GB2212244A - A method of producing a leaf spring assembly - Google Patents

Description

2212244 i A METHOD OF PRODUCING A LEAF SPRING ASSEMBLY.

The invention relates to methods of producing spring assemblies and more particulary but not exclusively to a method for producing a spring assembly of the type in which a number n of spring leaves of different length are clamped together in the order of their lengths so that their mid points are aligned and the longest leaf spring in the assembly may be connected with an structure, as for instance an automobile body, to be resiliently supported.

The conventional method of designing a laminated spring leaf assembly is on the basis that all superposed leaf cross sections are spbject to the same flexure. This assumption is however a rough estimation of the actual state of events taking place and therefore does not permit optimum utilization of the spring material.

Accordingly one object of the present invention is to devise a method for producing a laminated spring assembly in which on the basis of certain basic assumptions, the stress i-n the spring leaves is to be equal.

More specifically the invention may be said to have the aim of devising a method of designing a leaf spring assembly in which assuming the following: (a) a given overall spring rate (b) a given length and breadth or thickness of the longest spring leaf, (c) identical material with the same modulus of elasticity for a] leaves, (d) the stacked leaves to be placed in contact in the middle of the range in which they are held and at the support points, (e) thickness of a spring leaf to be constant along the entire effective,Iength and (f) the breadth of all leaves is to be equal along the effective length, the condition is complied with that on the application of a force to the assembly the maximum stress is to be equal in all spring leaves.

The invention may be said to consist in a method of designing a leaf spring assembly with a number of leaf springs of different length to be arranged in the order of their lengths and held together so that the mid points of their lengths are aligned, said leaf spring assembly being adapted to be mounted so that the two ends of the longest spring I eaf are engaged with a structure to be spring-mounted, characterized in that for the spring leaf assembly to be produced which is to have a given spring rate (C2) and spring leaves (n=1.... i) each of the same material with the same modulus of elasticity, firstly a master spring leaf assembly with the same number of spring leaves (n=1.... i) is computed, said master spring leaves serving as a datum for dimensioning the spring leaves of the spring leaf assembly to be produced and such computation being performed on the basis of the following assumptions, namely:

(a) all master spring leaves consist of the same material with the same modulus of elasticity, (b) all master spring leaves are in contact with each other respectively at points of mutual support and in a central holding zone, (c) the thickness of a master spring leaf is of the same size along the entire effective length thereof, (d) all master spring leaves have the same breadth along the entire effective length thereof, (e) the stress is respectively equal in all master spring leaves between points of support when the assembly is subjected to a force 1 j and each spring leaf is computed on the basis of a given length (12) and breadth (b2) or thickness (h2) of the longest spring leaf to be produced with respect to its dimensions from the master spring leaf which corresponds thereto on the basis of its numeration in the assembly, in 1 which respect on the basis of this master spring leaf (index 1) and the spring leaf (index 2) to be produced the ratio L=11/12 of the spring leaf lengths, the ratio B=bl/b2 of the spring leaf breadths, the ratio H=hl/h2 of the spring leaf thicknesses, the ratio E=El/E2 of the moduli of elasticity and the ratio C=Cl/C2 Of the spring rates are determined and after calculation using the formula C=E.O.B/L3 involving adjustment in accordance with the desired size and using the known data hl, 11, bl, Cl and El of the master spring leaf and of the given data C2, E2, 12 and b2 or h2 the dimension b2 or h2 still sought of the spring leaf to be designed is found and on the basis of the ratio values so computed thereafter each further spring leaf is computed and that on the footing of these values the spring leaves for the spring leaf assembly are produced.

Further features of the invention are defined in the claims.

In the method of the invention the first step is to compute a master spring leaf assembly with ideal ratios and on the basis thereof the dimensions for the spring leaves of the spring leaf assembly are calculated and then the assembly is produced on the basis of the values so obtained.

p The method of the invention will now be explained with the aid of the accompanying drawing. Figure I of the drawing shows the elastic flexure of a cantilever beam. Figure 2 is a diagram of conditions to be fulfilled in the method of the invention.

