Question

2. Mechanical Spring Analysis (30 points) A camshaft rotates, 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 an operating force F that varies from 300 N to 600 N as the spring length varies over a range of 25 mm. The helical compression spring is to be made of chrome-vanadium wire with a wire diameter d = 5 mm, spring index C = 12, and two constants m and A (m = 0.168, A = 2,005 MPa · mm^m). The helical spring has squared and ground ends. Given: Shear modulus of the spring G = 79 GPa, the fraction to overrun to closure ? = 0.15. (a) Determine the spring rate, k of the helical spring using the force-deflection relation (5 points) (b) Determine the number of active coils, Na needed for the helical spring (5 points) (c) Determine the total number of coils, Nt needed for the helical spring (5 points) (d) Determine the free length of the helical spring, L0 (5 points) (e) Determine a static factor of safety, ns based on the yielding of the spring if it is compressed to its solid height. Assume the spring has presetting and its torsional shear strength Ssy is 70% of the tensile strength Sut. (10 points) Type of Spring Ends Term Plain Plain and Ground Squared or Closed Squared and Ground End coils, Ne 0 1 2 2 Total coils, Nt Na Na + 1 Na + 2 Na + 2 Free length, L0 pNa + d p(Na + 1) pNa + 3d pNa + 2d Solid length, Ls d(Nt + 1) dNt d(Nt + 1) dNt Pitch, p (L0 - d)/Na L0/(Na + 1) (L0 - 3d)/Na (L0 - 2d)/Na

          2. Mechanical Spring Analysis (30 points)
A camshaft rotates, 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 an operating force F that varies from 300 N to 600 N as the spring length varies over a range of 25 mm. The helical compression spring is to be made of chrome-vanadium wire with a wire diameter d = 5 mm, spring index C = 12, and two constants m and A (m = 0.168, A = 2,005 MPa · mm^m). The helical spring has squared and ground ends.

Given: Shear modulus of the spring G = 79 GPa, the fraction to overrun to closure ? = 0.15.

(a) Determine the spring rate, k of the helical spring using the force-deflection relation (5 points)
(b) Determine the number of active coils, Na needed for the helical spring (5 points)
(c) Determine the total number of coils, Nt needed for the helical spring (5 points)
(d) Determine the free length of the helical spring, L0 (5 points)
(e) Determine a static factor of safety, ns based on the yielding of the spring if it is compressed to its solid height. Assume the spring has presetting and its torsional shear strength Ssy is 70% of the tensile strength Sut. (10 points)

Type of Spring Ends
Term Plain Plain and Ground Squared or Closed Squared and Ground
End coils, Ne 0 1 2 2
Total coils, Nt Na Na + 1 Na + 2 Na + 2
Free length, L0 pNa + d p(Na + 1) pNa + 3d pNa + 2d
Solid length, Ls d(Nt + 1) dNt d(Nt + 1) dNt
Pitch, p (L0 - d)/Na L0/(Na + 1) (L0 - 3d)/Na (L0 - 2d)/Na

$2. Mechanical Spring Analysis (30 points) A camshaft rotates, causing a follower to raise and lower once per revolution. The follower is to be held against the cam by a helical compression spring with an operating force F that varies from 300 N to 600 N as the spring length varies over a range of 25 mm. The helical compression spring is to be made of chrome-vanadium wire with a wire diameter d = 5 mm, spring index C = 12, and two constants m and A (m = 0.168, A = 2,005 MPa · mm^m). The helical spring has squared and ground ends. Given: Shear modulus of the spring G = 79 GPa, the fraction to overrun to closure ? = 0.15. (a) Determine the spring rate, k of the helical spring using the force-deflection relation (5 points) (b) Determine the number of active coils, Na needed for the helical spring (5 points) (c) Determine the total number of coils, Nt needed for the helical spring (5 points) (d) Determine the free length of the helical spring, L0 (5 points) (e) Determine a static factor of safety, ns based on the yielding of the spring if it is compressed to its solid height. Assume the spring has presetting and its torsional shear strength Ssy is 70% of the tensile strength Sut. (10 points) Type of Spring Ends Term Plain Plain and Ground Squared or Closed Squared and Ground End coils, Ne 0 1 2 2 Total coils, Nt Na Na + 1 Na + 2 Na + 2 Free length, L0 pNa + d p(Na + 1) pNa + 3d pNa + 2d Solid length, Ls d(Nt + 1) dNt d(Nt + 1) dNt Pitch, p (L0 - d)/Na L0/(Na + 1) (L0 - 3d)/Na (L0 - 2d)/Na$

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