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1、JIS JAPANESE I NDUSTRIAL STANDARD Design of Leaf Springs JIS B 2 7 1 0 - 1 9 8 6 Translated and Published by Japanese Standards Association UDC 621.826.23 Printed in Japan 13 S Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing
2、, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- J I S B*2710 8b m 4933608 OOI.12478 5 m , Translation without guarantee standard in Japanese is to be evidence in the event of any doubt arising, the original Copyright Japanese Sta
3、ndards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- JAPANESE INDUSTRIAL STANDARD Design of Leaf Springs UDC 621.826.23 J I S B 2710-
4、1986 1. Scope This Japanese Industrial Standard specifies design of leaf springs (including single leaf springs , hereinafter referred to as the “springs“), to be used for automobiles, railway vehicles, etc. Remark: The units and numerical values given in in this standard are in accordance with conv
5、entional unit, and are the . standard value. 2. Materials Materials to be used for springs shall be in accordance with Table 1 . Applicable Standards and Reference Standards: See page 21. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001
6、, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- J I S B*Z7i10 86 m 4933b08 0032480 3 = , 2 B 2710-1986 Table 1, Materials I Materials -.-.- For au tomobile s For railway vehicles Steel flats specified in JIS G 4801 Typ
7、e B sections or Type C sections of SUP 6, SUP 9, SUP 9 A or SUP 1 1 A As a rule, Type A section of SUP 3 Leaf Strength division of mechanical properties shall be in ac- cordance with either of 4.6, 6.8, 7T, 8.8, 10.9 specified in JIS B 1180, as appropriate. Center bolt clip bolt Strength division of
8、 mechanical properties shall be in ac- cordance with JIS B 1180, as appropriate. Nut Small size hexagon nut of Appendix of JIS B 1181 As a rule, SS 34 and SS 41 of JIS G 3101 clip I As a rule, S W R M 10 and SWRM SV 34 of JIS G 3104 and S W R M I 12 of JIS G 3505 1 10 of JIS G 3505 Rivet I B ac kle
9、S 10 C of JIS G 4051 or killed steel equivalent thereto Remark: Part materials other than those shown in Table 1, shall be agreed upon between the parties concerned. 3. Calculation 3.1 Symbols to Be Used for Design of Springs The symbols to be used for design of springs shall be in accordance with T
10、able 2. Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- Symbol 3-12 of vertical load acting on spring Mean
11、ing of symbol Unit Symbol I mm I I b d I Deflection of spring Meaning of symbol 1 i k % Z l Il 2P k I Spring constant Unit u I Bending stress T I Wind-up torque B I Rotary angle by wind-up I rad II 11 kT I Rotary spring constant N-mm/rad 1 1 kgf * mm/r ad n I Stress due to wind-up torque 3 B 2710-19
12、86 Symbols 1 1 -of 2. span ( ) Im Breadth of leaf Im Thickness of leaf I Geometrical moment of inertia I l U m 3 Modulus of section I- Total number of leaves l- Number of full length leaves Modulus of longitudinal elasticity (2) Notes ( l) Refer to 5.2. ( 2 , Generally, the value of 206X lo3 N / m 2
13、 I21 X lo3 kgf/m2 shall be used. 3.2 Basic Formulae to Be Used for Design of Springs Basic formulae to be used for design of springs shall be of two types of expansion method and leaf end method, and the basic formula for symmetric spring as shown in Fig. 1 shall be as follows: Remark: Out of symbol
14、s used in calculation formulae, the symbol appended with suffix r or i concerns the leaf of r-th or i-th counting from the shortest spring leaf. Further, the symbol appended with suffix n , concerned to the top plate. Fig. 1. Symmetrical Spring 2P Copyright Japanese Standards Association Provided by
15、 IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- JIS B*2730 8b m 4733b08 0032482 7 m 4 B 2710-1986 (1) Expansion Method Calculation formulae for spring constan
16、t and stress according to expansion method shall be as follows: (a) Where the springs are developed stepwise as given in Fig. 2 (1) 6EI, 1 1.S K k = - e- Ir 1. where A=- .=* . p . (3) 2 x 1 , ,=1 Fig. 2. Stepwise Development (b) Where the springs with a definite leaf thickness are developed to trape