In the case of an ideal spriny leaf assembly with the leaves 35 stacked to form a laminated structure the forces are, by definition, transmitted from one spring leaf to the next one only at the respective spring leaf ends. Furthermore the lengths of the individual spring leaves and the leaf thickness, which is constant along the full length of each leaf, are so set that in each spring leaf there is the same maximum marginal stress as far as the free leaf ends. 1 Accordingly for the spring leaf assembly to be produced the first step is to compute a master spring leaf assembly with the same number (n) equal to 1.... i leaves, this assembly serving as a master.

The computation of this master spring leaf assembly is performed on the following assumptions: (a) all master spring leaves consist of the same material with the same modulus of elasticity, (b) all master spring leaves are in contact with each other respectively at points of support and in a central holding zone, (c) the thickness of a master spring leaf is of the same size along the entire effective length thereof, (d) all master spring leaves have the same breadth along the entire effective length thereof, (e) the stress is respectively equjal in all master spring leaves between points of support when the assembly is subjected to a force.

Since a spring leaf behaves identically on the two sides of its line of symmetry when subject to a force, the computation of the features of the master spring leaf assembly may be based on the computation of elastic line of a cantilever beam which, as will be seen from figure 1, is loaded at the outer end by the force P and at a second point (corresponding to the support by the next smaller master spring leaf) by an opposing force U.

In the figure la(n) denotes the free length of the master spring leaf (n) in the range a from the central point of holding as far as the position of action of the force U. lb(n) denotes the Iree length of the master spring leaf (n) from the central position cf holding as far as the position of the action of the force P trier-c-,,.

On the basis of the expression E.J. M(x), in which M Q1 denotes the moment of flexure, E denotes the modulus of elasticity, J denotes the superficial moment of inertia (const.) and qdenotes the local flexure, the following equations may be derived for the first range (a) 0, < x < la(n):

1 (1) E.:3-, = KI6C,') - X) (r) E. 3. 1 = P ( L 6(,). X - 71) - U (L OL(.') X -9 Z) cl Z.

2_;< 3.!-2)-+Cl.X4C2 CIE) E.3 - -U-) 2_ 6 For the second range (b)]a 4 K \ lb(n) the following equations apply:

(m) E - j - L (Y-) E. 3 - P.((be-) -X) P. (1 R.1) X - 2) _ GS Z (YE) E - 3 TI ' X 3 4 C3 -X _+ C4 P.(L >""- c) 6('1) 2_C, The constants Cl, C2, C3 and C4 are to be obtained from the following marginal conditions, namely:

1 X = 0 > rt 0 2 X = 0 -> = 0 (no flexure) (horizontal tangent, zero s(ope-) 3 x la(n) - rUa) rUb) (at the point of application of the force., U) is 1 4 x]a (n)) (a) (b) (at the same point of application of force U, common tangent with same slope).

As a result it possible to derive the following equations for the elastic line of the beam of figure 1:

CSM) E.J.1 = valid for x <]a 2- 1 2 X) - u (3.x 3.1 U- b(h) - 6 valid for]a \< x \< lb.

-10L(O1)) In order to assure optimum utilization of the material there is the further basic condition that the force U be equal to the force P, because then the stress and the moment of flexure will be constant in the range (a) x < la- Following the above definition, the next larger master spring 30 leaf (n+ 1), which is to be designed by computation, will have to fulfill the following conditions (see figure 2), namely:

1 At the point x ' lb(n) la(n+l) it must have the same flexure as the given master spring leaf (n).

2 From the point x = 0 to the point of support (with the application of force U=P) by the master spring leaf n) the next master spring leaf (n+l) should have the same maximum marginal stress as the already known master spring leaf or leaves for the length la(n) The equations (VII) and (VIII) for the elastic lines apply 5 but with a d 1 ifferent length and a different leaf thickness h(n+l) in the same manner for the required next master spring leaf (n+l).

