Rotary fluid displacement device

June 24, 1952

2,601,397

M. F. HILL ET AL

ROTARY FLUID DISPLACEMENT DEVICE

Filed April 11, 1950 3 Sheets-Sheet 1

<img file="US2601397A_D0001.tif" />

June 24, 1952

2,601,397

M. F. HILL ETAL

ROTARY FLUID DISPLACEMENT DEVICE

Filed April 11, 1950

Sheets-Sheet 2

<img file="US2601397A_D0002.tif" />

June 24, 1952

2,601,397

M. F. HILL ETAL

ROTARY FLUID DISPLACEMENT DEVICE

Filed April 11, 1950 3 Sheets-Sheet 3

<img file="US2601397A_D0003.tif" />

Patented June 24, 1952

2,601,397

UNITED STATES PATENT OFFICE

2,601,397

ROTARY FLUID DISPLACEMENT DEVICE

Myron Francis Hill and. Francis A. Hill, 2nd, Westport, Conn.

Application April 11, 1950, Serial No. 153,176

Claims. (Cl. 103—126)

Our invention relates to rotary fluid displacement devices' employing rotors having novel tooth relations, the outer rotor having. a driving connection to maintain continuous· fluid pressure holding engagements between the teeth of rotor chambers as they close in pumps and as they open in motors.

This case, combined with added features, is a continuation of part of our application Ser.

No. 561,948, filed'Nov. 4, 1944, which in turn, 10 drive connection, 'maintains said engagement combined with new matter, is a continuationin-part Of our application Ser. No. 452,654, filed July 28, 1942, now: abandoned, which in turn, combined with new matter is a continuation-in-part of OUr application Sef. No. 227,954, filed Sept. 4, 1938, now Patent No. 2,386,896, issued October 16, 1945; our Patent No. 2,386,896 being a continuation-in-part Of said application 452,654; and our application 659,098, filed Apr. 2, 1946, now Patent No. 2,547,392, issued April 3, 1951, being also in part a continuation of our said applications

452,654, and 561,948 filed Nov. 4, 1944 allowed and abandoned; all of which, with rectified lines of division between them, comprise a step-bystep development over 'the years of this new art of rotary pump and engine constructions with fluid pressure holding tooth engagements between chambers opening and closing during rotation, ^;In this farnily tree of continuous con- 30 tact rotors having differences in tooth ratios of two or more, rotor teeth were based at first upon a difference of one tooth (reissue Patent 21,316), in which extra wide teeth on one rotor were split into two teeth by cutting a tooth space in the middle of each tooth, and putting an extra tooth, to match, in the extra' Wide tooth spaces of the other rotor. ' The result was a common - Center of curvature for. the off sides of any two consecutive teeth. This was based upon the difference of one tooth construction in 21,316, which had pressure angles of 30° to 50° more or less. The next most important development was designing teeth by the new Hill Theorem of geometry, described -herein, where the centers of .the sides were no longer like those in 21,316, but adapted to provide .pressure angles of 1° to 20 more or less, comparable to ordinary sgear practice.

This case also contains -descriptive matter which may be later divided out, including a method of truing our outer rotors for precision in manufacture the object of the division being to avoid too 'many factors and claims in one case.

........... 2 ... .

Our application is subordinate to our said application 659,098. In that case, specifically, the pinion has the driving connection, which in a pump maintains tight tooth relations of open5 ing chambers. Generically it maintains fluid pressure holding engagements between the teeth having a difference in number Of more than one . with a hunting relation between all the teeth. In this case the outer rotor, having the s between the teeth. Ports are shown and described for use with incompressible liquids and with compressible gases (including air). The Object is to maintain such engagements by ap15 plying the drive force to the outer rotor to engage the teeth of the pinion to maintain tightness of closing chambers of pumps and opening chambers of motors. Maintaining tightness between closing chambers provides 20 economical compression of gases, and between opening chambers utilizes expansion of pressure gases.

