Post on 22-Dec-2015
BK50A2200 BK50A2200 Design Methodologies and Design Methodologies and
Applications of Machine Applications of Machine Element DesignElement Design
Lecture 2Lecture 2
Introduction to the textbook:Introduction to the textbook:““Norton: Machine Design”Norton: Machine Design”
D.Sc Harri EskelinenD.Sc Harri Eskelinen
Goals of this lectureGoals of this lecture
Support the contents of the previous Support the contents of the previous lectures dealing with machine design lectures dealing with machine design approaches, reliability design and wear approaches, reliability design and wear phenomenaphenomena
To get familiar with the main designing and To get familiar with the main designing and dimensioning criteria of the most important dimensioning criteria of the most important machine elements (according to Norton)machine elements (according to Norton) Main consecutive designing steps and aspectsMain consecutive designing steps and aspects Fundamental dimensioning equations Fundamental dimensioning equations
Briefly about the bookBriefly about the book
The textbook presents an integrated approach The textbook presents an integrated approach to the machine elements by combining the to the machine elements by combining the usual set of machine element topics with a usual set of machine element topics with a series of case studies that illustrate the series of case studies that illustrate the relationships between force, stress and failure relationships between force, stress and failure analysis in real-world design.analysis in real-world design.
The book emphasizes the design and The book emphasizes the design and synthesis aspects of machine elements but it synthesis aspects of machine elements but it forms also a good balance between synthesis forms also a good balance between synthesis and analysis.and analysis.
The first part of the book presents The first part of the book presents the fundamentals of design, the fundamentals of design, materials, stress, strain, deflection, materials, stress, strain, deflection, failure and fracture theories.failure and fracture theories.
The second part treats of the aspects The second part treats of the aspects of machine element design, such as of machine element design, such as designing springs, shafts, gears, designing springs, shafts, gears, bearings etc.bearings etc.
PART 1.PART 1. FUNDAMENTALS FUNDAMENTALS
Chapter 1. Introduction to Chapter 1. Introduction to DesignDesign
This chapter partially supports the ideas of systematic This chapter partially supports the ideas of systematic design approach (see the yellow items below) : according to design approach (see the yellow items below) : according to Norton the design process consists of the following ten Norton the design process consists of the following ten stages:stages: 1 Identification of need1 Identification of need 2 Background research2 Background research 3 Goal statement3 Goal statement 4 Task specifications4 Task specifications 5 Synthesis5 Synthesis 6 Analysis6 Analysis 7 Selection7 Selection 8 Detailed design8 Detailed design 9 Prototyping and testing9 Prototyping and testing 10 Production10 Production
Chapter 2. Materials and Chapter 2. Materials and ProcessesProcesses
The contents of this chapter will be discussed in details The contents of this chapter will be discussed in details during the university course “Introduction to Material during the university course “Introduction to Material Technology”Technology”
Basic definitions of the most common material properties Basic definitions of the most common material properties are presented briefly:are presented briefly:
Modulus of elasticityModulus of elasticity Yield strengthYield strength Ultimate tensile strengthUltimate tensile strength Modulus of rigidityModulus of rigidity Fatigue strengthFatigue strength ToughnessToughness HardnessHardness
Most typical hardening and surface coating processes are Most typical hardening and surface coating processes are presented brieflypresented briefly
Basic information about some material groups is given:Basic information about some material groups is given: SteelsSteels Cast ironCast iron AluminiumAluminium TitaniumTitanium Copper AlloysCopper Alloys PolymersPolymers CeramicsCeramics CompositesComposites
Chapter 3. Load DeterminationChapter 3. Load Determination
The content of this chapter produce the The content of this chapter produce the fundamentals for the further stress, strain fundamentals for the further stress, strain and deflection analysis presented in chapter and deflection analysis presented in chapter 4.4.
