US2154249A - Internal combustion engine - Google Patents

Description

a April 11, 1939. o k- 2,154,249

INTERNAL COMBUSTION ENGINE Filed Nov. 12, 1934 Fig.1

N0, 2 1 N o. 3 INVENTOR.

Frederic R Porter ATTORNEY.

Patented Apr. 11, 1939 PATENT OFFICE INTERNAL COMBUSTION ENGINE Frederic P. Porter, Beloit, Wis., assignor to Fairbanks, Morse & 00., Chicago, 11]., a corporation of. Illinois Application November 12, 1934, Serial No. 752,598

Claims.

odd number of cylinders, or multiples thereof.

It is customary in the design and construction of the older prevailing engines of the types noted, to give the engine cranks an equal angular spacing, which would place the cranks of a five cylinder engine, which may be selected for illustration, at 72 degree intervals relative to the crank circle. Moreover, it is the usual practice to space the cranks equally along the axial length of the crankshaft, and further to provide piston and connecting rod structures of equal weight. The

above described engine arrangement has been found to give the best engine balance for an equal-angle spacing of the cranks. However, such an arrangement is subject to a number of pertinent objections, i. e., an engine having its cranks arranged as described above, is still considerably out of balance, and as a consequence, the operation of the engine results in considerable vibration and objectionable noise. It is, therefore, an object of the present invention to effect, througha method and means hereinafter to be describedya better balance of the engine assembly, and hence to efiect a substantial reduction in engine vibration, and the operating noises resulting therefrom, as caused by the unbalanced forces in the engine structure.

The present invention does. not of necessity involve any constructional differences over the existing arrangement of engine parts, other than a novel change in the relative angular settings of the several engine cranks. The particularly novel idea herein disclosed may thus be easily incorporated in existing engines or other reciprocating machinery of certain types, simply by changing the engine crankshaft and camshaft structure to provide for the best angular setting of the cranks as determined by the method presently to be described.

Further objects and advantages will appear from the following detailed description, and from the accompanying drawing, in which:

Fig. 1 is a longitudinal sectional elevation of a preferred form of five cylinder engine having a crankshaft structure embodying the improvements of the present invention; Fig. 2 is a diagrammatic showing of a crank angle setting for a five cylinder engine, illustrating the arrangement of the five cranks in the preferred crank sequence, the angles between adjacent cranks being designated by suitable indicia; Fig. 3 is a diagram of two superimposed crank angle settings, one thereof being in dotted lines and representing the equal angle spacing of the cranks according to the older practice, and the other being shown insolid lines and representing the preferred crank angle settings resulting from the improvements of the present invention, and Fig. 4 is a diagrammatic showing of a crank angle setting for a five cylinder engine, illustrating the arrangement of the five cranks in the preferred sequence, the angles between crank No. 1 as a reference, and each of the others being designated by suitable indicia.

Although my invention consists largely in the arrangement of certain of the engine parts as hereinafter described and particularly pointed out in the claims, yet I do not limit my invention to the precise arrangement of parts shown, inasmuch as various alterations may be made without changing the scope of my invention.

In order to present a clearer understanding of my improved construction and arrangement of certain of the engine parts, I prefer to give a brief statement of the considerations involved, which must be given careful attention if a true balance of the engine is to be effected.

It is well known to those skilled in the art to which this invention relates, that the moving parts of a reciprocating engine have inertia forces which might be neutralized or balanced against each other, in order to effect any desirable degree of engine balance, otherwise, as a result of the unbalanced forces, the engine assembly will tend to move in translation or rotation, or both. These inertia forces in each cylinder unit of the engine, result from the reciprocating movement of such engine parts as the piston, piston rings, pin, crosshead, etc., the movement of the connecting rod, and the rotative movement of such parts as the crank pin and webs. Hence it results that, in effecting a balanced engine, particular attention must be given to these elements of the engine structure. However, for present purposes, the balance of each of these elements need not be considered per se, but the balance characteristics of the engine may be found from a separate consideration of the effect of the several kinds of forces upon the translation and rotation of the engine considered as a rigid mass. The principal forces to be dealt with in effecting any satisfactory degree of engine balance are the primary reciprocating force, the secondary reciprocating force and the rotating force. From these forces and from their moments about a convenient point, the balance characteristics of an engine, when considered as a rigid mass, may be determined.

