US2628605A - Cam mechanism and method for manufacturing the same - Google Patents

Description

Feb. 17, 1953 J. F. JONES ET .AL n 2,628,605

CAM MECHANISM AND METHOD FOR MANUFACTURING THE SAME Filed Nov. 2, 1950 3 Sheets-Sheet 1 if; ,L

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Feb. 17, 1953 J. F. JONES ETAL 2,528,605

cAM MEcHANIsM AMD METHOD EoR MANUFACTURING THE sAME /aasa a 7a la fa 4a ,5a :a /a a IN V EN TOR.S. )g/f; 7X2 e s. F4557? C? Alk/424mm Feb. 17, 1953 ,vous

CAM MECHANISM AND METHOD FOR MANUFACTURING THE SAME' Filed NOV. 2, 1950 3 Sheets-Sheet 5 Mya/Lx MMA/4 Patented Feb. 17, 1953 CAM MECHANISM AND METHOD FOR MANUFACTURING THE SAME John F. Jones, Berkley, and Fred F. Timpner, Birmingham, Mich., and Robert C. Juvinall, Chicago, Ill., assignors to Chrysler Corporation, Highland Park, Mich., a corporation of Dela- Application November 2, 1950, Serial No. 193,632

This invention relates to cam mechanism and more particularly to cam surface contour and the dimensions to which the contour is formed for providing smooth and durable performance in service. The instant improvement is most needed in the valve train of high speed automotive engines which employ overhead valves, but is not necessarily limited to automotive engines and high speed cam trains of extended length having control over the operation of overhead valves.

Cams are traditionally cut to contours developed on the basis of circular arcs and straight line tangents in combinations such that the arcs are tangent at each end either to another circular arc or to a straight line tangent. True to be sure, the geometry and calculations are simple but the resulting behavior of the ordinary cam at high speeds is far from satisfactory where long trains are involved. High rate return springs for the cam follower are, of course, necessary to prevent bounce under such circumstances and even then other dynamic disturbances are likely to show up. Moreover, the excessively high rate of spring, to which resort must be made, is likely to cause pitting and galling at the cam nose owing to the maximum spring force being exerted over what turns out to be the minimum contact area exposed by the cam during its cycling.

According to a feature of the present invention, a cam is provided in which the maximum spring forcer and the maximum unit pressure on the cam facemay be held to allowable limits even though the cam train is relatively long and operating at high speeds.

4According to another feature, a cam is provided in which the acceleration forces applied to the cam follower are'applied gradually.

According to still another feature of the invention is the provision of a cam mechanism in which the force necessary to decelerate the inertia of the train without bounce varies according to the spring force available. That is to say, as contrasted with the traditional practice of designing the cam and then selecting the spring believed desirable for the cam, the improved practice makes provision whereby the cam is contoured to behave according to the operating characteristics of the spring.

Further features, objects, and advantages will either be speciiicaly pointed out or become apparent when for a better understanding of the invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings in which:

5 Claims. (Cl. 123-90) Figures 1 and 3 each show respectively, a conventional cam and the improved cam;

Figures 2 and 4 are charts representing a graphic analysis of the behavior of the respective conventionalcam and improved cam; and l Figure 5 is a fragmentary view of the improved cam applied to an overhead valve train.`

As particularly respects Figures 1 and 2, the conventional cam I0 is shown in order that by way of contrast due appreciation may be made of the merits of the improved cam later to be described in detail. Conventional cam I0 is provided with a base circle I2 from the surface of which there arises a ramp I4 which blends into a ank I6. It is the traditional function of the ramp I4 to take up the clearance between the cam and its follower and to cause the follower to commence movement at a relatively low constant velocity. Flank I6 may be indicated,l as shown in dotted lines, to have an infinite radius 23 such that the cam is ineffect straight-sided in the flank portion. What is preferred though as the usual variation in this practice, is for the flank to use a finite radius R such as indicated at 22 for the flank notwithstanding the fact that the end results approach one another as to the cam behavior. Flank-I6 is tangent to a circular arc nose 20 at the reversal point indicated at I8. In the center of the nose at point `2| is indicated the point of maximum lift which may also be called the point of dwell. Circular arc nose 20 is provided with a constant nose radius 24. Point I8, the point of reversal, so called, represents that point at which the motion of the follower abruptly undergoes the transition from acceleration to deceleration and is characterized by the fact that the follower tends to leave the surface of the cam but for the opposition of the follower spring. Follower 2B which cooperates with cam I0 is diagrammatically represented as adapted for rectilinear motion along the axis 3U and to be separated from the base circle of the cam by a clearance dimension indicated at 28. Curves 32, 34, and 36 in Figure 2 show the cam behavior from the standpoint of lift, velocity, and accelera.- tion respectively.