Main topics are:Main topics are: Different loading casesDifferent loading cases Free-body diagramsFree-body diagrams Static loadingStatic loading Dynamic loadingDynamic loading Vibration loadingVibration loading Impact loadingImpact loading Beam loadingBeam loading
Classification of loading casesClassification of loading cases
Constant Constant
LoadsLoadsTime-Varying Time-Varying LoadsLoads
Stationary Stationary elementselements
Class 1Class 1 Class 2Class 2
Moving Moving elementselements
Class 3Class 3 Class 4Class 4
Identification of different loading casesIdentification of different loading cases Identification of different loading cases in necessary Identification of different loading cases in necessary
to make it possible to use proper material properties to make it possible to use proper material properties as criteria during the material selection processas criteria during the material selection process Tension or compression Tension or compression tensile or compressive stress tensile or compressive stress Bending Bending bending stress bending stress Shear Shear shear stress shear stress Torsion Torsion torsion stress (shear strass) torsion stress (shear strass) Reverced loading Reverced loading endurance limit (for reverced stress) endurance limit (for reverced stress) Pulsating loading Pulsating loading endurance limit (for pulsating stress) endurance limit (for pulsating stress)
Pulsating loadingPulsating loading Reverced loadingReverced loading
Free-Body DiagramsFree-Body Diagrams Case example: Wire connector crimping toolCase example: Wire connector crimping tool
Chapter 4. Stress, Strain and Chapter 4. Stress, Strain and DeflectionDeflection
This chapter includes the basic theories of This chapter includes the basic theories of “strength “strength of materials”of materials”, the following topics are discussed , the following topics are discussed (the most important items are high-lighted with (the most important items are high-lighted with yellow):yellow): Principal stressesPrincipal stresses Axial TensionAxial Tension Bending stresses of beamsBending stresses of beams Deflection of beamsDeflection of beams TorsionTorsion Combined stressesCombined stresses Stress concentrationStress concentration Axial compressionAxial compression Stresses in cylindersStresses in cylinders
T1
Fa
FrFt
Combined loading:-Axial force-Radial force-Tangential force-Torque- combined stresses
A B C D
Critical cross-sections due tostress concentrations:-End of the keyseat at cross-section A-Cross-sections B, C and D of a smaller diameter
Chapter 5. Static Failure Chapter 5. Static Failure TheoriesTheories
Chapter 5 is divided in three main sections:Chapter 5 is divided in three main sections: Failure of ductile materials under static loadingFailure of ductile materials under static loading
The main failure mode is permanent yield under static The main failure mode is permanent yield under static loading loading yield strength of the material is exceeded yield strength of the material is exceeded
Critical material property is yield strengthCritical material property is yield strength Failure of brittle materials under static loadingFailure of brittle materials under static loading
Instead on yielding brittle materials fractureInstead on yielding brittle materials fracture Fully hardened steels, cast iron, materials in low Fully hardened steels, cast iron, materials in low
temperatures can behave like brittle materialstemperatures can behave like brittle materials Critical material property is toughness at certain Critical material property is toughness at certain
temperaturetemperature Fracture mechanicsFracture mechanics
This theory presumes the presence of a crack, which This theory presumes the presence of a crack, which starts to grow under the specific loading and finally starts to grow under the specific loading and finally leas to either ductile or brittle failureleas to either ductile or brittle failure
Toughness
Temperature
Brittlebehaviour
Ductilebehaviour
Transitionzone
Modes of crack displacementMode I = load tends to pull the crack open in tensionMode II = shear crack in-planeMode III = shear the crack out-of-plane
Loading
Chapter 6. Fatigue Failure Chapter 6. Fatigue Failure TheoriesTheories
The use of typical Wöhler’s strength-life- The use of typical Wöhler’s strength-life- diagrams is presenteddiagrams is presented
The main principles of the use of Paris-The main principles of the use of Paris-Equation are presentedEquation are presented
The use of Goodman’s diagram for fatigue The use of Goodman’s diagram for fatigue life analysis is presentedlife analysis is presented
Schematic fatigue-fracture surfaces of a Schematic fatigue-fracture surfaces of a shaft cross-sections are presented to shaft cross-sections are presented to support further failure mode analysis support further failure mode analysis
