Illustrated Sourcebook of Mechanical Components Part 4 pptx

5-16 slipping rpm, and the horscpowcr pcr 5hoc curve for hp vs p to determine the best value Foi p. Plot the (12) Q sin (CY - a) p, - F, = ______ sin a Solution Numerical example A centrifugal clutch shoe has a radius of 5.25 in. and a width of lining of 2.50 in. Lining pressurc is not to cxcccd 100 psi. Angulai- length of lining is 4 = 108 cleg, and the link is at an angle of a = 48 des. The shoe is pivoted at a distance h of 4 in. from the center. BY Eq (73 tall 8= p [(4)(5.25) (0.80902) -4(1.88496+0.95l0G)T _- 4 (1.88496-0.95106) =l.Sllp Total inward sprinq force of both springs is 15 Ib. BY Eq (2) Weight of shoc-is 7 Ib with its center- of -gravity al a AT,,= -($)(2 5)(5.25)(100)(2.8.3602) COS Q = - 1861 ('08 B radius of 4.6 in. As there are linings on the market with a diRerent coefficient of friction. for values of II. of 0.1. 0.2. 0.3, BY Eq (3) 0.4 and 0.5 find the corresponding v'alues ot' forccs Q, R, :ind F,-F,. Find the torque T, the corrcsponding N,,= -(i12.0 sin 0 2. Floating-link design Clutches P 0.1 5-17 ~~ tan 8 8 N,, NU F, F,, N,-F NAF, f ,,I- 0 1 0.15112 8'35.6' -18402 -91.6 9.2 -184.0 -1831 0 -275 6 75,960 1852 Then 0.2 0.3 also 0.30225 16'49.0' -1774.1 -177.3 35.5 -354.8 -j738 6 -532.1 283,130 I818 0.45337 24'23.3' -1695.1 -253.1 75.9 -508.5 -1619.2 -761.6 580,030 1789 Tn hp=- 63,000 0.4 0.5 %he calculations are bcst carried out in tabular form (see table). Thus, for the case of p = 0.1 tan 0 = 0.1511 0 = 8" 35.6'; ('OS 6 = 0.9888 N, N, = -612.9 (0.1494) = -91.6 lb -1861 (0.9888) = -1840.2 lb 0.60449 31' 9.2' -1592.7 -317.1 126.8 -637.1 -1465.9 -9542 910,500 1749 1 0.75562 37' 4.5' -1484.9 -369.5 184.7 -742.4 -1300.2 -1111.9 1,236,320 171 I , By Eq 4, 5, and 8 P, = -0.1 (-91.6) = 9.16 lb 0.1 0.2 P,, = 0.1 (-1840.2) = -184.0 lb ~~-~_____- 8 = Vi- 1840.2-t-9.16)2+(-91.6-18$.0)" 0.15052 8'33.6' 371 39'26.4' 0.63527 I583 1102 1598 2019 35.3 0.30605 17' 1.0' 716 30'59.0' 0.51478 I259 2126 1274 1-1 = 1852 lh BY Eq 9 0.3 0.4 -273.6 - 1831 tan 0 = -~ ~ - = 0.15052 0.47036 25'11.4' 1024 22'48.6' 0.38768 933 3046 948 1556 75.2 E 0.65093 33' 3.7' 1284 14'56.3' 0.25795 607 3517 622 1260 76.3 ~ /3 = 8" :3:3.(i' By Hq 11 and 12 P, = 1.382 + 15 = 1598 Ib Thus 1' = 11,140 (0 1) (0.9888) = 1102 lb-in. n = .io ,j 41598- = 2019 rpm I I I 0p 0.1 0.3 4. Variation of horsepower with coefi- cient of friction for the floating-link clutch analyzed in the numerical ex- ample. Note that best gripping power is obtained with shoe-linings having a coefficient of about 0.35%. Calculations for various iinings 1 0.5 1 0.85518 40'32.2' 1496 7'27.8' 0.12990 299 4448 314 1011 63.2 1 5-18 Small Mec for Precise Clutches used in calculating machines must have: (1) Quick response-lightweight moving parts; (2) Flexibility-permit multiple members to control operation; (3) Compactness-for equivalent capacity positive clutches are smaller than friction; (4) Dependability; and (5) Durability. Marvin taylor PAWL AND RATCHET SISGLE CYCLE CLUTCH (Fig. 1). Known as Dennis Clutch, parts B, C and D, aro primary components, R, heing the driving ratchet, C, the driven cam platc and, I), tho connecting pawl carryid by the cam plate. Normally the pawl is held disengaged by the lower portion of clutch arm A. When activated, arm A rocks counter-clockwise until it is out of tho path of rim F on cam plate C and permits pawl D under tho effect of spring E to engage with ratchet B. Cam plate C then turns clockwise until, near the end of one cyde, pin G on the plate strikes the upper part of arm A camming it clockwise back to its normal position. The lower part of A then performs two functions: (1) cams pawl D out of engagement with the dri+ing ratchet B and (2) hlocks fnrther motion of rim f and the cam plate. Fig. I PAWL AND RATCHET SINGLE CYCLE DUAL CONTROL CLUTCH-(Fig. 2). Principal parts are: driving rztohet, B, directly connected to the motor and rotating frccly on rod A; driven crank, C, directly connected to