408 TECHNICAL INFORMATION 1.3.3 Stress Correction Factor The stress correction factor relative to the spring index (C) can be determined by using the following formula or based on Fig.1. 3 4 5 6 7 8 910111213141516171819202122 1.0 1.3 1.2 1.1 1.4 1.5 1.6 d D c= Spring Index Stress Correction Factor (a) Closed End (Non-ground) (b) Closed End (Ground) (c) Closed End (Tapered) (d) Open End (Non-ground) (e) Open End (Ground) (f) Open End (Tapered) (g) Open End 3/ 4 Turn (Non-ground) (h) Tangent Tail End (Non-ground) (i) Pig Tail End (Non-ground) 1.3.4 Solid Length The solid length of a spring can normally be obtained by using the following simplified formula. Generally, the purchaser of a compression spring does not specify the solid length of the spring. As for those compression springs, both ends of which are shaped as shown in (b), (c), (e) or (f) of Figure 2 and for which the solid length needs to be specified, the following formula can be used to obtain the maximum solid length. However, the actual maximum solid length can be greater than the value thus calculated depending on the shape of the spring in question. HS=(Nt-1)d+(t1+t2) ··························································································(10) where, (t1+t2) is the sum of the thicknesses of the coil ends. HS=Nt×dmax ·······································································································(11) where dmax : Material diameter measured when the maximum tolerance is applied for d. 1.3.5 Initial Tension of Tension Springs Cold-formed solid-coiled tension springs are subjected to initial tension (Pi). The initial tension can be obtained using the following formula. Fig-2. Coil End Shape On solid-coiled piano wire, hard steel wire, and other steel wires that are not low-temperature annealed, the initial stress occurs within the hatched range shown in Fig.3. However, if materials other than steel wire are used, or the wire in question is low-temperature annealed, the initial stress taken from within the hatched range in Fig.3 should be corrected as follows. πd3 Pi= i ································································································ (12) 8D 1.3.7 Other Points to Note In spring design calculations, the following points should also be taken into account. (1) Spring Index Excessive local stress can result from too small spring index. Machinability should be considered if the spring index is too great or small. The spring index should be selected from the range of 4~15 when hot forming, and from the range of 4~22 when cold forming. (2) Slenderness Ratio In order to ensure the correct number of active winding, the slenderness ratio for a compression spring (Ratio of free height to coil mean diameter) should be 0.8 or greater. Furthermore, buckling considered, it is generally recommended that the slenderness ratio be selected from the range of 0.8 ~ 4 to prevent buckling. (3) Number of Active Winding The number of active winding should be 3 or more in order to stabilize spring characteristics. (4) Pitch Generally, when the pitch exceeds 0.5D, the spring deflection (load) increases to the extent that the coil diameter changes. This requires correction of the deflection and torsional stress values obtained by the basic formula. Therefore, the pitch should be 0.5D or smaller. The pitch can generally be estimated using the following simplified formula. L−HS p= +d ··································································································· (14) Na 1.3.6 Surging In order to prevent surging, the spring should be selected in such a way that its natural frequency does not resonate with any of the natural frequencies that may act upon the spring. The initial tension can be obtained using the following formula. Fig-1.Stress Correction Factor : Fig-3 Initial Stress : i (Spring formed from steel coil, not low-temperature annealed) 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 (8) (6) (4) (2) (0) (10) (12) (14) (16) (18) (20) 20 40 60 80 100 120 140 160 180 200 220 mm ) 2 (kgf/ i = mm 2 i N/ D d 0 Initial Stress Spring Index c (1) When using stainless steel wire, decrease the initial stress value for steel wire by 15%. (2) If the spring is low-temperature annealed after being formed, decrease the value by 20~35% for springs made of piano wire, hard steel wire, or other stainless steel wires, and by 15~25% for springs made of stainless steel wire. The following examples are for applications of this formula to obtain the initial tension. Reference In place of Fig.3, the following empirical formula can be used to establish the initial stress for springs before low-temperature annealing. G i= 100c (1) Piano Wire / Hard Steel Wire [G=78×103N/mm2 {8×103kgf/mm2}] G i= ×0.75 (0.75 by 25, reduction by low-temperature annealing). 100c Initial Stress Initial Tension πd3 Gd4 229d4 24d4 Pi= i= ×0.75 = 8D 255D2 D2 D2 { } (2) When using stainless steel wire [G=69×103N/mm2{7×103kgf/mm2}] G i= ×0.8(0.8 by 20, reduction by low-temperature annealing). 100c Initial Stress Initial Tension πd3 Gd4 216d4 22d4 Pi= i= ×0.8 = 8D 255D2 D2 D2 { } kg 70d G f=a =a ·············································································· (13) W πNaD2 where, i a= :when both spring ends are either free or fixed 2 2i-1 a= :When one spring end is fixed while the other end is free i=1,2,3 ···················· 4 G=78×103N/mm2 {8×103kgf/mm2}, w=76.93×10-6 N/mm3 {7.85×10-6kgf/mm3} If both spring ends are either free or fixed, the natural primary frequency of a spring can be obtained as follows. d f1= 3.56×105 ··············································································(13') NaD2 4c-1 0.615 = + ··························································(9) 4c-4 c Springs GeometricToleranceIndications
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