Wöhler’s diagramWöhler’s diagram
Schematic fatigue-Schematic fatigue-fracture surfacesfracture surfaces
Rotating bendingRotating bending Low nominal stressLow nominal stress Mild stress concentrationMild stress concentration
Paris-equationParis-equation
The crack growth “speed” is presented as a The crack growth “speed” is presented as a function of loading cycles:function of loading cycles:
WhereWhere a a = crack width= crack width N N = number of cycles= number of cycles A, n A, n = material coefficients= material coefficients ΔΔKK = stress intensity factor range = stress intensity factor range
DAMAGING
SPEED
Stress intensity
Region ICrack initiation stage
Region IICrack propagation
Region IIIUnstable fracture
Nocrackgrowth
Chapter 7. Surface FailureChapter 7. Surface Failure
This chapter contains the following topicsThis chapter contains the following topics Mathematical theory of surface contactsMathematical theory of surface contacts
Characteristics to describe the value of surface roughnessCharacteristics to describe the value of surface roughness Spherical contactSpherical contact Cylindrical contactCylindrical contact Dynamic contact stressesDynamic contact stresses Designing rules to avoid surface failureDesigning rules to avoid surface failure
Wear phenomena (discussed earlier during this course)Wear phenomena (discussed earlier during this course) Abrasive wearAbrasive wear Adhesive wearAdhesive wear Fatigue wear Fatigue wear Tribochemical wear or corrosive wear Tribochemical wear or corrosive wear
Mathematical definition of RMathematical definition of Raa:n:n
l
dx)x(ylaR01
Designing rules to avoid surface failureDesigning rules to avoid surface failure
11 Remember the rules which were presented during the Remember the rules which were presented during the special lesson dealing with wear phenomenaspecial lesson dealing with wear phenomena
2 2 Choose proper materialsChoose proper materials HardnessHardness Surface roughnessSurface roughness Use of coatingsUse of coatings
3 3 Choose proper lubricantsChoose proper lubricants Take care of EHD- or HD- lubrication (avoid boundary Take care of EHD- or HD- lubrication (avoid boundary
lubrication)lubrication) Use EP-lubricants if needed(extreme pressure)Use EP-lubricants if needed(extreme pressure)
44 Take care of cleanliness Take care of cleanliness Use proper sealing constructionsUse proper sealing constructions Select proper material pairs (e.g. hardness pairs)Select proper material pairs (e.g. hardness pairs)
55 Avoid and minimize stress concentrations Avoid and minimize stress concentrations Select proper stiffness and/or geometrySelect proper stiffness and/or geometry
6 6 Avoid fretting problems by taking care of possible vibrationAvoid fretting problems by taking care of possible vibration phenomena (near joints or fits)phenomena (near joints or fits)
Case example:Case example: How to minimize How to minimize the stress the stress concentrations concentrations in a cylindrical in a cylindrical roller bearing by roller bearing by using a proper using a proper geometry of the geometry of the roller elements.roller elements.
Case example: Case example: Fretting wear Fretting wear on a shaft on a shaft beneath a beneath a press-fit hub.press-fit hub.
PART 2.PART 2. Machine Design Machine Design
Chapter 8. Design Case StudiesChapter 8. Design Case Studies
This brief chapter is written just to form “a This brief chapter is written just to form “a bridge” between the theories of material bridge” between the theories of material science, strength of materials, failure science, strength of materials, failure theories (presented in part 1) and practical theories (presented in part 1) and practical dimensioning and analysing instructions of dimensioning and analysing instructions of some typical machine elements (to be some typical machine elements (to be presented in part 2).presented in part 2).
The iterative nature of designing process The iterative nature of designing process is emphasized.is emphasized.
Chapter 9. Shafts, Keys and Chapter 9. Shafts, Keys and CouplingsCouplings
Designing of shafts step-by-step (iterative analysis):Designing of shafts step-by-step (iterative analysis): 1 Determine the affecting loading cases1 Determine the affecting loading cases
E.g. gear forces, torque, forces due to belt drives etc.E.g. gear forces, torque, forces due to belt drives etc. 2 Collect contacting dimensions from the construction and select 2 Collect contacting dimensions from the construction and select
possble shaft materialspossble shaft materials E.g. shaft-hub joints, diameters of bearing seats, width of gears etc.E.g. shaft-hub joints, diameters of bearing seats, width of gears etc.
