selection of rolling element bearings
BEARINGS CONTENTS: • • • • • • •
INTRODUCTION SELECTION OF BEARINGS BEARING TYPES GENERAL BEARING DATA SELECTION OF ROLLING ELEMENT BEARINGS FRICTION AND LUBRICATION ROLLING BEARINGS INSTALLATION
INTRODUCTION
One of the earliest (stone age) rolling-element bearings is a set of logs laid on the ground with a large block of stone on top. As the stone is pulled, the logs roll along the ground with little friction. As each log comes out the back, it is moved to the front where the block then rolls on to it.
INTRODUCTION Archaeological excavation from Lake Nemi (about 60 BC) – revolving platform on trunnion-mounted bronze balls
INTRODUCTION Bearings allow a relative movement between components of machines and provide some type of location between them. (The function of the machinery bearings is the same as the function of the human joints). The relative motion of machine components can be: - rotation about a point
gimbals (double gimbals mounting)
ball on recessed plate
INTRODUCTION - rotation along a line
journal bearing
journal bearing with double thrust location
Another solutions: double conical bearing, screw and a nut (with axial translation) -
translation along a line
railway or crane wheel on a track
pulley wheel on a cable (wire rope)
INTRODUCTION - rotation in a plane
single thrust bearing
- translation in a plane
hovercraft
double thrust bearing
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 1. Dry rubbing bearing consists of a steel shaft supported in a bush made of: •Thermosets (phenolics, epoxies etc.) + fillers (e.g. textiles) •Thermoplastics (nylon, acetal etc.) + fillers •Thermoplastics – unfilled •PTFE + fillers •Carbon graphites (metal/epoxy filled) •Sintered bronze + PTFE and Pb
SELECTION OF JOURNAL BEARINGS
MAIN TYPES OF BEARINGS: 2. Porous metal bearing consists of a sleeve of pressed and sintered metal with a density of about 80-90% of those of the bulk material. Commonly used metal is bronze (about 90% Cu and about 10% Sn) that can incorporate graphite in original powder or can be impregnated with PTFE after sintering. In most cases, the sleeve is filled with a lubricating oil by a vacuum impregnation. The oil in the pores can last a very long time, even the service life of machine.
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 3. Fluid film plain bearing (hydrodynamic/HD bearing) needs for its successful operation a converging, wedge-shaped gap into which the viscous fluid is dragged by the motion of surface or surfaces of mating components.
Pressure generation in: a) radial bearing; b) axial bearing
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 4. Externally pressurised plain bearing (hydrostatic bearing) requires the supply pump that externally generates pressure in the gap between the loaded surfaces. The essential features of the single-pad hydrostatic bearings are shown in figure below for axial (a) and radial (b) bearing. Pump supplies fluid trough pipe and restrictor or compensator (e.g. capillary, orifice, constant flow valve) to the pocket or recess.
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 5. Rolling-element bearing provide close positioning of two loaded components and allows rotational or linear motion between them. Rolling-element bearing consists of the following main components: • inner ring/race • outer ring/race • retainer/cage • rolling elements
As rolling elements can act balls or rollers, thus the equivalent term for rolling-element bearing is ball and roller bearing. An another name is anti-friction bearing.
SELECTION OF JOURNAL BEARINGS Maximum load capacity of bearings (10000 h, l = d) Rolling element bearings Fluid film (HD) bearings Rubbing plain bearings of plastic Plain bearings of porous metal impregnated with a lubricant
BEARING TYPES The most widespread rolling element bearing is the deep groove ball bearing (Conrad bearing, single row ball bearing) in which the depth of the tracks in races is about one-quarter of the ball diameter. These bearings carry radial loads and also sustain modest thrust loads. These bearings (and some others too) can be made: • with shield(s) • with seal(s) • with retaining (snap) ring groove
BEARING TYPES Some another types of ball bearings are shown in following figures.
Double row deep groove ball bearing
Angular contact ball bearings: single row and double row one
BEARING TYPES
Precision Self-aligning angular contact ball bearing ball bearing
Thrust ball bearings (single direction)
BEARING TYPES There are many variants of cylindrical roller bearings. The double row, four-row and crossed cylindrical roller bearings are also produced.
BEARING TYPES Cylindrical rollers can be assembled without cage (full complement cylindrical roller bearing) or have enlarged length (needle roller bearings).
BEARING TYPES Another types of roller bearings are taper roller bearings, spherical roller bearings (single and double row) and spherical roller thrust bearings.
BEARING TYPES Most rolling-element bearings are for rotating or oscillating loads, but there are also linear bearing designs, e.g. linear ball bearings (ball guides) with limited and endless translation.
