BK50A2200 Design Methodologies and Applications of Machine Element Design

1. BK50A2200 Design Methodologies and Applications of Machine Element Design Lecture 2 Introduction to the textbook: “Norton: Machine Design” D.Sc Harri Eskelinen

2. Goals of this lecture • Support the contents of the previous lectures dealing with machine design approaches, reliability design and wear phenomena • To get familiar with the main designing and dimensioning criteria of the most important machine elements (according to Norton) • Main consecutive designing steps and aspects • Fundamental dimensioning equations

3. Briefly about the book • The textbook presents an integrated approach to the machine elements by combining the usual set of machine element topics with a series of case studies that illustrate the relationships between force, stress and failure analysis in real-world design. • The book emphasizes the design and synthesis aspects of machine elements but it forms also a good balance between synthesis and analysis.

4. The first part of the book presents the fundamentals of design, materials, stress, strain, deflection, failure and fracture theories. • The second part treats of the aspects of machine element design, such as designing springs, shafts, gears, bearings etc.

5. PART 1. FUNDAMENTALS

6. Chapter 1. Introduction to Design • This chapter partially supports the ideas of systematic design approach (see the yellow items below) : according to Norton the design process consists of the following ten stages: • 1 Identification of need • 2 Background research • 3 Goal statement • 4 Task specifications • 5 Synthesis • 6 Analysis • 7 Selection • 8 Detailed design • 9 Prototyping and testing • 10 Production

7. Chapter 2. Materials and Processes • The contents of this chapter will be discussed in details during the university course “Introduction to Material Technology” • Basic definitions of the most common material properties are presented briefly: • Modulus of elasticity • Yield strength • Ultimate tensile strength • Modulus of rigidity • Fatigue strength • Toughness • Hardness • Most typical hardening and surface coating processes are presented briefly • Basic information about some material groups is given: • Steels • Cast iron • Aluminium • Titanium • Copper Alloys • Polymers • Ceramics • Composites

8. Chapter 3. Load Determination • The content of this chapter produce the fundamentals for the further stress, strain and deflection analysis presented in chapter 4. • Main topics are: • Different loading cases • Free-body diagrams • Static loading • Dynamic loading • Vibration loading • Impact loading • Beam loading

9. Classification of loading cases

10. Pulsating loading Reverced loading Identification of different loading cases • Identification of different loading cases in necessary to make it possible to use proper material properties as criteria during the material selection process • Tension or compression  tensile or compressive stress • Bending  bending stress • Shear  shear stress • Torsion  torsion stress (shear strass) • Reverced loading  endurance limit (for reverced stress) • Pulsating loading  endurance limit (for pulsating stress)

11. Free-Body Diagrams • Case example: Wire connector crimping tool

12. Chapter 4. Stress, Strain and Deflection • This chapter includes the basic theories of “strength of materials”, the following topics are discussed (the most important items are high-lighted with yellow): • Principal stresses • Axial Tension • Bending stresses of beams • Deflection of beams • Torsion • Combined stresses • Stress concentration • Axial compression • Stresses in cylinders

13. T1 Fa Ft Fr A B C D • Critical cross-sections due to • stress concentrations: • End of the keyseat at cross-section A • Cross-sections B, C and D of a smaller diameter • Combined loading: • Axial force • Radial force • Tangential force • Torque •  combined stresses

14. Chapter 5. Static Failure Theories • Chapter 5 is divided in three main sections: • Failure of ductile materials under static loading • The main failure mode is permanent yield under static loading  yield strength of the material is exceeded • Critical material property is yield strength • Failure of brittle materials under static loading • Instead on yielding brittle materials fracture • Fully hardened steels, cast iron, materials in low temperatures can behave like brittle materials • Critical material property is toughness at certain temperature • Fracture mechanics • This theory presumes the presence of a crack, which starts to grow under the specific loading and finally leas to either ductile or brittle failure

15. Toughness Transition zone Ductile behaviour Brittle behaviour Temperature

16. Loading Modes of crack displacement Mode I = load tends to pull the crack open in tension Mode II = shear crack in-plane Mode III = shear the crack out-of-plane