In order to determine the balance characteristics of engines of a great variety of types, varying for example from each other as to physical dimensions, speed ranges, etc., the maximum values of the inertia forces enumerated above are stated in ratio form. These force ratios then, may be applied in the determination of the balance of substantially any engine, for example of five cylinder type. The primary reciprocating force ratio, which here may be represented by the symbol R1, is represented by the ratio of the maximum resultant reciprocating force to the maximum reciprocating force for the first cylinder assembly. The secondary reciprocating force ratio R11 and the rotating force ratio R111 may It will of course appear that the actual resultant forces and resultant moments should approach zero as closely as possible, so as to avoid shaking vibrations of the engine. It follows that the ratio of the resultants to the components should be zero, since zero divided by any finite quantity equals zero. From this it appears that the resultant moment ratio equations desirably appear as last stated above. It should be borne in mind that these equations do not, of themselves, define the invention, but serve to state a theoretically ideal condition of perfect balance or zero shaking forces.

In a five cylinder engine, there are twelve possible distinct firing orders and twelve mirror reflections considering reversible rotation, and for each distinct firing order, the primary, secondary and rotating force moments vary to a considerable extent. The following table for the conventional engine with equal crank angles, gives the possible crank sequences with the corresponding values for the moment ratios R4 R6) and R5, the corresponding force ratios R1, R2 and R3 being respectively equal to zero:

nk Crank ra sequence sequence reversed rotation From an examination of the above table, it will be found that the Number 1 crank sequence gives the best'engine balance. It will be noted that R is quite large, but since it has been found in practice that the secondary unbalanced moments represented thereby do not, in general, affect the engine balance to the same extent to which the primary moments of the same magnitude affect the balance, R5 may be overlooked in favor of the relatively small primary moment ratio obtainedin the cylinder crank sequence No. 1.

The above arrangement, however, does not effect a wholly satisfactory engine balance, as the primary and rotating force moments R4 and Re which are not minimized thereby still produce an objectionable unbalanced condition of the engine, causing vibration in the engine structure with the attendant noises set up thereby. There are three general methods by which these remaining unbalanced primary and rotating moments may be substantially reduced, namely, making the total weights at each crank of unequal values; providing an irregular cylinder spacing,

and by making the relative crank angles unequal in value. Common to all applications of the last noted method of attaining the desired degree of engine balance, is the practice of causing the pistons of the successively-firing cylinders, to attain corresponding piston-cylinder positions in successive time intervals, each or at least certain of which are not uniform, assuming of course, a given engine speed. These intervals, as represented in terms of crank angles, will in nearly all cases, be other than 72, and hence other than any small aliquot part of the total crank circle, of 360. The first two methods named are subject to the objection that substantial production and manufacturing difiiculties are created thereby. The third method is, however, quite feasible from a production and manufacturing standpoint.

As determined by experience, the extent to which the conventional crank angles or spacings are rendered unequal in value, is best determined mathematically, the procedure in calculations of this kind, such as the optimum angular relation between the cranks, being hereinafter referred to by way of general direction, indicating how the equations of balance can be set up for any engine to which the invention is applicable, the solution of the equations being evident to those skilled in the art of engine balancing, to which the present invention pertains. The solution indicated by the results shown by Fig. 3, when once determined for a five cylinder engine, is of course applicable to any homologous five cylinder engine of a type in which the cylinders are in line, and which also has the usual equal reciprocating and rotating weights from crank to crank, and the usual equal longitudinal cylinder spacing, irrespective of physical dimensions, load, speed or engine cycle.

Referring to the drawing by suitable characters of reference in Fig. 1 the numeral l0 designates, generally a preferred form of five cylinder internal combustion engine, which for example may be considered as of two-cycle type embodying the improvements of the present invention. The engine organization includes the cylinders l2, l3, l4, l5 and I 6 arranged in line, the pistons l1, 18, I9, 20 and 2| operable therein, respectively, the crankshaft structure 22, the piston connecting rods 24 and the spaced bearing structures 26 rotatably supporting the crankshaft. As before stated, the present invention may best be embodied in the crankshaft assembly and carried into effect through the relative angular settings of the several crank portions thereof. The crank portions are, by preference, numbered in order I to 5 inclusive, crank number I being the extreme left hand crank (Fig. 1) which is associated with the piston ll and its connecting rod 24, crank number 2 being next thereto and associated with piston l8, and so on through the assembly through crank number 5 and its associated piston 2|.

