A camshaft rotates 650 rpm, causing a follower to raise and lower once per revolution. The follower is to be held against the cam by a helical compression spring with

a force that varies between Fmin = 300 and Fmax = 600 N as the spring length varies over a range of AL = 25 mm. Ends are to be squared and ground. The material is chrome-vanadium ASTM A232, with Young's modulus E = 203 GPa and shear modulus G = 77 GPa. The wire diameter to be used is d = 6 mm. S sa + Se se S. sm Sa su =1, Homework 2 MAE 156A - Winter 2024 Cam Squared and ground ends, ASTM A232 spring wire n = 650 rpm I Key A + 25 a) Determine the spring rate k. b) Estimate the ultimate tensile strength Sut for the spring material using Table 10-4 at the end of the document. Also estimate the endurance limit as Se≈ Sut/2. Finally, calculate the ultimate shear strength as S = S/√√3 and the shear endurance limit as S = S/√√3 (according to von Mises criterion). su se c) Using Goodman's rule for shear stress, 600 N 600 N Shaft 300 N 300 N 25 mm allow Ssm determine the maximum allowable midrange shear stress as t m where Ssm is the midrange shear strength component, Ssa is the shear strength amplitude, and n is the safety factor. Use n = 1.2. n 2 Hint: Observe that Ssa/Ssm = Fa/Fm, where Fa = Fmax – Fmin and Fm = (Fmax + Fmin)/2 are the amplitude and midrange of the cyclic loading. allow d) Determine the coil diameter D so that m >1, the spring is absolutely stable. f₁ = 4c-1 0.615 4c-4 с = 1 Ik 2 Vm + C₂ E 2(E-G)' 9 is the Wahl stress C₂ = h) Compare the loading frequency with the natural frequency of the spring to assess the possibility of resonance (spring surge). Assume the mass density of the spring is p = 7.8 g/cm³. Hint: The natural frequency of the spring is given by 2π² (E-G) 2G+E are elastic where m pV is the mass and V is the wire volume (assume small pitch so that V = Al, where A is the cross section of the wire and / its length). Table 10-4 Constants A and m of Sut = A/dm for Estimating Minimum Tensile Strength of Common Spring Wires Source: From Design Handbook, 1987, p. 19. Courtesy of Associated Spring. Material Music wire* OQ&T wire* Hard-drawn wire Chrome-vanadium wire Chrome-silicon wirel 302 Stainless wire* ASTM No. A228 A229 A227 A232 A401 A313 Phosphor-bronze wire** B159 Exponent m 0.145 0.187 0.190 0.168 0.108 0.146 0.263 0.478 0 0.028 0.064 Diameter, in 0.004-0.256 0.020-0.500 0.028-0.500 0.032-0.437 0.063-0.375 0.013-0.10 0.10-0.20 0.20-0.40 0.004-0.022 0.022-0.075 0.075-0.30 A, kpsi - in™ 201 147 140 169 202 169 128 90 145 121 110 Diameter, mm 0.10-6.5 0.5-12.7 0.7-12.7 0.8-11.1 1.6-9.5 0.3-2.5 2.5-5 5-10 0.1-0.6 0.6-2 2-7.5 A, MPa.mm 2211 1855 1783 2005 1974 1867 2065 2911 1000 913 932 Relative Cost of Wire 2.6 1.3 1.0 3.1 4.0 7.6-11 8.0