Illustrated Sourcebook of Mechanical Components Part 8 doc

Springs 16-29 h Handre in maximum /' -, i ,I position ,.__ . ! I! SPRING-MOUNTED DISK changes ceri- ter position as handle is rotated to move friction drive, also acts as hailt-in limit stop. CUSHIONING device feature4 rapid 111 crease of spring tension because offhe small pyramid ;ingie. Rcbouricl i5 iniiiiiiiuni, too. HOLD-DOWN CLAMP ha5 flat spring as- hembled with initial twist to provide clamp- ing force lor thin iiralcrial. 16-30 12 Detents for Mechanical Movement Some of the more robust and practical devices for locating or holding mechanical movements are surveyed by the author. Louis Dodge FIXED HOLDING POWER IS CONSTANT IN BOTH DIRECTIONS ADJUSTABLE HOLDING POWER WEDGE ACTION COCKS MOVEMENT IN DIRECTION OF ARROW NOTCH SHAPE DICTATES DIRECTION OF ROD MOTION %& 4 LEAF SPR6NG PROVIDES LIMITED HOLDING POWER LEAF SPRING FOR HQBDlN6 FIAT PIECES Springs 16-3 1 DOMED PLUNGER HAS LONG LIFE Holding power is R = P tan a; for friction coeficient. F. at contact siirface R = P (tan a +- F) CONICAL OR WEDGE-ENDED DETENT Py 4 FRICTION RESULTS IN HOLDING FORCE POSITIVE DETENT HAS MANUAL RELEASE AUTOMATIC RELEASE OCCURS IN ONE DIRECTION, MANUAL RELEASE NEEDED IN OTHER DIRECTION LEAF SPRING DETENT CAN BE REMOVED QUICKLY 16-32 17 Ways of Testing Springs C. J. McClintock Clearance resf fengfh Scafe i Compression Torsion Extension spring spring W, should not Fig.1 spring touch block Fig. 2 touch block Fig. 1-Dead-weight testing. Weights are directly applied to spring. In the compression spring and the extension spring teeters, the test weights are guided in the -re to prevent buckling. Instead of using a linear scale, the spring deflection can be measured with a dial indicator. Fig. Mrdnance gage incorporates Wo-no-go” principle. Block is bored for specified test length L. Weight Wi is slightly less than the minimum specified load at L and therefore should not touch block W1 plus load tolerance W2 must touch block for the spring to be acceptable. b@ W / iTTp A Tension Compression (Rod ocfs as pivot paint - I.__- .__ ix and fixture for spring rm/////4 Torsion Fig. 3 Fig. 3-Pilot-beam testing. Fractional resistance offered to movement of parts is low. These testers are more sensitive than those in which the weight is guided in the -re. Many of the commercial testers are based on this principle. Fig. S-Spring against spring. (A) spring scales used in place of dead weights for testing short-run springs. (It) ,I Weights ,Pivot paint &ff 46 ,/” for zeroing in U I stop ,/ Coflar -adjusted for test length . - Ram rod Fig. 4 Fig. 4-Zero-gradient beam. Uses retked pivot-beam principle. Ram rod is pushed up with pedal or ak cylinder. Beam must not touch contacts A or B. Contacting A indicates spring too weak; B indicates spring too strong. X Y , Mavobfe I , ,. scale -clamped to plate Force - LTesf spring ‘\ “Calibrafed fcampressianl ‘\ spring \ Rate (8) ‘‘rest spring fextensionl Similar results obtained by using calibrated springs. Section x calibrated for deflection readings; y for load. Springs 16-33 Spring dimensions are based on calculations using empirical-theoretical equations. In addition, allow- ances are made for material and manufacturing tolerances. Thus, the final product may deviate to an important degree from the original design crite- ria. By testing the springs: (I) Results can be entered on the spring drawing, thus including actual per- formance data; this leads to more realistic future designs. (2) Performance can be checked before assembling spring in a costly unit. Shown below are I2 ways, Fig. I to 5, to quickly evaluate load-deflection characteristics; for more accurate or fully automatic testing, Figs. 6 and 7, describe 5 types of commercial testers. ,Weighing heads , Test weighf _- Detail of - Adjustable canracrs Fi 9.6 weighing head Fig. 6-Fully-automatic testing. Continually moving rotary springs that aIlow lower point to make contact are ejected table with three testing positions. Springs are loaded at position A; springs too strong ejected at B. All springs manually but tested and ejected automatically. Weak reaching point C are ejected as acceptable. Defleciion diol For extension (Ai 1 J I7 I Fig. 7-Commercial