BEARING TYPES Dimensions of rolling contact bearings are from millimetres (instrument/miniature bearings) to meters (slewing bearings).
GENERAL BEARING DATA The main dimensions of the rolling-element bearing do not concern the internal details.
The characteristic dimension of the rolling-element bearing is the bore diameter d.
GENERAL BEARING DATA The dimensions of bearings have been, in order to limit the number of produced bearings, standardised by the International Organisation for Standardisation (ISO). The basics of this system (the ISO Dimension Plan) for the most of radial bearings shows figure below. Note that the numbers shown occur in bearing symbols.
GENERAL BEARING DATA Symbols of the rolling-element bearings include type, diameter and width series and the characteristic diameter. The most important types are as follows: • deep groove ball bearings – 60, 62, 63 • self-aligning ball bearings – 12, 13, 22, 23 • angular contact ball bearings – 72, 73 • cylindrical roller bearings – N/NU/NJ/NUP 2/3 • spherical roller bearings – 222, 213, 232, 223 The characteristic diameter d represent the last two digits of the bearing symbol – beginning from the figure of 04 this diameter is to be determined by multiplying by 5. Example: symbol 6005 denotes the light deep groove ball bearing (60) with the nominal bore diameter of 25 mm (05x5).
GENERAL BEARING DATA The most common through-hardening steel used for rolling bearings is a carbon chromium steel (about 1% C and 1.5% Cr). The new material for rolling bearings is silicon nitride. The comparison below shows the significant advantages of this ceramic material. Ceramic coatings (TiN, TiC, DLC) on steel surfaces are also used. Property Steel Si3N4 Density [g/cm3]
7.8
3.2
Vickers hardness HV
700
1500
Young’s modulus [GPa]
210
320
12·10-6 300
3·10-6 1000
0.02
0.005
1
10
Thermal expansion coefficient [K-1] Maximum usage temperature [ºC] CLA [µm] Relative fatigue life
SELECTION OF ROLLING-ELEMENT BEARINGS Bearing type Suitability of bearing for:
radial load
++
++
axial load
++ +++ +++ +++
compensation for misalignment
+
-
++
-
+
-
+ -
--
++
++
--
+++
+++
-
-
-
-
-
high speed
+++ +++
++
low friction
+++ +++
++
-
+++
++
+
+++ +++ +++
-
radial stiffness ++
axial stiffness
+
++
+++ +++ +++ ++ +++ +++ +++
++ +++ +++ +++ +++ ++
+++ +++ +++ +++ ++
-
+
+++ ++
++
+
+
+
+
+
+++ +++ +++ +++ +++ +++ +++
--
+++ +++
--
++
--
+
+++ excellent; ++ good; + fair; - poor; -- unsuitable
--
+
--
++
++
++ +++ ++
+++
--
--
++ +++
--
--
--
+++
+
++
++
++
+
--
++
+++ +++ ++
--
++
-
--
++ +++ +++ +++
SELECTION OF ROLLING-ELEMENT BEARINGS One of the factors of selection is the permissible speed. The numbers in figure denote the type of bearing: 1 – deep groove ball bearing 2 – cylindrical roller bearing and self-aligning ball bearing 3 – angular contact ball bearing, single row 4 – angular contact ball bearing, double row 5 – taper roller bearing 6,7 – spherical roller bearing, single row,double row 8 – spherical roller thrust bearing 9 – angular contact thrust ball bearing 10 – thrust ball bearing 11 – cylindrical roller thrust b.
SELECTION OF ROLLING-ELEMENT BEARINGS Selecting bearing size using the life equations Bearing life can be calculated with various degrees of sophistication, depending on the accuracy with which the operating conditions can be defined. The most simple method of life calculation is to use the ISO equation of Lundberg and Palmgren for basic rating life which is
⎛C ⎞ L10 = ⎜ ⎟ ⎝P⎠
p
C 1/ p or = L10 P
where L10 basic rating life, millions of revolutions C basic dynamic load rating, N P equivalent dynamic bearing load, N p exponent of the life equation p=3 for ball bearings p = 10/3 for roller bearings
SELECTION OF ROLLING-ELEMENT BEARINGS It should be emphasised the statistical nature of life estimates. An example of the test results of the fatigue surface failure (pitting) of rolling-element bearings shows Weibull plot.
