1、Manual on Design and Manufaeture of Coned Disk Springr (Belleville Springs) and Spring Washers SAE HS 1582 7W Engineering Society =For Advancing Mobility I Land Sea Air and Space, Manual on Design and Manufacture of Coned Disk Springs (Belleville Springs) and Spring Washers SAE HS 1582 Report of the
2、 Spring Committee, issued June 1988. mw All SE slandard are -acted STANDARDS SEARCH Database and indexed in Um SAE I SAE Information Report First Edition, June 1988 Published by: Society of Automotive Engineers, Inc. 400 Commonwealth Drive Warrendale, PA 15096-0001 No part of this publication may be
3、 reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. ISBN 0-89883-424-4 Copyright 1 988 Society of Automotive Engineers, Inc. This report is published by SAE to advance the state of technical and engineering sciences. The use
4、 of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringe- ment arising therefrom, is the sole responsibility of the user. PRINTED IN U.S.A. SPRING COMMITTEE E. C. Oldfield (Chairman), Hendrickson Intl. G. A. Schremmer (Sponsor
5、), Schnorr Corp. K. Campbell, Ontario, Canada D. Curtin, General Motors Corp. B. E. Eden, N. I. Industries M. Glass, Service Spring Co. L. Godfrey, Associated Spring R. S. Graham, Rockwell Intl. R. A. Gray, Troy, MI D. J. Hayes, HolcroftLoftus P. W. Hegwood, Jr., GMC J. V. Hepke, GMC E. H. Judd, Ass
6、ociated Spring Corp. J. F. Kelly, Marmon Group Inc. M. Lea, GKN Composites D. J. Leonard, Firestone Tire and Rubber Co. J. Marsland, Chrysler Corp. W. T. Mayers, Peterson Amer. Corp. J. E. Mutzner, GMC W. C. Offutt, Key Bellevilles, Inc. J. P. Orlando, General Motors Corp. R. L. Orndorff, B. F. Good
7、rich W. Platko, General Motors Corp. H. L. Schmedt G. R. Schmidt, Jr., Moog Automotive Inc. A. Schremmer, Associated Spring-Barnes Group K. E. Siler, Ford Motor Co. R. W. Siorek, U.S. Army Tank-Auto. Command A. R. Solomon, Analytical Engineering Res. Inc. M. C. Turkish, Valve Gear Design Associates
8、F. J. Waksmundzki, Eaton Corp. CONED DISK SPRING SUBCOMMITTEE G. A. Schremmer (Chairman and Sponsor), Schnorr Corp R. E. Joerres, Barnes Group, Inc. W. C. Offutt, Key Bellevilles, Inc. PREFACE This manual is the latest edition in the group of spring manuals currently under the review of the SAE Spri
9、ng Committee. The preceding SAE manuals on coned disk springs were published in 1950 (First Edition), and 1955 (Second Edition). Developments during the past 30 years necessitated a complete revision. In addition to updating the treatment of Coned Disk Springs, material on other spring washers, not
10、directly related to the Coned Disk Spring, has been added. In accordance with current SAE practice, customary units have been replaced by metric SI units throughout this manual; for a conversion table see the Appendix. TABLE OF CONTENTS CHAPTER 1-INTRODUCTION . 1 CHAPTER 2-DEFINITION AND REPRESENTAT
11、ION . 3 1 .Definition . 3 2 . Representation 3 CHAPTER 3.NOMENCLATURE. UNITS 5 CHAPTER 4-CALCULATION AND FORMULAE. SINGLE DISK . 7 1 . Theory and Limitations 7 2 . Single Disk. Usual Force Application . 7 A . Force-Deflection . 8 B . Stress-Deflection . 8 C . SpringRate . 8 D . Energy Storage Capaci
12、ty . 8 E . Constants K,. K,. K, . 8 F . Load Acting Inside Edges . 8 G . Contact Bearing Flats 9 H . Initially Flat Disk Spring 9 CHAPTER 5-SINGLE DISK. LOAD-DEFLECTION DIAGRAMS . 11 CHAPTER 6-DESIGN CONSIDERATIONS 13 1 . Combination of Single Disks (Stacking) 13 2 . Stack Length 14 3 . Guiding and
13、Clearances, Lubrication 5 . Loading Beyond Flat . 14 6 . Frictional Hysteresis . 15 7 . Presetting, Recovery. Creep and Relaxation 14 4.Alignment 14 15 CHAPTER 7-DESIGN STRESSES 17 1 . Static and Quasi-Static Loading . 17 2 . Repetitive Loading (Fatigue) . 17 3 . “Ideal” Shape of Disk Springs . 18 4