Antifriction 'bearings insure the starting of this mechanism as a fluid motor operated with 25 suitable parts either by air, gas or liquid pressures as well as a pump. As a pump the successive closing chambers, each in turn coming into registration with the discharge port, forcibly eject their contents out thru that port, the chambers overlapping- each' Other in discharging, so that a steady stream is ejected. The discharge port pressure region is smaller than the low intake pressure region so that leakage over the ends of rotors is correspondingly less.

In our said application 659,098 in a pump the suction area is the smaller one, and is along opening chambers, so that with a liquid seal the leakage of gas over the ends of the rotors tending to reduce suction is less. The different driving systems are suited to different specific Objectives aimed at in the two cases.

In this case the numbers of teeth of the two rotors differ by the same two or more teeth, but it is the outer rotor that is connected to the drive shaft, not the inner rotor, so that in a gas puma the closing chambers are sealed from each other instead of the opening chambers. The discharge port of a compressor as compared’to a liquid , port, is shortened so that a closing rotor chamber ./compressing gas does not connect With it .preferably until its chamber pressure has risen to that in the discharge port. The intake port, instead of being short and sealed Off from the crescent space is connected to the crescent range thru back lash,

2,601,897 allowing more time for the chambers to fill with gas, thus increasing compressor efficiency. Likewise in a gas expansion motor, the outer rotor drive keeps the opening chambers sealed from each other so that the full expansive power in the gas may be utilized in exerting power instead of blowing thru open tooth contacts and failing to effect any great amount of power. A pinion drive in a gas motor would have the closing chambers (not the opening ones) sealed from each other and unable to utilize expansive energy.

An attempt to use our present. mechanism with a short intake high pressure port as a liquid motor would fail, since liquid has no expansive energy.

The numbers of teeth preferably vary by two for reasons below.

As a motor, with ports to suit, pressure enters thru the port which in a pump is the discharge port, expands the opening rotor chambers, causing them to rotate in the reverse direction from a pump, and leaves thru the pump intake port. Ports for these various operations are shown and described. Liquid motors are made reversible and also may act as reversible pumps. To avoid complexity our invention will be described first as a pump.

As related in our earlier application Serial No. 659,098, it was once believed that the difference of one tooth was an inherent factor in rotors having continuous contact until upon inspection of Pig. IX, of reissue patent to Μ. P. Hill No. 21,316, it became apparent that without changing the basic ratio of the teeth differing by one, an extra tooth could be inserted in each pinion tooth space, and an extra tooth space cut in each outer tooth to match. This doubled the numbers of teeth without changing the basic ratio, and with little loss of displacement. It provided smaller pressure angles, smoother driving, and greater durability.

It was also apparent that instead of one tooth being inserted in a pinion space, it was possible without changing the basic tooth ratio, to put two or more teeth in each pinion tooth space with a corresponding number of tooth spaces in each outer rotor tooth. The difference of three or more teeth however, radically reduced displacement and is mainly useful for high suction or minute displacement.

After doubling the numbers of teeth, the total numbers of teeth may be reduced with a correspondingly reduced diameter. By enlarging them to the original diameter again, the eccentricity between the centers of the two rotors is increased, which increases their displacement.

A difference of more than two teeth however greatly reduces displacement, so that the relation of the numbers of teeth to displacement is not one of degree but is critical, the difference of two teeth affording a greater displacement than any other ratio for a given diameter.

After these features became well understood, it appeared that one tooth of one rotor engaged only alternate teeth of the other rotor, and the next tooth of the one rotor engaged only the remaining teeth of the other rotor. Generation of pinion teeth required two separate operations. A cutting tool representing a tooth of the outer rotor cuts alternate teeth of the other rotor. After that operation is completed, the blank for the other rotor is indexed one half tooth division and the generation repeated to cut the remaining teeth. This indexing needs to be exact, perhaps to a ten-thousandth of an inch, to avoid noise and leakage between the teeth. It takes longer to manufacture ro(· tors so we discovered next that the addition of one more tooth to each rotor enabled the teeth to be completely generated at a single setting. The geometry proved that such an increase was possible. The resulting ratio com10 prises numbers of teeth based on a ratio of fractional numbers instead of integers differing by one, each number having no (whole) common divisor.