17、zoidal state Further, the diagram of formula (5) is shown in Fig. 4. ( 4 ) 6nEI 1 k = - . - 1 . K ( 5 ) 21+1(2-10ge1) 3 n where 8 = n . = I “ . p . ( 6 ) nZ Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Res
18、ale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- 5 B 2710-1986 Fig. 3. Trapezoidal Development Fig. 4. Shape Factor o. 2 0 . 4 O . 6 pL n O . 8 1.0 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/
19、1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- JIS B*Z10 8b 4933608 0032484 O = 6 B 2710-1986 (2) Leaf-End Method Calculation formulae or spring constant and stress according to leaf-end method shall be as f
20、ollows: (7) (8) ( 9 ) k = - 6EIn . 1 . In3 7jn 1,-1 R I3 . ,:-I n . (ui)c=-$l-pi- . i-i where 7 j i = , - a i - i i - i . ( a ) Bi = 1 + (1- pi - ,I3Kt I t - i &-i=- li 3i The diagram for leaf end shape factor is shown in Fig. 5. log,- 3(Ei-3O 2(5*-i)2 + (ti-i13 K,=-l + bi i=,f Ott: leaf breadths at
21、 leaf end parts are shown in Fig. 6. ti: leaf thicknesses at spring leaf are shown in Fig. 6. ( b ) pi-1 - %-1*Ai-i a,-i=- p i Di-i Ii-1 Ii (ai-i=- Di- 1 = (4-1 + vt - i ci-i= (UA: (3- pr- 1 ) p 2 1 - 1 (cl 2 stress at central part of i -th leaf ( N / m 2 Ikgf/m21 1 (do: stress at contact point betw
22、een i-th leaf and (i-1)th leaf ( N / m z kgf/m2 ) Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- 7 B 2710
23、-1986 Fig. 5. Leaf End Shape Factor O I e. =L O 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 . 9 1.0 t e ti 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 O. 8 O. 6 0 . 4 o. 2 Ki Fig. 6. Leaf Breadth and Leaf Thickness at Leaf End Part Copyright Japanese Standards Association Provided by IHS under license with JS
24、ALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- 8 B 2710-1986 Remark: Calculation of spring constant and stress shall be carried a out according to the following procedures: When eleme
25、nts of spring are decided, the values of At+ B, and Cz-, are determined, and therefore %=O is clear. Therefore, at first, 11 is obtained from formula (a), and by inserting it into formula (e), 4 is obtained, further by inserting it into formula (b), RI is obtained. By inserting this Hereinafter , by
26、 repeating the similar calculation , is obtained at last. By inserting 1% into formula (7) , the spring constant is obtained. Further, obtained in the midway of the above calculation is entered in formulae (8) and (9), the stress is obtained. , into formula (a), 12 is obtained. 3.3 Calculation Formu
27、lae to Be Used for Design of Taper Leaf Springs An example of symmetrical single leaf spring having leaf breadth of a definite 6 and the shape changing linearly in leaf thickness is shown in Fig. 7. Load applied at the center of spring is defined as 2 P, and the symbols expressing shape of spring ar
28、e decided as given in Fig. 7. Fig. 7. Taper Leaf Spring The calculation formulae of spring constant shall be as follows: where The calculation formulae of stresses shall be as follows. Provided that u0 is the stress at loading point, and u(=) is the stress at taper part. PI uo= 7 Copyright Japanese
29、Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- 9 B 2710-1986 3.4 Items to Be Considered in Design 3.4.1 Calculation of Unsym
30、metrical Spring The calculation formulae for spring constant of unsymmetrical spring shall be as follows: . n(l+W (12) (i +n) (i +CR*) k=(k,+k,) k, and k, are respectively spring constants of IA side and Z , side, and are f of spring constant to be obtained by applying formulae (1) , (4), (7) and (1
31、0) to symmetrical spring having spring compositions of zA side and ZB side respectively. In the case where the number of leaves andratio of length for zA side and Z , side are equal, the spring constant shall be as given in the following formula: (13) . k=k,A(l+ A) = (k-+k,)7 A(l+A) 1+R The relation
32、 drawing between k and R is shown in Fig. 9. For calculation of stresses, the reactive forces due to vertical load 2 P at both ends shall be calculated from the following formulae, and formulae (3), (6), (8), (9) and (li) shall be applied. . (14) (15) 1 1+R R 1+R PA=%?- . Y,=2P- where PA: reactive f