3 Produce the free-body diagram and calculate the teaction forces3 Produce the free-body diagram and calculate the teaction forces 4 Draw loading (force), shear and moment diagrams4 Draw loading (force), shear and moment diagrams 5 Find the critical cross-sections of the shaft5 Find the critical cross-sections of the shaft
E.g. key seats, changes of the diameters, grooves, threads etc.E.g. key seats, changes of the diameters, grooves, threads etc. 6 Calculate the affecting stresses and deflections6 Calculate the affecting stresses and deflections
E.g. tensile stress, bending stress, shear stress,E.g. tensile stress, bending stress, shear stress, 7 Calculate the critical rotating speed due to vibration and 7 Calculate the critical rotating speed due to vibration and
resonanceresonance 8 Calculate safety factors8 Calculate safety factors
Constant and time-varying loadingConstant and time-varying loading
The dimensioning procedure of The dimensioning procedure of shafts is based on ASME-method:shafts is based on ASME-method: Soderberg’s hypothesis Soderberg’s hypothesis
(in Finland several hypothesis are used and (in Finland several hypothesis are used and usually compared in university text books)usually compared in university text books)
Goodman’s line Goodman’s line (in Finland the use of Smith’s diagram is (in Finland the use of Smith’s diagram is
more common)more common)
Some rules of thumbsSome rules of thumbs
Estimation of shaft diameter:Estimation of shaft diameter:
d d = required shaft diameter= required shaft diameter TTmaxmax = affecting torque= affecting torque TTsallsall = allowed shear stress of the = allowed shear stress of the
materialmaterial
Critical angular velocity:Critical angular velocity: Bending vibrationBending vibration
nncrcr = critical angular velocity= critical angular velocity δδmaxmax = maximum deflection of the shaft= maximum deflection of the shaft
Critical angular velocity:Critical angular velocity: Torsinal vibrationTorsinal vibration
ffcrcr = critical angular velocity= critical angular velocity kkvv = torsional stiffness coefficient= torsional stiffness coefficient JJ11 = moment of inertia (input)= moment of inertia (input) JJ22 = moment of inertia (output)= moment of inertia (output) dd = diameter of the shaft= diameter of the shaft GG = modulus of rigidity= modulus of rigidity LL = length of the shaft= length of the shaft mm = weight of (each) component= weight of (each) component rr = rotating radius of (each) component= rotating radius of (each) component
Loading cases of shaft-hub-jointsLoading cases of shaft-hub-joints
Torque
FrFt
Fa
Moment
Torque
If the joint is able to withstand also axial loading, its torque If the joint is able to withstand also axial loading, its torque transmission capacity can be estimated according to the following transmission capacity can be estimated according to the following equation:equation:
WhereWhere TTtheortheor = = theoretical maximum allowed torque which joint theoretical maximum allowed torque which joint
could transmit without any axial loadingcould transmit without any axial loading TT = = torque, which can be transmitted even though Fa torque, which can be transmitted even though Fa
is affecting simultaneously (usually the value is affecting simultaneously (usually the value which is calculated)which is calculated)
FFatheoratheor = = theroretical maximum allowed axial force, which theroretical maximum allowed axial force, which joint could transmit without any torque joint could transmit without any torque
loadingloading FFaa = = axial load, which is decreasing the torque axial load, which is decreasing the torque
transmission capacity (“the disturbing factor”)transmission capacity (“the disturbing factor”)
Dimensioning of parallel keys is based on Dimensioning of parallel keys is based on SFS-standards (we skip the presentation SFS-standards (we skip the presentation presented by Norton):presented by Norton):
Main designing steps are as follows:Main designing steps are as follows: Check the maximum surface stress of the hubCheck the maximum surface stress of the hub Check the maximum surface stress of the keyCheck the maximum surface stress of the key Check the maximum shear stress of the keyCheck the maximum shear stress of the key Ensure that the required torque transmission Ensure that the required torque transmission
capapacity is achievedcapapacity is achieved
Chapter 10. Bearings and Chapter 10. Bearings and LubricationLubrication
This chapter includes the following This chapter includes the following important topics:important topics: Lubricants and types of lubricationLubricants and types of lubrication Briefly about sliding bearings and their Briefly about sliding bearings and their
material combinationsmaterial combinations Rolling-element bearingsRolling-element bearings Failure of rolling-element bearingsFailure of rolling-element bearings Selection of rolling bearingsSelection of rolling bearings
Types of lubricationTypes of lubrication
Hydrodynamic lubrication (HD or HL)Hydrodynamic lubrication (HD or HL) HD refers to the supply of oil to the sliding interface to allow the HD refers to the supply of oil to the sliding interface to allow the
relative velocity of the mating surfaces to pump oil within the relative velocity of the mating surfaces to pump oil within the gap and separate the surfaces on the dynamic film of liquid.gap and separate the surfaces on the dynamic film of liquid.
