MEC613 Machine Design I 2021 Winter Semester 1 Instructor: Dr. Shudong Yu Office: EPH321 Phones: x557687 (O); 416 888 0962 (cell) Email: syu@ryerson.ca TAs: TBD 2 Course Briefing Course Outline (available in the course D2L; minor revision) Textbook Shigley’s Mechanical Engineering Design , 11th ed. © 2019, McGraw Hill Richard Budynas and J. Keith Nisbett. regular print can be purchased through Ryerson bookstore. Also available: 180 days unrestricted electronic access at $61.50. Lectures: 4 hrs/wk (Mon 1-3, 4-6; Wed 3-5, 6-8) Tutorials weeks 2-13: 1 hr/wk by GAs Counselling hours: Wed 10-12, Thursdays 2-4, Additional upon request. 6 sets of homework (0%) – for better understanding of course materials and good preparation for the test and exam. Fatigue Hardware Lab and Report (5%0%, demonstration only) Surprise in-class assessment (5 in total, 5% in weight) Design Project (30%, challenges with use of gears!) 2 hr Term Test (20%, week 7, after reading week; outside the regular class) 3 hr Final Exam (45%) This semester, we will focus more on problem solving. 3 Scope A mechanical system (or electrical, electromechanical, structural, etc.) consists of many components joined together rigidly or kinematically at various locations to deliver its intended functions. Deformations and stresses (static, quasi-static, and dynamic) are experienced by all components as a result of direct application of loads (forces/moments) and/or transfer via joints. Loads can include gravity and other effects: inertial, thermal, flow, etc. This course is concerned with design for rigidities (the allowable deformations of components, e.g., a shaft) and design for strengths (allowable stresses, static, quasi-static, and dynamic) 4 Methods Analytical methods and hand calculations for determination of nominal values of stresses by incorporating various modifying factors to account for complicating effects (e.g., local stress concentration due to key/keyway, hole, fillet) without conducting comprehensive tests – experimental or computational (FEM, CFD, FSI). This is important in initial design stage during which frequent modifications are necessary to address various functionalities and constraints. Use of codes and standards like ASTM (general material properties), SAE (fatigue and material props for automotive industry), ASME (piping, machine tools), ABMA (bearings) and AGMA (gears) for design of specific machine components against common failures. Skills/knowledge – math, statics, stress, dynamics, fluid mechanics, heat transfer, FEM, etc. Designer often needs rounds of iterations/modifications to resolve conflict and make compromises (less optimal) before a design is finalized. Use of analytical skills in connection with the industry-specific codes and standards help speed up the completion of each iteration. Examples of Failures and Consequences 5 Florida International University pedestrian bridge collapse (2018) The Nipigon River Bridge (built and commissioned in Nov. 2015, broke in Jan. 2016, due to “mechanical” failure) 6 Fatigue failure of a food processor blade Many other … Design for Static Strength 7 Failure criteria Ductile materials (Yield criteria): Distortion Energy, Maximum Shear Stress, Coulomb-Mohr f (, S ) 0 S Brittle Materials: Maximum Normal Stress,critical effective stress strength Coulomb-Mohr, modified Mohr Design Formula n>1 factor of safety, industrydependent, ASME, SAE codes and standards Find some time to review chapters 1-5 of the textbook. S n Example 1: A poor cleat design 8 Design of cleats to supporting spare tires for a truck. Problem: Cleat fractured; causing the bogie along with the tires to fly out of control. It had caused damages to other vehicles and human lives. The contributed to a series of “flying tire accidents on Ontario highways during 1997-98 as a result of poor mechanical design. One lawsuit case went to a Provincial Court in Kingston. Side View Back Cleat Front Cleat Circular Cross Bar Transferring loads to the Chasse/Frame Spare tire assembly (bogie) Weight Initial design 9 Analysis done by Manufacturing Co. a Design Engineer at XX Truck Assumed that the total load (W/2) was uniformly distributed across the interface line of cleat-beam contact. The Jr.-Eng. determined that the maximum principal stress in the cleat is 50% of the yield strength. His conclusion: safe for steel cleat and shock load (a safety factor of 2). What’s wrong? Front View and Mechanical Model Side View Back Cleat Front Cleat Back Cleat W/2 – total load Circular Cross Bar Transferring loads to the Chasse/Frame Spare tire assembly (bogie) Weight Beam Line of contact before deformation Re-examination 10 FE Analysis by ANSYS Cleat – shell elements Cross bar – beam element Lateral contact elements along the line of contact Findings: the maximum stress in the cleat is 30 ksi! Yield strength for typical steel is about 30 ksi. My conclusion: unsafe for shocking load. Back Cleat deformation is small. Beam W/2 – total load Line of contact after deformation (unknown load distribution) Where majority of load is concentrated. Example 2: Solving Conflicts – CANDU Fuel Element 11 A CANDU 6 fuel bundle (FB) 4 rings of 37 fuel elements welded to two endplates