Machine Design I (MCE-C 203) Mechatronics Dept., Faculty of Engineering, Fayoum University Dr. Ahmed Salah Abou Taleb Lecturer, Mechanical Engineering Dept., Faculty of Engineering, Fayoum University 1

2 loads mechanical  forces, moments… thermal  chemical changing in place/ time … static cyclic dynamic

3 loads & stresses Tension load. Compression load. Shear load. Bending load. Torsion load. Compound load

Stresses 4

5

Tension 6

7 Below the yield stress Strength is affected by alloying, heat treating, and manufacturing process but stiffness (Modulus of Elasticity) is not.

8 Tension From Hooke’s Law: From the definition of strain: Equating and solving for the deformation, With variations in loading, cross-section or material properties,

9 Determine the deformation of the steel rod shown under the given loads. SOLUTION: Divide the rod into components at the load application points. Apply a free-body analysis on each component to determine the internal force Evaluate the total of the component deflections. Tension Example

10 Tension Example SOLUTION: Divide the rod into three components: Apply free-body analysis to each component to determine internal forces, Evaluate total deflection,

11 Bending Pure Bending: Prismatic members subjected to equal and opposite couples acting in the same longitudinal plane

12 Eccentric Loading: Axial loading which does not pass through section centroid produces internal forces equivalent to an axial force and a couple Transverse Loading: Concentrated or distributed transverse load produces internal forces equivalent to a shear force and a couple Bending

13 A cast-iron machine part is acted upon by a 3 kN-m couple. Knowing E = 165 GPa and neglecting the effects of fillets, determine (a) the maximum tensile and compressive stresses, (b) the radius of curvature. SOLUTION: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. Apply the elastic flexural formula to find the maximum tensile and compressive stresses. Calculate the curvature Bending Example

14 Bending Example SOLUTION: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia.

15 Apply the elastic flexural formula to find the maximum tensile and compressive stresses. Calculate the curvature Bending Example

16 Torsion Interested in stresses and strains of circular shafts subjected to twisting couples or torques Generator creates an equal and opposite torque T’ Shaft transmits the torque to the generator Turbine exerts torque T on the shaft

17 Torsion The results are known as the elastic torsion formulas, Equating the expressions for shearing strain and solving for the angle of twist,

18 Shaft BC is hollow with inner and outer diameters of 90 mm and 120 mm, respectively. Shafts AB and CD are solid of diameter d. For the loading shown, determine (a) the minimum and maximum shearing stress in shaft BC, (b) the required diameter d of shafts AB and CD if the allowable shearing stress in these shafts is 65 MPa. SOLUTION: Cut sections through shafts AB and BC and perform static equilibrium analysis to find torque loadings Given allowable shearing stress and applied torque, invert the elastic torsion formula to find the required diameter Apply elastic torsion formulas to find minimum and maximum stress on shaft BC Torsion Example

19 SOLUTION: Cut sections through shafts AB and BC and perform static equilibrium analysis to find torque loadings Torsion Example

20 Torsion Example Apply elastic torsion formulas to find minimum and maximum stress on shaft BC Given allowable shearing stress and applied torque, invert the elastic torsion formula to find the required diameter

21 Design Factor Analysis Design

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence 22

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence How many will be produced? What manufacturing methods will be used? What are the consequences of failure? Danger to people Cost Size and weight important? What is the life of the component? Justify design expense? 23

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence Temperature range. Exposure to electrical voltage or current. Susceptible to corrosion Is noise control important? Is vibration control important? Will the component be protected? Guard Housing 24

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence Nature of the load considering all modes of operation: Startup, shutdown, normal operation, any foreseeable overloads Load characteristic Static, repeated & reversed, fluctuating, shock or impact Variations of loads over time. Magnitudes Maximum, minimum, mean 25

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence What kind of stress? Direct tension or compression Direct shear Bending Torsional shear Application Uniaxial Biaxial Triaxial 26

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence Material properties Ultimate strength, yield strength, endurance strength, Ductility Ductile: %E  5% Brittle:%E < 5% Ductile materials are preferred for fatigue, shock or impact loads. 27

Factors Effecting Design Factor Application Environment Loads Types of Stresses Material Confidence Reliability of data for Loads Material properties Stress calculations How good is manufacturing quality control Will subsequent handling, use and environmental conditions affect the safety or life of the component? 28

Recommended Design Factors Confidence in material properties, analysis, loads, the environment, etc. See Mott, pages

Design Factor 30