testers: (A) Balanced-beam tester uses dead weights for loads. Pantagraph linkage keeps weighing head vertical irrespective of beam movement. Load capacity: 10 Ib. Baldwin-Lima-Hamilton Corp. (B) Calibrated spring tester available in several models for testing loads up to 1000 lb. Load applied manually through gear and rack; motor-driven units can be attained for applying heavier loads. Link Engineering Co. (C) Pneumatic-operated tester uses torque bar system for applying loads and a differential transformer for accurately measuring displacements. Wide table permits tests on leaf springs. Load capacity: 2000 Ib. Tinius Olsen Testing Machine Co. (D) Electronic micrometer tester has sufficient sensi- tivity (0.0001 in.) to measure drift, hysteresis and creep as well as load deflection. Adjustments made by large micrometer dial; contact indicated by sensitive electronic circuit. Load capacity: 50 Ib. J W Dice Co. 16-34 Overriding Spring Mechanisms for low-Torque Drives Henry L. Milo, Jr Extensive use is made of overriding spring mech- anisms in the design of instruments and controls. Anyone of the arrangements illustrated allows an incoming motion to override the outgoing motion whose limit has been reached. In an instrument, for example, the spring device can be placed between Drive_ ~. pin Bracket FIG. 1 Driving shaft Upper drlve Arbor Stop A ! stop e I 25’’ hro &.I Pin, \ L im __-_ Lower spring ‘Spacer FIG. 2 Spring A I Fig. I-Unidirectional Override. The take-off lever of this mechanism can rotate nearly 360 deg. It’s movement is limited by only one stop pin. In one direction, motion of the driving shaft also is impeded by the stop pin. But in the reverse direction the driving shaft is capable of rotating approximately 270 deg past the stop pin. In operation, as the driving shaft is turned clockwise, motion is transmitted through the bracket to the take-off lever. The spring serves to hold the bracket against the drive pin. When the take-off lever has traveled the desired limit, it strikes the adjustable stop pin. However, the drive pin can continue its rotation by moving the bracket away from the drive pin and winding up the spring. An overriding mechanism is essential in instruments employing powerful driving elements. such as bimetallic elements, to prevent damage in the overrange regions. Fig. 2-Two-directional Override. This mechanism is similar to that de- scribed under Fig. 1, except that two stop pins limit the travel of the take-off lever. Also, the incoming motion can override the outgoing motion in either direction. With this device, only a small part of the total rotation of the driving shaft need be transmitted to the take-off lever and this small part ma); be anywhere in the range. The motion of the driving shaft is transmitted through the lower bracket to the lower drive pin, which is held against the bracket by means of the spring. In turn, the lower drive pin transfers the mo- tion through the upper bracket to the upper drive pin. A second spring holds this pin against the upper drive bracket. Since the upper drive pin is attached to the take-off lever, any rotation of the drive shaft is transmitted to the lever, provided it is not against either stop A or E. When the driving shaft turns in a counterclockwise direction, the take-off lever linally strikes against the ad- justable stop A. The upper bracket then moves away from the upper drive pin and the upper spring starts to wind up. When the driving shaft is rotated in a clockwise direction, the take-off lever hits adjusrahie stop B and the lower bracket moves away from the lower drive pin, winding up the other spring. Although the principal uses for overriding spring arrangements are in the field of instrumentatioh, it is feasible to apply these devices in the drives of major machines by beefing up the springs and other members. Spr/ng I Take off Brackef Take off /ever / Arbor’ /ever / . I I stop B I I Stop A Spring B / FIG. 5 Arbor pin Arbor Fig. 5-Two-directional, 90 Degree Override. This double overriding mechanism allows a maximum overtravel of 30 deg in either direction. As the arbor turns, the motion is carried from the bracket to the arbor lever. then to the take-off lever. Both the bracket and rhe