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