Turning now to Fig. 2, which illustrates, diagrammatically the preferred crank sequence for the cranks of a five cylinder engine, the arrangement shown is in accordance with the number I crank sequence, appearing in the crank sequence table hereinabove set out. Starting from crankNo.

I ,the preferred sequence is 1 4 3 2 5 fora clockwise crankshaft rotation, or the reverse 1 5 2 3 4 for the opposite direction of rotation. The angularspacing of the cranks is designated by the angles A, B, C, D and E between the cranks l4, 4-3, 3-2, 25 and 5I respectively.

According to established practice in the case of five cylinder engines, the several cranks are generally given an equal angular setting with respect to each other, and hence in the older forms of this type of engine, the angles A, B, C, D and E would each equal 72 degrees. I have found that by giving at least some of the adjacently firing cranks an angular setting slightly greater or slightly less than that represented by the usual heretofore prevalent practice, an engine of any type to which the present invention is applicable, may be balanced to a very high degree.

The results of my work in improving the balance of an engine of the type under discussion,

are diagrammatically illustrated in Fig. 3, in

which the solid lines indicate the preferred crank sequence. From this view, it will be seen that the angles A and D are each 85 degrees, while angles B and C are each 6'7 degrees, and angle E 56 degrees. From these angular settings of the five cranks, it will be observed that, relative to the usual equal-angle settings of the cranks, as indicated by the dotted lines, crank number I has been shifted in a counter-clockwise direction, substantially 8 degrees, crank number 4 substantially 5 degrees in a clockwise direction, crank number 3 remains unshifted, crank number 2 substantially 5 degrees in a counterclockwise direction, and crank number 5 substantially 8 degrees in a clockwise direction. It is to be understood, of course, that the above angular crank settings apply tothe particular engine illustrated in Fig. 1, and that for engines of other types, the crank settings may advantageously be varied within limits of a few degrees from those given herein. However, the method of securing engine balance by providing the cranks with unequal angular settings as clearly described herein, remains substantially the same for all engines having inherent unbal ance with equal angles between cranks, equally spaced, in-line cylinders, and equal weights at each crank.

The procedure in determining the best angular relation of engine cranks for an engine of given type, will be illustrated as applied to a five cylinder engine. As an example within the invention, this engine will have five cylinders with their centerlines substantially in one plane, with the five cranks of equal radius, and equally spaced longitudinally, that is, along the length of the crankshaft, and will have equal reciprocating and equal rotating weights, respectively, from crank to crank.

Tabulating the symbols representing the force and moment ratios, let

R1 =primary reciprocating force-ratio,

R11 =secondary reciprocating force-ratio, R111=rotating force-ratio,

R4 :primary reciprocating force moment-ratio,

R5 =secondary reciprocating force momentratio,

Rs =rotating force moment-ratio,

and referring to Fig. 4 of the drawing, let b equal the unknown angle between cranks H and J, and c the unknown angle between cranks H and K, and d the unknown angle between cranks H and L, and e the unknown angle between cranks H and M. For convenience, crank I-I" is taken as crank #l, crank J, crank No. 4, crank K as crank No. 3, crank L as crank No. 2, and crank M as No. 5, and the use of symbols H, J, K, L, and M may thus express a preferred crank sequence.

Let a equal the variable angle through which the crankshaft has rotated from its position with crank H vertical.

Let Pr equal the total shaking force due to the reciprocating weights at any one crank, and let P equal the centrifugal force which would exist if this total weight rotated around the crank circle.

We then have the well-known formula:

Pr=P cos ak cos 2a), where P, the centrifugal force is .00002842 radius (R. P. M.) W, k is a constant, and W the reciprocating weight.

As is well-known, the primary reciprocating force at any one cylinder therefore varies as P cos a, while the secondary force varies as P it cos 2a.

Assume the crankshaft rotating counterclockwise, then the resultant primary force F1 is found by adding components of the primary force at each crank projected onto the vertical axis Y-Y, Fig. 4, as follows:

Expressions of the form Pcos(ab) can be transposed to the equivalent P cos a cos b+P sin a sin b.

Performing all these transpositions and rearranging, we have:

F1=P(sin b+sin c+sin d-l-sin e sin a+ P(1+cos b+cos c+cos cl+cos e) cos 0.