take-off lever are held against the arbor lever by means of springs A and B. When the arbor is rotated counterclockwise, the take- off lever hits stop A. The arbor lever is held stationary in contact with the take- off lever. The bracket, which is soldered to the arbor, rotates away from the arhor lever. putting spring A in tension. When the arbor is rotated in a clockwise di- rection, the take-off Iewr comes against stop B and the bracket picks up the arbor lever, putting spring B in tension. , II Take off Stop lever bd FIG. E Springs 16-35 the sensing and indicating elements to provide over- range protection. The dial pointer is driven posi- uvely up to its limit, then stops; while the input shak is free to continue its travel. Six of the mech- anisms described here are for rotary motion of vary- ing amounts. The last is for small linear movements. A Arbor A ,I’ Spring E IY dj * Arbor lever r9 A Take OH m., lever I U Y _ Spring E __Arbor fever FIG. 3 , ,v - - Stop E Oc Stap A Take’ off lever Fig. %Two-directional, Limited-Travel Override. This mechanism per- forms the same function as that shown in Fig. 2, except that the max- imum override in either direction is limited to about 40 deg, whereas the unit shown in Fig. 2 is capable of 270 deg movement. This device is suited for uses where most of the incoming motion is to be utilized and only a small amount of travel past the stops in either direction is required. As the arbor is rotated, the motion is transmitred through the arbor lever to the bracket. The arbor lever and the bracket are held in contact by means of spring B. The morion of the bracket is then transmitted to the take-off lever in a similar manner, with spring A holding the take-off lever and the bracket together. Thus the rotation of the arbor is imparted to the take-off lever until the lever engages either stops A or B. When the arbor is ro- tated in a counterclockwise direction, the take-off lever eventually comes up against the stop B. If the arbor lever continues to drive the bracket, spring A will be put in tension. Arbor d’ Drive pin Spring /’ Adjustable rbor {’ vpr rtop A, le. \ \ Toke off lever FIG. 4 Fig. &Unidirectional, 90 Degree Override. This is a single overriding unit, that allows a maxi- mum travel of 90 deg past its stop. The unit as shown is arranged for over-travel in a clockwise direction, but it can also be made for a counter- clockwise override. The arbor lever, which is se- cured to the arbor, transmits the rotation of the arbor to the take-off lever. The spring holds the drive pin against the arbor lewr until the take- off lever hits the adjustable stop. Then, if the arbor lever continues to rotate, the spring will be placed in tension. In the counterclockwise direc- tion, the drive pin is in direct contact with the arbor lever so that no overriding is possible. Fig. &Unidirectional, 90 Degree Override. This mechanism operates exactly the same as that shown in Fig. 4. However, it is equipped with a flat spiral spring in place of the helical coil spring used in the previous version. The advantage of the flat spiral spring is that it allows for a greater override and minimizes the space required. The spring holds the take-off lever in contact with the arbor lever. When the take-off lever comes in contact with the stop, the arbor lever can continue to rotate and the arbor winds up the spring. Fig. 7-Two-directional Override, Linear Motion. The previous mechanisms were overrides for rotary motion. The device in Fig. 7 is primarily a double override for small linear travel although it could be used on rotary motion. When a force is applied to the input lever, which pivots about point C, the motion is transmitted directly to the take-off lever through the two pivot posts A and B. The take-off lever is held against these posts by means of the spring. When the travel is such the take-off lever hits the adjustable stop A, the take-off lever revolves about pivot post A, pulling away from pivot post B and putting additional tension in the spring. When the force is diminished, the input lever moves in the opponire direction, until the take-off lever contacts the stop B. This causes the take-off lever to rotate about pivot post B, and pivot post A is moved away from the take-off lever. FIG. 7 16-36 Deflect a Spring Sideways Formulas for force and stress when a side load deflects a vertically loaded spring. W. H. Sparing There arc iiian!. dcsignr in which one end of a helical spring must lie mo\.ccl laterally rclati\-c to the other cnd. IIow iiitich force will hc requircd to do this? \Vhat cleflcctiori \vi11 tlic force cause? \\'hat .