50% of the bearings tested had failed by more than 100 million cycles 10% of the bearings tested had failed by less than 20 million cycles
SELECTION OF ROLLING-ELEMENT BEARINGS
Basic dynamic load rating for radial ball bearings according to DIN standard
SELECTION OF ROLLING-ELEMENT BEARINGS For bearings operating at constant speed it may be more convenient to deal with a basic rating life L10h expressed in operating hours using the equation
L10 h
1000000 = ⋅ L10 60 ⋅ n
where n is the rotational speed in r/min. In case of the road and rail vehicles the life L10s can be expressed in millions of kilometres travelled
L10 s =
π ⋅D
1000
⋅ L10
where D is the wheel diameter in metres.
SELECTION OF ROLLING-ELEMENT BEARINGS If a bearing does not rotate but oscillates from a central position through an angle of ±γ as shown in figure, then the basic rating life L10osc expressed in millions of cycles is
L10osc
180 = ⋅ L10 2 ⋅γ
where γ is the oscillation amplitude (angle of maximum deviation from centre position in degrees.
SELECTION OF ROLLING-ELEMENT BEARINGS The required basic rating life depends on the type of machine and the requirements regarding duration of service and operational reliability. Some values for L10h are: 300 ... 3000 h household machines, agricultural machines, instruments 3000 ... 8000 h machines used for short periods or intermittently 10000 ... 30000 h machines used 8 hours per day 40000 ... 50000 h machines for continuous use 24 hours per day 60000 ... 100000 h big machinery (power plants, vessels) for continuous use 24 hours per day Figures for L10s are: 300000 km private cars 800000 km commercial trucks 1500000 km tramcars 3000000 km passenger carriages 5000000 km locomotives
SELECTION OF ROLLING-ELEMENT BEARINGS Equivalent bearing load Radial bearings are often subjected to simultaneously acting radial and axial loads. The equivalent dynamic bearing load P can be calculated from the following general equation
P = X ⋅ Fr + Y ⋅ Fa where Fr radial bearing load, N Fa axial bearing load, N X radial load factor Y axial load factor Load factors are given in bearing catalogues.
SELECTION OF ROLLING-ELEMENT BEARINGS The same general equation is to be applied for thrust bearings that can take both axial and radial loads (spherical roller thrust bearings). If the magnitude of the bearing load fluctuates, its average value, the constant mean load Fm, is to be calculated
Fm where F1, F2, ... U
3 3 F1 ⋅ U1 + F2 ⋅ U 2 3 =
+ ...
U
constant loads during U1, U2, .... revolutions total number of revolutions
SELECTION OF ROLLING-ELEMENT BEARINGS Selecting bearing size using the static load carrying capacity Bearing size should be selected on the basis of the basic static load rating instead of on bearing life when one of the following conditions pertains: • • • •
bearing is stationary bearing makes slow oscillating movements bearing rotates at very slow speed bearing has to sustain heavy shock loads
In all these cases, the permissible load for a bearing is determined not by material fatigue but by the permanent deformation caused by the load at the contact of the rolling element with raceway.
SELECTION OF ROLLING-ELEMENT BEARINGS Loads comprising radial and axial components must be converted into an equivalent static bearing load P0. This is defined as that load (radial for radial bearings and axial for thrust bearings) which, if applied, would cause the same permanent deformation in the bearing as the actual load. It is obtained from the general equation
P0 = X 0 ⋅ Fr + Y0 ⋅ Fa where Fr Fa X0 Y0
radial bearing load, N axial bearing load, N radial load factor axial load factor
FRICTION AND LUBRICATION
Friction in a rolling bearing is the determining factor where heat generation in the bearing is concerned and consequently for the operating temperature. The friction depends on the load and on several other factors, the most important of which are the bearing type and size, the operating speed, the properties of the lubricant and the quantity of lubricant. The total resistance to rolling in a bearing is made up of the rolling and sliding friction in the rolling contacts, in the contact areas between rolling elements and cage as well as in the guiding surfaces for the rolling elements or the cage, the friction in the lubricant and of the sliding friction of rubbing seals in the case of sealed bearings.
FRICTION AND LUBRICATION Estimation of frictional moment Under certain conditions (bearing load P/C ≈ 1, good lubrication, normal operating conditions) the frictional moment can be calculated with sufficient accuracy using a constant coefficient of friction µ from the following equation
M = 0 .5 ⋅ µ ⋅ F ⋅ d where M frictional moment, N·mm µ coefficient of friction for the bearing F bearing load, N d bearing bore diameter, mm
FRICTION AND LUBRICATION Coefficient of friction for different bearings types Bearing type
µ
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Deep groove ball bearing.................................0.0015 Self-aligning ball bearing.................................0.0010 Angular contact ball bearing - single row......0.0020 Angular contact - double row..........................0.0024 Four-point contact ball bearing.......................0.0024 Cylindrical roller bearings with cage..............0.0011 Full complement cylindrical roller bearing.....0.0020 Needle roller bearing.........................................0.0025 Spherical roller bearing....................................0.0018 Thrust ball bearing............................................0.0013 Cylindrical/needle roller thrust bearing..........0.0050 Sphericaliroller thrust bearings.......................0.0018
FRICTION AND LUBRICATION Grease lubrication is generally used when rolling-element bearings operate at normal speeds, loads and temperature conditions. For normal application the bearings and housings should be filled with grease up to 30-50% of the free space. Overpacking with grease will cause overheating. When selecting a grease, the consistency, rust-inhibiting properties and temperature range must be carefully considered. The most important characteristic of grease is its consistency, an empirical measure of the flow ability.