14、 . Minimum Preload . 18 CHAPTER 8-MATERIALS AND FINISHES 19 1 . Spring Materials . 19 2 . Surfaces 20 A. Blank. Oiled . 20 Zinc Phosphate. Black Oxide 20 Shot Peening 20 Teflon Coating . 20 F . Other Coatings 20 B . C . Plating for Corrosion Protection 20 D . E . C”TR 9-DESIGN EXAMPLES . 23 1 . Stat
15、ic Loading . 23 2 . Repetitive Loading . 24 C“TER 10-MANUFACTURING AND TOLERANCES 25 1 . Manuiacturing Methods 25 2 . Tolerances 25 A . Thickness Tolerances 25 B . Diameter Tolerances . 25 C . Overall Height Tolerances 25 D . Force Tolerances 25 E . Reference Dimensions 26 CHAPTER 1 1 -STANDARDIZATI
16、ON 27 CHAPTER 12-MODIFIED DISK SPRING SHAPES . 29 1 . The “Open“ Disk Spring . 29 2 . Radially Tapered Disk Spring . 30 3 . Slotted Disk Spring 30 4 . Serrated Spring Washers . 31 CHAPTER 13-SPRING WASHERS . 33 1 . Curved Washer 33 2 . Wave Washer 33 3 . Finger Washers 34 CHAPTER 14-REFERENCES 35 AP
17、PENDIX-CONVERSION TABLE . 36 . Chapter 1 Introduction Coned disk springs, also known as Belleville Springs, have a long history. In 1835, one Timothy Hackworth, in England, received acknowledgment for an application in a safety valve. A Frenchman, Julian F. Belleville, secured a British patent in th
18、e 1860s for a particular application. At that time, these springs were mainly used in the buffer parts of railway rolling stock and for recoil mechanisms of guns, etc. Whenever space is limited, particularly in the presence of high forces, the use of coned disk springs will be of advan- tage. Linear
19、, regressive, and even progressive load- deflection characteristics can be obtained by varying the basic dimensions or by stacking. A large number of standard off-the-shelf sizes is available, so that custom sizes may not be required. For these reasons, coned disk springs are used today in virtually
20、 all branches of engineering with new applications surfacing all the time. 1 Chapter 2 Definition and Representation 1. Definition F Di - 1 F S Disk springs have the shape of conical washers (shells of truncated cones), with normally rectangular cross sections. Their geometry is defined by the outsi
21、de diameter De, the inside diameter Di, the thickness t, and the overall height L, usually written in the form De X Di X T, L = . mm. A disk spring with De = 50 mm, Di = 25.4 mm, T = 3 mm, and L = 3.6 mm for example can, therefore, be designated as Disk Spring 50 x 25.4 X 3, L = 3.6 mm. For further
22、description, material, surface finish, etc., have to be added. The overall height L is taken as T + H, that is, thick- ness + dish height. A mathematically more correct relation- H T ship is L = H + T cos a, Fig. 4.4. I H. Initially Flat Disk Spring The initially flat disk spring of constant thickne
23、ss (Fig. 4.5) is of little practical interest, mainly because of the need for special loading supports. Equations (2a), (3) to (6) with H = O can be used for calculations. Fig. 4.4-Disk spring cross section, regular (left), with bearing flats (right) B. Width of flats A spring with flats can be calc
24、ulated by using equations (2a), (3) to (6), substituting T for T and H for H. H is the disk height before the flats are machined. A common flat width of B = DJ150, H can be calculated as: H L - 0.9 T (13) In addition, loads and deflections should be corrected with equations (12a) and (12b), Section
25、F, because the loads will be acting inside the edges by the size of the flat width B. The results of such calculations, particularly the stresses, should be taken as a guide only. For standardized sizes with flats, see manufacturers cat- alogs (Ref. 4, 5, 6). Fig. 4.5-Cross section of an initially f
