Spring problems

1. Identical springs are to be designed to support a machine in order to isolate vibrations.
   The static load on each spring is 7 kN under which the deflection should be not less than 50 mm, and the outside coil diameter must not exceed 150 mm. The shear yield strength of the material selected is 690 MPa, which may be assumed independent of wire size.
   Determine the springs' manufacturing dimensions based upon a design factor of 1.5.
    
2. A spring has a mean coil diameter of 76 mm, a wire diameter of 12.5 mm, and 5 active coils with a free length of 140 mm. The material is ASTM A229 oil tempered wire.
   ( a)   Determine the spring's stiffness;     [ 110 N/mm]
   ( b)   Check the solid stress;     [ 619 MPa]
   ( c)   Calculate the factor of safety for a load which fluctuates between 2 and 3 kN.     [ 1.3]
    
3. A spring from ASTM A229 oil tempered wire is required which will fit inside a guide tube of 70 mm bore, exert a minimum force of 1 kN, and when compressed a further 30 mm exert a load not exceeding 1.5 kN.
   Determine the manufacturing dimensions of a suitable spring to last indefinitely.
                     [ wire dia. 8 mm, mean coil dia. 51 mm, total turns 20.5, free length 263 mm ]
    
4. Is there a feasible solution to the previous problem if the guide tube's bore is 40 mm?
    
5. A helical compression spring is required to have infinite life when subjected to a load which fluctuates between 250 and 500 N. Wire having   S_ut = 1250; S_us = 1000; S_ys = 680 MPa and a zero- to- maximum torsional endurance limit of 550 MPa will be used. These values apply to the size range and surface finish of the spring.
   What wire size should be used if the spring index is 7 ?     [ 4 mm ]
    
6. A cam rotates at 10 Hz and imparts a sinusoidal oscillation to its follower. Follower total lift is 20 mm and the mass of the oscillating parts is 9 kg.
   A return spring is required to overcome the inertia of the oscillating parts and to maintain contact between follower and cam. To fit the space available, the spring inside diameter must be at least 25 mm and the outside diameter no more than 50 mm.
   Ascertain the manufacturing dimensions of a spring made from music wire and with indefinite life.