the main shaft of the machine and also free on A; and spring loaded ratchet pawl, D, which is carried by crank, C, and is normally held disengaged by latch E. To activate the elutch, arm F is raiscd, permitting latch E to trip and pawl D to engage with ratchet E. The left arm of clutch latch 6, which is in tho path of the lug on pawl D, is normally permitted to move out of interferrnre by the rotation of the camming edge of era& C. For certain operations block W is temporarily lowered, preventing niotion of latch C, resulting in dismgagement of thc clutch after part of the cycle until subsequent raising of block H pcrmits motioii of latch C and resumption of the cyele. PLANETARY TRANSWISSION CLUTCH (Fig. 3). A positive clutch with external control, two gear trains to provide hi-directional drive to a calculator for qcling the machine and shifting the carriage. Gear A is the driver, gear I. the driven member is directly corxneeted to planet carrier F. The planet consists of integral gears B and C; E3 meshing with sun gear d and free-wheeling rtng gear 6, and C meshing wirh free-whceling gear D. Gears D and C carry projecting lugs, E and H respectively, which can contact formings on arms J and K of the control yoke. When the machine is at rest, the yoke is centrally positioned 50 that the arms J and K are out of the path of the projecting lugs permitting both D and G to free-wheel. To engage the drive, the yoke rocks elockwise as shown, until the forming on arm K engages lug H blocking further motion of ring gear C. A solid gear train is thereby established driv- ing F and L in the same direction as the drive A and at the same time altering the speed of D as it continues counter-clockwise. A reversing signal rotates the yoke coun- ter-clockwise until arm J encounters lug E blocking further motion of D. This actuates the other gear train of the Same ratio. FlQ 2 Fig. 3 L Clutches 5-19 € 'E! Shift clutch F I OVERLOAD RELIEF CLUTCH (Fig. 6). This is a simply constroered, double- plate, spring loaded, friction coupling. Shaft G drives collar E which drives slotted plates C and D and formica disk. B. Spring H is forced hy the adjusting nuts, which are serewed on to collar E, to maintain the nnit under axial pressure against the shoulder at the left end of the collar. This enables the formica disks B to drive through friction against both faces of the gear whieh is free to turn on the collar, eausing output pinion J to rotate. If the machine should jam and pin- ion J prevented from turning, the motor can continue rnnning without overloading while alippage takes place between formica plates B and the gear. MULTIPLE DISK FRICTION CLUTCH (Fig. 4). Two multiple disk friction clutches are combined in a single two-position unit which is shown shifted to the left. A stepped cylindrical housing C enelos- ing both clutches is carried hy solf-lubricated hrar- ing E on shaft J and is driven by the transmission gear W meshing with the housing gear teeth K. At either end, the housing carries multiple metal disks Q that engage keyways Y and can make frictional contact with formica disks N which, in turn, can contact a set of metal Jisks P which have dotted openings for coupling with flats on sleeves B and W. In the position hhown, pressure is exerted &rough rollers L forcing the housing to the left making the left clutch compact against adjusting nuts R, thereby driving gear A via sleeve B which is connected to jack shaft J by pin U. When the carriage is to he shifted, rollers L force the hous- ing to rhe right, first relieving the pressure between the adjoining disks on the left clutch then passing through a neutral position in which both clutches are disengaged and finally making the right clutch compact against thrust bearing F, thereby driving gear G through sleeve W which rotates freely on the jack shaft. SINGLE PLATE FRICTION CLUTCH (Fig. 5). The hasic clutch elements. formica disk A, stcel plate B and drum 6, are normally kept separated by spring washer