\tress will rcsult from conihincd 1;iteral and .i.crtical loads? IIerc are forinulas that find the answers. It is assunicd tlut the spring cncls arc hcld parallcl hy a \utiea1 forcc P (which docs not appcx in thcsc formulas), mid that the spring is long cnotigh to allow ovcrlooking the cffcct of closed cnd-turns. Lateral load for ;I stccl spring whcrc JI = iiunilicr of tnriis = (h'd) - 1.2. D = incan dia in., A = corrcction factor. Lateral deflection '4V.rLI) [0.204 (I, - d;' + 0.265 = ~- ~~ ~~~~ . 1wa4 ?'he corrcction factor A caii iic\'cr be unity (sec chart on continuing page); also P can never be zero. This is lxcawc thcrc will always he sonic vertical deflection, and a sidc load will alaays c;iusc a resultant \.crtical force if the ends arc held p:i~"llel and at right anglcs to thc original cciitcr linc. Combined stress whcrc f = vertical-load strcss. Acciiratc within 10'96, thesc foriiiulas show that thc nearer a spring ap- proaches its solid position, thc greater tlic discrcpancy bctwccii calculated and actual load. This results froiii premature closing of thc cnd-tunis. It is best to provide stops to prevent the spring from being com- pressed solid. An example shows the combined stress at the stop position may cvcn be higher than the solid stress caused by vertical load only. A Working Example '4 spring Iix, tlic follou iiig di~~lc~~hioi~.s, 111 iiiclics: Out,sidc clia. 9 Ear dis (d). 1 15/16 Free hright (H) Solid hcight (h) I3 Stop helght. 13 3/4 16 lj2 1,oadcd hoight (L). . , , . . Lateral d(:flcction (&I,) , . . I4 5/lfi 1 1 /2 From thcsc diinci~sionr coillputc \.alucs at loaded licight and stop height. I>oad(YI Stop position position I). 7.0625 7.062.5 n 5.51 5.5 1 y (vcrtical drflcction). 2.1873 2.73 H - tl. 11.,563 L - tl .12.375 (H - d)/D 2.06 2.06 y/(H - d), 0.1.70 0.189 A 1.30 1.40 Q 9400 Ih 9310 lh 11.5li3 11.813 From standard formulas for vertical loads only: Solid load. 36,300 lb Load at stop, 28,500 lb Stress f when solid. 111,500 psi Stress j at stop, .I1 1,200 psi Springs 16-37 A - FAC llllllllllllllllllllll~ llllll 1 2 3 4 5 From the combined-stress formula f, = 111,200 X 1.759 Generally, combined strcss under the worst condi- tioii anticipated should not exceed the solid stress caused by vertical load only. A stop at a reasonable height above solid height is thus desirable-otherwise, spring may have to be modified. = 195,600 psi This stress is so high that settling in service would This particular spring should be redesigned. occur. 16-38 Ovate Cross Sections Make Better Coil Spring Egg shape proves more efficient that conventional round configuration while also saving space and weight. Analysis also casts light on which materials store energy best. Nicholas P. Chironis Almost since helical coil springs were invented, they have conven- tionally been made of round wire. Few engineers have been aware that round wire does not perform as effi- ciently as it should, and that other cross sections often used in helical springs, such as square or rectangular wire, give even poorer results. Now, however, the proposal of a new cross-sectional shape of wire to bring out the best performance in a coil spring is focusing attention on this aspect of spring design. Accord- ing to H. 0. Fuchs, a Stanford Univ. professor, the ideal cross section, based on fatigue tests, is a blend of a circle with an ellipse (drawing). Such egg-shaped wire, Fuchs con- tends, can store more elastic energy than the conventional round wire in a spring taking up the same space. Thus, less spring weight is needed to absorb or store a given amount of energy. Moreover, an egg-shaped or “stress-equalized” spring wire will have a higher resonant frequency than a round wire and will be less subject to flutter. Egg-shaped wire for coil springs is not especially costly to make. What- ever the cross-sectional shape, the