17. Chapter 6. Fatigue Failure Theories • The use of typical Wöhler’s strength-life- diagrams is presented • The main principles of the use of Paris-Equation are presented • The use of Goodman’s diagram for fatigue life analysis is presented • Schematic fatigue-fracture surfaces of a shaft cross-sections are presented to support further failure mode analysis

18. Wöhler’s diagram

19. Schematic fatigue-fracture surfaces • Rotating bending • Low nominal stress • Mild stress concentration

20. Paris-equation • The crack growth “speed” is presented as a function of loading cycles: • Where • a = crack width • N = number of cycles • A, n = material coefficients • ΔK = stress intensity factor range

21. D A M A G I N G S P E E D Region I Crack initiation stage Region II Crack propagation Region III Unstable fracture No crack growth Stress intensity

22. Chapter 7. Surface Failure • This chapter contains the following topics • Mathematical theory of surface contacts • Characteristics to describe the value of surface roughness • Spherical contact • Cylindrical contact • Dynamic contact stresses • Designing rules to avoid surface failure • Wear phenomena (discussed earlier during this course) • Abrasive wear • Adhesive wear • Fatigue wear • Tribochemical wear or corrosive wear

24. Mathematical definition of Ra:n

25. Designing rules to avoid surface failure • 1 Remember the rules which were presented during the special lesson dealing with wear phenomena • 2 Choose proper materials • Hardness • Surface roughness • Use of coatings • 3 Choose proper lubricants • Take care of EHD- or HD- lubrication (avoid boundary lubrication) • Use EP-lubricants if needed(extreme pressure) • 4 Take care of cleanliness • Use proper sealing constructions • Select proper material pairs (e.g. hardness pairs) • 5 Avoid and minimize stress concentrations • Select proper stiffness and/or geometry • 6 Avoid fretting problems by taking care of possible vibration phenomena (near joints or fits)

26. Case example: How to minimize the stress concentrations in a cylindrical roller bearing by using a proper geometry of the roller elements.

27. Case example: Fretting wear on a shaft beneath a press-fit hub.

28. PART 2. Machine Design

29. Chapter 8. Design Case Studies • This brief chapter is written just to form “a bridge” between the theories of material science, strength of materials, failure theories (presented in part 1) and practical dimensioning and analysing instructions of some typical machine elements (to be presented in part 2). • The iterative nature of designing process is emphasized.

30. Chapter 9. Shafts, Keys and Couplings • Designing of shafts step-by-step (iterative analysis): • 1 Determine the affecting loading cases • E.g. gear forces, torque, forces due to belt drives etc. • 2 Collect contacting dimensions from the construction and select possble shaft materials • E.g. shaft-hub joints, diameters of bearing seats, width of gears etc. • 3 Produce the free-body diagram and calculate the teaction forces • 4 Draw loading (force), shear and moment diagrams • 5 Find the critical cross-sections of the shaft • E.g. key seats, changes of the diameters, grooves, threads etc. • 6 Calculate the affecting stresses and deflections • E.g. tensile stress, bending stress, shear stress, • 7 Calculate the critical rotating speed due to vibration and resonance • 8 Calculate safety factors • Constant and time-varying loading

31. The dimensioning procedure of shafts is based on ASME-method: • Soderberg’s hypothesis • (in Finland several hypothesis are used and usually compared in university text books) • Goodman’s line • (in Finland the use of Smith’s diagram is more common)

32. Some rules of thumbs • Estimation of shaft diameter: • d = required shaft diameter • Tmax = affecting torque • Tsall = allowed shear stress of the material

33. Critical angular velocity: • Bending vibration • ncr = critical angular velocity • δmax = maximum deflection of the shaft

34. Critical angular velocity: • Torsinal vibration • fcr = critical angular velocity • kv = torsional stiffness coefficient • J1 = moment of inertia (input) • J2 = moment of inertia (output) • d = diameter of the shaft • G = modulus of rigidity • L = length of the shaft • m = weight of (each) component • r = rotating radius of (each) component

35. Fa Torque Torque Moment Ft Fr Loading cases of shaft-hub-joints

36. If the joint is able to withstand also axial loading, its torque transmission capacity can be estimated according to the following equation: • Where • Ttheor = theoretical maximum allowed torque which joint could transmit without any axial loading • T = torque, which can be transmitted even though Fa is affecting simultaneously (usually the value which is calculated) • Fatheor = theroretical maximum allowed axial force, which joint could transmit without any torque loading • Fa = axial load, which is decreasing the torque transmission capacity (“the disturbing factor”)