Elastohydrodynamic lubrication (EHD or EHL)Elastohydrodynamic lubrication (EHD or EHL) When the contacting surfaces are nonconforming, as with gears When the contacting surfaces are nonconforming, as with gears
or cam mechanisms, it is difficult to form a full film of oil.The or cam mechanisms, it is difficult to form a full film of oil.The affecting load creates a contact area from the elastic deflections affecting load creates a contact area from the elastic deflections of the surfaces. This area can be large and flat enough to of the surfaces. This area can be large and flat enough to provide full hydrodynamic film if the relative sliding velocity is provide full hydrodynamic film if the relative sliding velocity is high enough. This is possible, because the high pressure high enough. This is possible, because the high pressure between the surfaces increase the viscosity of the fluid.between the surfaces increase the viscosity of the fluid.
Boundary Lubrication (BL)Boundary Lubrication (BL) Either the insufficient geometry, too high load level, low velocity Either the insufficient geometry, too high load level, low velocity
or insufficient oil quantity may prevent hydrodynamic lubrication or insufficient oil quantity may prevent hydrodynamic lubrication and cause metallic contacts between the surfaces (e.g. at the and cause metallic contacts between the surfaces (e.g. at the beginning or end of the rolling)beginning or end of the rolling)
Selection of rolling bearingsSelection of rolling bearings Allowed Allowed
dynamic dynamic loadload
Allowed Allowed maximum maximum angular angular velocityvelocity
Allowed Allowed frictionfriction
Allowed Allowed static loadstatic load
Required Required stiffness stiffness and and accuracyaccuracy
Required Required reliabilityreliability
Facilities of the Facilities of the selected bearing typeselected bearing type
Ability to withstand Ability to withstand axial loadsaxial loads
Ability to withstand Ability to withstand axial bending axial bending moments or angular moments or angular assembly errorsassembly errors
Some examplesSome examples
A detailed guide to select an appropriate A detailed guide to select an appropriate bearing type will be given out as a hand-out…bearing type will be given out as a hand-out…
Tapered roller bearings-Especially for cases in which good axial load standing capacity is required
Spherical roller bearings-Especially for cases in which bending moment could cause additional loading on the bearing or where possible assembly errors may cause some misaligning of the shaft
Basic equations of bearing designBasic equations of bearing design P = P = combined dynamic equivalent load of the bearingcombined dynamic equivalent load of the bearing
FFrr = applied radial load = applied radial load FFa a = applied axial load = applied axial load X = a radial factorX = a radial factor Y = an axial factorY = an axial factor
p = p = exponent, the value depends on the exponent, the value depends on the bearing typebearing type
Ball bearings p=3Ball bearings p=3 Roller bearings p= 10/3Roller bearings p= 10/3
LL10h10h = = Nominal life-time (e.g. 20 000 h)Nominal life-time (e.g. 20 000 h) CC == Dynamic load ratingDynamic load rating
Chapter 11. Spur GearsChapter 11. Spur Gears
Spur gears are used to present principles of gear Spur gears are used to present principles of gear dimensioning in generaldimensioning in general Specialized terminology is presented in detailsSpecialized terminology is presented in details Gear tooth theory is discussedGear tooth theory is discussed Equations for dimensioning gears are presentedEquations for dimensioning gears are presented Also gear manufacturing processes are presented brieflyAlso gear manufacturing processes are presented briefly
Different casting processesDifferent casting processes MachiningMachining Powder metallurgical processes (sintering)Powder metallurgical processes (sintering) Extruding and cold drawing processesExtruding and cold drawing processes Different finishing processesDifferent finishing processes
The presentation is based on standards published The presentation is based on standards published by the American Gear Manufacturers Association by the American Gear Manufacturers Association (AGMA)(AGMA)
T1
T2
Fa
Fa
Fr
Fr
Ft
Ft
At first the applying forces on gear teethmust be established!