wire is, in smaller diameters, drawn through dies with an opening of the desired shape or, in larger diameters, roll-formed to any configuration. Anti-surgc auxiliary. Fuchs, work- ing with John G. Schwarzbeck, a consulting engineer, has also devel- oped an auxiliary coil spring (draw- ing, page 87) that gives anti-surge pro- tection without requiring any more space than the main spring takes up. The turns of the auxiliary coil in- terlace with those of the main stress- equalized spring, which is modified by flattening of its rounded surfaces. As the turns of the larger coil move together during compression, they are frictionally engaged by the turns of the bumper, or anti-surge, spring. Being more flexible, the auxiliary spring contracts as a unit, taking up the surge energy by bending to a slightly smaller radius. Stress peaks. In conventional coil springs with circular cross section, efficiency is curtailed by stress peaks at points on surfaces of the coil turns during deflection of the spring. At the inside of the coil, for example, direct shearing stresses augment the torsional stresses while the shorter metal fibers are twisted through the same angle as the longer fibers at the outer side of the turn. Thus, total stresses are higher at the inner side than at the outer side of the coil. In a round wire, the increased stress at the inside of the turn is ap- proximately 1.6/C times the average surface stress, where C is the spring index, equal to the mean coil diame- ter divided by the wire diameter. A spring index of 5, therefore, means there is about 30% greater peak stress at the inside of the coil turn, over and above the average surface stress. Moreover, spring efficiency is pro- portional to the square of the per- missible stress. So the efficiency of such a spring in fatigue loading, where maximum stress range is the determining factor, is only 60% of the efficiency of the same spring in static loading, where average stress is the determining factor. Differing curvature. In the egg- shaped cross section, the curvature on the inside of a coil turn is sharper than that on the outside. The differ- ence between the two curvatures is calculated to equalize substantially the stresses produced on the surfaces of the coil during axial deflection. The centroid of the cross section is toward the outside of the midpoint between the inner and outer surfaces. Overall length and width dimen- sions of the egg-shaped cross section are approximately related to the coil’s inner and outer diameters by the expression: Circle blends with ellipse to equalize stresses during flexing in new wire shape. 1.2 - =1+- t C where w = overall length of the section in a radial direction normal to the coil axis t = overall width thickness of the section in a direction parallel to the coil axis c =Do + DI 2w Do = outer diameter of coil D, = inner diameter of coil The exact equation for the w/t ratio is a much more involved rela- tionship, but the error in use of the above approximate relationship is slight (graph, page 88). For design purposes, it is important to know the relationship between the radii of in- ner and outer curvatures: f 2r where - - I defines the “egginess” of the oval sec- tion. When t = r, the egginess will, of course, be zero. For the section shown in the drawing (above and right), ,t = 0.6, r = 0.15, and w = 0.9, which works out to an egginess of 1. Fuchs has also worked out the four other formulas needed to design an egg-shaped spring : Stress equation Loa,d-deflection equation Area of section Coil diameter to centroid where A = area of cross section, D = coiI diameter (of centroid of section), f = deflection, G = shear modulus, N = number of active coils, P = load, S = maximum shear stress. S/P = 2.55D/wt2 P/f = Gt4[2.1 (w/t) - 1.1]/8ND3 A = .Irwt/4 D = O.S(Do + Di) + 0.152(w-t) [...]... one-third of the corabout intermediate cases and triaxial respondiny stresses for steel Glass states of stress Fuchs defines R as fiber, which has even lower value of energy stored per unit volume, main- modulus and of density seems to be ly to dodge the nuisance of working worthy of serious consideration only with pounds force and pounds mass for special applications, according to The units of R are... modulus of torsion, Ib/in.