407 1. Calculation 1.1 Symbols Used in Spring Design Formulas Symbols used in spring design formulae are shown in Table 1. 1.2 Basic Formulas Used in Designing of Springs 1.2.1 Compression Springs, and Tension Springs without Initial Tension 1D D L d P 2D (Average Dia.) 1 D D d 2D L (Average Dia.) Reference:L=Na·P+1.5d Reference:L=Na·d+2(D2−2d) 1.3 Points to Note when Designing Springs 1.3.1 Shear Modulus of Elasticity Shear modulus of elasticity (G) listed in Table 2 is recommended for the designing of springs. 1.3.2 Number of Active Winding The number of active winding can be determined as follows. (1) Compression Springs Na=Nt−(X1+X2) Where X1 and X2 are the number of turns at each end of the coil. (a) When only the end of the coil is in contact with the next free coil [Corresponding to (a) ~ (c) in Fig.2] X1=X2=1 Therefore, Na=Nt-2 (b) When the end of the coil is not in contact with the next coil, and the spring end has of a turn. [Corresponding to (a) ~ (e) in Fig.2] X1=X2=0.75 Therefore, Na=Nt-1.5 (2) Tension Springs The number of active winding can be determined as follows. But hooks are ignored. Na=Nt 8NaD3P = ····························· (1) Gd4 = 0 ··········································· (5) P Gd4 k= = ······················ (2) 8NaD3 8DP 0= ································ (3) πd3 Gd 0= ····························· (4) πNaD2 Gd4 Gd4 Na= = ··················· (7) 8D3P 8D3k P k 2 U= = ··························· (8) 2 2 1.2.2 Tension Springs with Initial Tension (Where P>Pi) 8DP 8DP d=3 =3 ················· (6) π 0 π 8NaD3(P−Pi) = ··················(1') Gd4 = 0 ·········································· (5') P−Pi Gd4 k= = ············(2') 8NaD3 8DP 0= ·······························(3') πd3 Gd 0= + i ·····················(4') πNaD2 Gd4 Gd4 Na= = ··········· (7') 8D3k 8D3(P−Pi) (P+Pi) U= ···························· (8') 2 8DP 8DP d=3 =3 ················ (6') π 0 π Table 1 Meaning of Symbols Note (1) In spring calculations, a gravitational acceleration of 9806.65mm/s2, is used. Table 2 Shear Modulus of Elasticity (G) Symbol Meaning of Symbols Unit d Diameter of Material mm D1 Inner Diameter of a Coil mm D2 Outer Diameter of a Coil mm D D1+D2 Coil Mean Diameter= 2 mm Nt Total Number of Winding − Na Number of Active Winding − L Free Length(Length) mm HS Solid Length mm p Pitch mm Pi Initial Tension N{kgf} c D Spring Index c= d − G Shear Modulus of Elasticity N/mm2{kgf/mm2} P Load on Spring N{kgf} Spring Deflection mm Spring Constant N/mm{kgf/mm} Torsional Stress N/mm2{kgf/mm2} Corrected Torsional Stress N/mm2{kgf/mm2} i Initial Stress N/mm2{kgf/mm2} Stress Correction Factor − f Frequency Hz U Spring-Retained Energy N·mm{kgf·mm} Per Unit Volume Material Weight kg/mm3 W Mass of Moving Parts kg Gravitational Acceleration (1) mm/s2 Material G Value N/mm2 (kgf/mm2) Symbol Spring Steel 78×103{8×103} SUP6, 7, 9, 9A, 10, 11A, 12, 13 Hard Steel Wire 78×103{8×103} SW-B, SW-C Piano Wire 78×103{8×103} SWP Oil Tempered Steel Wire 78×103{8×103} SWO, SWO-V, SWOC-V, SWOSC-V, SWOSM, SWOSC-B Stainless Steel Wire SUS 302 69×103{7×103} SUS 302 SUS 304 SUS 304 SUS 304N1 SUS 304N1 SUS 316 SUS 316 SUS 631 J1 74×103{7.5×103} SUS 631 J1 Springs Spring Calculations
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