shaft dimension dmax=d11+es=20+0,0065=20,0065
mm;
Minimum limit of shaft dimension:
dmin=d11+ei=20+(-0,0065)=
=19,9935 mm;
+ mm
+21
H7
+6,5
0
0
Dmax
js6
dmax
Dmin
dmin
Smax
Nmax
-6,5
- mm
Fig. 4. Tolerance zones scheme of fit 20 H7/js6
Hole limit deviations:
ES=+0,021 m, EI= 0;
Maximum limit of hole dimension: Dmax=d11+ES=20+0,021 =
= 20,021 mm;
Minimum limit of hole dimension: Dmin=d9+EI=20+0 =20,000 mm.
Maximum clearence Smax=ES – ei=0,021 – (– 0,0065) =0.0275 mm;
Maximum interference Nmax= es – EI =0,0065 – 0 = 0,0065 mm.
Probability calculation of clearence and interference:
mean shaft: dm=(dmax+dmin)/2=(20,0065+19,9935)/2=20,000 mm;
mean hole: Dm=(Dmax+Dmin)/2=(20,021+20)/2=20,0105 mm;
mean clearence: Sm=Dm-dm=20,0105-20=0,0105 mm=10,5 m;
shaft tolerance: Td=es – ei=6,5 – (–6,5) = 13 m;
hole tolerance: TD=ES – EI=21 – 0 = 21 m;
fit tolerance: Ts=TD+Td=21+13=34 m;
standard deviation of the fit:
m
Smax=27,5
Sm=10,5 m
Nmax= -6,5 m
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
= TD 2  Td 2 / 6  212  132 / 6  24,7 / 6  4,12 m;
3=3*4,12=12,4m;
6=6*4,12=24,8m;
Sm + 3=10,5 + 12,4=
=22,9 m;
Sm - 3=10,5 – 12,4= = –1,9 m;
In fig. 5 filled area shows interference probability. The rest area
shows clearance probability.
Clearance probability P(S) =
=0,5 + F(Sm/)=
=0,5 + F(10,5/4,12)=
=0,5 + F(2,55)=
=0,5 + 0,4946=0,9946.
Clearance
Ávarþos
Tarpai
Interference
s
5 pav. Diagram of clearance and interference of fit 20H7/js6
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We accept P(S) =0,99 or 99% as clearance probability. Then the interference is P(N) =0,01
or 1%.
3.3. Connection of gear 12 and hub 13. Diameter d8
Hub is pressed into gear.
Basic fit parameters:
Submited torsion moment – Ms=200Nm;
Basic connection diameter – d8=28 mm;
Connection length – l= 25 mm (Fig.1);
Inner diameter of hub – d1pr= 20 mm (Fig 1 );
Diameter of gear hob – d2pr=40 mm (Fig 1 );
Mechanic properties of gear – E=2,1E11 Pa, e=85E7 Pa, =0,3;
Mechanic properties of hub – E=0,9E11 Pa, e=20E7 Pa, =0,33;
Roughness parameter of hub – Ra=0,8 m;
Roughness parameter of gear – Ra=1 m;
Factor of friction when pressing – f=0.15.
We use the computer programm „Matavima“. After calculation according to the connection
data we get necessary minimal interference Nmin=9,26x10-5 m, interference Nmax=8,21x10 m
that the pressed hub can withstand. As the necessary condition Nmax>Nmin is not satisfied, we
change the connection parameters. We enchance hub enlarging outer diameter d8=32 and
reducing torsion moment to Ms=100 Nm. We enlarge gear hob diameter to d2pr=45 mm.
New calculation results: Nmax= 9,41x10-5 m=94,1 m , Nmin=3,90x10-5m=39,0 m.
From fit tables we select interference fit that matches requirements Nmax>=Nmaxlent and
Nmin<=Nminlent. The fit H8/x8 with Nmin=41 m ir Nmax=119m. matches these
requirements.