Functions:Functions: To transimitTo transimit
TorqueTorque Angular Angular
velocityvelocity
Main Main dimensioning dimensioning criteria:criteria: Bending Bending
stresses of stresses of the teeththe teeth
Surface Surface stresses of stresses of the teeththe teeth
Main Main characteristiccharacteristics:s: Gear ratio Gear ratio
i=Zi=Z11/Z/Z22 Module Module
m=dm=d11/Z/Z11 Contact Contact
ratioratio
Equations are Equations are based on based on experimental experimental factors, factors, parameters and parameters and characteristics characteristics describing e.g.:describing e.g.:
Geometric Geometric accuracy of accuracy of gearsgears
Lubrication Lubrication conditionsconditions
Material Material properties of properties of gears gears
Stress Stress concentration concentration phenomenaphenomena
Surface Surface properties of properties of gearsgears
Loading Loading conditions of conditions of gearsgears
Basic equations for spur gear designBasic equations for spur gear design
Power transmission capacity according to allowed Power transmission capacity according to allowed bending stresses of the teethbending stresses of the teeth
Power transmission capacity according to allowed Power transmission capacity according to allowed surface stresses of the teethsurface stresses of the teeth
Chapter 12. Helical,Bevel and Worm Chapter 12. Helical,Bevel and Worm GearsGears
Helical gearsHelical gears Teeth are angled with respect to the axis Teeth are angled with respect to the axis
of rotationof rotation Contact surface between teeth is increasedContact surface between teeth is increased Axial load component is causedAxial load component is caused
Bevel gearsBevel gears Shafts are located usually at 90 degrees Shafts are located usually at 90 degrees
angleangle Worm gearsWorm gears
Shafts are located at crossing position and Shafts are located at crossing position and high gear ratios are achievedhigh gear ratios are achieved
The dimensioning of helical gears is based on The dimensioning of helical gears is based on the equations of spur gears, so-called virtual the equations of spur gears, so-called virtual number of teeth should be established and number of teeth should be established and then the theory of spur gears is appliedthen the theory of spur gears is applied
For bevel gears either the theories of For bevel gears either the theories of dimensioning of spur or helical gears can be dimensioning of spur or helical gears can be applied:applied: Straight bevel gears Straight bevel gears spur gears spur gears Spiral bevel gears Spiral bevel gears helical gears helical gears
Two main additional aspects of tooth geometry should be Two main additional aspects of tooth geometry should be consideredconsidered Use of single- or double-enveloping tooth formsUse of single- or double-enveloping tooth forms Number of teeth in contact with worm and worm wheelNumber of teeth in contact with worm and worm wheel
Worm gears are discussed very briefly, however the main Worm gears are discussed very briefly, however the main dimensioning aspects consist of four main steps:dimensioning aspects consist of four main steps: Durability against pitting (surface fatigue)Durability against pitting (surface fatigue) Durability against wear (abrasive wear due to different Durability against wear (abrasive wear due to different
material properties of the worm and the worm wheel)material properties of the worm and the worm wheel) Durability against overheatDurability against overheat Allowable bending deflection of the worm (shaft) Allowable bending deflection of the worm (shaft)
Example of dimensioning equations of worm gear Example of dimensioning equations of worm gear designdesign
Safety factor Safety factor SSWW against wear against wear
WlimWlim = kulumislujuus= kulumislujuus
WWPP = kulumisparikerroin (mm. kovuus)= kulumisparikerroin (mm. kovuus)
WWRR = pinnankarheuskerroin= pinnankarheuskerroin
WWvv = liukunopeuskerroin= liukunopeuskerroin
ZZEE = materiaalikerroin (E= materiaalikerroin (E1 1 ja Eja E22))
ZZ = kosketuskerroin (kierremuoto)= kosketuskerroin (kierremuoto)
Materials wear strength
Coefficient depending on materials hardness
Coefficient depending on surface roughnesses
Coefficient depending on the sliding velocity
Coefficient depending on modulus of elasticity
Coefficient depending on the tooth geometry
Chapter 13. Spring DesignChapter 13. Spring Design Main contents of this chapter:Main contents of this chapter:
Definition of the spring rate is presentedDefinition of the spring rate is presented Various spring configurations and Various spring configurations and
materials are presented brieflymaterials are presented briefly Dimensioning and designing criteria is Dimensioning and designing criteria is
presented for the following spring presented for the following spring configurations:configurations:
Helical compression springs Helical compression springs Helical extension springsHelical extension springs Helical torsion springsHelical torsion springs Belleville spring washersBelleville spring washers