For example, doubling a 5 to 4 ratio makes 16 it 10 to 8, and adding 1 to each makes it 11 to 9.

VZhile this ratio seems radically different from the 5 to 4 ratio, it is not so much different because it is really 5½ to 4½. It restores the ratio difference of unity between the numbers of 20 teeth as required in our earlier rotor patents, only this time with fractions instead of whole numbers. The ratio 7 to 5 for example, in reality, is a basic fractional ratio of 3½ to 2%, thus differing by one, while the actual teeth 25 have a difference of two; and 9 to 7 teeth have a basic ratio of 4½ to 3½ and so on. These manipulations increase displacement.

The great advantage of this odd series of ratios is that a tool representing a tooth of 30 one rotor will, in a single setting of a blank for the other rotor in a generating machine, generate all the teeth and tooth spaces of the other, thus also providing the hunting relation between all the teeth. This hunting relation 35 differs from that of rotors having a difference of one tooth in which generation proceeds seriatim. In a tooth ratio based on fractional ratio with a difference of two teeth each tooth of one rotor enters alternate spaces of the other zo rotor jumping over the intervening space in doing so. As this operation proceeds, the tool representing a tooth during one rotation enters only half of the tooth spaces of the other rotor and enters the remaining tooth spaces during the next revolution.

ⁱ⁵ For example, a tool representing a tooth of an outer rotor having eleven teeth engages a tooth space of a pinion having nine teeth, which we may call the first tooth space, travels in an anti-clockwise direction along the contour of ^,&gt;0 the pinion tooth, say, to the left until it reaches its top, forming that side of this pinion space and tooth and then skips over the next, or second, tooth space until it reaches the top of the third tooth. Then it travels down along ⁰⁵ the far side of that tooth into the third tooth space, of the pinion. It then repeats the operation over the next tooth to the left, skips the fourth tooth space and enters the following or fifth tooth space, after which it proceeds in the same way, skipping alternate tooth spaces, entering the seventh, and then the ninth—all during one rotation. Then during the second rotation it leaves the ninth space, enters the second, then the fourth, then the sixth and the eighth, back to the starting point in the first tooth space. This requires two revolutions to complete the generation of all the teeth and tooth spaces of a nine tooth pinion. It is believed that this method is entirely novel in continuous tooth contact generation. The “hunting” relation is important in the operation of pump and motor mechanisms and particularly in compressors where perfection of tooth contacts determines volumetric efficiency. Any es2,601,397 cape crevice between teeth compressing gas has a disastrous result upon volumetric efficiency. The hunting relation tends to keep the wear upon all the teeth equal. This action of each tooth of one rotor entering . . . all the tooth spaces of the other rotor expresses the idea of the “hunting” relation.

Another advantage was discovered after these factors were established, namely that the curves of the contours could be adjusted to different angles and different radii of curvatures to improve the pressure angles and rolling drive relations between the teeth in the driving region at full mesh. Smaller pressure angles result from tooth contour of relatively larger radii than possible in the aforesaid patents.

This doubled tooth system does hot heed the same extreme precision of manufacture as that involved in the manufacture of Gerotors having a difference in numbers of teeth of one in which all the tooth contacts are tight within a tenth of a thousandth of an inch and have to be carefully and patiently “run in” to slide over each other without heat before they may be delivered to a purchaser. Unless handled with extreme care and patience, running in of such air compressor rotors would result in heat, expansion, binding and torn surfaces.