The values just enumerated are plotted against degrees of cam opening indicated at 38. In lift curve 32 the ramp portion 40 merges with the flank portion 42 and flank portion 42 inturn merges with nose portion 44. The lift behavior for the nose is interrupted in Figure 2 along the dwell axis 45 and the lift curve may be symmetrical on the other side or not as desirable. The nose portion 44 and, if desirable, the flank portion 42 of curve 32, may comprise cosine waves. In velocity curve 34 the nose portion 58 of curve 34 will be seen to follow accordingly a sine wave. Flank portion 54 of velocity wave 44 may be either straight or conform to a relatively unpronounced sine wave. It will be noted that the ramp portions 4G and'48 in velocity curve 34 are formed such that the cam brings the follower up to the velocitv indicated along the constant velocity portion 48 at a constant rate of change. In acceleration curve 36, the ramp portions 50 and 52 correspond to the ramp portions 4R and 48 to velocitv curve 34. It will be seen in the acceleration curve 36 that for a part oF the ramp travel acceleration is constant as indicated at 50, and then reduces back to vero at 52 throughout the period of constant velocitv of the cam mechanism. Bv constant velocitv of the mechanism is meant constant' velocitv of travel of the cam follower inasmuch as the calculations here involved are based on the theory of constant cam rotation. In accelera tion curve 36 a flank portion IR of the cam will be seen to produce a constant acceleration along portion 5R to yield a constant rate of acceleration of value indicated at 68. Since for a given inertia the force necessary is proportional to the acceleration reouired, it will be seen that the cam train bv conventional design is subiected alnost immediately from no force to an appreciable accelerating force corresponding value of acceleration indicated at 68. The reversal point |8 of Figure l corresponds to the line of reversal 66 'on the acceleration curve 36. The acceleration in this instance drops instantaneously from avalue indicated at l'i8 to the decelerative value of B6. The cam opening forces then are no longer effective andit is the decelerative force of the cam train spring which is active to bring about the deceleration throughout travel across the cam nose. The decelerating portion 60 of acceleration curve 3G conventionally follows a cosine wave of rather nat proportions. As noted previously, since acceleration is in. effect a measure of force involved, it has been convenient to superimpose curves of spring resistance in units of force as indicated at 62 and 64. With proportional coordinates, it may be observed that at all points the curves 62 for one high rate spring performance and 84 for another high rate spring performance must at all times be spaced from the decelerating curve 60 in order to prevent valve bounce. It has been observed that as the spring rate :is-increased either by virtue of the relatively high inertia of a long valve train or because of the; relatively high speed to which a long valve train must be operated, the spring force curves become more and more steep relative to the comparatively ilat cosine wave G0. The graphical analysis of Figure 2 then will bring out the fact that the excessive force available with the relatively steep curve as shown at 64 attains its maximum value at the tip of the nose of cam I0, notablyat point 2| in Figure 1. tively smallest surface area of the cam is active when the tip of the nose is-contacting the cam and with maximum spring force being there exerted, the unit pressures may be expected to reach values such as to cause failure 'and galling in the vicinity ofthe cam nose. Moreover, even though-the spring force and the decelerating Iorcenecessary may be near enough to be compatible, still a broad consideration will show that Yet the rela- 4 the accelerating and the decelerating forces between curve portions 52 and 56 and curve portions 56 and 60 respectively will tend to cause dynamic disturbances later to show up in phases of the valve operation particularly in long value train arrangements.