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Dmax
Dmin
d8
Nmin
dmin
dmax
Nmax
Basic fit parameters:
Basic dimension d8=32 mm;
Shaft limit deviations:
es=+119 m, ei= +80 m;
Maximum limit of shaft dimension: dmax=d8+es=32+0,119=32,119 mm;
Minimum limit of shaft dimension: dmin=d8+ei=32+0,080= =32,080 mm;
+ mm
119
Hole limit deviations: ES=+0,039m,
EI= 0;
x8
Maximum limit of hole dimension:
Dmax=d8+ES=32+0,039
= 32,039 mm;
80
Minimum limit of hole dimension:
Dmin=d8+EI=32+0 =32,000 mm;
Minimum interference:
39
Nmin=ei – ES=0,080 – 0,039 =0.041mm=
=41 m;
H7
Maximum interference:
0
0
Nmax= es – EI =0,119 – 0 = 0,119 mm=
=119
m.
- mm
Tolerance zones scheme of fit 32 H8/x8 is
shown
in Fig. 6.
Fig. 6. Tolerance zones scheme of fit 32 H8/x8
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3.4. Calculation of cylindrical fixed limit gauges
We calculate the gauges dimensions of fit 32H8/x8.
The schemes of the gauges tolerance zones for shaft and hole are given in Fig. 7. The
schemes are given in literature [4]. The shape of schemes belongs on the basic dimension, grade
of tolerance and purpose (for shaft or hole).
d-K-GO
Hp
Ring
gauges
d-K-NOGO
K-NOGO
Hp
D-NOGO
d-K-Wear
Hp
z1
D-GO
H1
H1
Dmin
K-GO
NOGO
Gab
gauges
Wear
limit
Y1
Shaft tolerance zone
dmax
Dmax
GO
x8
dmin
z
H8
Y
H
d-GO
GO
Hole tolerance zone
H
d-NOGO
NOGO
Plug
gauges
K-Wear
Wear
limit
7 pav. Gauges tolerance zones schemes of fit 32 H8/x8
Gauges tolerances and deviations are found in literature [4]:
plug gauges z=6 m, y=5m, H=4m;
gab gauges z1=6 m, y1=5m, H1=7;
ring gauges Hp=2,5m.
Roughness of gauges work surfaces: plugs and gabs Ra=0,08 m and control rings - 0,04
m [7].
The grade IT3 of gauges work surfaces form is taken from standard GOST 24853. Flatness
tolerance is lygi 1,2 m and cylindric tolerance is 2 m [ 5].
From the subsection 3.3:
basic dimension
maximum limit of size of shaft
minimum limit of size of shaft
maximum limit of size of hole
minimum limit of size of hole
d8= 32 mm;
dmax= 32,119 mm;
dmin=32,080 mm;
Dmax=32,039 mm;
Dmin=32,000 mm.
Gauges limit and production dimensions are calculated in table 2.
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Table 2
Gauges limit and production dimensions
Name of gauge
GO
Plugs
NOGO
GO
Gabs
NOGO
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New gauges dimensions, mm
Maximum limit of size
Minimum limit of size
Dmin+z+H/2=
Dmin+z-H/2=
=32,000+0,006+0,004/2=
=32,000+0,006-0,004/2=
=32,008 mm
=32,004 mm
Dmax+H/2=32,039+0,004/2= Dmax-H/2=32,039-0,004/2=
=32,041 mm
=32,037 mm
dmax-z1+H1/2=
dmax-z1-H1/2=
=32,119-0,006+0,007/2=
=32,119-0,006-0,007/2=
=32,1165 mm
=32,1095 mm
dmin+H1/2=
dmin-H1/2=
=32,080+0,007/2=
=32,080-0,007/2=
=32,0835 mm
=32,0765 mm
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In drawing
32,008-0,004
GO gauge wear limit
Dmin-y=
=32,000-0,005=
=32,995 mm
32,041-0,004
32,1095+0,007
32,0765+0,007
dmax+y1=
=32,119+0,005=
=32,124 mm
4. SELECTION OF UNIVERSAL MEASURING MEANS
We select the universal measuring means for the fit. We use literature [4]. In table 6.7 the
measuring error is =10 m. The dial micrometer MP and dial gab CP is used as measuring
means for the shafts. We choose the dial micrometer MP50, the scale interval of which is 2 m,
measurement limits are 25 – 50 mm, permissible error is 3 m, measurement force is 6 1 N.