FRICTION AND LUBRICATION Penetration test apparatus consists of grease container, a two-stage cone cone and a displacement indicator. The container is filled with the grease and the top surface of the grease is smoothed over. The cone is placed so that its tip just touches the grease surface and a dial indicator is set to zero at this position. When the test starts the weight of the cone will cause it to penetrate into the grease. After a specific time interval the depth of penetration (expressed in tenths of mm) is measured. The test procedure is internationally standardised.
FRICTION AND LUBRICATION On the base of the grease penetration tests a classification of their consistency has been made by the US National Lubricating Grease Institute (NLGI grades) NLGI Grade
Penetration
Appearance
000
445-475
fluid
00
400-430
fluid
0
355-385
very soft
1
310-340
soft
2
265-295
moderately soft
3
220-250
semi-fluid
4
175-205
semi-hard
5
130-160
hard
Grades 1 through 4 are often used in rolling element bearings where grades 2 and 3 are the most common.
FRICTION AND LUBRICATION The relubrication times for typical greases
FRICTION AND LUBRICATION Oil lubrication is used when operating conditions such as speed or temperature preclude the use of grease. Figure gives a guide to suitable oil viscosities for rolling-element bearings taking into account the bearing size and operating temperature. In the figure d is bearing bore diameter in mm and n denotes the rotational speed in rev/min. An example is shown on the graph by means of the lines of dashes. Generally the oil viscosity for medium and large size bearings should not be less than 12 centistokes (mm2/s) at the operating temperature. For small high-speed bearings less viscous oils are used in order lo keep friction to a minimum. The viscosity measurements will be discussed in chapter Hydrodynamic Bearings.
FRICTION AND LUBRICATION
ROLLING BEARING INSTALLATION Shaft and housing design - rigidity • Check the shaft slope at the bearing positions due to load •
•
deflection, unless self-aligning bearings are to be used Check that the housing gives adequate support to the bearing outer ring, and that housing distortion under load will not cause distortion of the bearing outer ring. Design the housing so that the resultant bearing slope is subtractive
ROLLING BEARING INSTALLATION Shaft and housing design - alignment • For rigid-type bearings, calculate the shaft and housing slopes due to load deflection • Determine the errors of housing misalignment due to tolerance build-up • Ensure that the total misalignment docs not exceed the values given below Approximate maximum misalignments for rigid bearings Radial ball bearing.......................................1.0 mrad Angular contact ball bearing......................0.3 mrad Radial roller bearing....................................0.3 mrad Needle roller bearing...................................0.1 mrad
ROLLING BEARING INSTALLATION Shaft and housing design – recommended fits
ROLLING BEARING INSTALLATION
Bearing mountings – horizontal shaft
ROLLING BEARING INSTALLATION Bearing mountings – horizontal shaft
ROLLING BEARING INSTALLATION Bearing mountings – vertical shaft
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods Shaft – screwed nut provides positive clamping for the bearing inner ring . Housing – the end cover should be spigoted in the housing bore, and bolted up uniformly to positively clamp the bearing outer ring.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods Circlip location can reduce cost and assembly time. Shaft – use a spacer if necessary to provide a suitable abutment. Circlips should not be used if heavy axial loads are to be taken or if positive clamping is required (e.g. paired angular contact unit). Housing shows mounting for snap ring type of bearing.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods
Interference fit ring
Interference fit rings are sometimes used as a cheap and effective method of locating a bearing ring axially. The degree of interference must be sufficient to avoid movement under the axial loads that apply.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods
Bearing with tapered clamping sleeve. This provides a means for locking a bearing to a parallel shaft.
Tapered clamping sleeve
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Shielded bearing (steel shields)
Sealed bearing (rubber seals)
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Brand rubbing seal (Simmering)
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Labyrinth closure (the running clearances should be about 0.2 mm and filled with a grease to improve the seal effectiveness).
