Question

A laminated semi-elliptic leaf spring under a central load of 12 kN is to have an effective length of 1 m and is to deflect not more than 80 mm. The spring has 14 leaves, three of which are full length, and have been pre-stressed so that all leaves have the same stress after the full load has been applied. All leaves have the same width and thickness. The maximum stress in the leaves is not to exceed 350 MN/m² . Calculate the width and thickness of the leaves. Modulus of elasticity of the spring material is 210 GPa. Also, determine the width and thickness of the leaves if the leaves are not pre-stressed, the other parameters remaining the same.

Answer 1

& Solution, equal airen condition, in the leaves. To spring semi- Teatt spring the stresses are all Tale thus, consider the as two cantilever-f De connee tel as s. = 1000 mm 4 = 500 mm A 4 12 6XION B P/2=6*10N P=12x 10°N Arrangement of beams we consider the portion Bc of the beam as the cantilever-type leaf spring with load P/ & length La. Applying the stress e deflection equations & by noting that stresses are all equal in the leares, we get Ex Smare = 6M. - 6 ( 2 ) _ 3PL nbt? a nbta anbt2 Where, n, is the total number of leares.be denotes plate width & t is plate thickness. - Note that the stresses Because of the above equation is applied as in the leaves are all equal pressing.

350 3x 12 x 103 103 2 x 14 x bte bt? = 3x12x106 2x14x350 or 6+2 = 3673.5 mm ) --- by putting f/2 & 4 in place of ubix p & L respec putting we get. spectively, Smee = 12000 od to sa Ebt (3 ne tane) w far to PLB. 4 Ebt (3n6 tango 3 & PLB to let 4 mar ( 304+ 2106) 3 12x(10) x (10@ gje 4 210 HO je x (80) ( 3x3 + 2x11) bt² = 17281.1 mm – – – 12 from equation & we Ubt 17281-1 mmk bevool 3673.5 mm It = 1 b = 4.7 mm 165.gg 7 166mm)

Pege No. Date & other b) It leaves are not pre-stressed parameters are same. then . Usually the stress in master Teat is the decading foretor as its stress is 50% more than that in the strad leated leaves kTo on = 18PL bt² ne tang so, the thickness of leaf spring considering the width is same ta I smb 3n+20G 18 AL 1 aces putting the values mm 18x12x110) x 1000 350x 166x4 W (3x3 + 2x117 - 10.95 mm Tb= 166 mm t = 5.47 mm