1. Determine reasonable design values for the number of active coils, the wire and coil diameters...

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1. Determine reasonable design values for the number of active coils, the wire and coil diameters of an infinite-life helical compression spring with a minimum load of 12 lb force and a maximum load of 25 lb force, with an accompanying compression of 0.2 in. between them. The spring is for a food-service (kitchen) equipment and is ASTM A313 (302 stainless steel) so that the maximum stress is 0.455, since presetting is not required. The outside diameter of the coil cannot exceed 0.5 in. and the free length cannot exceed 2 in. Include a 10% clash allowance. Use shear modulus G = 11.5 x 106 psi. Use C = 5 to start your iteration. Buckling prevention criterion is ignored. (a) (3 marks) List the governing equations with their dependence on C intact for the iteration to arrive at the recommended design values. How many governing equations are there? (b) (2 marks) What is the main reason for the iteration need? (c) (3 marks) Obtain the first-iteration design values using the equation that does not depend on C nor N (but you still use C = 5 to start your iteration). Hint: Such equation can be obtained by converting the inequality that does not depend on C nor N into an equation. (d) (2 marks) Is there a need for second iteration? If yes, obtain the second-iteration design values. If no, state the first-iteration design values. Table 10-4 Constants & and m of S = Ald" for Estimating Minimum Tensile Strength of Common Spring Wires Material Music wire OQ&T wire Hard-drawn wire Chrome-vanadium wirel Chrome silicon wire!! 302 Stainless wire Phosphor-bronze wire" ASTM No. Exponent m A228 A229 A227 A232 A401 A313 BI59 0.145 0.187 0 0.190 0.168 0.108 0.146 0.263 0.478 0.028 0.064 Surface is smooth, free of defects, and has a bright, lustrous finish Has a slight heat-treating scale which must be removed before plating Surface is smooth and bright with no visible marks Aircraft-quality tempered wire, can also be obtained annealed Tempered to Rockwell C49, but may be obtained untempered Type 302 stainless steel "Temper CASIO Source Data from Design Handbook, 1987, p. 19. Diameter, in 4. kpsi - 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 0.075-0.30 201 147 140 169 202 169 128 90 145 121 110 A, Diameter, mm MPa - 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 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 1. Determine reasonable design values for the number of active coils, the wire and coil diameters of an infinite-life helical compression spring with a minimum load of 12 lb force and a maximum load of 25 lb force, with an accompanying compression of 0.2 in. between them. The spring is for a food-service (kitchen) equipment and is ASTM A313 (302 stainless steel) so that the maximum stress is 0.455, since presetting is not required. The outside diameter of the coil cannot exceed 0.5 in. and the free length cannot exceed 2 in. Include a 10% clash allowance. Use shear modulus G = 11.5 x 106 psi. Use C = 5 to start your iteration. Buckling prevention criterion is ignored. (a) (3 marks) List the governing equations with their dependence on C intact for the iteration to arrive at the recommended design values. How many governing equations are there? (b) (2 marks) What is the main reason for the iteration need? (c) (3 marks) Obtain the first-iteration design values using the equation that does not depend on C nor N (but you still use C = 5 to start your iteration). Hint: Such equation can be obtained by converting the inequality that does not depend on C nor N into an equation. (d) (2 marks) Is there a need for second iteration? If yes, obtain the second-iteration design values. If no, state the first-iteration design values. Table 10-4 Constants & and m of S = Ald" for Estimating Minimum Tensile Strength of Common Spring Wires Material Music wire OQ&T wire Hard-drawn wire Chrome-vanadium wirel Chrome silicon wire!! 302 Stainless wire Phosphor-bronze wire" ASTM No. Exponent m A228 A229 A227 A232 A401 A313 BI59 0.145 0.187 0 0.190 0.168 0.108 0.146 0.263 0.478 0.028 0.064 Surface is smooth, free of defects, and has a bright, lustrous finish Has a slight heat-treating scale which must be removed before plating Surface is smooth and bright with no visible marks Aircraft-quality tempered wire, can also be obtained annealed Tempered to Rockwell C49, but may be obtained untempered Type 302 stainless steel "Temper CASIO Source Data from Design Handbook, 1987, p. 19. Diameter, in 4. kpsi - 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 0.075-0.30 201 147 140 169 202 169 128 90 145 121 110 A, Diameter, mm MPa - 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 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