To measure the hole we select the dial internal gauge 109, which measurement limit is 18 –
50, scale interval is 2 m, maximum measurement depth is 150 mm, measurement error is 3,5
m, measurement force is 4,5 N.
5. THE FITS OF BALL BEARINGS
We select the fits of the first ball bearing. It is said in assignment that overloading of the
bearings is up to 150%, normal impacts and vibration.
As the shaft turns, we press the inner bearing ring and assemble the outer bearing ring
leaving a small clearance. We choose the fit 10 L0/m6 for the inner bearing ring, and 30 H7/l0
for the outer one.
Deviations of bearings diameters [4]:
inner diameter of inner ring: ES=0, EI= –0,008 mm,
outer diameter of outer ring: es=0, ei= – 0,008 mm.
Upper deviation of shaft 10m6 is es= + 0,015 mm, lower deviation - ei = + 0,006 mm.
Upper deviation of hole 30H7 is ES= + 0,015 mm, lower – EI = 0.
Schemes of bearings fits tolerance zones are given in Fig.8.
limit
+ mm
+ mm
0
L0
¨ 30
Shaft
tolerance Zone
-8
- mm
Inner ring of bearing
toleranc lzone
- mm
0
-8
Outer ring of bearing
tolerance zone
Hole of base
tolerance zone
l0
+6
0
Nmin=6
Smin=0
0
m6
Smax=23
H7
Nmax=23
+15
¨ 10
+15
Fig.8. Tolerance zones of bearing rings
Structure of bearing unit is shown in Fig.9, and parts joined to bearing No.200 – in Fig. 10
and 11.
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Form and location tolerances of surfaces
joined to bearings:
cylindric tolerance of shaft cylindric surface– 0,003 mm,
tolerance of complete axial runout of the
shaft plane to which the bearing is attached is
0,006 mm,
cylindrical tolerance of the hole to which
the bearing is mounted is 0,0045 mm,
¨ 10L0/m6
¨ 30H7/l0
Fig.9. Structure of bearing unit
perpendicularity tolerance of the hole end plane is 0,009 mm.
Roughness of surfaces connected to bearings:
for cylindrical surfaces of the shaft and hole – Ra1,25,
for end surfaces of the shaft and hole – Ra2,5.
0,009 A
A
¨ 30H7
0,006 A
Ra1,25
0,003
Ra2,5
0,003 A
¨ 10 m6
Ra2,5
¨ 9,5
3
0,0045
A
1,6x45°
Ra1,25
11
R0,6max
Fig. 10 Hole to which the bearing is mounted
Fig. 11 Shaft to which the bearing is mounted
6. FITS OF PRISMATIC KEY CONNECTION
Gear 22 and shaft 20 are connected by the prismatic key (see Fig. 1). According to the shaft
diameter 18 mm the prismatic key 6x6x16 GOST 23360 is chosen [4]. We choose the normal
prismatic key connection. Schemes of connection tolerance zones are shown in Fig. 12. Hight
tolerance of key is 6h11( - 0,075). Length tolerance of key is 16h14(-0,43). Tolerance of the cut
length in shaft is 16H15(+0,7).Dimension of the cut depth in shaft is t1=3,5(+0,1). Dimension of
the cut depth in gear is t1=2,8(+0,1). Numerical values of deviations are taken from [4].
+ mm
0
Tolerance
zone of cut width
in
Išdrožos
krumpliaratyje
pločio
gear
tolerancijos laukas
Išdrožos velene pločio
Tolerance zone of cut
+15
tolerancijos
laukas
width in shaft
0
Js9
N9
-15
h9
- mm
6
-30
Tolerance
of key
Pleištozone
pločio
width
tolerancijos laukas
Fig. 12. Tolerances zones for width of key connection
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According to [6] 234 p. simetric tolerance of key cut is Ts = 2*Tp = 2*0,03 = 0,06 mm and
parallelism tolerance of simetric plane according to the shaft axis is Tlyg = 0,5 Tp = 0,5*0,03 =
0,015 mm.
