Question

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.

Answer 1

rbt 0.005 14 002875h é = reby 0 00G08 roy 0.005m Solution: The direction that the ball roll is x-direction. rax ray=0.005m-5mm ebx =D rby - 6:08 min = -0.00608m ! = 1 & I - I & I Rx = 0.005m. rax 1 + ooom + ky doom + o2815 R=0.004 LA = Ry - 0.02815m = 5.630 ke – Lill - (5.630) It – 3.000 Note that we al so f and { are Calematen et (I-1) Indr - It + (I-1) en (5.630) = 2.557 = 1 + (1 - 1) – It (I-1) - 110 5.630 E- 2 2 1- Var + 1 - V6h - 1.82 th e Ea E. T – 220 G Pa 200 GPa 1-0.32 004 Dy= 2 (DERW) - 2 63 % Vol 2 060425 + = 2.27 x10 to 0.2270m TE T + 220 - 4 7x10 m = 0.22thm 16x1.101x 4 x 0.00425 2 F 26EWR (Tkc E TX3 X 220 = 7.57 xlon = 0.075 man Umat = F/9 / W 12 7112 ZER (TKCE) = 2.5579 X16 m 2x H01X 0:00 425 TUX3x2.200 max= 0.391 Hm Pomoc 6W T DxPY - 6x4 = 0.445 Gila. TX 0.0757mm x 0.227mm.