37. Dimensioning of parallel keys is based on SFS-standards (we skip the presentation presented by Norton): • Main designing steps are as follows: • Check the maximum surface stress of the hub • Check the maximum surface stress of the key • Check the maximum shear stress of the key • Ensure that the required torque transmission capapacity is achieved

38. Chapter 10. Bearings and Lubrication • This chapter includes the following important topics: • Lubricants and types of lubrication • Briefly about sliding bearings and their material combinations • Rolling-element bearings • Failure of rolling-element bearings • Selection of rolling bearings

39. Types of lubrication • Hydrodynamic lubrication (HD or HL) • 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 gap and separate the surfaces on the dynamic film of liquid. • Elastohydrodynamic lubrication (EHD or EHL) • When the contacting surfaces are nonconforming, as with gears or cam mechanisms, it is difficult to form a full film of oil.The affecting load creates a contact area from the elastic deflections of the surfaces. This area can be large and flat enough to provide full hydrodynamic film if the relative sliding velocity is high enough. This is possible, because the high pressure between the surfaces increase the viscosity of the fluid. • Boundary Lubrication (BL) • Either the insufficient geometry, too high load level, low velocity or insufficient oil quantity may prevent hydrodynamic lubrication and cause metallic contacts between the surfaces (e.g. at the beginning or end of the rolling)

41. Allowed dynamic load • Allowed maximum angular velocity • Facilities of the selected bearing type • Ability to withstand axial loads • Ability to withstand axial bending moments or angular assembly errors • Allowed friction • Allowed static load • Required stiffness and accuracy • Required reliability Selection of rolling bearings

42. 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 • Tapered roller bearings • Especially for cases in • which good axial load • standing capacity is • required Some examples • A detailed guide to select an appropriate bearing type will be given out as a hand-out…

43. Basic equations of bearing design • P = combined dynamic equivalent load of the bearing • Fr = applied radial load • Fa = applied axial load • X = a radial factor • Y = an axial factor • p = exponent, the value depends on the bearing type • Ball bearings p=3 • Roller bearings p= 10/3 • L10h = Nominal life-time (e.g. 20 000 h) • C = Dynamic load rating

44. Chapter 11. Spur Gears • Spur gears are used to present principles of gear dimensioning in general • Specialized terminology is presented in details • Gear tooth theory is discussed • Equations for dimensioning gears are presented • Also gear manufacturing processes are presented briefly • Different casting processes • Machining • Powder metallurgical processes (sintering) • Extruding and cold drawing processes • Different finishing processes • The presentation is based on standards published by the American Gear Manufacturers Association (AGMA)

45. T1 Fa Ft Fr Fr Fa T2 Ft At first the applying forces on gear teeth must be established!

46. Equations are based on experimental factors, parameters and characteristics describing e.g.: • Geometric accuracy of gears • Lubrication conditions • Material properties of gears • Stress concentration phenomena • Surface properties of gears • Loading conditions of gears • Main dimensioning criteria: • Bending stresses of the teeth • Surface stresses of the teeth • Main characteristics: • Gear ratio i=Z1/Z2 • Module m=d1/Z1 • Contact ratio • Functions: • To transimit • Torque • Angular velocity

47. Basic equations for spur gear design • Power transmission capacity according to allowed bending stresses of the teeth • Power transmission capacity according to allowed surface stresses of the teeth

49. Chapter 12. Helical,Bevel and Worm Gears • Helical gears • Teeth are angled with respect to the axis of rotation • Contact surface between teeth is increased • Axial load component is caused • Bevel gears • Shafts are located usually at 90 degrees angle • Worm gears • Shafts are located at crossing position and high gear ratios are achieved

50. The dimensioning of helical gears is based on the equations of spur gears, so-called virtual number of teeth should be established and then the theory of spur gears is applied • For bevel gears either the theories of dimensioning of spur or helical gears can be applied: • Straight bevel gears  spur gears • Spiral bevel gears  helical gears