G. To engage the drive, the left end of a control arm is raised, causing ears F, which sit in slots in plates H, to rock clockwise spreading the plates axially along sleeve F. Sleeves E and P and plate B are keyed to the drive shaft; all other members can rotate freely. The axial mo- tion loads the assembly to the right through the thrust ball bearings K against plate L and adjust- ins nut M, and to the left through friction surfaces on A, B and C to thrust washer S, sleeve E and against a shoulder on Ehaft D, thus enabling plate A to drive %he drum C. 5-20 Serrated Clutches an S L. N. Canick F Fig. I (A) Toothed clutch Driving rorque Fl (5) Detent i Where : rn =ratio of tooth thickness to tooth n = number of teeth in wheel spoce ot radius R r/ R f =T/R IN THE DESIGN OF straight toothed components such as serrated clutches, Fig. 1 (A), and detent wheels, Fig. 1 (B) , the effective pitch radius is usually set by size considera- tions. The torque transmitting capacity of the clutch, or the torque resisting capacity of the detent wheel, is then obtained by assigning suitable values ro the engaging force, tooth angle, and coefficient of friction. The nomogram, Fig. 2, is designed to be a convenient means for considering the effect of variations in the values of tooth angle and coefficient of friction. For a given coeff- cient of friction, there is a tooth angle below which the clutch or detent is self-locking and will transmit torque limited only by its structural strength. Where T = torque transmitted without clutch slip, or torque resisted R = edective clutch, or detent wheel, radius, in. F = axial, or radial, force, lb .f = tangential force acting at radius R, lh N = reaction force of driven tooth, or detent. :irtiiiq norm:il to by detent wheel, lb in. tooth face, Ih ,u = coefficient of friction OI tooth rn:i tei.i:il 0 = see Fig. 1(R: = angle of tooth face, ~PN f< = (1 A I* tiin O,/(t,zzn ij - u) a statement of the conditions of equilibrium for the forces acting on a clutch tooth will lead to the following equation 1' = it F K (1 A similar statement of the conditions of equilibrium for the forces acting on a 100th of the detent wheel shown in Fig. 1(B) will lead to the following equation: '/'= (2, From Eqs (1) and (2), when all other rerins hnve cow stant values, it is obvious that the required axial force, cr the radial fo:ce, diminishes as the value of K increases. Dependent upon the values of 0 and p, the value of K can vary from zero to infinity. The circular nomogram shown in Fig. 2 relates the values of the parameters I(. 0, rind that satisfy the basic equation Ir' 11, l(c~rs w' '%I - air1 \- Clutches 5-2 1 R = (1 + p tan @)/(tan e - p) EXAMPLE I. Find the maximum tooth angle for a self- lodting clutch, or for which K is infinity, taking the coeffi- cient of friction as 0.4 minimum. SOLUTION I. Line I through these values for K and p on the nomogram gives a maximum tooth angle slightly less than 22 deg for the self-locking condition. EXAMPLE 11. Find the minimum value of K to be expected for a clutch having a tooth angle of 30 deg and a coefficient of friction of 0.2 minimum. SOLUTION IL Line I1 through these values for 8 and p on the nomogram gives a value for K of 3 approximately. EXAMPLE 111. Find the value of K for a flat-face (8 equals 90 deg) friction clutch, the face material of which has a coefficient of friction of 0.2. Compare its torque transmit- ting capacity with that of the toothed clutch of Example 11. SOLUTION 111. Line 111 through these values for 0 and p on the nomogram gives a value for K of 0.2. Torque transmitting capacity of flat-face clutch : Torque transmitting capacity of toothed-clutch : T= 3RP Thus for equal effective radii and engaging forces, the torque capacity of the toothed-clutch is 3/02, or 15, times greater than that of the flat face clutch. T = 0.2RF 40 Fig. 2 5-22 Spring Bands Grip Tightly to Drive Overrunning Clutch New spiral-band clutch Roller clutch Sprag clutch actuates clutch Spiral-band