INTRODUCTION SELECTION OF BEARINGS BEARING TYPES GENERAL BEARING DATA SELECTION OF ROLLING ELEMENT BEARINGS FRICTION AND LUBRICATION ROLLING BEARINGS INSTALLATION
INTRODUCTION
One of the earliest (stone age) rolling-element bearings is a set of logs laid on the ground with a large block of stone on top. As the stone is pulled, the logs roll along the ground with little friction. As each log comes out the back, it is moved to the front where the block then rolls on to it.
INTRODUCTION Archaeological excavation from Lake Nemi (about 60 BC) – revolving platform on trunnion-mounted bronze balls
INTRODUCTION Bearings allow a relative movement between components of machines and provide some type of location between them. (The function of the machinery bearings is the same as the function of the human joints). The relative motion of machine components can be: - rotation about a point
gimbals (double gimbals mounting)
ball on recessed plate
INTRODUCTION - rotation along a line
journal bearing
journal bearing with double thrust location
Another solutions: double conical bearing, screw and a nut (with axial translation) -
translation along a line
railway or crane wheel on a track
pulley wheel on a cable (wire rope)
INTRODUCTION - rotation in a plane
single thrust bearing
- translation in a plane
hovercraft
double thrust bearing
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 1. Dry rubbing bearing consists of a steel shaft supported in a bush made of: •Thermosets (phenolics, epoxies etc.) + fillers (e.g. textiles) •Thermoplastics (nylon, acetal etc.) + fillers •Thermoplastics – unfilled •PTFE + fillers •Carbon graphites (metal/epoxy filled) •Sintered bronze + PTFE and Pb
SELECTION OF JOURNAL BEARINGS
MAIN TYPES OF BEARINGS: 2. Porous metal bearing consists of a sleeve of pressed and sintered metal with a density of about 80-90% of those of the bulk material. Commonly used metal is bronze (about 90% Cu and about 10% Sn) that can incorporate graphite in original powder or can be impregnated with PTFE after sintering. In most cases, the sleeve is filled with a lubricating oil by a vacuum impregnation. The oil in the pores can last a very long time, even the service life of machine.
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 3. Fluid film plain bearing (hydrodynamic/HD bearing) needs for its successful operation a converging, wedge-shaped gap into which the viscous fluid is dragged by the motion of surface or surfaces of mating components.
Pressure generation in: a) radial bearing; b) axial bearing
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 4. Externally pressurised plain bearing (hydrostatic bearing) requires the supply pump that externally generates pressure in the gap between the loaded surfaces. The essential features of the single-pad hydrostatic bearings are shown in figure below for axial (a) and radial (b) bearing. Pump supplies fluid trough pipe and restrictor or compensator (e.g. capillary, orifice, constant flow valve) to the pocket or recess.
SELECTION OF JOURNAL BEARINGS MAIN TYPES OF BEARINGS: 5. Rolling-element bearing provide close positioning of two loaded components and allows rotational or linear motion between them. Rolling-element bearing consists of the following main components: • inner ring/race • outer ring/race • retainer/cage • rolling elements
As rolling elements can act balls or rollers, thus the equivalent term for rolling-element bearing is ball and roller bearing. An another name is anti-friction bearing.
SELECTION OF JOURNAL BEARINGS Maximum load capacity of bearings (10000 h, l = d) Rolling element bearings Fluid film (HD) bearings Rubbing plain bearings of plastic Plain bearings of porous metal impregnated with a lubricant
BEARING TYPES The most widespread rolling element bearing is the deep groove ball bearing (Conrad bearing, single row ball bearing) in which the depth of the tracks in races is about one-quarter of the ball diameter. These bearings carry radial loads and also sustain modest thrust loads. These bearings (and some others too) can be made: • with shield(s) • with seal(s) • with retaining (snap) ring groove
BEARING TYPES Some another types of ball bearings are shown in following figures.
Double row deep groove ball bearing
Angular contact ball bearings: single row and double row one
BEARING TYPES
Precision Self-aligning angular contact ball bearing ball bearing
Thrust ball bearings (single direction)
BEARING TYPES There are many variants of cylindrical roller bearings. The double row, four-row and crossed cylindrical roller bearings are also produced.
BEARING TYPES Cylindrical rollers can be assembled without cage (full complement cylindrical roller bearing) or have enlarged length (needle roller bearings).
BEARING TYPES Another types of roller bearings are taper roller bearings, spherical roller bearings (single and double row) and spherical roller thrust bearings.
BEARING TYPES Most rolling-element bearings are for rotating or oscillating loads, but there are also linear bearing designs, e.g. linear ball bearings (ball guides) with limited and endless translation.