As respects' Figures 3 and 4, the improved cam |00 is provided with portions and 2, which together constitute a ramp |02. The flank is constituted by portions 3, 4, 5, 6, and 1 and blends with a nose portion |94. The intermediate angles of rotation corresponding to portions l, 2, 3, etc. correspond generally with the intermediate angles e1, 412, qu. The follower of the nat face type is indicated at |05 cooperating with the cam along the instantaneous point of contact |08. Cam |00 is provided with a base circle radius and a dimension of maximum lift ||2 indicated along the dwell YY for the cam. The other principal axis for the cam XX is seen to be disposed at an angle es with XX axis for follower |06'. lThe Y'Y axis for follower |06 istheaxis along which cam |66 is adapted for rectilinear movement by action ofV cam 00. Angle A rcpresents portions 5, 6, l, and the nose collectively; the intermediate angles throughout the entire angle i are indicated as 5, qbs, qu, and pa which range between the limits respectively set at a.,T,T, and 9. in Figure 4, curve |20 corresponds to the lift curve for cam |00. Curve |22 corresponds to the velocity curve for cam |00. Curve |24 corresponds to the acceleration curve for the cam |00. Curve |25 corresponds to the rate of change of acceleration of the cam |00, and curve |28 brings out those points at which the rate of change of acceleration of the cam is constant. As particularly regards acceleration curve |24 in Figure 4, a spring force curve has been superposed adjacent to it at |34. Both spring force curve |34 and the acceleration curve portion |24 are shown in a relatively at disposition but such showing is purely for convenience and the same principle would apply to the spring force curve V of the steeper slope |35. One primary object of the instant invention being to correlate the cam behavoir to the physical behavior of the spring, it is desirable that the force required to decelerate the valve train be equal to or less than the force actually exerted by the spring. In equation form, for critical speed this statement may be represented as follows:

As is well known in the art the force required may be readily expressed in equation form thusly:

wenn

FREQ. :Espa

where Wzequivalent weight at valve.

K=spring design factor.

f t)=lift curve at valve, or maximum lift M less instantaneous lift Lv.

Where Bzspring load at maximum lift. R=spring rate lb./in.

aoaaeou" From equations 1, 2, and 3 the value .#(t) :nay be solved for by'diierential equations such as to yield:

where:

"l radan=9 degrees In Figure 3 the sliding point of contact |08 has a Y' coordinate equal to the instantaneous value of lift L. Therefore, y" may be equated. to the value for L in equation 5:

Since tappet velocity numerically equals the distance of the sliding contact point |08 from the),

Y'VY' axis the other coordinate for point |08 of value may be expressed as follows:

The coordinates of the point of sliding contact |08 with reference to the cam axis XX, YY at the angle @sa to axes XX, YY may be formulated as follows:`

(11) 11:11' sin ps-Hl cos ps Sutable dfferentiatons will yield:

@a dg--n (12) daz-gi tan dda (13) @fr En dwz-dard@ da: 1

Appropriate substitution of the values of the rst and second derivatives Equations l2 and 13 into the general equation for the radius of curvature of a curve y=f m) will yield:

Since p, generally Works out greater than one for high speed V*engine work the mlmmum radius of The velocity on: the nose maylbe rewritten inl terms of degrees rather than radians:-

ll' Tr L im ,E ns1 i CLR KW 3N KW N f .l

Acceleration on the nose then is:..

Where es is the instantaneous angularlty of rota? tion vof the cam on the nose: rSince inertia forces vary with the square of the `speed of a moving object such as a valve train, inertia problems become increasingly importantninhigh speed engine Work; acceleration being a direct measure of the instantly active'inertia forces; it is of advantage to have the acceleration increase gradually rather than to be applied and withdrawn suddenly. It is the function of the ank portion of the improved cam of Figures 3 and 4 to accomplish this acceleration 'gradually and atA the same timeV to blend smoothly with the noseportion just discussed. 'The ramp |02 is conventional in that, as is a factlthat curves |20',v |22, and |24 will bring out, thecam mechanism undergoes constant acceleration A1 for an instant, then zero acceleration and constant velocity V2. At some point during the theoretically constant velocity V2 period the clearance is taken up. As depends on the point at which thisrclearance is taken up then, the value for lift at the end of portion I is:

1 1 (l 8) L1=A1 At the end of portion 2 at constant velocity, the lift is: y

(19) Lz=Vz5z|^Li=Vrin"l- illh2 Portions 3 and 4 bring the cam train to maximum acceleration in a gradual fashion such that the rate of change of acceleration on portions 3 and 4 of the cam is constantly increasing at the rate K as is indicated at |39 and is constantly decreasing at the rate K xas is indicated at |40 on curve I 26. Hence for portion 3: i

Ka3 't 1,2)954 t KQ'is 't V23 t V22+ /iduz The magnitude of the acceleration A4, velocity V4, and lift L4 at the end of portion 4 are then readily determinable by assigning real values in Equations 25, 2'7, Vand 29 fOr K, p4, du, V2, and A1 aS appropriate. In accordancewith the plan of the invention, on portion 5 the angle es varies from zero value to value a; the acceleration A5 is constant and equals acceleration A4 at the end of portion 4 previously discussed. Further let the rate of change of acceleration decrease constantly at rate K for T degrees on portion 6, and on portion 'l increase constantly at rate K for T degrees.