Our new rotors with the open mesh crescent space and back lash between the teeth, with the usual manufacturing tolerances, are loose when assembled and are capable of running themselves in without attention to perform the very best, of service. Furthermore they can be operated in service at the very start, and improve their efficiency as they lap themselves into each other’s contours. The shifting of a side Of the teeth of a rotor towards the other side a few thousandths of an inch reduces the anguar length of a tooth and provides the back lash that eliminates contacts between opening chambers, and makes possible running new rotors (in either direction) without creating troublesome heat. Convex tops of narrow teeth having sharper curves wear more rapidly in running-in than rotor tooth curves so that the latter predominate in “wearability.” These factors set forth in our earlier application Ser. No. 659,098 apply likewise to this invention, similar rotors being usable.

To eliminate rubbing friction and its heat is of prime value in compressors. Compressors require a liquid seal over the end of the rotors. After years of experiment it was discovered th;at a mixture having the characteristics of twenty parts or more of water with one part of a non-foaming cutting oil spray into the intake of a compressor effectively seals leakage crevices. A fine spray at 70° F. with its high specific heat keeps the temperature of 100 lbs. compression down to 110° F. instead of a normal adiabatic temperature of 475° F.

A 50 cu. ft. Gerotor compressor having a difference of one tooth (8 to 7 teeth) ran steadily daytimes for some 3 months at over 84% mechanical efficiency, in perfect condition. It was shipped some 60 miles by freight, and when set up again developed so much heat internally as to vaporize the liquid spray and exclude the intake of air. The eccentricity (maintained by large dowels) had been altered perhaps, a few ten-thousandths of an inch perhaps. The teeth at open mesh rubbed heavily upon each other their heat creating steam vapor that excluded air and caused binding. It was apparent that improvement was needed. Rotoids having a crescent space at open mesh, and back Tash solved the problem. They could get hot while running in without needing attention.

At full mesh the driving angles are adjusted for nearer a pure rolling action to eliminate heat there. It has taken years to 'perfect this double tooth system just as it took years to develop the original Gerotor system. When run-in, a compressor develops no -substantial mechanical friction and heat between its teeth, which contributes to high volumetric as Yfell as mechanical efficiency.

There is no limit theoretically to the highest numbers of teeth possible with our ratios having a difference of two or more teeth. The least number of teeth is determined by the driving relation that provides steady ratio speeds with continuous fluid tight engagements for rotor chambers between the teeth-performing fluid pressure functions. A ratio of 7 to 5 teeth’provides an excellent driving relation between the teeth. A ratio of 5 to 3 is possible, due to the long driving contact across full mesh of a rolling character though it is assisted in part of the driving range by a slight slide between the teeth. A number of modifications lie within the scope Of our invention.

Continuous engagement is possible with one tooth contact, not two or three. But irregular curves have unsteady contact relations. Only correct contours based en the circroidal addition make possible steady speeds. They are according to the tooth ratio.

Efforts have been made to approximate the contours of our rotors with circular arcs, parts of cycloids, or ellipses or oval curves or a combination Of one or more of them. They are useless unless patterned to follow our correct contours, hence, being made possible thru the light of our invention, they lie' within its scope.

In the drawings:

Fig. I is a right-hand view of ’Fig. II with a casing member removed to show rotors having 7 to 5 teeth, with ports in solid and dotted lines suitable for a fluid pump or compressor.

Fig. II is a section of Fig. I on line II—II showing pump and motor casings containing rotors, a driving plate, and an antifriction thrust bearing carrying the outer rotor to withstand fluid thrust pressures of either·, gas or liquid in the rotor chambers.

Fig. Ill shows a sector of the outer rotor and its driving plate in side elevation.

Fig. IV shows a type of tooth curve for the outer rotor.

Fig. V is a plan view of Figs. I and II.

Fig. VI illustrates construction details possible for an outer rotor.

Fig. VII shows successive positions of an outer rotor tooth curve rolling on a pinion tooth curve.

Fig. VUI illustrates an oil system for a compressor or gas motor to seal crevices and absorb the heat of compression including a valve for the compressor or a pump for the motor to supply water containing latent heat, to expanding pressure gases.

Fig. Villa shows a detail.

Fig. IX shows another form of rotors having and 9 teeth, and indicates bearing means with parts broken away.

