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P 1
Basic Design principles:
 The shaft and other rotating parts should be axially located/clamped in
both the directions.
 The bearing arrangement should be able to accommodate relative axial
expansion between the shaft and the housing.
 Selection of fits on shaft and housing should be able to take care of
mounting requirements, load conditions and rotation.
 Proper lubrication system to provide adequate lubrication to bearings,
retention should be used.
 Spur and double helical gears will transmit only Tangential and radial
forces. Select bearings appropriately
 Helical gears, All bevel gears and Worm gears will transmit Axial force in
addition to tangential and radial forces. Select bearings with axial load
carrying capacity.
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 Bearing arrangements used in the Gear box assemblies,

Locating/non-locating bearing arrangement:

 To accommodate thermal expansion and
contraction of a shaft.
 locating bearing: Axial location of the shaft
relative to the housing.
 Non-locating Bearing: to accommodate axial
displacements due to thermal elongation of the
shaft relative to the housing. This avoids
induced internal loads.
 It can be used for short and long shafts also.

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 Bearing selection guidelines
Spur Gears or Gears without any Axial force

Method1:
 Spur gears or double helical/Herringbone gears
choose Ball bearings on Both ends of shaft.
 Locating bearing means ,the bearing has to be
clamped axially in both directions.
 Inner ring Interference Fit, Outer ring Sliding /
transition fit.
 Axial expansion accommodated at outer ring of
ball bearing at non locating end. Locating Non Locating
 No Axial Load. Bearing Bearing

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 Bearing selection guidelines
Spur gears or gears without any Axial force
Method 2:
 If one of the Ball bearing load carrying capacity is not
sufficient use Cylindrical Roller bearing in its place.
 Keep roller bearing as Non locating bearing and Ball
bearing as Locating bearing.
 Inner ring Interference Fit,Outer ring Sliding / transition fit.
 Axial expansion accommodated on inner ring of the roller
bearing. Locating Bearing Non Locating Bearing

Method:3
 If both sides Cylindrical Roller bearing has to be used,
Use NUP type bearing on locating side.
 NUP bearing, Due to shoulder on inner race, can take
certain amount of axial load.
 Axial expansion accommodated on inner ring of the NU
NUP
roller bearing
Locating Bearing Non Locating Bearing
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 Bearing selection guidelines
Helical gears,bevel gears and worm gears

Helical gears, Bevel gears and worm gears develop/produce

axial force in addition to Tangential and separating(Radial)
forces.
Hence bearings having capability of carrying axial /Thrust load
should be selected.
Locating bearing should be capable of taking axial load in both
directions .
Direction of axial load changes with direction of rotation.
If axial load is unidirectional , only one bearing is used at locating
side.
However if it is bidirectional, Two bearings have to be used at
Locating side to take carry axial load in both direction.

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 Bearing selection guidelines
Helical gears,bevel gears and worm gears

Method 1:
 When Helical gears are selected, use Double row or
matched pair Angular contact Ball bearings on locating side.
 Cylindrical Roller bearing on Non locating side of the shaft.
 Inner ring Interference Fit, Outer ring Sliding / transition fit.
 Radial load at both bearings.
 Axial load in both directions at Locating bearing.
Locating Bearing Non Locating Bearing
Method 2:
 If axial load is high ,use matched pair of Taper roller
bearings in place of Angular contact Ball bearings on
locating side.
 Cylindrical Roller bearing on Non locating side of the shaft.
 Inner ring Interference Fit, Outer ring Sliding / transition fit.
 Radial load at both bearings.
 Axial load in both directions at Locating bearing

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 Bearing selection guidelines
Helical gears,bevel gears and worm gears

Adjusted bearing arrangement:

 It is mainly used for short length shafts.
 The shaft is located axially in one
direction by one bearing support and in
the opposite direction by the other.
 Either Angular contact ball bearings or
Taper roller bearings are used on Both
ends of shafts.
 No provision for Axial expansion of shaft.
 Adequate lubrication to be provided to
overcome Thermal expansion.

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1. Calculate Equivalent dynamic load acting on Bearing(P)
P= X*Fr+Y*Fa
• Select X and Y from the Bearing catalogues. Bearing type Xo Yo
• For bearings operating at constant speed: Ball Bearing 0.6 0.5
•Bearing life in hours(L) = (106/60n)(C/P)e
Angular contact
•e = 3 for Ball bearings and 10/3 for roller bearings 0.5 0.46
bearing
• For bearings operating at Different speeds :
• Bearing Life in hours(L)= 1/[(t1/L1)+(t2/L2)+ …..(tn/Ln)]. Taper Roller
0.5 0.8-0.9
•t1,t2,t3…% of total time for which the above load is acting. bearing
•L1,L2,L3--- : life in hours corresponding to load P1.P2,P3…
2. Calculate equivalent static load acting on Bearing(Po)
• Po= Xo*Fr+Yo*Fa
• Co > Po for Average working condition, smooth and
vibration free running is assured.
• C0>2Po for Shock loads and for quiet running.