Next, replace the sum in the first parenthesis by an arbitrary symbol A1 and the sum in the second parenthesis by B1 and since we want to find only the ratio between F1, the resultant primary force, and P the primary force at one cylinder, we can divide by P and obtain:

F1/P=A1 sin a-i-Bi cos a This can be written:

F1/P=1/A12+B12 cos (la-tan" g) or F /P=R cos (er-tan 1 where R1=1/A1 +B1 and is the primary reciprocating force ratio as previously defined. It is thus seen that for R1 to be zero, both A1 and B1 must be zero. This gives two simultaneous equations for primary reciprocating force balance, namely:

sin b+sin c+sin d+sin e=0 l+cos b+cos c+cos d+cos e=0 Similarly, the resultant secondary reciprocating force F11 is found to be:

11 cos (2a tan u) and and The moment ratio equations of balance are set up next, using algebraic designations for the several cranks, so that the equations are general for all crank sequences. Let S be the distance between adjacent cylinders, and taking moments about the first cylinder (related to crank H) the lever-arm of the unbalanced force at any cylinder K about the reference point, is the number of spaces S intervening. If K is the third cylinder, namely K :3 on the crank sequence diagram (Fig. 4), then the lever-arm is (K1)S or 28, being the distance between the 1st and 3rd cylinders. In general then, the lever arm at any crank at will be (a:l)S.

Next, to find the balance equations for the primary reciprocating force moments, the resultant moment M4 is expressed in terms of the cylinder-spacing S, the algebraic crank-numbers H, J, K, L and M, the angle of rotation a, and the unknown desired crank-angles b, c, d, e, as follows:

M4=0+(]1)SP cos (ab)+ (K1)SP cos (a-c)+ (L1)SP cos (a-d)+(M1)SP cos (a-e) [(Note that moment of first cylinder H about itself is 0.)

Since the ratio of the resultant moment M4, to the moment of the first cylinder H about the second cylinder (PS), is desired, the quantity PS in the above equation is divided out, and since cos(a-b)=cos a cos b+sin a sin b the primary reciprocating force moment ratio M4/SP becomes (]1) cos a cos b+(]l) sin a sin b+ (K1) cos a cos (K1) sin a sin c+(L1) cos a cosd-l- (L-1) sin a sin d-l- (M1) cos a cos e+(M- 1) sin a sin e which can be segregated into 1) sin b+(K- 1) sin c+(L-- 1) sin d+ (M- 1) sin e) sin a+ 1) cos b+(K- 1) cos c+(L 1) cos d-l- (M 1) cos e) cos a This expression is again of the form A4 sin a+B4 cos a,

which as shown. above, is equivalent to:

Where which is the primary reciprocating moment. ratio as previously defined. To reduce this moment ratio R4 to zero, both A4 and B4 must be reduced to zero simultaneously, as previously described for R1.

The equations of balance for the secondary reciprocating moment ratios are determined in the same manner, and are of the same general form as tabulated below:

A; R cos (Za-tan 1) Next to set up the equations of balance for the rotating forces, these are balanced when their vertical resultant Fv and their horizontal resultant Fh are zero at any angular position of the crankshaft.

Assuming the first crank vertical, and taking the vertical components, we have, using Pu to designate the rotating force at each cylinder, and where Pu=.00002842 u(R, P. M.) Wu,

and Wu=rotating weights at radius u:

Fv=Pu+Pu cos b+Pu cos c-i-Pu cos d-i-Pu cos eand taking. the horizontal components, we have Fii=0+Pu sin b+Pi1 sin C+Pu sin d-i-Pu sin e To make the solution general and independent of size of engine, force ratios are expressed instead of forces, as before. The horizontal rotating force ratio is then Fh/Pii=sin b+sin c+sin d+sin e= A111 And. the vertical rotating force ratio is MD=0'+(J1) PuS cos b+(K-1) PMS cos c +(L1) PuS cos d+(M-1) PuS cos e Mn=0+(J-1) PuS sin b+(K-1) PuS sin c +(L-l) PuS sin d-]-(Ml) P'uS sin e The vertical and horizontal rotating moment raties are. obtained by dividing by PuS thus:

