Helical torsion springs problem

1. Design a concentric spring for an air craft engine valve to exert a maximum force of 5000 N under a deflection of 40 mm. Both the springs have same free length, solid length and are subjected to equal maximum shear strees of 850 MPa. The spring index for both the springs is 6. [ Ans.d1 = 8 mm ; d2 = 6 mm ; n = 4 ]

Answer:

Load each spring

P1 : P2 = (d1 : d2)2 P1 : P2 = (8 : 6)2 = 1,69 mm2

P1 + P2 = 5000 (1,69 . P2) + P2 = 5000

2P2 = 2958,6

P2 = 1479,3 P1 = 3520,7

Mean diameter

k1 = k2 = (4C – 1) : (4C – 4) + 0,615 : C

= (4.6 – 1) : (4.6 – 4) + 0,615 : 6 = 1,2525

Max shear stress 1

850 = k1 (8.P1.C) : ( phi.d12) 850 = 1,2525 ( 8.(3520,7).6 : (phi..d12)

d1 = 8.9 mm

D1 = C.d1 = 6.8,9 = 53,4 mm

Max shear stress 2

850 = k2 (8.P2.C) : ( phi.d12) 850 = 1,2525 ( 8.(1479,3).6 : (phi.d22)

d2 = 5,7 mm

D2 = Cd2 = 6.5,7 = 34,2 mm

2. The free and of a torsional spring deflects through 90ᵒ when subjected to a torque of 4 N-m. The spring index is 6. Determine the coil wire diameter and number of turns with the following data : Modulus of rigidity = 80 GPa ; Modulus of elasticity = 200 GPa ; Allowable stress = 500 MPa. [ Ans. 5 mm ; 26 ]