* Sp = stress a t minimum compressed height, psi H I = assembled height, in H, = minimum compressed height,V = volume of spring material, in." in W = weight of spring material, Ib H,, = free height, in p = density of spring material, N = number of active coils lb/in.:{ - = 7.5 Step M a l c u l a t e the active solid height Solid height, H , = ( N 8. 5 (.092) = 0. 782 in + =... (50) (11.5) (IO6) - (80 ,000)* ~~ = 0. 18 in.3 the wire diameter, Eq 2: Step 2-Find = 87 3 + 1.000 = 1 .87 3 h For required final load Designing for minimum weight Step 3 4 a l c u l a t e the number of coils, Eq 1: N = (11.5) (lo6)(0.115)4(1.0) 8 (0.95)3-(50T Step 4-Determine height H, = = (N = 5.9 the active solid For required initial load + 1) d 6.9 (0.115) = 1.1H.g 1.1 (.794) = 0 .87 3h Fz H F = Hz = +... MOUNTPIN Figure 2 16- 48 Nonlinear Springs Two forms of nonlinear systems offer improved working characteristics in a wide range of applications Design equations are given for each William A Welch M ANY of today's products that use spring sys- springs for valves, latches, escapements), reciprocating tools tems will function better if a nonlinear type is employed in place of one of the usual linear springs... which describes the rapidity of the change of t h e spring rate, k , with changes in deflection = elastic modulus, psi = harmonic force amplitude, Ib = cross section moment of inertia, in.4 = spring rate, Ib/in P E x x ' x" y z w of application are the vibrating conveyors and sorters, Fig 2 Such machines are tuned, by proper choice of springs, to the operating frequency of the drive motor = free length,... [23-3 (Lo-z)P 2+2 ( L o - z ) ] The bilinear spring can be any of the usual types of springs, arranged so that one of two springs engages the mass when x = a , Fig 1 In such an arrangement, the spring constant of the second portion, k 2 , is the sum of the two spring rates acting together 16-52 Friction-Spring Buffers Here’s a new way of teaming springs to dissipate kinetic energy in rapid, high-impact,... series The buffer spring takes most of the deflection during impact, while the friction unit, installed ahead of the buffer spring, absorbs most of the impact energy 16-53 Springs inst;tlled between 1 ) a resilient bufter spring supported at the closed end of the housing and 2) an axially movahlr plunger for transmission of external forces (Fig I ) Camniing angles of 30 and 36 deg 1s have been found... load; E = modulus of elasticity, psi; b = width of material, in.; t = thickness of material, in and R , = natural radius of curvature, in From this we see that load is directly proportional to width, thus any change in the width of the band will vary the load proportionately Thus, by shaping the bands, springs and spring motors can deliver selective constant or controllable torques of any simple mathematical... resultingofmomentcharacterisis the tics If sum o both characteristhe gradients are identical graphical f and the gradients are locked tics If output shafts are identical together, the sum are locked toand output shafts of the moments of each the sum of the moments of gether, spring remains constant as both springs remains constant as both each springare deflected If are deflected springs one spring is offset... one spring is offset by prewinding orspring is offsetrelative to the If one unwindirig by prewindother spring, a relative to the ing or unwindingnew sum of the moments of a individual springs other spring, thenew sum of the mo- re- ments of the individual springs re- 16-61 Springs s u l k and this rcniains constant as both springs are deflected However the offset decreases the available stroke I n the . the travel of the take-off lever. Also, the incoming motion can override the outgoing motion in either direction. With this device, only a small part of the total rotation of the driving. Area of section Coil diameter to centroid where A = area of cross section, D = coiI diameter (of centroid of section), f = deflection, G = shear modulus, N = number of active. testing. Fractional resistance offered to movement of parts is low. These testers are more sensitive than those in which the weight is guided in the -re. Many of the commercial testers