assembly releases clutch Contact area with pulley (typical each clutch band) Spiral bands direct force inward as outer ring drives counterclockwise. Roller and sprag types direct force outward. A new type of overrunning clutch that takes up only half the usual space employs a series of spiral- wound bands instead of the conven- tional rollers or sprags to transmit high torques. The new dcsign (draw- ings, above) also simplifies the as- sembly, cutting costs as much as 40% by eliminating more than half the parts in conventional clutches. The key to the savings in cost and bulk is the new design’s freedom from the need for a hardened outer race. Roller and sprag types must have hardened races because they transmit power by a wcdging action between the inner and outer races. Role of spring bands. Overrun- ning clutches, including the spiral- band type, slip and overrun when reversed-in drawing above, when outer member is rotated clockwise and inner ring is the driven member. The new clutch, developed by Na- tional Standard Co., Niles, Mich., contains a set of high-carbon spring- steel bands (six in the design illus- trated) that grip the inner mcmbcr when the clutch is driving. The outer member merely serves to rc- tain the sorine anchors and to Dlav a part in actuating the clutch. Since it isn’t subject to wedging action, it can be made of almost any mate- rial, and this accounts for much of the cost saving. For example, in the automotive torque converter in the drawing at right, the bands fit into the aluminum die-cast reactor. Reduced wear. The bands are spring-loaded over the inner mem- ber of the clutch, but they are held and rotated by the outer member. Thc centrifugal force on the bands thus releases much of the force on the inner member and considerably dccreases the overrunning torque. Wear is, therefore, greatly reduced. The inncr portion of the bands fits into a V-groove in the inner member. Whcn the outer member is reversed, the bands wrap, creating a wedging action in this V-groove. This action is similar to that of a spring clutch with a helical-coil spring, but the spiral-band type has very little unwind before it over- runs, compared with the coil type. Thus it responds faster. Edges of the clutch bands carry the entire load, and there is also a conmound action of one band uDon I converter Stator- n Spiral clutch bands can be bought separately to fit in user’s assembly. another. As the torque builds up, each band pushes down on the band beneath it, so each tip is forced more firmly into the V-groove. National Standard plans to sell the bands as separate components, without the inner and outer clutch members (which the user customar- ily builds as part of his product). The bands are rated for torque ca- pacities from 85 to 400 ft lb. Ap- plications includc auto transmissions and starters and industrial machin- ery. 0 Clutches 5-23 Accurate Solution for Disk-Clutch Torque Capacity Nils M. Sverdrup IN COMPUTING TORQUE CAPACITY, the mean radius R of the clutch disks is often used. The torque equation then assumes the following form: T = PpRlL (1) Where T = torque, in lb P = pressure, lb. p = coefficient of friction R = mcan radius of disks, in. n = no. of friction surfaces This formula, however, is not math- ematically correct and should be used cautiously. The formula’s accuracy varies with the ratio D,/D,. When DJD, approaches unity, the error is negligible; but as the value of this ratio decreases, the induced error will increase to a maximum of 33 percent. By introducing a correction factor, 9, Eq (1) can be written T = PpRn4 (2) The value of the correction factor can be derived by the calculus derivation of Eq (2). ’ Sketch above represents a disk clutch with n friction surfaces, pres- sure between plates being p psi. In- side and outside diameters of effective friction areas are D, and DO in., re- spectively. Since the magnitude of pressure on an element of area, dA, at distance x from center is pdA, the friction force is