In order then that the acceleration and velocity curves at the end of portion 'I intersect the 'nose contour, then acceleration Av must equal the acceleration yielded by Equation 17 for the nose and the Velocity V7 must equal the velocity yielded by Equation 16 for the velocity at the nose. Let the final value for the acceleration in Equation 17 be represented as A7 and the final value for the velocity in Equation 16 be indicated as V1. Let the end value for the nose angle equal 0 degrees:

A value of T is to satisfy the simultaneous Equations 31 and 32 is found to be:

From Equations and 33:

By appropriate integration:

The angle 0s increasing from zero value to value As to portion 5:

(3s). 4 ,dwg

41) Le:-Kaw/taw(AMM/oma The angle @e increasing from zero value to valuev T as to portion 1:

The angle p7 increasing from zero value to value T. It will be appreciated that when the assumed values for and 0 satisfy the conditions of Equation 34 for the value a the radius of curvature of the nose portion may be easily computed from Equation 14 inasmuch as the angle'ca in Equation 14 varies from the value zero" to the value 0. The lift curves for the ramp and flank blending into the nose may be readily computed according to the lift curves of the respective portions into which the ramp and flank are divided. Equations 18 and 19 yield the lift curves for the appropriate values of qu and A1 assumed and for the appropriate values of (p2 and V2 assumed. The lift curves for the rst portions of the flank may be determined in accordance with Equations 23 and 29 once the values for angles Lpg, K, and 4 are established. Equations 33 and 35 yield respectively the values of T and Ks by means of which the lift curves for portions 5, 6, and 1 of the flank may be computed through appropriate substitution in Equations 37, 41, and 45. A cam could then, according to the foregoing limits, behave in the manner desired. In particular regard to Figure 5 a cam, according to the instant invention, is shown in an appropriate setting. Cam |00 and follower |06 of the flat face type coact to operate a push rod |50 on the end of which is an adjustable cam tappet 52. Tappet |52 cooperates With a rocker arm pivoted about pivot |58 and having arms |54 and |56 of relative lengths corresponding to the rocker arm ratio C. Arm |56 contacts the end of an overhead valve |60 seating at |62 over the end of a uld passage |66. The cam mechanism causes opening of valve |60 and valve seating as occasioned by the action of a valve spring |64. Cam |00 is cut to the contours according to the chart ot Figure 4 and will operate as follows. On the opening side of the cam the behavior is divided broadly into three categories as best brought out 1n. curve |24. That is, after. the initial ac.

-celeration on the ramp, the valve |6015 opened .'rst at the constant acceleration indicated at |45, which is zero, secondly, at the constant acceleration indicated at p5 which is a constant maximum, and thirdly, along the portion of curve |24 indicated at |46 on the nose, which is of negative acceleration or deceleration. During the latter named portion |46, it will be noted that the decelerative value-or force generally parallels the spring force |34 which is available inasmuch as according to Equation 1 foregoing, the cam is cut so as to have such behavior as to the nose portion. In order to prevent dynamic disturbances from showing up in the cam trainas, for instance, would be occasioned by push rod |50 compressing as a spring instantaneously and later expanding such that the action of valve |60 does not follow exactly the operation of actuating cam |00, the transition from zero acceleration portions |45 on curve |24 to the maximum constant acceleration A4 will be observed to be a grad- -ually acting contour.

change of acceleration is shown at curve |26 in constant but of a negative'character as at |40. It is to be observed that rather than have the acceleration vary instantaneously from zero vto maximum value as in a conventional cam,

the improved cam |24 manifests the behavior of a gradual transition to maximum acceleration. This gradual transition is of prime importance.

vOn the decelerating side of the accelerating curve |24, another gradual transition is effected ,i

from the portion of constant maximum accelthe acceleration throughout the portion p6 willA be observed on curve |26 to be constant and`` of a negative character that is minus K slope throughout the portion pv on curve |24 the rate of change of slope will be observed to be constant and of a positive character plus K. Hence in curve |28 the second derivative of the acceleration at die will be observed to be constant and the second derivative of the acceleration at qbv will be observed to be constant. Since the lift formulas were set up on the premise of the acceleration and velocity curves of portion 1 blending in with the nose, a smooth contour will result at the respective points Lv, V7, and A7 on curves |20, |22 and |24 respectively. The duration of these respective portions as best se'en in curve |22, is accurately determined by for-- mula such that the angle A is always equal to the sum of the respective duration angles a, T, T, and 0. As particularly regards curve |24, since the companion portions cpa and 4 and also the companion portions s and er are complementary in the respect that where one is of constant rate of change of acceleration of one character, the other is of constant rate of change of acceleration of the opposite character. The build-up then from zero acceleration to maximum acceleration and from maximum acceleration to deceleration as indicated by nose portion |46 is gradual and hence the forces applied will be gradual as contrasted with the theoretical instantaneous application of. these 'same forces in` the conventional cam. Since the lift curves and the curve for the radius of curvature of the improved cam are explicit as set forth in the foregoing, the cam'contour may be accurately cut to produce a cam acting in accordance with the behavior graphically shown by the chart of Figure 4. Such approach to the problem is of advantage in ironing out dynamic disturbances, bounce, and coil oscillation as may be manifested when conventional cams are attempted to be used in the environment of a long overhead valve train operating at high speeds.