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Bearing Assembly selection for this gear box:
 As selected gears are helical gears we have to use
bearings with axial load carrying capacity.
 We will select two angular contact bearings on both
ends , as shaft length is small(<< 700mm).
 Select bearing size , same or more than the size of
Min. Shaft dia required to transmit gear forces.
 Make drawing/ layout of the gear box and fix
bearing sizes.
 Calculate Bearing life, after estimating the Radial
and axial forces acting on each bearing.
 Bearing life should be Min.20000hrs.

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 Radial and Axial loads On Bearings

Axial
Shaft Gear Bearing Radial load,N
load,N
Number Position Fr Fa
B1 1222 647
Motor Shaft(I) 1
B2 1407 0
B3 1290 0
Output shaft(II) 2
B4 1864 647

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  Radial load acting on Angular contact or Taper roller bearing induces
additional Axial force(Fra).
 Fra=0.5Fr/Y
 Fr= Radial force acting on Bearing,N
 Y= Axial factor of the selected Bearing.

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 Taper roller bearing
Case 1: Back to back assembly

Cal. Induced Axial force(Fra) in both bearings.

Additional axial Force on Bearing 1=Fra1
Additional axial Force on Bearing 2=Fra2

Load case Axial force Axial force

on Bearing 1 on Bearing 2
Fra1>Fra2 Fra1 Fa+Fra1
Bearing 2 Bearing 1
Fra1<Fra2 Fa+Fra2 Fra2

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 Case 2: Face to Face assembly

Cal. Induced Axial force(Fra) in both bearings.

Additional axial Force on Bearing 1=Fra1
Additional axial Force on Bearing 2=Fra2

Load case Axial force on Axial force on

Bearing 1 Bearing 2
Bearing 1 Bearing 2

Fra1>Fra2 Fa+Fra2 Fra2

Fra1<Fra2 Fra1 Fa+Fra1

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 Motor shaft
 For 7207 ; f0:13.9
 For B1: ifoFa/Cor: 1*13.9*647/20100=
0.45.
 e =0.43
 Fa/Fr : 647/1222=0.52 > e =0.43
 X=0.44:Y=1.30
 For B2: Fa=0; X=1;Y=0
Bearing Bearing loads Selected bearing
Dynamic Load Static load
Radial Axial Bearing Bore, consta Dynamic
position carrying carrying
load,N load,N No. mm nt load factors
capacity, N capacity, N
Fr Fa Cr Cor e X Y
B1 1222 647 7207 35 29700 20100 0.43 0.44 1.30
B2 1407 0 7207 35 29700 20100 0 1 0
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 Motor shaft

In The gear box the Bearing arrangement is Face to face, As Gears are in between
bearings.
Fra1= 0.5*Fr1/Y=0.5*1222/1.3=470N
Fra2= 0.5*Fr2/Y=0.5*1407/0=0N; Hence Fra1>Fra2
Total Axial force(Fat1)On bearing 1(Fat1)=Fa+Fra2=647+470=1117N
Total Axial force(Fat2)On bearing 2(Fat2)= Fra2=0N.
Bearing 1:
Fat1/Fr1=1177/1222=0.96>e=0.43. X=0.44;Y=1.30
Equivalent dynamic load(P)=X*Fr1+YFat1=0.44*1222+1.3*1117=1940N.
Life of bearing(Lh)= (29700/1944)^10/3x(10^6)/(60*720)=82546hours.
Lh=82546>20000.Hence safe.
Bearing 2:
Fat2/Fr2=0/1151=0 ; X=1Y=0
Equivalent dynamic load(P)=Fr2 =1407N.
Life of bearing(Lh)= (29700/1407)^10/3x(10^6)/(60*720)=217722hours.
Lh=217722>20000.Hence safe
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 Second shaft
 For 7210 ; f0:14.5
 For B3: Fa=0; X=1;Y=0
 For B4:
 ifoFa/Cor: 1*14.5*647/41500= 0.23.
 e =0.38
 Fa/Fr : 647/1864=0.35 < e =0.38
 X=1:Y=0
Bearing Bearing loads Selected bearing
Dynamic Load Static load
Radial Axial Bearing Bore, consta Dynamic
position carrying carrying
load,N load,N No. mm nt load factors
capacity, N capacity, N
Fr Fa Cr Cor e X Y
B3 1290 0 7210 50 41500 31500 0 1 0
B4 1864 647 7210 50 41500 31500 0.38 1 0
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 Second shaft
In The gear box the Bearing arrangement is Face to face, As Gears are in between
bearings.
Fra3= 0.5*Fr3/Y=0.5*1290/0= 0N
Fra4= 0.5*Fr4/Y=0.5*1864/0=0N;
Bearing 3:
Fat3/Fr3=0/1290=0 ; X=1Y=0
Equivalent dynamic load(P)=Fr3 =1290N.
Life of bearing(Lh)= (41500/1290)^3x(10^6)/(60*720)=770710hours.
Lh=770710>20000.Hence safe
Bearing 4:
Fat4/Fr4=0/1864=0 ; X=1Y=0
Equivalent dynamic load(P)=Fr4 =1864N.
Life of bearing(Lh)= (41500/1864)^3x(10^6)/(60*720)=255459hours.
Lh=255459>20000.Hence safe

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