design of elements machine, bearing, shaft, spur gear and others, superficie profile, lubrication,...
TRANSCRIPT
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7/25/2019 Design of elements machine, bearing, shaft, spur gear and others, superficie profile, lubrication, friction
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson
201 !"! #ress
Chapter 8: Lubrication, Friction and Wear
...among all those who have writtenon the subject of moving forces,probably not a single one has givensufficient attention to the effect offriction in machines...
Guillaume Amontons
Greases are a necessary lubricant for many applications,including rolling element bearings, for the reduction offriction and wear.Source:Courtesy of SKF USA, Inc.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson
201 !"! #ress
Surface Profiles
Figure 8.1: Surface profile showingsurface height variation relative to
mean reference line.
Two common surface measures:
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Typical Surface Roughness
Figure 8.2: Typical arithmeticaverage surface roughness(Ra) for various
manufacturing processes andmachine components.Source:Adapted from Kalpakjianand Schmid [2010] andHamrock, et al. [2004].
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Conformal and Nonconformal
Figure 8.3: Conformal surfaces.Figure 8.4: Nonconformal surfaces.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
NonconformalGeometry
Figure 8.5: Geometry of contactingelastic solids.
Effective radius:
where
Radius ratio:
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Sign Convention
Figure 8.6: Sign designations for radii of curvature. (a) Rolling elements; (b) ballbearing races; (c) rolling bearing races.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Hertz Pressure Distribution
Figure 8.7: Pressure distribution inellipsoidal contact.
Pressure distribution:
wherepmaxis the central pressure:
Note: no general solution, onlyparticular solutions for point andline contacts.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Simplified Contact Equations
Define the ellipticity parameter as:
The contact diameters are:
The maximum deflection is:
where
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Simplified Contact
Figure 8.8: Variation of ellipticityparameter and elliptic integrals offirst and second kinds as function ofradius ratio.
Table 8.1: Simplified ellipticalcontact equations.Source:FromHamrock and Brewe [1983].
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Rectangular (Line) Contacts
The Hertz solution for Rectangular contacts is as follows. The contactsemiwidth is:
The dimensionless load is
The maximum deflection is
The maximum contact pressure, or Hertz pressure, is:
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Metallic Bearing Materials
Table 8.2: Physical and mechanical properties of selected white metal bearing alloys.Source:From Hamrock et al. [2004].
Table 8.3: Mechanical properties of selected bronze and copper alloy bearingmaterials.Source:Abstracted from Hamrock, et al.~[2004].
Material Designation
Tensile Maximum Allowablestrength, temperature, stress,
MPa C MPa
Copperlead SAE480 25 55.2 177 13.8High-leadtinbronze AMS4840 48 172.5 204 20.7Semiplasticbronze SAE67 55 207 232 20.7Leadedredbronze SAE40 60 242 232 24.2
Bronze SAE660 60 242 232 27.6Phosphorbronze SAE64 63 242 232 27.6Gunmetal SAE62 65 310 260 27.6NavyG SAE620 68 276 260 27.6Leadedgunmetal SAE63 70 276 260 27.6Aluminumbronze ASTMB148-52-9c 195 621 260 31.1
Brinellhardness
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Non-metallic Bearing Materials
Table 8.4: Limits of application of nonmetallic bearing materials.
Material
Allowable Maximum Maximum pustress, temperature, speed, limit,MPa C m/s N/m-s
Carbongraphite 4.1 399 12.7 525 103
Phenolics 41.4 93 12.7 525 103
Nylon 6.9 93 5.1 105 103PTFE(Teflo
n) 3.4 260 .51 35103
ReinforcedPTFE 17.2 260 5.1 350 103
PTFEfabric 414.0 260 .25 875 103
Polycarbonate(Lexan) 6.9 104 5.1 105 103
Acetalresin(Delrin) 6.9 82 5.1 105 103
Rubber 0.34 66 7.6 525 103
Wood 13.8 66 10.2 525
103
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Bearing Materials and Forms
Figure 8.9: Phenolic laminate bearings.
(a) Tubular bearing; (b) circumferentiallylaminated bearing; (c) axially laminated
bearing; (d) stave bearing; (e) moldedbearing.Source:From Hamrock, et al.[2004].
