spherical joint where the ball has a radius of 20 mm and socket has a radius...
1). Two spherical balls are contacting each other due to a pair of compressive forces F = 50 N. The bigger ball with a radius of R2 = 20 mm is made of a steel with elastic modulus of 210 GPa and Poisson's ratio of 0.3. The smaller ball with a radius of R1 = 5 mm is treated as a rigid body. According to Hertz contact theory, what is the pressure distribution along a radial path in the contact...
8.3 A single ball rolling in a groove has a 10-mm diameter and a 4-N normal force acting on it. The ball and the groove have a 200-GPa modulus of elasticity and a Poisson's ratio of 0.3. Assuming a 6.08-mm-radius groove in a semi-infinite steel block, determine the following: (a) Contact zone dimensions Ans. Dy = 0.227 mm, D = 0.0757 mm. (b) Maximum elastic deformation Ans. Omax = 0.391 um. (c) Maximum pressure Ans. 0.445 GPa.
The ball-outer-race contact of a ball bearing has a 17-mm ball diameter, an 8.84-mm outer-race groove radius, and a 44.52-mm radius from the bearing axis to the bottom of the groove. The load on the most highly loaded ball is 10,000 N. Calculate the dimensions of the contact ellipse and the maximum deformation at the center of the contact. The race and the ball are made of steel. Ans. Dy = 6.935 mm, Dx = 0.9973 mm.
Question 1 (20 points) Determine the components of reaction at the ball-and-socket joint A and the tension in each cable necessary for equilibrium of the rod. .4m N/M D 150 om 400 N
Question 1 (20 points) Determine the components of reaction at the ball-and-socket joint A and the tension in each cable necessary for equilibrium of the rod. .4m 150 N/m D B E 400 W
Shape FilB Convert to Picture Shapes Text Arrange Quick MENG 3505 Mechanics of Materials Spring 2018 Example, Contact of Spherical Surfaces Two carbon steel spherical surfaces, each 30 mm in diameter, are pressed together by a force F Find the maximum values of the principal stresses and the maximum shear stress if F = 50 N, v = 0.3, and E-207 GPa. Contact Po area 2a E2 al Bonus #3: solve this example. Course Material for MENG 3505
b) A 150mm diameter shaft has a 25mm diameter ball rolling circumferentially around the outside with a normal load of 1200N. The ball is made of silicon nitride (E = 314GPa, v = 0.26) and the shaft is made of steel (E = 206 GPa, v = 0.30). Apply Hertzian contact analysis to determine the, Curvature sum (include a diagram(s) to define the contact geometry considered) [4 Marks] ii. Dimensions of the contact ellipse [6 Marks] Maximum elastic deformation in...
Consider the Laplace equation for a ball of radius R described in spherical coordinates (r, 0) 2 1 cot 72 0= n where is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w:= cos e given by 2 F" (r) +2rF (r) - n(n + 1) F, (r) = 0, (1 w2)G (w) - 2wG", (w) +n(n +1)G, (w) 0. (n 0,1,2,....
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2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0, uee 7:2 where is the zenith angle and assume u is independent on the azirnuth angle o. a) By separation of variables, derive two ordinary differential equations of r and w=Cos given by r2 F(r)2r F(r)-n(n+ 1)F(r) 0, (1- w2)G (w)- 2wG (w)n(n +1)G(w) 0. (n 0,1,2,.) b) Find Fn (r) and Gn (w) satisfying Gn(1) =1 for...
4.A thin-walled cylindrical column carries a weightless arch and is loaded as shown in Figure 4. The column has an internal diameter of 250 mm with a thickness of 2 mm Given: E-200 GPa and 0.3 The answer to each part of the question is to be used for subsequent parts (a)Determine the stresses on the outer surface of the cylinder at points A and B due to (8 marks) (b) Determine the minimum internal pressure p required if the...