Example: Designing steps of helical Example: Designing steps of helical compression springscompression springs
1 Decide spring configuration1 Decide spring configuration 1.1 Length1.1 Length 1.2 End details and number of active coils1.2 End details and number of active coils 1.3 Tentative material selection 1.3 Tentative material selection
2 Establish functional properties2 Establish functional properties 2.1 Sprind index C = D/d (coil diameter/wire diameter)2.1 Sprind index C = D/d (coil diameter/wire diameter) 2.2 Spring deflection y2.2 Spring deflection y 2.3 Spring rate k = F/y2.3 Spring rate k = F/y
3 Loading cases and stress analysis3 Loading cases and stress analysis 3.1 Shear stress3.1 Shear stress 3.2 Torsional shear stress3.2 Torsional shear stress 3.3 Stress concentrations 3.3 Stress concentrations 3.4 Residual stresses due to manufacturing stages (e.g coiling into the 3.4 Residual stresses due to manufacturing stages (e.g coiling into the
form of helix causes tensile stress)form of helix causes tensile stress) 3.5 Buckling 3.5 Buckling 3.6 Vibration and resonance phenomena3.6 Vibration and resonance phenomena 3.7 Fatigue analysis3.7 Fatigue analysis 3.8 Final material selection3.8 Final material selection
Chapter 14. Screws and Chapter 14. Screws and FastenersFasteners
This chapter deals with the following This chapter deals with the following topics:topics: Standardized thread dimensionsStandardized thread dimensions Power screwsPower screws Screw fastenersScrew fasteners Stresses in threadsStresses in threads
Tensile, torsion and shearTensile, torsion and shear Joint stiffnessJoint stiffness Preloaded fastenersPreloaded fasteners
A bolted assemblyA bolted assembly
A bolted assemblyA bolted assembly
The clamped construction may include two or more pieces and The clamped construction may include two or more pieces and they may be of different material. they may be of different material.
Also a long bolt usually has threads over only a portion of its Also a long bolt usually has threads over only a portion of its length having at least two different cross-sectional areas.length having at least two different cross-sectional areas.
These different stiffness-sections act as springs in series and their These different stiffness-sections act as springs in series and their function can be described according to the following equation:function can be described according to the following equation:
When we know the dimensions and geometry of the bolt and When we know the dimensions and geometry of the bolt and pieces to be joined it is possible to calculate the partial spring pieces to be joined it is possible to calculate the partial spring rates and combine them according to this simple equation.rates and combine them according to this simple equation.
Analogical with spring analysis we can now write the relationship Analogical with spring analysis we can now write the relationship between the total spring rate, deflection and applying force.between the total spring rate, deflection and applying force.
Other dimensioning aspects of bolted jointsOther dimensioning aspects of bolted joints 11 Washers Washers
Decrease the surface stresses at the jointDecrease the surface stresses at the joint Ensure the tightness of the jointEnsure the tightness of the joint Prevents the possible bending moment of the bolt due to Prevents the possible bending moment of the bolt due to
slant surfaceslant surface 22 Bolt’s straight length without threads Bolt’s straight length without threads
The stress concentration at the end of the straight The stress concentration at the end of the straight length before the first thread could be criticallength before the first thread could be critical
The straight length is planed to function “as a spring”The straight length is planed to function “as a spring” 33 Parts to be clamped together Parts to be clamped together
In many cases the friction coefficient between In many cases the friction coefficient between the parts to be clamped together is in key-rolethe parts to be clamped together is in key-role
There should be enough distance between the mounting There should be enough distance between the mounting holes of the screws and edges of the parts to be holes of the screws and edges of the parts to be clamped to avoid fractures of the base materialclamped to avoid fractures of the base material
Possible failure modes of bolted jointsPossible failure modes of bolted joints 11 The bolt breaks under the static tensile The bolt breaks under the static tensile
loading loading Tensile stress exceeds the ultimate tensile Tensile stress exceeds the ultimate tensile
strength of the boltstrength of the bolt The first thread of the bolt is cut offThe first thread of the bolt is cut off The first thread of the nut is cut offThe first thread of the nut is cut off
22 The fatigue strength of the bolt is exceeded The fatigue strength of the bolt is exceeded Typically the fatigue limit is only 10% of screw Typically the fatigue limit is only 10% of screw
