Values of [s]
Degree of accuracy of design loads, analytical models, and mechanical characteristics |
[S] |
High |
1.2-1.5 |
Approximate (shafts of most general-purpose mechanisms) |
1.5-1.8 |
Reduced(also for shafts with d>200 mm) |
1.8-2.2 |
Condition is satisfied.
8. Analysis of the rolling contact bearings
In our case for the output shaft we will use Single - Row Radial Ball Bearings 210 (50×90×20); n = 272.676 rpm; RxA= 1067.306 N, RyA= 1493.392 N,RxC = 1067.306 N, RyC= 2414.155 N Cr =35.1 kN, C0 = 19.8 kN.
8.1. Determine the total radial reacting forces which act on the bearings
;
.
8.3. Determine factor V which is used to take into account what ring of the bearing is movable.
– for bearings with movable inner ring V = 1;
8.4. Determine safety factor Kswhich allows for the load nature. It may be ranged from 1 to 2.5 depending upon the type of designing machine. For general purpose speed reducers the safety factor is assumed as 1.3.
8.5. Determine temperature factor Kt
As a rule in general purpose speed reducers the working temperature of bearings is less than 100 ºC.
8.6.
Determine the radial force factor X
and axial force factor Y
for both supports. For this purpose it is necessary to find ratio
for every support and compare with axial load parameter e.
If
then Xi
=1
and Yi
=
0. Otherwise Xi
and
Yiare
determined according to table 11.1.
In
our case: V
=1;
Ks=1.3;
Kt
=1;
,
then X1
=1
and Y1
=
0;
,
then X2
=1
and Y2
=
0.
11.7. Determine the equivalent radial loads for both supports
Pr1 = X1VFr1 KsKt=1∙1∙1835.581∙1.3∙1=2386.255 N,
Pr2 = X2VFr2 KsKt=1∙1∙2639.562∙1.3∙1=3431.431 N.
8.8. Determine the rated life in million revolutions for the most loaded support
,
wherem
= 3 for ball bearings and m
=
for roller bearings.
8.9. Determine the rated life in hours
.
For general purpose speed reducers Lh min=12000 hours.
If the last inequality is not carried out it is necessary to reselect the bearing of more heavy series and make all calculations once more.
In
our case
.
Condition is satisfied and we can use this type of bearings.
9.Calculation of keyed joints.
Dimensions of keys are chosen according to table depending upon the shaft diameter. The length of the key should be less than the hub length by 5…10 mm and correspond to the standard series.
Standard Sunk Keys
The length of the key is chosen according to the following series: 6; 8; 10; 12; 14; 16; 18; 20; 25; 28; 32; 35; 40; 45; 50; 56; 63; 70; 80; 90; 100; 110; 125; 140; 160; 180; 200.
In general-purpose speed reducer keyed joints are usually calculated to prevent bearing stresses.
where T is the torque in N∙mm; d is the diameter of the shaft in mm; h is the height of the key in mm; t1 is the of the slot in the shaft; ld is the design length of the key in mm ( for keys with round sides ld = l – b; for keys with square sides ld = l, where l is the length of the key; b is the width of the key); [σbear] is the allowable bearing stress (for cast-iron hubs [σbear]=60…80 MPa; for steel hubs [σbear]=100…120 MPa).
Input shaft:
Shaft diameter d=22mm
b=8mm;
h=7;
t1=4;
t2=3.3;
l=56 mm
Output shaft:
Shaft diameter d=50mm
b=12mm;
h=8;
t1=5;
t2=3.3;
l=50mm
Shaft diameter d=36
b=14mm;
h=9;
t1=5.5;
t2=3.8;