pdAp and the moment of this force around the center is Integrating within limits D,/2 and DO/2 and multiplying by 12 friction surfaces, the expression for total torque in in lb is obtained. Hence PdAP. T =g:2 pdApxn (3) but Substituting in Eq (3) dd = 2?rxdx (4) or T = 0.262 ppn (Dos - D?) (5) If the total pressure acting on clutch disks be P lb, the expression for pres- sure per unit area is P = (xj4) (DO* - D1’) Substituting this value for p in Eq (5) Do2 + Do DI + D? (6) Do + Di T = 0,333 Ppn Now let Dl m so that, D1 = m DO (7) DO -= Substituting in Eq (6) (8) Similarly, by substituting value of Dl from Eq (7) in Eq (2), and hav- ing 1+m2+m lfm T = 0.333 PpnDo DO + m Do 4 nd T= Pp Or T = 0.25 Ppnd Do (1 + m) 0.25 Ppnd DO (1 4- m) = 0.333 Ppn DO +m (9) Equating expressions (8) and (9) l+m*+m and solving for +, the result is 1 -I- m2 + m (1 + m)* .$ = 1.333 X With various diameter ratios, the values for were computed and rep- resented in graph herewith. By using this graph and Eq (2), accurate values I of torque can be easily determined. I L LU S T RAT E D S OU RC E B 0 0 K of ME C HAN I CAL C 0 M P 0 N E NTS SECTION 6 EALS Rubber Seals for Oil Retention Non-Rubbing Seals for Oil Retention How to Seal Air Ducts that Separate More Seals for Ducting that Separate Window Awning Unit Sealing Window Casement Unit Seals Multiple Seals & Bonding for Dam Retrofitting 6-2 6-4 6-6 6-8 6-10 6-1 1 6-12 Seals & Packings 6-3 abrasive surroundings. Types that are held against the rotating member by spring pressure can be used where there is a pressure head of fluids within the assembly or on the exterior. For high pressure stuffing box and O-ring type seals are used. O-rings are also used for zero leakage. Bronze ,bearing I \ \ Housing - Shaft I \ \ Housing haft L I- (- - - - -/Garter or stomped - -) Bronze bearing Housing 4austing stud ,/and nul FIG. &Rubbing seals, of the type shown, (A), have wide- spread use in all types of equipment. The spring tension and sealing ring material may be varied so that a variety of applieations can be handled. Small units can be had where the 0. D. is the same as the 0. D. of the sleeve bearing, (B), thus eliminating the counterboring operation on the housing. The seal may be reversed and used to keep foreign matter out of the assembly. A drain hole may be provided to earry away surplus lubricant. Retention is by press fit on the outside diameter. FIG. 5-Rubbing seals of the stuffing box type (A), are used where high pressure are encountered. It can be used for all types of motion and the packing material can be varied de- pending upon the fluid to be sealed and the application. For rotating motion some leakage is necessary so it cannot be used when permissible leakage is zero. O-rings can also be used for rotary motion if the speed is slow. Special designs use O-ring seals (B), when zero leakage is demanded for either stationary or reciprocating motion. This ring is made of natural rubber or synthetic rubber de- pending on the type of solution resistance required. Synthetic rubber, such as buna or neoprene, is resistant to aromatic hydrocarbons, while natural rubber resists the action of alco- hol and glycerine. 0-rings ean be located either in the shaft or in the housing and any movement or pressure forces the ring to one side, thereby forming a tight seal. -I . .\ ,o-r'"P ,', !$! I. [...]... Fasteners 9 -40 Lanced Metal Eliminates Separate Fasteners 9 -42 Lanced Sheetmetal Parts 9 -44 Joining Circular Parts without Fasteners 9 -46 Joining Sheetmetal Parts without Fasteners 9 -48 Fastening Sheetmetal Parts by Tongues, Snaps or Clinching 9-50 Retainers for Circuit Boards 9-52 Handles for Printed Circuits 9-60 Friction Clamping Devices 9- 64 Clamping Devices for Aligning Adjustable Parts 9-66 How... degrading effects when heat-treated parts are involved Precision of parts can be maintained because thickness of the lubricating film can be specified between 15 and 40 millionths of an inch, with a tolerance of 5 