Fig. X illustrates a motor construction for a hydraulic drive or gas expansion drive (depending on ports) both rotors being mounted c-n antifriction bearings.

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Fig. XI is a section of Fig. X on line XI—XI.

Fig. XII shows a hardening fixture for truing outer rotors.

Fig. XIII shows 11 to 9 rotors and a comparison with our earlier types of rotor teeth.

Fig. XIV shows a left-hand elevation of Fig. XI with parts broken away.

Figs. XV and XVI illustrate the novel Hill theorem of geometry by which rotors are designed to maintain continuous tooth contacts at steady speeds.

Figs. I and II show a casing I bolted at la to an end bell 2 of a motor to drive it. A motor shaft 3 (see also Fig. VIII) enters a bore 4 in a rotor back plate 5( Figs. Π and III) where it is keyed at Ga. The shaft is mounted on antifriction bearings 7 at one end (Fig. VIII) and 8' at the other end (Fig. II) between suitable hardened steel collars and rings. The balls 8 are held in position longitudinally between thrust collars 5a and 5t&gt;, and radially between bearing rings 5.c and 5d. The back plate 5 carries the teeth G of the outer rotor housed in a bore 9 of the casing I with just enough looseness not to conflict with the ball bearing 8. These rotors have seven and five teeth. The teeth of the outer rotor may be manufactured by inserting hardened teeth G in the plate 5 by means of tongues 11 in slots 12. The tongues may be coated with solder of type metal, lead, silver or other fusible metal which upon heating joins the parts solidly together. The teeth are pressed into close union with the plate 5 while cooling. Thus the teeth become practically integral with the plate 5. The teeth themselves may be made by production methods separately. Other methods of making the outer rotor are well known, tho not with our continuous contact teeth, which are described later.

Fig. IV shows a curve design for the outer rotor teeth. It has side tooth curves 13 and 14, being arcs of circles centered at ί3α and (4a. They are identical in reverse but do not have to be. They are connected together by a small nose curve 15 because sharp points on the generating master tools cannot be maintained in production manufacture. The curve 15 may be continuous with the side curves (3 and (4 if its center is at the junction of the radii 16 and (7, tho whatever the curve, the tool that generates the pinion curve has a corresponding curve on it. It shapes portions of the pinion teeth. The curves 13, 14 and (5 constitute the outer rotor teeth and the tool that generates the teeth and tooth spaces of the pinion suitable for pumps and hydraulic motors. The space at 18, Fig. I is objectionable for compressors and gas motors as it is what is termed “clearance” that results in losses of volumetric efficiency. It is quite acceptable for liquid mechanisms.

Outer rotors of the preferred type are first made with teeth of the desired number and size in accordance with the description in connection with Figs. XV and XVI, described later.

A tool of the right form (Figs. I and IV, representing a tooth of a rotor) will generate a mating rotor capable of maintaining continuous contacts at steady speeds inverse to the numbers of the tooth ratio. Ordinarily both rotors rotate in the same direction, the pinion faster than the annular rotor due to its lesser number of teeth. To assist better comprehension of generation, one rotor is considered as being fixed and the other rolling around on it or in it. We may at present consider the outer rotor as being fixed and the pinion revolving around in it. The tool has the form and size of a tooth of the outer rotor, Fig. IV for example. A pinion rotor blank is set up on a first shaft. This shaft is adapted to turn in an eccentric bore of a second larger shaft, all mounted upon a suitable base, as set forth in the Bilgram-Hill Patent 1,798,059. The bore is off-center in the larger shaft a distance equal to the eccentricity of the rotors (or the ratio or pitch circles) and the larger shaft also turns in a bearing. The two shafts are geared to each other at the tooth ratio to revolve the inner shaft and its blank at the same relative speeds that the completed pinion revolves if rolled around in the outer rotor.