Fuel elements are separated by spacer pads at various axial cross sections for adequate coolant flow in all sub-channels During operations, FB rests on the inside of a pressure tube (PT) through bearing pads Design of fuel element or fuel rod 12 A C6 fuel element a thin and hollow Zircaloy sheath a number of solid UO2 pellets Pellet R 1 Pellet R Np/2 sheath Midplane endcap two end-caps Design A • Perfect for heat transfer • Terrible for containing harmful fission products • Lack of integrity for fuel handling Coolant UO2 Coolant UO2 Thin Zircaloy Design A: no cladding Design B: with cladding Coolant 13 Cont… UO2 Coolant UO2 Thin Zircaloy Design A: no cladding Design B: with cladding Design B Reduced heat transfer rate (gap, Zircaloy thermal conductivity, degradation of irradiated Zircaloy) Secured fission product containment (<0.1% failure rate for CANDU fuel bundles) Increased fuel integrity Increased fuel element stiffness or rigidity Key is to determine the right thickness to balance the conflict between heat transfer engineers and stress engineers while considering manufacturability and cost. Use common engineering sense and set achievable and affordable tolerance Mention the impact on tightening thickness tolerances on collapse pressure and cost. Example 3:Design for rigidity and minimization of contact force – Fuel Bundle CANFLEX Bundle 43 fuel elements; 2 end plates Bearing pads are introduced to the outer elements at three axial locations to reduce contact areas between fuel bundle and the pressure tube for efficient heat transfer. Why three locations? Not two? Benefits and issues with 3 arrays of BPs Benefits and issues with 2 arrays of BPs Decision 14 Example 4 Design for Optimal Support to Minimize Max Bending Stress or Max Lateral Deflection Want to locate the supports so that the maximum deflection is minimized. • Uniform load is q. • Beam flexural rigidity is EI in plane bending) • Ignore shear deformation • Euler-Bernoulli beam theory Quick analysis of Single Span Beam • Symmetry Load q • Two ends? • Midspan? Beam or shaft 15 Design for rigidities - Fuel bundle bending as a background application Case A (ends, ref case) max, A 5qL4 qL4 0.01302 384EI EI Case A: supports are at the two ends. Case B (Mid,) max, B q(0.5L) 4 qL4 0.0078125 8EI EI 60% of max ref deflection Case C (0.32L from either end, optimal locations) max, B Case B: supports are at the midspan. ends. qL4 0.003694 EI 28% of max ref deflection Case C: supports are at optimal locations 16 Design for Natural Frequencies 17 Operating speed 3540 rpm (59 Hz) Design the supporting beam-motor system so that its fundamental frequency is outside the range (<50 Hz or >68Hz) to avoid resonance. AC Motor Supported by a Simply supported Beam Strengths Other constraints (clearance, cost, etc.) Theory (EB?, Timoshenko, Reddy, Etc.) Selection of material, cross section, support, etc.) Different Cross Sections y x Neutral axis Beam 18 Wind induced vibration example Design of Insertion Shape for Minimizing 19 Membrane Stresses in Pressure Vessel It is common practice to weld a variety of attachments support pads, lifting lugs, instrument ports and reinforcements to the pressure boundary of the vessel. 20 Impact of attachments and optimization Attachments locally stiffen the vessel shell and alter the membrane stress (hoop and axial) field due to internal pressure in the vicinity of the attachment. Depending on the type of weld and geometry of the weld footprint, the local stress field in the vessel shell at the attachment boundary can increase significantly. Question: Does an optimal shape of attachment (insertion) exist so that the impact on local stress along the boundary is minimized? If so, what is the optimal shape? 21 Optimal shape of rigid attachment in a biaxial stress field (Gordon Bjorkman) 22 ANSYS Simulations: max principal stress 11.9 kpsi Design of Optimal Hole Shape for Minimizing 23 Membrane Stresses Similar to attachments, membrane stresses increase significantly near the hole boundary. Question: Does an optimal shape of hole exist so that the impact on local stresses on the boundary is minimized? If so, what is the optimal shape? Optimal shape of hole in a biaxial stress field (Gordon Bjorkman) 24 25 A circular hole: non-optimal Nominal max principal stress w/o hole: 10 ksi An “non-optimal” circular hole : max principal stress 25.5 ksi Increase by 155% 26 An optimal elliptical hole (a/b=2): max principal stress: 15.3 kpsi, 53% increase Optimal shape of airplane window 27 Treat the fuselage as an cylindrical pressure vessel Hoop stress vs axial stress Shape: elliptical or near What is the optimal ratio of height to width, or ratio major to minor axes? Design of a Machine Component Based on Static Load Forces Moments Loads Geometry: 1,2,3D Materials: Constraints: Machine Component DE, MSS, Mohr, MNS u,,,Pcr Methods of Solution: Buckling, Rigidity, Temperature, etc. Analytical, FEM Design Criteria Static Response Modifications 28 Met? Yes Stop No 29 Home Work Read Chapter 1-5 for Some Fundamentals of Mechanical Engineering Design Units (SI, Imperial) Stress and Strength Tolerances and Costs Uncertainty Reliability (redundancy) Calculations and Significant Figures