BEARING TYPES Dimensions of rolling contact bearings are from millimetres (instrument/miniature bearings) to meters (slewing bearings).
GENERAL BEARING DATA The main dimensions of the rolling-element bearing do not concern the internal details.
The characteristic dimension of the rolling-element bearing is the bore diameter d.
GENERAL BEARING DATA The dimensions of bearings have been, in order to limit the number of produced bearings, standardised by the International Organisation for Standardisation (ISO). The basics of this system (the ISO Dimension Plan) for the most of radial bearings shows figure below. Note that the numbers shown occur in bearing symbols.
GENERAL BEARING DATA Symbols of the rolling-element bearings include type, diameter and width series and the characteristic diameter. The most important types are as follows: • deep groove ball bearings – 60, 62, 63 • self-aligning ball bearings – 12, 13, 22, 23 • angular contact ball bearings – 72, 73 • cylindrical roller bearings – N/NU/NJ/NUP 2/3 • spherical roller bearings – 222, 213, 232, 223 The characteristic diameter d represent the last two digits of the bearing symbol – beginning from the figure of 04 this diameter is to be determined by multiplying by 5. Example: symbol 6005 denotes the light deep groove ball bearing (60) with the nominal bore diameter of 25 mm (05x5).
GENERAL BEARING DATA The most common through-hardening steel used for rolling bearings is a carbon chromium steel (about 1% C and 1.5% Cr). The new material for rolling bearings is silicon nitride. The comparison below shows the significant advantages of this ceramic material. Ceramic coatings (TiN, TiC, DLC) on steel surfaces are also used. Property Steel Si3N4 Density [g/cm3]
7.8
3.2
Vickers hardness HV
700
1500
Young’s modulus [GPa]
210
320
12·10-6 300
3·10-6 1000
0.02
0.005
1
10
Thermal expansion coefficient [K-1] Maximum usage temperature [ºC] CLA [µm] Relative fatigue life
SELECTION OF ROLLING-ELEMENT BEARINGS Bearing type Suitability of bearing for:
radial load
++
++
axial load
++ +++ +++ +++
compensation for misalignment
+
-
++
-
+
-
+ -
--
++
++
--
+++
+++
-
-
-
-
-
high speed
+++ +++
++
low friction
+++ +++
++
-
+++
++
+
+++ +++ +++
-
radial stiffness ++
axial stiffness
+
++
+++ +++ +++ ++ +++ +++ +++
++ +++ +++ +++ +++ ++
+++ +++ +++ +++ ++
-
+
+++ ++
++
+
+
+
+
+
+++ +++ +++ +++ +++ +++ +++
--
+++ +++
--
++
--
+
+++ excellent; ++ good; + fair; - poor; -- unsuitable
--
+
--
++
++
++ +++ ++
+++
--
--
++ +++
--
--
--
+++
+
++
++
++
+
--
++
+++ +++ ++
--
++
-
--
++ +++ +++ +++
SELECTION OF ROLLING-ELEMENT BEARINGS One of the factors of selection is the permissible speed. The numbers in figure denote the type of bearing: 1 – deep groove ball bearing 2 – cylindrical roller bearing and self-aligning ball bearing 3 – angular contact ball bearing, single row 4 – angular contact ball bearing, double row 5 – taper roller bearing 6,7 – spherical roller bearing, single row,double row 8 – spherical roller thrust bearing 9 – angular contact thrust ball bearing 10 – thrust ball bearing 11 – cylindrical roller thrust b.
SELECTION OF ROLLING-ELEMENT BEARINGS Selecting bearing size using the life equations Bearing life can be calculated with various degrees of sophistication, depending on the accuracy with which the operating conditions can be defined. The most simple method of life calculation is to use the ISO equation of Lundberg and Palmgren for basic rating life which is
⎛C ⎞ L10 = ⎜ ⎟ ⎝P⎠
p
C 1/ p or = L10 P
where L10 basic rating life, millions of revolutions C basic dynamic load rating, N P equivalent dynamic bearing load, N p exponent of the life equation p=3 for ball bearings p = 10/3 for roller bearings
SELECTION OF ROLLING-ELEMENT BEARINGS It should be emphasised the statistical nature of life estimates. An example of the test results of the fatigue surface failure (pitting) of rolling-element bearings shows Weibull plot.
50% of the bearings tested had failed by more than 100 million cycles 10% of the bearings tested had failed by less than 20 million cycles
SELECTION OF ROLLING-ELEMENT BEARINGS
Basic dynamic load rating for radial ball bearings according to DIN standard
SELECTION OF ROLLING-ELEMENT BEARINGS For bearings operating at constant speed it may be more convenient to deal with a basic rating life L10h expressed in operating hours using the equation
L10 h
1000000 = ⋅ L10 60 ⋅ n
where n is the rotational speed in r/min. In case of the road and rail vehicles the life L10s can be expressed in millions of kilometres travelled
L10 s =
π ⋅D
1000
⋅ L10
where D is the wheel diameter in metres.