M;,/P,,S=*(]l) sin b+(K-1) sin 0+ (L1) sin d+(M 1) sin e=A M,/P,,S=(]-1) cos b+(K-l) cos c-l- (L-l) cos cl-l-(.M1) cos e=B Ravm Collecting andtabulating all of the above forceratio and moment-ratio equations, as applied to a five cylinder engine within the invention (cylinders in line, equal crank spacings and equal Weights .at each crank, and cranks spaced equally around 360. degree circle except for increments for balance) and of any sizeand any crank sequence, there is obtained:

For balance: of primary reciprocating forces, there must be satisfied simultaneously the two equations:

sin b+sin c+sin d+sin e=0' 1+cos b+cos c+cos d-l-cos e=0 For balance. of secondary reciprocating forces,

there must be satisfied simultaneously the two equations:

(3) sin 2b+sin 2c+sin 2d(+sin 2e=0 (4) 1+cos 2b+cos 2c+cos 2d+cos 2e=0 (5) (1-1) sin b-l-(K l) sin c+(L1) sin d-|-(M--1) sin e= (6) (J-l) cos b+ (K-l) cos c+(L1) cos d+(M-1) cos e=0 For balance of secondary reciprocating force mements, there must be satisfied simultaneously the two equations:

(7) (J-1) sin 2b+(K1) sin 20+(L-1) sin 2d+ (M1) sin 26:0

(8) (J-1) cos 2b+(K-1) cos 20+(L-1) cos 2d3+(M1) cos 2e=0 For balance of rotating force moments, there must be satisfied simultaneously the two Equations and 6 above.

Illustrating the use of these equations, assume it is desired to balance the primary reciprocating forces and the primary reciprocating force moments, the rotating forces and the rotating force moments, of a five cylinder engine with crank sequence 14325 such as illustrated in Fig. 2. Specifically, it is desired to determine the increments from the aliquot 72 degrees of Fig. 2, which will effect the specified balance. Broadly, it is desirable to balance the secondary forces and secondary-force moments as well, but this would require satisfaction of all eight of the equations of balance, whereas the foregoing involves only four variables, namely, the unknown angles b, c, d and e. In the usual case, the primary and rotating forces and moments are more apt to cause noticeable disturbance in the supporting substructure, such as the hull of a ship, or the terrain adjacent the foundation of a stationary enine, and it is therefore chosen to eliminate the primary and rotating force and moment unbalances as above stated. To do so, Equations 1 and 2 and 5 and 6 must be satisfied simultaneously.

Equations 1 and 2 do not contain the symbols H, J, K, etc. designating the cranks, hence are the same regardless of crank sequence. Whereas Equations 5 and 6 vary with the crank sequence. For the crank sequence 14325 above assumed, Equations 5 and 6 become:

Since J=4, K=3, L=2, and M=5,

(5') 3 sin b+2 sin c-l-sin (1+4 sin e=0 (6) 3 cos 5+2 cos c+cos d+4 cos e=0 There are now presented for solution, four simultaneous equations with four unknowns, namely, the four angles 1), c, d and 2. Their direct or graphical solution is a purely mathematical operation which will be evident to the skilled mathematician. The solution of the four Equations 1, 2, 5, and 6', for the specific engine used for illustration, gives 21:85 degrees 20 minutes and 45.51 seconds 0:152 degrees 33 minutes and 5.57 seconds (1:219 degrees 45 minutes and 25.63 seconds 6:305 degrees 6 minutes and 11.14 seconds With these values of b, c, d and e, the primary force, primary forcemoment, rotating force and rotating force moment unbalances are all zero, while the secondary reciprocating force ratio is 0.7505 and the secondary reciprocating force moment ratio is 4.935.

With the usual equal-angle arrangement (cranks 72 degrees apart in the present five-cylinder illustration) the unbalance ratios would be: Primary and rotating force ratio equals zero.

Primary and rotating force moment ratios, re-' spectively are 0.4490, and the secondary reciprocating force ratio equals zero, and the secondary reciprocating force moment ratio is 4.980.

The utility of the present procedure will be" readily apparent, since in most cases the secondary shaking forces and moments are relatively unimportant, while the elimination of the primary forces, force moments and rotating forces and force moments are of vital practical:

importance. It will be understood also that the invention is applicable to cases in which a resonance condition exists between the secondary forces and moments, and the hull or other substructure supporting the engine, with the primary and rotating forces out of resonance. By the method hereinabove described, a different set of unequal crank-angles is obtained, which will serve to eliminate the secondary disturbing.

forces and moments, and therefore eliminate the resonant vibration.