The contact condition thus leads to the following equation (IX):

11 E. h3 c 6("4 1) - 1 b(")) (-i-i) - P. 12 3 -Lb(,j Lix,1)) (0 (n)Obeying the further requirement for equal edge stress the following further equation (X) obtained:

P' (16(".1) - 16C.J p R Q01) In the equations (IX) and (X) the formulas for the superficial moments of inertia J and the moment of resistance W of the rectangular cross section assumed for the spring leaf have been incorporated, in which J = b.h3/12 and W = b.h216 with the breadth b and the thickness h.

These two equations (R) and (X) may now be resolved for the with respect of the two unknowns, namely the length lb(n+l) and the thickness h(n+l) so that we have the equation (XI):

1. (16(' 1 3. ib(m)) - CkAs')) h(, ', 1) L (") ( 7- 3b( 1,) - 3 - 1 o. (s.,) and the equation (XII):

2- k (h -t-1) C, Taking as a starting point a first master spring leaf (n) whose length lb(n), breadth b and thickness h(n) are able to be freely selected, in which the length]a is then zero,it is then possible to compute the respective next master spring leaf (n+l) on the basis of the equations (Xl) and(XII). In order to avoid any misinterpretation, it is to be borne in mind that every master spring leaf whose dimensions are computed in this manner with the equations (Xl) and (M1) is to be used for the computation of the next successive master spring leaf as a basic spring leaf and thus its dimensions indexed (n) are to be put in the equations.

It remains to be noted in addition that in the case of this manner of computation with the result lb(n+l) in each case only half of the length of the master spring leaf is produced; the actual length is equal to twice the value Of lb(n+l).

Using the above described computation of the ideal master spring leaf assembly n master spring leaves are designed whose dimensions are not as a rule able to be used directly in a production run.

For this reason each spring leaf of a leaf assembly to be produced is computed, which is to have a certain overall spring rate C2 and to have spring leaves n = 1 i of the same material with the same modulus of elasticity. Such computation is on the basis of a given length and breadth or thickness of the longest spring leaf to be produced on the basis of its dimensions in accordance with its numeration n in the assembly taking into account the same master spring leaf. This method will now be described in more detail.

On the basis of a master spring leaf n_designed by computation whose dimensions are denoted with the index 1, in respect 1 -z of a spring leaf is to be designed, whose dimensions have the index 2, it is possible to work out the modulus of elasticity ratio E El/E2, the spring leaf length ratio L = 11/12, the spring leaf thickness ratio H = hl/h2, the spring leaf breadth ratio B = bl/b2 5 and the spring rate ratio C = Cl/C2.

In accordance with the computation of the spring rate of a cantilever beam it is possible to derive from the formula C=11.O.B/L3 with conversion in accordance with the size sought and after putting in the values El, hl, 11, bl and Cl of the master spring leaf and E2, C2, 12 and b2 or h2 already known of the leaf to be produced n the ideal dimension of the latter. Accordingly on the basis of this computation the ratio values E, L, B, and H, which remain constant, are established for the longest spring leaf to be produced, such values remaining constant for each spring leaf n of the spring leaf assembly to be produced.

On the basis of the values so obtained it is then possible to produce the spring leaves. In the case of direct production using these dimensions there will then be a constant and thus optimum utilization of the material. However, as a rule the values to be found, more especially the thickness will be such that no commercial stock will be available with such dimensions. In such cases it is then necessary to round off the computed dimensions to comply with those of commercial stock. These departures from the computed values should be as small as possible since it is only in this manner that it is possible to achieve the aim of optimum material utilization, at least to a substantial extent.

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Claims (1)

