Design of Helical Springs

Transcription

1 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm Design of Helicl Springs The design of new spring involves the following considertions: Spce into which the spring must fit nd operte. Vlues of working forces nd deflections. Accurcy nd relibility needed. Tolernces nd permissible vritions in specifictions. Environmentl conditions such s temperture, presence of corrosive tmosphere. Cost nd qulities needed. The designers use these fctors to select mteril nd specify suitble vlues for the wire size, the number of turns, the coil dimeter nd the free length, type of ends nd the spring rte needed to stisfy working force deflection requirements. The primry design constrints re tht the wire size should be commercilly vilble nd tht the stress t the solid length be no longer greter thn the torsionl yield strength. urther functioning of the spring should be stble. Stbility of the spring (Buckling) Buckling of column is fmilir phenomenon. Buckling of column is fmilir phenomenon. We hve noted erlier tht slender member or column subjected to compressive loding will buckle when the lod exceeds criticl vlue. Similrly compression coil springs will buckle when the free length of the spring is lrger nd the end conditions re not proper to evenly distribute the lod ll long the circumference of the coil. The coil compression springs will hve tendency to buckle when the deflection (for given free length) becomes too lrge. Buckling cn be prevented by limiting the deflection of the spring or the free length of the spring. Indin Institute of Technology Mdrs

2 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm The behvior cn be chrcterized by using two dimensionless prmeters, criticl length nd criticl deflection. Criticl deflection cn be defined s the rtio of deflection (y) to the free length free to tip (Lf) of the spring. The criticl length is the rtio of free length (Lf) to men coil dimeter (D) fixed end () Non prllel ends constrined prllel The criticl deflection is function of criticl length nd hs to be below certin limit. As could be noticed from the figure bsolute stbility cn be ensured if the criticl length cn be limited below limit. fixed end (b) prllel ends igure 4.16 Indin Institute of Technology Mdrs

3 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm stble unstble stble unstble prllel ends nonprllel ends rtio of free length/men dimeter L /D f (b) () igure 4.17 Similrly compression coil springs will buckle when the deflection (for given free length) becomes too lrge. The condition for bsolute stbility cn be given s: 1 πd 2(E G) L 2 o < α 2G + E or steels this cn be simplified s: L o < 2.63 D α Where α is constnt relted to the nture of support of the ends simply referred s end constnt Indin Institute of Technology Mdrs

4 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm Spring Surge nd Criticl requency If one end of compression spring is held ginst flt surfce nd the other end is disturbed, compression wve is creted tht trvels bck nd forth from one end to the other exctly like the swimming pool wve. Under certin conditions, resonnce my occur resulting in very violent motion, with the spring ctully jumping out of contct with the end pltes, often resulting in dmging stresses. This is quite true if the internl dmping of the spring mteril is quite low. This phenomenon is clled spring surge or merely surging. When helicl springs re used in pplictions requiring rpid reciprocting motion, the designer must be certin tht the physicl dimensions of the spring re not such s to crete nturl vibrtory frequency close to the frequency of the pplied force. The finl eqution for the nturl frequency, derived from the governing eqution of the wve motion, for spring plced between two flt prllel pltes is given by: f = d G. g πd 2 N 32. ρ or steels this cn be simplified s: 4 d f = N D 2 The fundmentl criticl frequency should be from 15 to 20 times the frequency of the force or motion of the spring in order to void resonnce with hrmonics. If Indin Institute of Technology Mdrs

5 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm the nturl frequency is not high enough, the spring should be redesigned to increse k or decrese the weight W. tigue Loding The springs hve to sustin millions of cycles of opertion without filure, so it must be designed for infinite life. Helicl springs re never used s both compression nd extension springs. They re usully ssembled with prelod so tht the working lod is dditionl. Thus, their stress-time digrm is of fluctuting nture. Now, for design we define, mx min = 2 mx + min = 2 Certin pplictions like the vlve spring of n utomotive engine, the springs hve to sustin millions of cycles of opertion without filure, so it must be designed for infinite life. Unlike other elements like shfts, helicl springs re never used s both compression nd extension springs. In fct they re usully ssembled with prelod so tht the working lod is dditionl. Thus, their stress-time digrm is of fluctuting nture. Now, for design we define, Then the stress mplitude nd men stress vlues re given by: if we employ the Goodmn criterion, then The best dt on torsionl endurnce limits of spring steels re those reported by Zimmerli. He discovered the surprising fct tht the size, mteril nd tensile strength hve no effect on the endurnce limits (infinite life only) of spring steels in sizes under 10mm(3/8 inches). or ll the spring steels in tble the corrected Indin Institute of Technology Mdrs

6 Mchine Design II Prof. K.Gopinth & Prof. M.M.Myurm vlues of torsionl endurnce limit cn be tken s: = 310 Mp (45.0 kpsi) for unpeened springs= 465 Mp (67.5 kpsi) for peened springs. The stress mplitude nd men stress vlues re given by: 8 D 8 m D τ = K c nd τ m = K 3 s πd πd 3 If we employ the Goodmn criterion, then τ τ m 1 S s.s + = or n = e su S se S su n τ.s su +τ m.s su The design or resulting fctor of sfety will depend on the spring mteril selected nd their endurnce strength. In the bsence of dt on the endurnce limit, the best dt on torsionl endurnce limits of spring steels re those reported by Zimmerli. He discovered the surprising fct tht the size, mteril nd tensile strength hve no effect on the endurnce limits (infinite life only) of spring steels in sizes under 10mm(3/8 inches). or ll the spring steels the corrected vlues of torsionl endurnce limit cn be tken s: = 310 MP for unpeened springs = 465 MP for peened springs. Indin Institute of Technology Mdrs