material’s yield strengthmaterial’s yield strength 33 The failures of the parts to be clamped The failures of the parts to be clamped
The shear stress is too large near the edges The shear stress is too large near the edges
Means to improve the fatigue strength of the Means to improve the fatigue strength of the bolted joint:bolted joint: Select a taller nut (to increase the number of Select a taller nut (to increase the number of
load standing threads)load standing threads) Select more suitable material pair for the nut and Select more suitable material pair for the nut and
the bolt combination (lower coefficient of the bolt combination (lower coefficient of elasticity for the nut compared to that of the elasticity for the nut compared to that of the screw’s e.g. aluminium or cast iron for nuts with screw’s e.g. aluminium or cast iron for nuts with and steel for bolts)and steel for bolts)
Use sufficient pre-loading of the bolts (equalize Use sufficient pre-loading of the bolts (equalize the stresses applying at each thread of the bolt the stresses applying at each thread of the bolt and nut)and nut)
Improve the surface quality of the bolt, Improve the surface quality of the bolt, Select the bolt (and thread) geometry with the Select the bolt (and thread) geometry with the
smallest stress concentration coefficientsmallest stress concentration coefficient Select the advantageous manufacturing Select the advantageous manufacturing
technology of the bolts (usually cold forming is technology of the bolts (usually cold forming is recommended)recommended)
Chapter 15. Clutches and BrakesChapter 15. Clutches and Brakes
This chapter forms only a brief overall picture of various This chapter forms only a brief overall picture of various types of clutches and brakes to give the reader a sight of types of clutches and brakes to give the reader a sight of possible constructions.possible constructions.
Classification according to the actuation Classification according to the actuation (impulse to start the function)(impulse to start the function) Electrical (press the button)Electrical (press the button) Mechanical (push the bedal)Mechanical (push the bedal) Pneumatic or hydraulicPneumatic or hydraulic AutomaticAutomatic
Classification according to the function Classification according to the function (what phenomenon the contact is based on)(what phenomenon the contact is based on)
Friction between (two) surfacesFriction between (two) surfaces Locked geometry (e.g. toothed components)Locked geometry (e.g. toothed components) MagneticMagnetic Fluid couplingFluid coupling
Load determination and different load cases
• utilization of free-body diagrams• static or dynamic loading• vibration loading - bending vibration - torsional vibration• impact loading• tension, compression, bending shear or torsion• reversed or pulsating loading
Failure theories
• Static failure theories - ductile materials - brittle materials• Fracture mechanics theory• Fatigue failure theories - Wöhler - Paris –Eguation - Soderberg - Goodman• Surface failure theories - wear - surface contact theories
Stress, strain and deflection
• allowed stress and deflection• due to affecting load cased • combined stresses• stress concentrations
Material properties
• metallic materials - steels - aluminium - cast iron• polymers• ceramics• composites• nanomaterials
SUMMARY : STRESS AND DEFLECTION ANALYSIS
Pulsating loadingPulsating loading Reverced loadingReverced loading
Exercise 2 Exercise 2 Exercise 2AExercise 2A
Present typical applications of power transmission or guiding shafts under Present typical applications of power transmission or guiding shafts under different loading cases. Explain the reasons for the affecting combined loading. different loading cases. Explain the reasons for the affecting combined loading. Use illustrative figures. Present at least the following loading cases: Use illustrative figures. Present at least the following loading cases:
Tension or compression + bending Tension or compression + bending Tension or compression + bending + torsionTension or compression + bending + torsion Bending + torsionBending + torsion Shear + any other loading caseShear + any other loading case Reversed loadingReversed loading Pulsating loadingPulsating loading
Exercise 2BExercise 2B Compare different fatigue failure theories and approaches by presenting typical Compare different fatigue failure theories and approaches by presenting typical
applications of different types of mechanical components or constructions. applications of different types of mechanical components or constructions. Compare at least the following approaches:Compare at least the following approaches:
Wöhler’s strength-life-theoryWöhler’s strength-life-theory Goodman’s theoryGoodman’s theory Paris-equationParis-equation Utilization of schematic fatigue-fracture surfaces Utilization of schematic fatigue-fracture surfaces Fracture mechanicsFracture mechanics