Figure 8.10: Different forms of bearingsurfaces. (a) Solid bearing; (b) lined
bearing; (c) filled bearing; (d) shrink-fitbearing.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Viscosity
Figure 8.11: Slider bearing illustratingabsolute viscosity.
Viscosity:
Viscosity depends on: Pressure
Temperature Shear strain rate
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Viscosity Conversion Factors
Table 8.5: Absolute viscosity conversion factors.
To conert To!rom cP
Multipl" b"
cP 1kgf-s/m2 1N-s/m2 103
reyn,orlb-s/in.2 1
#g!-s/m$ N-s/m$ lb-s/in%$
9.807 103
6.90 106
1.02 10-4
1.02 10-1
7.03 102
9.8071
6.9 103
10-3
1.45 10-7
1.422 10-3
1.45 10-4
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
FluidViscosities
Figure 8.12: Absoluteviscosities of a number offluids for a wide range oftemperatures.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Viscosity of Fluids
Table 8.6: Absolute and kinematic viscosities of various fluids at atmospheric
pressure and different temperatures.Source:From Jones, et al. [1975].
&luidTemperature, C
'( )) *+) '( )) *+)
Advancedester 0.0253 0.00475 0.00206 2.5810 5 0.5110 5 0.2310 5
Formulatedadvancedester 0.0276 0.00496 0.00215 2.8210 5 0.5310 5 0.2410 5
Polyalkylaromatic 0.0255 0.00408 0.00180 3.010 5 0.5010 5 0.2310 5
Syntheticparaffini coil 0.375 0.0347 0.0101 44.
710
5
4.
0410
5
1.
310
5
Syntheticparaffini coil 0.375 0.0347 0.0101 44.710 5 4
.0410 5 1
.310 5
plusantiwearadditiveC-ether 0.0295 0.00467 0.00220 2.510 5 0.4110 5 0.2010 5
Superrefine dnapthenicmineraloil 0.0681 0.00686 0.002.74 7.810 5 0.8210 5 0.3310 5
Synthetichydrocarbon(tractionflui d) 0.0343 0.00353 0.00162 3.7210 5 0.4010 5 0.1910 5
Fluorinatedpolyether 0.181 0.0202 0.00668 9.6610 5 1.1510 5 0.410 5
inematic iscosit"atp.,
m$/s
Absoluteiscosit"atp. ,
, N-s/m$
Temperature, C
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Pressure-Viscosity Coefficients
Table 8.7: Pressure-viscosity coefficients of various fluids at different temperatures.Source:From Jones, et al. [1975].
&luid
Temperature, C'( )) *+)
Pressure-iscosit" coe!!ici ent ,, m$/N
Advancedester 1.2810 8 0.98710 8 0.85110 8
Formulatedadvancedester 1.3710 8 1.0010 8 0.87410 8
Polyalkylaromatic 1.
5810
8
1.
2510
8
1.
0110
8
Syntheticparaffini coil 1.9910 8 1
.5110 8 1
.2910 8
Syntheticparaffini coil 1.9610 8 1.5510 8 1.2510 8
plusantiwearadditiveC-ether 1.8010 8 0.98010 8 0.79510 8
Superrefine dnapthenicmineraloil 2.5110 8 1.5410 8 1.2710 8
Synthetichydrocarbon(tractionflui d) 3.1210 8 1.7110 8 0.93910 8
Fluorinatedpolyether 4.1710 8 3.2410 8 3.0210 8
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Single Grade Oils
Figure 8.13: Absolute viscosities of SAE lubricating oils at atmospheric pressure. (a)Single grade oils;
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Multigrade Oils
Figure 8.13: Absolute viscosities of SAE lubricating oils at atmospheric pressure. (b)multigrade oils.
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Viscosity of Single Grade Oils
Table 8.8: Curve fit data for SAE single grade oils for use in Eq. (8.26).Source:FromSeirig and Dandage [1982].
A0 1rade ConstantC* ConstantC$
re"n N-s/m$
10 1.5810 8 1.0910 4 1157.520 1.3610 8 9.3810 5 1271.6
30 1.4110
8
9.7310
5
1360.040 1.2110 8 8.3510 5 1474.450 1.7010 8 1.1710 4 1509.660 1.8710 8 1.2910 4 1564.0
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Regimes of Lubrication
Figure 8.14: Regimes of lubrication. (a) Fluid filmlubrication - surfaces completely separated by bulklubricant film. This regime is sometimes further
classified as thick or thin film lubrication; (b)partial lubrication - both bulk lubricant andboundary film play a role; (c) boundary lubrication- performance depends essentially on a boundaryfilm.
