1、 Chapter 9 Springs 9.1 Types and Characteristics of Springs9.2 Potential Failure Modes9.3 Spring Materials 9.4 Axially Loaded Helical-Coil Springs; Stress9.5 Deflection and Spring Rate9.6 Buckling Analysis of Helical Compression Springs9.7 Procedure and General Guidelines for Spring Design 9.1 Types

2、 and Characteristics of SpringsSprings may be broadly defined as structures or devices that exhibit elastic deformation when loaded, and recover their initial configuration when the load is removed. Usually the term spring denotes a resilient device specially configured to exert desired forces or to

3、rques, to provide flexibility, or to store potential energy of strain for release at a later time. Springs include helically coiled wire loaded by a force along the axis of the helix or by torsional moments about the axis of the helix, thin flat beams loaded in bending, and round bars or tubes loade

4、d in torsion. The commonly used mechanical springshelical-coil springsspiral torsion springMultileaf springsRubber springsPneumatic springsring springBelleville washers (coned-disk springs) 9.2 Potential Failure ModesSprings of all types are expected to operate over long periods of time without sign

5、ificant changes in dimensions, displacements, or spring rates, often under fluctuating loads. The potential failure modes include yielding, fatigue, corrosion fatigue, fretting fatigue, creep, thermal relaxation, buckling, and/or force-induced elastic deformation. 9.3 Spring Materials Candidate mate

6、rials for springs should have high strength (ultimate, yield, and fatigue), high resilience, good creep resistance, and, in some applications, good corrosion resistance and/or resistance to elevated temperatures. Materials meeting these criteria include carbon steel, alloy steel, stainless steel, sp

7、ring brass, phosphor bronze, beryllium copper, and nickel alloys. Any of these spring materials may be formed into bars, wire, or strip by various hot-forming or cold-forming processes. Cold-formed spring wire is produced by cold drawing the material through carbide dies to produce the desired size,

8、 surface finish, dimensional accuracy, and mechanical properties. Spring wire may be obtained in annealed, hard-drawn, or pretempered conditions. Springs are usually cold-formed when wire diameters are less than 10 mm, and hot-wound when wire diameters exceed 16 mm.Music wire Oil-tempered steel valv

9、e spring wire Oil-tempered steel spring wire Hard-drawn steel wire Alloy steel wire Stainless-steel wire Beryllium copper wire Nickel alloy wireSpring wire materials that are widely usedStrength properties of many materials are strongly size dependent, ultimate strength properties for many of these

10、materials may be closely approximated by the empirical expression Sut=Bda (9-1)where Sut = ultimate strength in tension d = wire diameter a = exponent B = coefficientThe exponent a and coefficient B may be evaluated for five of the materials, as shown in Table 9.1. 9.4 Axially Loaded Helical-Coil Sp

11、rings; StressThe design of helical-coil springs involves selection of a material, and determination of the wire diameter, d, mean coil radius, R, number of active coils, N, and other spring parameters (see Figure 9.2) so that the desired force-deflection response is obtained, without exceeding the d

12、esign stress under the most severe operating conditions.For open-coil axially loaded helical springs The primary stress developed in the wire is torsion, whether the load produces extensionor compression. The free body that results when a section is cut through the helically coiled bar, as shown in

13、Figure (b), indicates that the bar experiences a torsional moment T = FR, and in addition, a transverse shear force F. Torsional shearing stressesThe torsional shearing stresses induced in the wire are the primary stresses, but transverse shearing stresses in helical-coil springs are important enoug

14、h to consider. The maximum torsional shearing stress over the surface of the wire is The transverse shearing stress has been shown to reach a maximum value at the midheight of the wire cross section, and to have the magnitudeBecause of coil curvature, a slightly larger shearing strain is produced (b

15、y the torsion) at the inner (shorter) fiber of the coil than at the outer (longer) fiber, inducing a slightly higher torsional shearing stress at the inner fiber. This stress-increasing curvature factor, Kc, may be estimated as where the spring index, c, is defined to be Curvature effectThe maximum