SELECTION OF ROLLING-ELEMENT BEARINGS If a bearing does not rotate but oscillates from a central position through an angle of ±γ as shown in figure, then the basic rating life L10osc expressed in millions of cycles is
L10osc
180 = ⋅ L10 2 ⋅γ
where γ is the oscillation amplitude (angle of maximum deviation from centre position in degrees.
SELECTION OF ROLLING-ELEMENT BEARINGS The required basic rating life depends on the type of machine and the requirements regarding duration of service and operational reliability. Some values for L10h are: 300 ... 3000 h household machines, agricultural machines, instruments 3000 ... 8000 h machines used for short periods or intermittently 10000 ... 30000 h machines used 8 hours per day 40000 ... 50000 h machines for continuous use 24 hours per day 60000 ... 100000 h big machinery (power plants, vessels) for continuous use 24 hours per day Figures for L10s are: 300000 km private cars 800000 km commercial trucks 1500000 km tramcars 3000000 km passenger carriages 5000000 km locomotives
SELECTION OF ROLLING-ELEMENT BEARINGS Equivalent bearing load Radial bearings are often subjected to simultaneously acting radial and axial loads. The equivalent dynamic bearing load P can be calculated from the following general equation
P = X ⋅ Fr + Y ⋅ Fa where Fr radial bearing load, N Fa axial bearing load, N X radial load factor Y axial load factor Load factors are given in bearing catalogues.
SELECTION OF ROLLING-ELEMENT BEARINGS The same general equation is to be applied for thrust bearings that can take both axial and radial loads (spherical roller thrust bearings). If the magnitude of the bearing load fluctuates, its average value, the constant mean load Fm, is to be calculated
Fm where F1, F2, ... U
3 3 F1 ⋅ U1 + F2 ⋅ U 2 3 =
+ ...
U
constant loads during U1, U2, .... revolutions total number of revolutions
SELECTION OF ROLLING-ELEMENT BEARINGS Selecting bearing size using the static load carrying capacity Bearing size should be selected on the basis of the basic static load rating instead of on bearing life when one of the following conditions pertains: • • • •
bearing is stationary bearing makes slow oscillating movements bearing rotates at very slow speed bearing has to sustain heavy shock loads
In all these cases, the permissible load for a bearing is determined not by material fatigue but by the permanent deformation caused by the load at the contact of the rolling element with raceway.
SELECTION OF ROLLING-ELEMENT BEARINGS Loads comprising radial and axial components must be converted into an equivalent static bearing load P0. This is defined as that load (radial for radial bearings and axial for thrust bearings) which, if applied, would cause the same permanent deformation in the bearing as the actual load. It is obtained from the general equation
P0 = X 0 ⋅ Fr + Y0 ⋅ Fa where Fr Fa X0 Y0
radial bearing load, N axial bearing load, N radial load factor axial load factor
FRICTION AND LUBRICATION
Friction in a rolling bearing is the determining factor where heat generation in the bearing is concerned and consequently for the operating temperature. The friction depends on the load and on several other factors, the most important of which are the bearing type and size, the operating speed, the properties of the lubricant and the quantity of lubricant. The total resistance to rolling in a bearing is made up of the rolling and sliding friction in the rolling contacts, in the contact areas between rolling elements and cage as well as in the guiding surfaces for the rolling elements or the cage, the friction in the lubricant and of the sliding friction of rubbing seals in the case of sealed bearings.
FRICTION AND LUBRICATION Estimation of frictional moment Under certain conditions (bearing load P/C ≈ 1, good lubrication, normal operating conditions) the frictional moment can be calculated with sufficient accuracy using a constant coefficient of friction µ from the following equation
M = 0 .5 ⋅ µ ⋅ F ⋅ d where M frictional moment, N·mm µ coefficient of friction for the bearing F bearing load, N d bearing bore diameter, mm
FRICTION AND LUBRICATION Coefficient of friction for different bearings types Bearing type
µ
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Deep groove ball bearing.................................0.0015 Self-aligning ball bearing.................................0.0010 Angular contact ball bearing - single row......0.0020 Angular contact - double row..........................0.0024 Four-point contact ball bearing.......................0.0024 Cylindrical roller bearings with cage..............0.0011 Full complement cylindrical roller bearing.....0.0020 Needle roller bearing.........................................0.0025 Spherical roller bearing....................................0.0018 Thrust ball bearing............................................0.0013 Cylindrical/needle roller thrust bearing..........0.0050 Sphericaliroller thrust bearings.......................0.0018
FRICTION AND LUBRICATION Grease lubrication is generally used when rolling-element bearings operate at normal speeds, loads and temperature conditions. For normal application the bearings and housings should be filled with grease up to 30-50% of the free space. Overpacking with grease will cause overheating. When selecting a grease, the consistency, rust-inhibiting properties and temperature range must be carefully considered. The most important characteristic of grease is its consistency, an empirical measure of the flow ability.
