CHAPTER 12 SPRINGS Summary Close-coiled springs (a)Under axial load w Maximum shear stress set up in the material of the spring 2WR 8WD =Tmax= nd3 Total deflection of the spring for n turns 4WR3n 8WD3n =6= Gr4= Gd4 where r is the radius of the wire and R the mean radius of the spring coils. W Gd4 i.e. Spring rate=δ-8nD (b)Under axial torque T 4T32T Maximum bending stress set up omax nd3 8TRn 64TDn Wind-up angle =0= Er4 Ed4 nEd4 .∴.Torque per turn= 0/2π32Dn The stress formulae given in (a)and(b)may be modified in practice by the addition of'Wahl' correction factors. Open-coiled springs (a)Under axial load W Deflection 6=2nnWR3 sec a cos2a sin2a GJ+EI Angular rotation 2mnWR2 sina [11 297CHAPTER 12 SPRINGS Summary Close-coiled springs (a) Under axial load W Maximum shear stress set up in the material of the spring 2WR 8WD - Tmax= __ = - xr3 xd3 - Total deflection of the spring for n turns 4WR3n 8WD3n Gr4 Gd4 - -6=- =- where r is the radius of the wire and R the mean radius of the spring coils. i.e. W Gd4 Spring rate = - = ~ 6 8nD3 (b) Under axial torque T 4T 32T Maximum bending stress set up = omax = - = __ xr3 xd3 8TRn 64TDn Wind-up angle = e = - E ___ Er4 Ed4 T xEd4 0/2x 32Dn :. Torque per turn = ~ - ~ The stress formulae given in (a) and (b) may be modified in practice by the addition of ‘Wahl’ correction factors. Open-coiled springs (a) Under axial load W cosza sin’a Deflection 6 = 2xn WR3 sec a Angular rotation 0 = 2xn WRz sin a [t - - - :I] 297