26、lat disk spring 9 Chapter 5 Single Disk, Load-Deflection Diagrams Disk springs are non-linear. The ratio H/T determines the actual shape of the load-deflection diagram (Fig. 5. I). As can be seen, disk springs with H/T - ratios smaller than 0.6 are practically linear over a wide deflection range. Th
27、e diameter ratio R = DJD, has no influence on the shape of the curves. Fig. 5.1 shows, in a non-dimensional representation, these curves up to 100% deflection (S/H = l), that is, up to the flat, bottomed out state. Loading beyond flat is possible with specifically shaped supports. The characteristic
28、s for these large deflections will be point-symmetrical with re- spect to the flat-load point, as long as the spring works within an acceptable stress range. Force F/F, 1.6 1.4 1.2 1 .o .OB 0.6 0.4 0.2 O Deiflection S/H Fig. 5.1 -Calculated characteristics (nondimensional) for disk springs with dier
29、ent ratios HTT. (Compare also Fig. 4.2) (FH: load at flat position) 11 Chapter 6 Design Considerations 1. Combination of Single Disks (Stacking) Disk springs can be stacked in different configurations. This may increase the load, the deflection, or both: Parallel Stacking: This will increase the loa
30、d proportional to the number of springs in parallel, Fig. 6.1. The deflection will remain un- changed. (Friction between disks in parallel is treated in Section 6.5.) FtOM = n.F (n: number of springs in par- allel) Lo = L + (n - 1) T unloaded height of parallel stack Stotal = s Force H Deflection 4
31、in parailei (c) I LO I 2 in parallel (b) I LO T L Series Stacking: Fig. 6.1-Parallel stacking of disk springs. (FH: load at flat, single disk) Disk springs in series will result in in- creased deflection, proportional to the number of disks, Fig. 6.2. Statal = i.S (i: number of disks in series) Lo =
32、 i.L unloaded height of stack in se- ries Fto, = F I 4L .- lu I single disk 2 in series 4 in series Deflection Fig. 6.2-Series stacking of disk springs. (FH: load at flat, single disk) Ftocal = n-F total Force Lo = i L + (n - 1) TI unloaded height Parallel-Series Statal = i.S total deflection H 2H 3
33、H 4H Ci Deflection Fig. 6.3-Parallel/series stacking of disk springs (FH: Load at flat, single disk) (a) Single disk (n = 1) (b) Two disks in parallel (n = 2) (c) n = 2, i = 4 Another combination is shown in Fig. 6.4, resulting in a progressive characteristic. Fig. 6.5 shows a preassembled stack wit
34、h n = 3, i = 25. Force 4FHmj 13 3FH 2FH FH H 2H 3H 4H Deflection Fig. 6.4-Stacking for progressive characteristic (FH: load at flat, single disk) Single disk n = 1 (a) (b) n = 2 (c) n = 3 (d) n = 4 (e) combination Fig. 6.5-Preassembied disk spring stack n=3,=25 For more examples of stacking, see Ref
35、. 4. Springs with ratios WT 1.4 show a force maximum before flat. If such springs are combined in stacks, individ- ual disks may snap through, even before the nominal force maximum is reached, due to tolerance variations of individ- ual disks. For this reason, practically all standard sizes are limi
36、ted to H/T 1.3. Not all disk springs can be flattened out without set be- cause of stress limitations. 2. Stack Length Long stacks may show uneven deflection of the individ- ual disks under load. This effect is more noticeable when disks with a relatively large ratio WT are used. Typically, the disk
37、s close to the moving end will show higher than proportional deflection (with fatigue life consequences, Chapter 7, Section 2), and disks at the non-moving end may appear to undergo very little or no deflection, see Section 4. This is caused mainly by friction between the disks and the guide element
38、 (see also Sections 3 and 4). As a rule, the total length of a stack should not exceed 2 to 3 times its outside diameter. Long stacks also tend to “buckle” under load. Guides prevent large sideways movements, but resulting forces per- pendicular to the direction of the load may cause additional fric