The shafts are caused to rotate, and the tool representing the tooth of the non-rotating outer rotor, is caused to reciprocate up and down to cut the edge of the pinion blank as a vertical shaper, cutting parallel to its axis. The blank, revolving upon the two axes of the two shafts, advances into the path of the cutter and away again, generating a tooth space. It cuts a complete space, including the side of one tooth, then the tooth space and then the near side of the next tooth. As the two shafts continue to rotate, the next time the blank advances against the cutter, another complete space is cut, but not the next Space adjoining the first space. After cutting the first space, the cutter passes by the second space position and cuts the third space, then in succession the fifth, the second and the fourth spaces, thus completing the pinion with five spaces and teeth.

If it is a seven-tooth pinion, the order of cutting is 1, 3, 5, 7, 2, 4 and 6. If it is a nine-tooth pinion it is 1, 3, 5, 7, 9, 2, 4, 6 and 8. In the case the outer rotor is to have tooth spaces like those in Figs. X and ΧΠΙ the bottoms of the tooth spaces of the outer rotor loosely fit the pinion teeth. Liquid in outer tooth spaces is splashed around preventing compressed air or gas from leaking over to a suction port, expanding there and interfering with intake of gas.

In practice the convex contours of the outer rotor tooth form only are used in generating the pinion. The contour of the outer rotor tooth spaces, the concave portion, if wanted, may be generated by using a cutter having the form of the convex tops of the pinion teeth. The bottoms of these space curves of the outer rotor may be deepened to avoid contact with the pinion teeth to prevent noise.

As a summary, any tooth form selected for one rotor may within the limits of the circroidal addition, be used to generate the entire contour of the other rotor, and in some cases, a tooth form of the other rotor may be used to generate the entire contour of the first rotor.

Rotors are best designed on a drafting board on a large scale to determine the sizes and strengths wanted. The geometry in Figs. XV and XVI guide tooth relations. Trial generation may be resorted to, trying different curves and inclinations until the contours meet the requirement as to the circroidal addition.

One side of all the teeth of one rotor engages only one side of all the teeth of the other rotor, and the other sides of the teeth of both rotors need not maintain continuous contacts or engagements unless for reversibility of rotors themselves or for tightness in rotation in opposite directions.

Whatever the driving rotor contour may be it must obey the principle of the circroidal addi2,801,397 tion g,s described in reissue Patent 21,316; that is, it must be at least far enough from the central axes to be able to generate or outline curves on the other rotor without undercutting those portions necessary for the contact service intended. The driving contours do not have to be circular arcs since, they may be any regular or irregular curve or curves subject to the conditions recited: elliptical,, oval, hyperbolic, parabolic, or other geometrical curves of various angular inclinations; or mongrel curves, or combinations with one or more of the foregoing curves, within the limits stated.

If during, outlining or generating, they undercut curves needed for the service intended, they may be shifted outward until, undercutting disappears. It had always been supposed by those skilled in the art that the curves of gears had to have their centers on ratio circles, but that is. unworkable. When, instead, the curves themselves (not their centers) are distributed along ratio circles, particularly the driving curves at full mesh, they avoid angular slip and friction.

Rotors are mounted in a pump and “run-in,” that is, run. one against the other as in final use, and their contours worn to a running fit, after which tops of teeth slide gently into engagements. If inaccuracies of tolerances of manufacture bear heavily, powdered sulphur as an abrasive wears away interfering surfaces except at full mesh where the rolling driving action occurs that makes them more durable. Many abrasives would “charge” the rotor surfaces and permanently grind against each other, but sulphur- soon loses its abrasive action.

Figs. I, IX, and X illustrate rotors having backlash by which only the teeth of opening or closing chambers can have continuous sealing contacts (or pressure holding engagements) during rotation, but not both. A broken line 19 along a pinion tooth in Fig. X indicates a normal generated tooth curve. The curve 20 in solid lines may on each tooth be the same curve swung around its rotor axis far enough to clear the teeth of the other rotor during rotation, to provide back lash. In reversible mechanisms such as a rotor maintains continuous contacts in either direction, there always being back lash so that the other side of the tooth is out of contact with the other rotor. Except for reversibility the shape of the curve 20, as long as it keeps out of contact with the other rotor, is important only as it affects displacement volume. Arrows indicate driving rotors. A compressor running clockwise with teeth in contact, on one side of a center line thru the rotor axes is reversed when it runs anticlockwise with teeth in contact on the other side of the center line. If running anticlockwise with tooth contacts tight on the same side, it becomes ah expansion motor, a case of functional reversibility. Reversing a liquid pump accordingly may still leave it a pump or a hydraulic motor.