millionths, plus or minus Because of its simplicity, the process can be applied to parts after they have been assembled MPB is already looking into the possibility of using Dicronite on its customers’... that the molecules of the metallic coating are bonded directly to the metal substrate This souping-up of the surface seems to increase life ot parts by three to seven times The lubricating film has a lower coefficient of friction than that of graphite It is highly resistant to wear and has withstood pressures to 300.000 psi, temperatures from -40 0 to 900 F in air, and temperatures to 240 0 F in vpcuum... Laboratories hit upon the idea of coating the boundary surfaces of a bearing (drawing, page 45 ) with a film that has a critical surface tension of wetting below that of the surface to which it is applied and that of the liquid to be retained The Navy tested several chemical compositions and found the fluorinated methacrylates, manufactured under various trade names, to be the bcst type Use of such barrier films... they must be designed to fit the particular installation REFERENCE: Which Bearing and W h y ? by Arnold 0 DeHart, Senior Researcl Engineer, Research Laboratories, General Motors Corporation, Warren, Mich Paper presented at the 1959 Design Engineering Conference, Philadelphia, Pa Paper No 59-MD-12 ILLUSTRATED SOURCEBOOK of MECHANICAL COMPONENTS SECTION 9 Various Methods of Locking Threaded Members 9-2... 225 F For MPB’s tests, bearings made of AIS1 44 OC were selected because they need only a 72-hr soak, compared with 360 hr for parts made of SAE 52100 steel T C P works well with lubricating oils and can be used in team with barrier films to improve bearing performance One word of caution, however, was given to the Bearing Conference by C H Hannan, MPB’s manager of research: Don’t expect TCP to noticeably... contact with hub and shaft, Ib -Radius of shaft, in p Coefficient of friction e -Friation angle (tan 0 = 1) C Y -Ring angle (16' 40 ' used in example) n - Number of ring sets PI -Radial thrust of &st ring set, lb S, - Compressive stress, psi D - Shaft dimeter, i n T - approximately 0.16, the torque equation shows that the first ring set will transmit approximately 50% of the theoretical torque value obtainable... based on these 4 types, gives axial load necessary to produce a given torque For example, a 1-in shaft that must transmit 3 hp, or 630 1b.inT requires an axial force of approximately 3000 Ib in a Type 1 mounting Types 2 and 3 would require 240 0 Ib and Type 4, 1500 Ib Radial thrust of the first outer ring against the hub is given by the cquation: PI = tan (a +FA .-.- tan e e) + For values of the ring angle... or the outer one In either case, the existence of the whirl phenomenon often causes severe damage through random or continuous torque surges Tests by Split Ballbearing Div., Lebanon N.H., indicate that stability of retainers is improved by designing square instead of round pockets in them As C A Griffiths, manager of the company’s product enpincerins department, told the Bearing Conference: Whirl can... coefficient of sliding friction = film thickness, in = length, in direction of flow, in = supply pressure, psi = pressure, psi = velocity, in per sec = force, Ib = eccentricity ratio = coeffiFient of absolute viscosity, lb-sec/ sq in = AE= b = c = e F 1s h L Bearings, 3 V A R I A T I O N OF po p 1‘ Yo W FATIGUE L I F E O F BALL BEARINGS c p 240 0 0 c _ t _200 w ! O O O lb rodid/- l0,OOO lb lhrusf L U 2,000 4, 000 . -612.9 (0. 149 4) = -91.6 lb -1861 (0.9888) = -1 840 .2 lb 0.6 044 9 31' 9.2' -1592.7 -317.1 126.8 -637.1 - 146 5.9 -9 542 910,500 1 749 1 0.75562 37' 4. 5' - 148 4.9 -369.5. angle of a = 48 des. The shoe is pivoted at a distance h of 4 in. from the center. BY Eq (73 tall 8= p [ (4) (5.25) (0.80902) -4( 1.8 849 6+0.95l0G)T _- 4 (1.8 849 6-0.95106). tan 0 = -~ ~ - = 0.15052 0 .47 036 25'11 .4& apos; 10 24 22&apos ;48 .6' 0.38768 933 3 046 948 1556 75.2 E 0.65093 33' 3.7' 12 84 14& apos;56.3' 0.25795 607 3517