39、tional hysteresis (Section 6). Flat washers can be used to break up a long stack. Such washers should operate with very low guide clearance and have to be thick enough to prevent cocking. 3. Guiding and Clearances, Lubrication Disk spring stacks require guides, either on the inside or on the outside
40、. The diametrical clearance between springs and guides should be about 1% of the respective diameter, possibly as low as 0.5% for springs with very low WT - ratios. Springs with standard rectangular cross-sections (Fig. 1.1) and small radii will not change their diameters perceptibly when loaded. Th
41、e inside diameter may even get larger and the outside diameter smaller under load, unless springs with very high H/T ratios are considered. Very small clearances are desirable when springs are as- sembled on rotating shafts in order to minimize imbalances. Small clearances will also facilitate align
42、ment (Section 4). The guides and the end thrust faces should be smooth and harder than the springs, for example, 55 HRC or more. This is particularly important for repetitive loading. For static or quasistatic loading (Chapter 7, Section i), hardening of guides may not be necessary. Practical consid
43、erations also determine if the outside or the inside diameter of the first and last spring in a stack should contact the supporting face. Lubrication should be provided for repetitively loaded stacks, both between individual springs in parallel and be- tween springs and guides. Extreme pressure, ant
44、i-seize lu- bricants are used for this purpose. 4. Alignment The alignment of springs or spring stacks with respect to the guide should be as perfect as possible. Insufficient align- ment may be the cause of uneven deflection (Section 2) or increased frictional hysteresis (Section 6). If assembled a
45、nd preloaded stacks are accessible, alignment may be possible with a straight edge or by the use of a rubber mallet. If a stack is not accessible, onetime loading to flat will improve alignment. 5. Loading Beyond Flat Sometimes it is desirable to load springs beyond flat, in order to increase the tr
46、avel per disk or to utilize the near zero-spring rate in this deflection range for springs with larger ratios WT (see Fig. 5.1 and Chapter 5). Fig. 6.6 shows a possible arrangement, using guide rings. Advantages are the larger deflection range, possibly with a near zero spring rate and the inherent
47、self-centering feature. Disadvantages are the increase in unloaded height and the higher costs of such an arrangement. Depending on the actual dimensions of the guide rings, the springs will be supported inside the edges as they be- come “flat”. .For load corrections, necessary beyond this point, th
48、e method described in Chapter 4, Section F can be used. 14 I IF single disk 2 in parallel 3 in parallel 4 in parallel I I2 to 3% -C4 to 6% +6 to 9% I8 to 12% Force 5 in parallel Deflection flat I10 to 15% Fig. 6.8-Hysteresis of disk spring stacks. (Also shown: typical boitom-out effect) II 4 in para
49、llel 3 in parallel 2 in parallel single disk Fig. 6.6-Disk spring stack for loading beyond flat Most standard stock sizes can safely be taken to flat position, but may be overstressed when taken beyond flat, resulting in a more or less pronounced set. 6. Frictional Hysteresis Friction results when disk springs slide along the guide under load. In long stacks this may lead to uneven deflection (Section 2), so that the last disks, that is, the non-moving end of the stack, may see little or no deflection at all. If a single spring is loaded between flat plates (Fig. 6.7), th