33、orce at I, side end due to vertical load 2 P (Nikgf) P8: reactive force at 6 side end due to vertical load 2 P (N kgf I) Fig. 8. Unsymmetrical Spring Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03
34、/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- J I S Bsi12730 86 = 4933608 0032488 8 10 B 2710-1986 Fig. 9. Diagram of Relation between k and R 1.0 0.4 O. 8 O . 7 k kA $- ks O . 6 O . 5 .- - “ i u O . 5 O . 6 0.7 O . 8 O . 9 I. o /z 3.4.2 Friction between
35、 Leaves Because the friction between leaves gives large effect on dynamic characteristics of spring, in design of spring number of leaves and insertion of spacer between leaves shall be considered with sufficient care. 3.4.3 Fretting Corrosion Because the fretting corrosion is likely generated at th
36、e central clamping part of spring, it is desirable to preventit by inserting resin or mild steel plate between leaves. Remark: The spring could be broken at U bolt, due to affect of fretting corrosion. 3.4.4 Variation of Span The relation between the camber and the span as shown in Fig. 10 shall be
37、in accordance with the following formulae: . (16) 1 S2 1- (C-e(C+Se 3 s z R- 2(C-e) XC-1 (C+&) (17) 3 9 1 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or netw
38、orking permitted without license from IHS -,-,- 11 B 2710-1986 where R: radius of curvature (mm) c: camber (mm) e: of eye diameter (mm) 2s: span at level (mm) 21 : span at camber C (mm) The diagrams between c and I , and C and L using f- as parameter are respectively shown in Fig. 11 and Fig. 12. Fi
39、g. 10 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networking permitted without license from IHS -,-,- JIS B*Z7l10 86 = 4733608 0032490 b sl 12 B 2710-1986
40、 Fig. Il. Diagram of Relation between c and R 50 40 30 20 10 - 5 - 4- 3- 2- I - 0 . 0 4 0.05 o. I o. 2 0.3 0 . 4 I C S - -5 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo re
41、production or networking permitted without license from IHS -,-,- 13 B 2710-1986 Approx. 60 ti of backle width B e e e Railway ve hicle s 1 S - Fig. 12. Diagram of Relation between C and 1.00 r 0.M /g=o.os 0.q6 0.44 0.42 0.40 0.88 : F 0.82 0.04 G C S - 1 3.4.5 Equivalent Length of Non-Active Part du
42、e to Central Champing The equivalent length of non-active part due to central clamping method as shown in Fig. 13 and Fig. 14 (indicate an example respectively) shall be in accordance with Table 3. Table 3. Equivalent Length of Non-Active Part Use Equivalent length of non-active length Method for ce
43、ntral clamping Automobiles Rigid clamp of U bolt 40 to 60 % of distance of u of I U bolt (Fig. 13) Backle Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or netw
44、orking permitted without license from IHS -,-,- J I S B*E7LO 8b W 4933608 0032492 T 14 B 2710-1986 Fig. 13. Central Clamping of Spring Fig. 14. Central Clamping of Spring for Automobiles for Railway Vehicles 3.4.6 Wind-up As shown in Fig. 15, the rotary spring constant and stress shall be calculated
45、 according to the following formulae and the relation drawing is shown in Fig. 16. . (18) (19) tt T 4 ( 1 +KA) (l+A)(l+A) kT=k12* l + R UTt-7 Further, in the case where number of leaves and L e length ratio at ld. side and the following formula: side are equal, the rotary spring constant shall be ob
46、tained from 4 2 .(20) (i+) (i+n kT = kl Fig. 15. In the Case Where Wind-up Torque T Acts on Spring 21 Copyright Japanese Standards Association Provided by IHS under license with JSALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/15/2007 20:50:36 MDTNo reproduction or networki
47、ng permitted without license from IHS -,-,- 15 B 2710-1986 Fig. 1.2 I. I 1. O 0.9 kr - kl 0 . 8 0.7 0.6 0 . 5 16. Diagram of Relation between k, and R I - i I I h , x=1.5 x=2 I 7 I l i l ShaDe of Each Part of SDring. 1 In the Case of Spring for Automobiles 4.1.1 plates shall be as shown in Figs. 17 to 19. Shape of End Part of Top Plate The main shapes of end parts of Fig. 17. Upturned Eye Fig. 18. Berli