Torsion Bar Springs Probably the simplest form of spring Common applications >Automotive suspension springs >Counterbalancing springs for car hoods and trunk lids >Doors Fixed end Bearirng Spline Torsion bar portion Generous radius d Bearing Spline (a) (b) Torsion bar with splined ends Rod with bent ends serving as torsion bar spring (type used in auto suspensions,etc.) (type used for auto hood and trunk counterbalancing.etc.l
Torsion Bar Springs • Probably the simplest form of spring • Common applications ¾Automotive suspension springs ¾Counterbalancing springs for car hoods and trunk lids ¾Doors
Torsion Bar Springs Shear stress T 16T T三 πd3 ·Angular deflection TL 32TL 0= 二 JG πd4G ·Spring rate JG πd4G k= L 32L ·T=F*D/2=torque ·r=wire radius ·J=πd4/32=polar moment of inertia A=wire cross-sectional area
Torsion Bar Springs • Shear stress 3 Tr T 16 J d τ π = = • Angular deflection 4 TL TL 32 JG dG θ π = = • Spring rate 4 32 JG dG k L L π = = • T = F ∗D/2 = torque • r = wire radius • J = π d 4/32 = polar moment of inertia • A = wire cross-sectional area
Stresses in Coil Springs Consider spring shown below and free body diagram of cut portion (b (a)
Stresses in Coil Springs • Consider spring shown below and free body diagram of cut portion
Stresses in Springs o Removed portion exerts force F and torsion T on remaining part Maximum stress in wire is: Tr F 十 max 士 A ·T=F*D/2=torque ·r=wire radius ·J=πd/32=polar moment of inertia A=wire cross-sectional area
Stresses in Springs • Removed portion exerts force F and torsion T on remaining part • Maximum stress in wire is: max Tr F J A τ =± + • T = F ∗D/2 = torque • r = wire radius • J = π d 4/32 = polar moment of inertia • A = wire cross-sectional area
Stresses in Springs ·Thus 8FD 4F max πd3 nd2 Positive sign indicates stress on inside fiber of spring. ·D=spring diameter ·d=wire diameter
Stresses in Springs • Thus max 3 2 8 4 FD F d d τ π π = + • D = spring diameter • d = wire diameter • Positive sign indicates stress on inside fiber of spring