FRICTION AND LUBRICATION Penetration test apparatus consists of grease container, a two-stage cone cone and a displacement indicator. The container is filled with the grease and the top surface of the grease is smoothed over. The cone is placed so that its tip just touches the grease surface and a dial indicator is set to zero at this position. When the test starts the weight of the cone will cause it to penetrate into the grease. After a specific time interval the depth of penetration (expressed in tenths of mm) is measured. The test procedure is internationally standardised.
FRICTION AND LUBRICATION On the base of the grease penetration tests a classification of their consistency has been made by the US National Lubricating Grease Institute (NLGI grades) NLGI Grade
Penetration
Appearance
000
445-475
fluid
00
400-430
fluid
0
355-385
very soft
1
310-340
soft
2
265-295
moderately soft
3
220-250
semi-fluid
4
175-205
semi-hard
5
130-160
hard
Grades 1 through 4 are often used in rolling element bearings where grades 2 and 3 are the most common.
FRICTION AND LUBRICATION The relubrication times for typical greases
FRICTION AND LUBRICATION Oil lubrication is used when operating conditions such as speed or temperature preclude the use of grease. Figure gives a guide to suitable oil viscosities for rolling-element bearings taking into account the bearing size and operating temperature. In the figure d is bearing bore diameter in mm and n denotes the rotational speed in rev/min. An example is shown on the graph by means of the lines of dashes. Generally the oil viscosity for medium and large size bearings should not be less than 12 centistokes (mm2/s) at the operating temperature. For small high-speed bearings less viscous oils are used in order lo keep friction to a minimum. The viscosity measurements will be discussed in chapter Hydrodynamic Bearings.
FRICTION AND LUBRICATION
ROLLING BEARING INSTALLATION Shaft and housing design - rigidity • Check the shaft slope at the bearing positions due to load •
•
deflection, unless self-aligning bearings are to be used Check that the housing gives adequate support to the bearing outer ring, and that housing distortion under load will not cause distortion of the bearing outer ring. Design the housing so that the resultant bearing slope is subtractive
ROLLING BEARING INSTALLATION Shaft and housing design - alignment • For rigid-type bearings, calculate the shaft and housing slopes due to load deflection • Determine the errors of housing misalignment due to tolerance build-up • Ensure that the total misalignment docs not exceed the values given below Approximate maximum misalignments for rigid bearings Radial ball bearing.......................................1.0 mrad Angular contact ball bearing......................0.3 mrad Radial roller bearing....................................0.3 mrad Needle roller bearing...................................0.1 mrad
ROLLING BEARING INSTALLATION Shaft and housing design – recommended fits
ROLLING BEARING INSTALLATION
Bearing mountings – horizontal shaft
ROLLING BEARING INSTALLATION Bearing mountings – horizontal shaft
ROLLING BEARING INSTALLATION Bearing mountings – vertical shaft
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods Shaft – screwed nut provides positive clamping for the bearing inner ring . Housing – the end cover should be spigoted in the housing bore, and bolted up uniformly to positively clamp the bearing outer ring.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods Circlip location can reduce cost and assembly time. Shaft – use a spacer if necessary to provide a suitable abutment. Circlips should not be used if heavy axial loads are to be taken or if positive clamping is required (e.g. paired angular contact unit). Housing shows mounting for snap ring type of bearing.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods
Interference fit ring
Interference fit rings are sometimes used as a cheap and effective method of locating a bearing ring axially. The degree of interference must be sufficient to avoid movement under the axial loads that apply.
ROLLING BEARING INSTALLATION Bearing mountings – fixing methods
Bearing with tapered clamping sleeve. This provides a means for locking a bearing to a parallel shaft.
Tapered clamping sleeve
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Shielded bearing (steel shields)
Sealed bearing (rubber seals)
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Brand rubbing seal (Simmering)
ROLLING BEARING INSTALLATION Bearing mountings – sealing arrangements
Labyrinth closure (the running clearances should be about 0.2 mm and filled with a grease to improve the seal effectiveness).