7. CALCULATION OF DIMENSIONS CHAIN
Skaičiuojame matmenų grandinę A, parodytą 1 pav. Matmenų grandinės schemoje (žr. 15
pav.)
We calculate the dimensions chain A, shown in Fig. 1 and in scheme of dimensions chain
(see Fig.13).
A3
A4
A2"
A5
A
A1
Fig. 13. Scheme of dimensions chain
In chain width of bearing 16 – 0,12 is marked by the letter A“. We will calculate the chain by
program MGML are given in table 3.
Data for the chain calculation lentelė
Basic dimension, Factor of impact
mm
A2“ =16
-1
A1=150
-1
A3=145
1
A4=1
1
A5=20
1
A= 2
Table 3
Upper
0
Deviations, mm
Lower
-0,12
Fundamental
pz
js
js
js
0
-1,5
In the table 3 the factor of impact for reducing members is -1 and for increasing members is
1. In the fundamental column the letters „pz“ mean that deviations of this member will be
corrected in the case the calculated number of tolerance units doesn‘t coincide with standard
tolerance units number for any grade of tolerance. Date and calculation results are given in Fig.
14.
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a}
b)
Fig. 14. a – initial data; b – calculation results.
We check if the sum of chain members tolerances equals the tolerance of closing member.
4
1
i 1
i 1
 TA   TA"  (670+400+100+210)+120 = 1380 + 120 = 1500 m.
The tolerance of closing member also equals to 1500 .
8. DATA FOR SHAFT DRAWING
1. The length of span measurement across several teeth of geared part of the shaft.
Span measurement across several is measured between the opposite profiles of teeth. The
formulas for calculation are taken from [3].
The gear module m=2,5 mm, teeth number z=30. 7-C GOST 1643 – 81 is chosen as
precision of the gear.
The length of span measurement across several teeth.
W=m*W‘,
W‘=10,753 mm – The length of span measurement across several teeth, when m=1 mm and
z=30 [3. 429 p.].
W=2,5*10,753=26,88 mm.
Four teeth are involved in measurement.
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2. Find the precision of span measurement across several teeth.
The lower deviation of span measurement across several teeth is Ews= -100 mm
[3. 464 p. 37 table].
The tolerance of cinematic deviation is Fr=36 m , when gear is at the 7th precision grade
and pitch diameter d= 75 mm.
The tolerance of span measurement across several teeth T=70 m [3. 466p.. 40 table].
-0,100
The length of span measurement across several teeth is 26,88 -0,170.
LITERATURE
1. Stasiūnas R., Naginevičienė L., Maršaitis D.Technologinių matavimų pagrindai.
Tolerancijos ir suleidimai: Paskaitų konspektas. – Kaunas: „Technologija“, 1994.
2. Anurjev V. Spravočnik konstruktora mašinostrojitelia: V 3 – ch tomach, T. 1, 2001.
Elektroninis variantas.
3. Anurjev V. Spravočnik konstruktora mašinostrojitelia: V 3 – ch tomach, T. 2, 2001.
Elektroninis variantas.
4. Inžinieriaus mechaniko žinynas / B. Dragūnas, K. Pilkauskas, A. Stasiūnas, R. Stasiūnas.
– V.: Mokslas, 1988.
5. Допуски и посадки: Справочник: В 2-х ч. / В.Д. Мягков и др. – М.:
Машиностроение, 1982. – Ч1.
6. Допуски и посадки: Справочник: В 2-х ч. / В.Д. Мягков и др. – М.:
Машиностроение, 1983. – Ч2.
7. Petronis V., Ramonas Z. Pakeičiamumo, standartizacijos ir techninių matavimų kursinis
darbas: Metodiniai nurodymai. – Kaunas: KTU, 1990.
8. Petronis V. Pakeičiamumo, standartizacijos ir techninių matavimų kursinio darbo
užduotys: Metodiniai nurodymai. – Kaunas: „Technologija“, 1992.
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