# Topics In Machine Elements Mit Opencourseware-Books Pdf

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Images by Silberwolf Red Rooster, ruizo and Aspectomat at Wikimedia. Commons and i am indisposed, and David on LRM on Flickr. Massachusetts Institute of Technology 2 017, downstream. Massachusetts Institute of Technology 2 017, Critical speed of a shaft with a mass. synchronous case slowest, 1 steady state, configuration.
x x deflection grows, linearly with time, Shaft has stiffness k at the location of the flywheel. is eccentricity, ADDITIONAL formulas, In steady state. available for multiple, masses on a shaft, x m 2 k m 2. 2 1 2 where m, Massachusetts Institute of Technology 2 017. Circular shafts, diameter d, in combined T, loading V x.
Polar moment of inertia J d4 32, Bending moment of inertia I d4 64 J 2. Angular deflection TL JG, Bending shear stress V x. Bending moment dM x dx V x, Max shear stress at shaft surface max Tr J 16T d3. Max bending stress at top bottom surface b x M x r I 32 M x d3. Transverse shear stress on u d centerline t x 16 V x 3 d2. and don t forget stress concentration, Massachusetts Institute of Technology 2 017. Just what you need Mohr stress, s1 s2 xy max sqrt s22 xy2.
s max tan 2 xy s2, tan 2 s2 xy, s 2 s1 max, 2 0 2 principal stresses. Massachusetts Institute of Technology 2 017, Fatigue of Engineering Materials. Basquin s equation L kb b where L is the lifetime cycles at stress level. kb b are determined from test data, Curve fits data for cycles at a given constant stress level. For loading at multiple levels, Consider Miner s equation. N1 L1 N2 L2 1, Peak alternating bending stress S kpsi log.
Li is the lifetime at stress level i, Ni is the number of cycles actually. 16 executed at i, 14 Permanent mold cast, Sand cast Concept Accumulation of. 103 104 105 106 107 108 109, Life N cycles log, Simplified approach does not take. into account the sequence of, Figure by MIT OpenCourseWare Adapted from Fig 6 11 in Shigley Mischke. loading levels, Massachusetts Institute of Technology 2 017.
L1 1000 1 81ksi, very light loading, very heavy loading. q twice the standard deviation of the underlying Gaussian stress. Massachusetts Institute of Technology 2 017, Four Bar Linkage Kinematics. l length of longest link, s length of shortest link. coupler p q lengths of intermediate links, frame Grashof s theorem. If s l p q then at least one link will revolve, If s l p q then all three links are rocking.
r2 Categories, l s p q double crank if s is the frame. l s p q rocker crank if s is one side, r4 1 l s p q double rocker if s is coupler. l s p q change point, l s p q triple rocker, Let i be the absolute angle of link ri vector as shown. The chain satisfies, X loop r1cos 1 r2cos 2 r3cos 3 r4 0 note 4 0. Y loop r1sin 1 r2sin 2 r3sin 3 0, Two equations two unknowns 2 3 if 1 given use a nonlinear solver.
Massachusetts Institute of Technology 2 017, rocker rocker. S S Driver, double crank L S P Q crank rocker, L S P Q rocker crank. Courtesy of Alex Slocum Used with permission, B Paul Kinematics and dynamics of planar machinery 1984. Massachusetts Institute of Technology 2 017, Inversions of the Scotch Yoke. a Scotch Yoke b Oldham Coupling, Ellipse P 4, c Elliptic Trammel.
Figure by MIT OpenCourseWare Adapted from Fig 1 51 1 in Paul Burton Kinematics. and Dynamics of Planar Machinery Englewood Cliffs NJ Prentice Hall 1979. Massachusetts Institute of Technology 2 017, Slider Crank r. Kinematics e, X loop r cos L cos s 0, Y loop r sin L sin e 0. Two equations two unknowns s if is given, smax s1 sqrt L r 2 e2. smin s2 sqrt L r 2 e2, at smax 1 arcsin e L r, at smin 2 arcsin e L r. Slider moves to the right smin smax 2 1, Slider moves to the left smax smin 1 2.
So time ratio TR captures quick return characteristic. Massachusetts Institute of Technology 2 017, Inversions of Slider Crank Mechanism. a Ordinary slider crank b Whitworth quick return, c Crank shaper ordinary quick return d Hand pump. Figure by MIT OpenCourseWare Adapted from Fig 1 42 1 in Paul Burton Kinematics. and Dynamics of Planar Machinery Englewood Cliffs NJ Prentice Hall 1979. Massachusetts Institute of Technology 2 017, Radial Ball Bearings. Ball Bearings in radial loading, Load rating is based on fatigue. Basic Rating Load C causes failure in 10 of bearings at 1 million cycles. Hardness and finish of balls and rollers is critical. Use e g high carbon chromium steel 52100 min 58 Rockwell. Finish balls to 50nm typical races to 150nm typical. Quality indexed by ABEC rating 1 to 9, Examples of Ratings.
102 15mm bore 9x32mm dia 4 3 kN C 2 4 kN static, 108 40mm bore 15x68mm dia 13 6 kN C 10 9 kN static. 314 70mm bore 20x110mm dia 80 kN C 59 kN static, Note static load rating dynamic load rating. Scaling life goes as load cubed, Decreasing the load by will increase expected life by 8 fold etc. Massachusetts Institute of Technology 2 017, Effect of Axial Loading on Radial Bearings Equivalent Pa ZiD2 X Y. radial load, 25 0 56 2 3, Max 1 2Pr 1 2XPr YPa, 50 0 56 2 0.
where Pr and Pa are axial and radial loads and X Y. 100 0 56 1 7, Service factor C1 1 3 to account for shock loads 200 0 56 1 5. Max 1 2C1Pr 1 2C1XPr C1YPa 500 0 56 1 2, 1000 0 56 1 0. Concept of accumulated damage Miner s equation, applies Z number of balls. i number of rings, Use tapered roller bearings for large combined loads D ball diameter. Radial bearings and thrust bearings separately, 1D separation Ack.
Confidence levels, adjustment to lifetime, 3D separation Ahhh 95 0 62. Machine Elements Massachusetts Institute of Technology 2 017 Images by Silberwolf Red Rooster ruizo and Aspectomat at Wikimedia Commons and i am indisposed and David on LRM on Flickr Massachusetts Institute of Technology 2 017 downstream upstream u u Massachusetts Institute of Technology 2 017 Critical speed of a shaft with a mass synchronous case slowest x x Shaft has stiffness k

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