Film parameter:
Note: Boundary lubrication, < 1 Partial lubrication, 1 < 3
Hydrodynamic lubrication,3 Elastohydrodynamiclubrication},3 < 10
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Lubrication Effect
Figure 8.15: Bar diagram showingcoefficient of friction for variouslubrication conditions.Source:FromHamrock, et al. [2004].
Figure 8.16: Wear rate for variouslubrication regimes.Source:FromBeerbower [1972].
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Hydrodynamic Lubrication
Figure 8.17: Characteristics ofhydrodynamic lubrication.Source:From Hamrock, et al. [2004].
Figure 8.18: Mechanisms of pressure
development for hydrodynamic lubrication. (a)Slider bearing; (b) squeeze film bearing; (c)externally pressurized bearing.Source:FromHamrock, et al. [2004].
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Fundamentals of Machine Elements, 3rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Elastohydrodynamic Lubrication
Figure 8.19: Characteristics of hardelastohydrodynamic lubrication.
Figure 8.20: Characteristics ofsoftelastohydrodynamic lubrication.
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Fundamentals of Machine Elements, 3
rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
FrictionValues
Table 8.9: Typical coefficients offriction for combinations ofunlubricated metals in air.
Material Coe!!ici ent
o!!riction, 3/el!-matedmetalsinair
5.2dloG1-8.0revliS
1niT
2.1-8.0munimulA 4.1-7.0reppoC2muidnI5.0muisengaM5.1daeL5.0muimdaC4.0muimorhC
Puremetalsandallo"sslidingonsteel 4.%*'5carbon6inair
5.0revliS5.0munimulA4.0muimdaC8.0reppoC5.0muimorhC
2muidnI2.1daeL2.0dael%02-reppoC8.0)desabnit(latemetihW
Whitemetal(leadbased) 0.5-brass(copper-30%zinc) 0.5Leaded/ brass(copper-40%zinc) 0.2
4.0noritsacyarGMidsteel(0.13%carbon) 0.8
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Fundamentals of Machine Elements, 3
rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Sliding and Rolling Friction
Figure 8.21: Friction force in (a) sliding and (b) rolling.
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Fundamentals of Machine Elements, 3
rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Adhesive and Abrasive Friction
Figure 8.22: Conical asperity havingmean angleplowing through asofter material. Also simulatesabrasive wear.
Figure 8.23: Adhesive wear model.
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Fundamentals of Machine Elements, 3
rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Wear Coefficients
Table 8.10: Coefficients of rubbing friction and adhesive wear constant for ninerubbing materials.
Coe!!ici en t o! Adhesiewear
,noitcir!slairetamgnibbu7 coe!!ici ent , k15.2dlognodloG2.1reppocnoreppoC6.0leetsdlimnoleetsdliM3.0leetsdrahnossarB2.0leetsnodaeL
Polytetrafluroethylene(teflon )onsteel 0.2
Stainlesssteelonhardsteel 0.5Tungstencarbideontungstencarbide 0.35
5.0leetsnoenelyhteyloP 5 10-8
2 10-5
2 10-5
2 10-5
10-2
10-3
0.01-0.10.1-1
10-6
Archard Wear Law:
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Fundamentals of Machine Elements, 3
rd
ed.Schmid, Hamrock and Jacobson 201 !"! #ress
Fatigue Wear
Figure 8.24: Fatigue wearsimulation. (a) Machine elementsurface is subjected to cyclicloading; (b) defects and cracksdevelop near the surface; (c) thecracks grow and coalesce,
eventually extending to thesurface until (d) a wear particleis produced, leaving a fatiguespall in the material.
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Fundamentals of Machine Elements, 3rded.Schmid Hamrock and Jacobson 201 !"! #ress
Orthopedic Implants
Figure 8.25: Examples of common orthopedic implants. (a) Total hip replacement,using a metal-on-metal interfaceSource:Courtesy DePuy, Inc.; (b) total kneereplacement using a metal-on-polymer interface.Source:Courtesy Zimmer, Inc.