Variations within the spirit and scope of the invention described are equally comprehended by the foregoing description.

What is claimed is: l. Mechanism including a curved cam andfollower comprising a sliding pair in which the lift isin accordance with the following formula:

Where:

L=Lift at cam.

`1M=Maxirnum lift at valve.

B=Total spring load at maximum valve lift. R=Spring rate.

K :Spring factor.

ifi/:Valve gear equivalent weight.

.N=Engine R. P. M.

s=Cam degreesv from maximum lift. C=Ratio of valve lift to cam lift.

2. A slidingpair comprising a cam and follower 0f which the lift of the latter varies during a. cycle of the former as corresponds to the rotative position thereof, in which each cycle comprises three lift periods viz., a constantly increasing rate of change of acceleration, a constantly decreasing rate of change of acceleration, and a relatively high constant acceleration, in whichv the said three periods are obtained by employing a curved .cam' surface and flat faced vfollower cooperating to produce an acceleration whereof the second derivative yielded is constant during each said period.

3. A sliding pair comprising a cam and follower of which the lift of the latter varies during a. cycle of the former as corresponds to the rotative position thereof, in which each cycle comprises a rising phase comprising three lift periods viz., -a lift period of constant zero acceleration. a lift period of constant relatively high acceleration, and a lift period of negative acceleration, and transition periods therebetween, in which the aforesaid periods are obtained by employing a iiat face on the cam follower in contact with Working arcuate surfaces on the cam whereof the transition portions of the latter tangentially merge into the liit period portions cut for the aforesaid lift periods to produce consecutively adjacent segments of equal duration and amount of eiect, one segment of each pair affording a. change of rate of change of acceleration at constant increase and the other segment of each pair affording a change of rate of change of acceleration at constant decrease.

4. In the method of cam lifting a cam follower included in a train of valve gear comprising a normally closed valve connected to the cam follower and a valve spring opposing movement of opening of the valve caused by the lifting of the cam follower, the improved single step comprisking the lifting of the cam followerraccording .to

theY following formula:

where L=1ift at cam.

C=ratioof valve lift to cam lift.

M :Maximum lift.

B=spring load at maximum lift.

R=springrate lb./in.

g=386 in./sec2.

K=spring design factor of safety.

W=equiva1ent weight of valve gear at valve.

s=cam degrees on cam nose from maximum lift increasing in the direction of rotation (negative values on opening side of cam), and

N=engine R. P. M.

so as -to maintain a constant spring factor at all points of the cam follower on the cam nose between point of reversal and point of full lift and thereby maintain the spring resistance proportionately constant at al1 points.

5. In the method of cam lifting a cam follower included in a train of value gear comprising a normally closed valve connected to the cam follower and a valve springopposing movement to open the valve caused by the lifting of the cam follower, the improvement comprising the steps of providing a cam having a radius of curvature on the nose in accordance with the general case of the expression:

,Ti 60%)] KW Nr (Rio) (Spring Factor) (Valve. Gear Equiv. Wt.)

60 (1r) (BJP-QM.)

12 andthereby lifting the cam follower by meanszcf rotating the cam nose thercagainst according. to the expression;

L=lift.at cam.

C=ratio of valve lift to camlift.

so as to maintain aA constantspring factor and thereby maintaining the spring resistance exerted directly proportional to the valve gear deceleration.

JOHN F. JONES.

FRED F. TIMPNER.

ROBERT C. JUVINALL REFERENCES CITED The following references areV of record in the file of this patent:

UNITED STATES PATENTS Name Date Walti V Aug. 1,1. 1942 OTHER REFERENCES Valve Gear Design by Michael C. Turkish.

Eaton Mfg. Co., Wilcox-Rich Division, Detroit, Michigan, 1946 (Div. 28).

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