1. Claims

   1 A method of designing a leaf spring assembly with a number of leaf springs of different length to be arranged in the order of their length and held together so that the mid points of their lengths are aligned, said leaf spring assembly being adapted to be mounted so that the two ends of the longest spring leaf are engaged with a structure to be springmounted, characterized in that for the spring leaf assembly to be produced which is to have a given spring rate (C2) and spring leaves (n=l. ...i) each of the same material with the same modulus of elasticity, firstly a master spring leaf assembly with the same number of spring leaves (n=1.... i) is computed, said master spring leaves serving as a datum for dimensioning the spring leaves of the spring leaf assembly to be produced and such computation being performed on the basis of the following assumptions, namely: (a) all master spring leaves consist of the same material with the same modulus of elasticity, (b) all master spring leaves are in contact with each other respectively at points of support and in a central holding zone, (c) the thickness of a master spri'ng leaf is of the same size along the entire effective length thereof, (d) all master spring leaves have the same breadth along the entire effective length thereof, (e) the stress is respectively equal in all master spring leaves between points of mutual support when the assembly is subjected to a force, and each spring leaf is computed on the basis of a given length (12)and breadth (b2) or thickness (h2) of the longest spring leaf to be produced with respect to its dimensions from the master spring leaf which corresponds thereto on the basis of its numeration in the assembly, in which respect on the basis of this master spring leaf (index 1) and the spring leaf (index 2) to be produced the ratio L=11/12 of the spring leaf lengths, the ratio B=bl/b2 of the spring leaf breadths, the ratio H=hl/h2 Of the spring leaf thicknesses, the - 11 ratio E=El/E2 of the moduli of elasticity and the ratio C=Cl/C2 Of the spring rates are ascertained and after calculation in using the formula C=E.O.B/L3 involving adjustment in accordance with the desired size and using the known data hl, 11, bl, Cl and El of the master spring leaf and of the given data C2, E2, 12 and b2 or h2 the dimension b2 or h2 still sought of the spring leaf to be designed is found and on the basis of the ratio values so computed thereafter each fur-her spring leaf is computed and that on the footing of these values the spring leaves for the spring leaf assembly are produced.

   2 A method as claimed in claim 1 wherein each master spring leaf is computed on the basis of the formulas for the elastic line of a cantilever beam which at its free end is subjected to a force P at a distance lb(n) and to an opposite force at a distance la(n) in accordance with the following equations (VII) and (VIII), respectively:

   E. J- 1 = P ( 3. 11,(,1) - X) U 6 ( 3. 1 a(n) - X) va(c- Tor X < 1 a 2P2d (3. L X) - U- (3x - 1 11.l-T 6 6(") - 6 C',(-1)) a < x \< 1 b - 3 A method as claimed in claim 2 wherein the next larger master spring leaf indexed (n+l) fulfills the following conditions, namely:

   1 At the point x " lb(n) la(n+l) it must have the same flexure as the given master spring leaf (n), 2 From the point of holding to the point of support by the previousy computed leaf (n) the next master spring leaf (n+l) should have the same maximum marginal stress as the master spring leaf (n), the force P being equal to the force U so that the stres and the moment of flexure are constant in the range (a) x 4 la- 4 A method as claimed in claim 3 wherein the equations(V11) and (VIII) for the elastic lines, but with different lengths and with a different spring thickness h(n+l) also apply br the desired next master spring leaf (n+l), the following equation (M) being derived from the contact condition, that is to say:

   (M+.I) 2- ( 1 h(M+.1) - 1 b(,-%)) - 3 1 3 IIX$141) E - (ti) - 6 6 and the following equation (X) being derived from the condition for equal marginal stress, that is to say:

   (X) P - L b(.i)) z 0I.+.I) -P-( Lben) - lrtc,,)) PIZ (61) into which respectively the formulas for the superficial moment of inertia J = b.h3/12 and for the moment of resistance W = b.h216 have been incorporated for the rectangular cross section assumed for the 11 J t spring leaf.

   A method as claimed in claim 4 wherein the equations (R) and (X) after rearrangement to give the two unknowns, namely the length lb(n+d) and the thickness h(n+l), in the desired next master spring leaf (n+l) make possible computation in accordance with the following equations (M) and (XII) respectively, namely:

   2 (X1) k 3. 16ch). (1 b(n) - 1 Q(,,)) and (xl) C6C14.1) 6 A method as claimed in claim 1 substantially as described herein.

   7 A spring leaf assembly as produced by the method as claimed in any one of the preceding claims.

   1 Published 1989 at The Patent Office, State House, 6671 High Holborn, London WClR4TP. FuMher copies maybe obtained from The Patent Office. Sales Branch, St Mary Cray, Orpington. Kent BR.5 3RD Printed by multiplex techniques ltd. St Mary Cray, Kent, Con. 1/87