MAE 322 Machine Design Dr. Hodge Jenkins Mercer University
What is this Machine Design course really about? What you will learn: How to design machine elements 1) Design so they won t break under varying loads 2) How to apply and select standard machine components If you apply all you learn here, you can still build an awful machine that does not work well. 1) Function can be very different from breakage. A good functional machine takes more than just good parts. But, you need good parts and components to build a good functional machine.
You will learn: Component Design Philosophies and Guidelines General, good approaches to design machine elements not to fail under various loadings Transmit power, torque or force, Transform kinematic motion Common Commercial Standards Design Rules of thumb (experience)
First: Let s Define Failure for our purposes For Materials: Break in to piece, deform permanently, crack Part function: to much elastic deformation (too flexible), wear, surface damage
Failure: Stress > Strength Typically we will limit ourselves to examining stress Stress: 1-D, 2-D, 3-D σ= Normal (compression or tension), τ= Shear Loading: Static, Dynamic, Cyclic Strength: strength values for materials, determined experimentally
Static Material Strength Usually necessary to design using published strength values Experimental test data is better, but generally only warranted for large quantities or when failure is very costly (in time, expense, or life) (e.g., aircraft nuclear reactors) Methods are needed to safely and appropriately use published strength values for a variety of situations In many instances it use depends on whether a material is ductile or brittle Shigley s Mechanical Engineering Design
Normal Stress vs. Strain (σ vs. ε) Material tests In General: ductile materials are limited by their yield strengths and fail in shear Brittle materials are limited by their ultimate strength (tension and compression). Each will have their own failure theory.
Need for Static Failure Theories Failure theories propose appropriate means of comparing multi-axial stress states to single strength Usually based on some hypothesis of what aspect of the stress state is critical Some failure theories have gained recognition of usefulness for various situations S Y = material yield stress in uniaxial tension S UT = material ultimate tensile stress in uniaxial tension Shigley s Mechanical Engineering Design
Reminder: Use Stress Concentration to find the maximum stresses Localized increase of stress near discontinuities K t is Theoretical (Geometric) Stress Concentration Factor Shigley s Mechanical Engineering Design
Need for Static Failure Theories Uniaxial stress element (e.g. tension test) Multi-axial stress element One strength, multiple stresses How to compare stress state to single strength? n Strength Stress S Shigley s Mechanical Engineering Design
Maximum Normal (Principal) Stress Theory Theory: Yielding begins when the maximum principal stress in a stress element exceeds the yield strength. n=factor of safety n = Strength Stress = S Y σ MAX For any stress element, use Mohr s circle to find the principal stresses. Compare the largest principal stress to the yield strength. Often the first theory to be proposed by engineering students. Is it a good theory?... Depends. Shigley s Mechanical Engineering Design
Maximum Normal (Principal) Stress Theory 2-D (Plane Stress) Experimental failure data shows the theory is unsafe in the 4 th quadrant. This theory is not safe to use for ductile materials. So, time for a better failure theory. Shigley s Mechanical Engineering Design
Statics Load Failure Theories to Study and Understand Maximum Normal Stress Maximum Shear Stress Distortion Energy Coulomb-Mohr
Maximum Shear Stress Theory (MSS) Theory: Yielding begins when the maximum shear stress in a stress element exceeds the maximum shear stress in a tension test specimen of the same material when that specimen begins to yield. For a tension test specimen, the maximum shear stress is 1 /2. At yielding, when 1 = S y, the maximum shear stress is S y /2. Could restate the theory as follows: Theory: Yielding begins when the maximum shear stress in a stress element exceeds S y /2.
Maximum Shear Stress Theory (MSS) For any stress element, use Mohr s circle to find the maximum shear stress. Compare the maximum shear stress to S y /2. Ordering the principal stresses such that 1 2 3, Incorporating a factor of safety n Or solving for factor of safety n S y /2 max Shigley s Mechanical Engineering Design
Maximum Shear Stress Theory (MSS) To compare to experimental data, express max in terms of principal stresses and plot. To simplify, consider a plane stress state Let A and B represent the two non-zero principal stresses, then order them with the zero principal stress such that 1 2 3 Assuming A B there are three cases to consider Case 1: A B 0 Case 2: A 0 B Case 3: 0 A B Shigley s Mechanical Engineering Design
Maximum Shear Stress Theory (MSS)Plane Stress ( C = 0) Case 1: A B 0 For this case, 1 = A and 3 = 0 reduces to A S y Case 2: A 0 B For this case, 1 = A and 3 = B reduces to A B S y Case 3: 0 A B For this case, 1 = 0 and 3 = B reduces to B S y Shigley s Mechanical Engineering Design
Maximum Shear Stress Theory (MSS) Plot three cases on principal stress axes Case 1: A B 0 A S y Case 2: A 0 B A B S y Case 3: 0 A B B S y Other lines are symmetric cases Inside envelope is predicted safe zone Fig. 5 7
Maximum Shear Stress Theory (MSS) Comparison to experimental failure data Conservative in all quadrants Commonly used for design situations Good, safe theory for design, but could be more accurate Shigley s Mechanical Engineering Design
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