16、shearing stress occurs at the mid-height of the wire at the inner coil radius, and may be estimated by: The maximum shearing stressFor most springs, c will range from 4 to 12. The end loops of helical-coil extension springs must be separately analyzed because stress concentration at the point where

17、the end loop is bent up see Figure 9.4(b), and at the inner radius of the hook see Figure 9.4(a). Stress concentration effect at the end loop 9.5 Deflection and Spring RateAxial deflection of a helical-coil spring under axial load may be found by first determining the magnitude of the relative angul

18、ar rotation between two adjacent cross sections of the wire, spaced a distance dL apart, produced by an applied torque T = FR.The total axial deflection and the spring rateExtending the results for the small segment to the entire flexible spring, we can obtain the total axial deflection and the spri

19、ng rate, respectively:For helical-coil compression springs, Nt, is determined by adding the number of inactive coils, Ni, to the number of active coils N, to obtainFigure 9.6 gives the number of inactive coils associated with each of the more common end conditions used for helical-coil compression s

20、prings. End coil configuration influences on overall spring flexibilityFor the case of extension springs, the end loops contribute additional elasticity to the springs, depending upon the end-loop configuration. The effective number of active coils, N, is obtained by adding the equivalent coils for

21、both end loops, Ne, to the number of coils in the length over coils, Nc, to obtain N=Nc+Ne Helical-coil springs loaded in compression will buckle if axial deflections become too large. Equations for prediction of critical buckling deflection, ycr, developed in a manner similar to column-buckling equ

22、ations, may be expressed in terms of free length Ly, mean coil radius R, and the method of constraining the ends of the spring (see Table 9.2). 9.6 Buckling Analysis of Helical Compression SpringsFig.9.8 shows critical deflection ratio plotted versus slenderness ratio for springs with both ends hing

23、ed ( = 1) and springs with both ends fixed ( = 0.5). Potential buckling failure should be checked using the curves of Fig.9.8. If the deflection ratio for the proposed spring exceeds the critical value read from the curve, the spring should be redesigned.To contain the spring inside a closely fittin

24、g guide cylinder;To insert an internal cylindrical guide mandrel; A diametral clearance of approximately 10 percent of the cylinder or mandrel diameter is commonly used to avoid rubbing between the spring and its guide.An alternative buckling solution1) Design Procedures(1) Based on functional speci

25、fications and contemplated system configuration, generate a first conceptual sketch for the proposed spring, approximately to scale. (2) Identify potential failure modes(3) Select a tentative spring material (4) Select an appropriate design safety factor (5) Calculate the design stress9.7 Procedure

26、and General Guidelines for Spring Design(6) Determine wire diameter, d, mean coil radius, R, and number of active coils, N, so that shearing stress and deflection are independently satisfied.(7) Using the tentative values of d, R, and N, determine spring rate, k, and check to assure that it also mee

27、ts any other functional requirements for k.(8) Select an appropriate end configuration and determine the number of inactive coils (for compression springs) or equivalent extra coils (for extension springs). Calculate total number of coils in the spring.(9) Determine solid height, free height, and op

28、erational deflection to make sure that no design requirements are violated.(10) Check potential buckling of compression springs. (11) Continue to iterate until all design requirements are satisfied. Summarize the final specifications for material, heat treatment, and dimensions. a. If the spring is

29、guided (to prevent buckling), allow a minimum diametral clearance between the spring and the guiding hole or mandrel, or approximately 10 percent of the coil diameter. b. Calculate material strength data with (9-1), if applicable. Otherwise, use procedures for multiaxial states of nonzero-mean cycli

30、c stress to determine failure strength. c. For initial selection of wire diameter, d and mean coil radius, R, try to proportion the spring so that spring index c will lie in the range between 4 and 12; 2) Experience-based guidelines d. If designing a compression spring, closed and ground ends are usually a good choice. If designing an extension spring, the use of full end loops, over center is usually a good choice, unl