In manufacturing practice, the usual crankangle tolerance is plus or minus one-half degree; this fact considered'with other phases of manufacture enables the angles shown by Fig. 3 to be considered as a final practical result, as demonstrated with substantial success in the building of engines. For these practical angles, the primary and rotating force ratios are 0.01557 instead of zero, and the primary and rotating force moment ratios are 0.04828 instead of zero, these differences however being pratically insignificant. In fact a variation of a few degrees from the practically-ideal angles, such as illustrated by Fig. 3, still largely reduces the undesired types of unbalance, and yet falls clearly within the intended scope of the invention.

It will be obvious to those skilled in engine design, that certain incidental changes will be required to correspond to the improved crankangle arrangements heretofore referred to; as an example, it is obvious that the cam angles of the engine camshaft will require some deviation from heretofore prevailing designs, but these and other changes incident to the adoption of the hereindescribed practice, are thought to be apparent and hence not necessary to be illustrated and described in any greater detail than heretofore referred to.

The present invention is applicable generally to five cylinder engines of either 2-cycle or 4- cycle types having inherent unbalance with equal angles between cranks, cylinders arranged in line with their centerlines in one plane, and equally spaced longitudinally of the engine, and having equal reciprocating and equal rotating weights at each crank. According to the crank arrangement now disclosed and as hereinafter claimed, engines as above characterized may be effectively dynamically balanced to a high degree, whereby to greatly improve the operating balance characteristics of such engines.

What I claim is:

1. In a five-cylinder engine in which the cylinders are in line, a power piston operable in each cylinder, a crankshaft assembly including a plurality of cranks each operatively connected to" one of: said pistonsysaid cranks being so. angula'rlyflrelated: onusaid crankshaft that the cranks disposed'between the outer or' end cranks are equally angularly spaced, relative to each other, 5 atsan. angle less' than 72, but exceeding 65,

whereby to effect an improved dynamic balance oft-the engines;

2. In a five-cylinder engine in which the cylinders are aligned, power pistons operable in the cylinders, and acrankshaftdassembly including cranks: each 'operatively'connected to one of said pistons, said cranks beingso angularly related on said crankshaft that the adjacent pair of cranks nearw'each end of said crankshaft are equally angularly' spaced, the value. of the angle thereb'etween, for one direction of rotation, being represented by 144 degrees plus; an algebraic increment of. other than zero but less than 20 degreeawhereby to effect an. improved dynamic I balance of the engine.

3. In a five-cylinder engine in which the cylinders" are aligned, pistons? operable in the cylinders, and a crankshaft assembly including cranks each operatively connected to one of said IIT'DiStOI'IS, said cranks being .so angularly related on'said crankshaft that the adjacent pair of cranks near eaclr end of. the crankshaft are related by an angle of 144' degrees, plus an algebraic increment between zero and 20 degrees, and

3a: theremaining pairs of; cranks thereof by an angle of 72degrees, plus an algebraic increment between zero and 1Qdegrees', whereby to secure an improved dynamic balance of the engine.

4. In a five-cylinder engine in whichthe 'cylinders are aligned, pistons operable inwthe cyl-n inders, and .a crankshaft assembly including cranks each operatively connected to one of said pistons, said cranks being so angularly related on said crankshaft, and so, related toother elements of the engine as to effect a firing.

order of 1-4-3-2-5, and the positions of the cranks being ,such thatv the adjacent pair of cranks near each end of the crankshaft are related by an angle of 144 degrees plus an alge-v braic increment between 1 and 20 degrees, and the intermediate pairs of cranks byan angle of '72 degrees plus an algebraic increment between 1 and 15 degrees, whereby to effectv an improved dynamic balance of the engine.

5. In a five-cylinder engine in which the cylinders are aligned, pistons operable in the cylinders, and a crankshaft assembly including cranks each operatively connected to one of said pistons,-said cranks being so angularly related on said crankshaft" that the adjacent pair of cranks near each end of the crankshaft are related by an angle of 14.4 degrees, plus an algebraic increment between zero and 20 degrees, and the remaining-intermediate crank is related to the adjacent crank on each side thereof, byan'angleof 72 degrees, plus an algebraic increment -between zero and degrees, whereby to secure an improved dynamic balance of. the engine.

FREDERIC P. PORTER.

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