The ratios of our earlier rotors mainly had a difference of one between integers. This meant a difference of one tooth. In this present case as already noted, the ratios have, a difference of two teeth thus apparently violating the rule laid down in those cases that a ratio of a difference of one tooth was essential, for continuous contacts or engagements between the teeth. Instead of the difference of one being between the numbers of teeth in this case, it is between the numbers of the basic ratio. That is in a 7 to 5 ratio there is a difference of two teeth. But the basic ratio is

3½ to 2½. restoring the difference of one. It is the basic ratio that must have the difference of one, not the numbers_: of teeth. The numbers of teeth are the product of the basic fractional ratio multiplied by the denominator of the fraction. Multiplying the 3½ to 2½ ratio by the denominator 2, gives 7 to 5 teeth. Similarly in a ratio of 41/3 to 3y₃, the numbers of teeth are 13 to 10.

When in liquid mechanisms the teeth 6 have circular arcs as at 22 and 23a, and tooth spaces as at 18, unless primed, reduce suction. Concave generated curves like those in the outer rotor in Figs. X and ΧΠΙ are then desirable.

As long- as extra spaces fill with liquid, suction and volumetric efficiency are not impaired. On the other hand, at high speeds tooth spaces i8 facilitate centrifugal discharge of liquid approaching full mesh where the chambers between the teeth are closing. For gas (including air of course) the tooth space in Figs. X and XIH may be shaped to fit the tops of pinion teeth at full mesh, tho relieved to avoid actual contact with the pinion teeth to avoid noise. The construction in Fig.: I permits smaller diameters (see the bore 9 in Figs. I and II) than that in Fig. X for example.

As the size of the outer rotor teeth 6 in Fig. I is also the size of a master cutting tool for machining, the pinion contours, the larger it is the faster it will generate the pinion. Also, such teeth predominate in wearing as against a pinion of equal hardness, the teeth of which are smaller.

Fig. IX has outer rotor teeth predominating by being of harder material than the pinion teeth.

As the teeth rotate they part company along a crescent 24 in Fig. I and along other crescents in other figures referred to later.

Pressure angles and rolling action at full mesh where the actual drive occurs (after running in) are conducive to high speed. They are indicated in Fig. XVI between an outer rotor tooth curve M-i and a pinion tooth curve T.

The pinion 25 is journalled on a stub shaft 23 fixed in the casing t, Fig. II, The_: distance between the axis A (Fig. I) of the pinion and the axis B of the outer rotor, the so-called “eccentricity” is greater than that in our earlier 7 to 6 rotors of the same outside diameter having a difference of one tooth. Except for the crescent 24 at open mesh the displacement, varies as the square of the eccentricity, i. e. as 25 to 9. While the crescent modifies this relation, rotor eccentricity is, a basic factor in rotor displacement. Without an antifriction bearing, a plain bearing tight enough to. keep the rotor teeth in contact might heat and seize. The pinion 25 has equal pressures upon its sides so that pressure or wear on its ends is not noticeable. The balls 8 keep the rotors running freely in the casing and keep the back plate 5 (Fig. H) from touching the wall 26, The driving plate 5, is centered in its casing by the balls running between race rings 5c and 5d and between the collars 5a and 5 b, The balls roll in a diagonal direction.

In a hydraulic or gas operated motor, Figs, X and XI, antifriction bearings 12 are needed to keep the back plate 73 from clutching the wall 7 ®c and preventing rotation. By centering the outer rotor to run free of contact in the surrounding wall of the casing 19, a clutching action there, that would prevent rotation, is avoided. Without some such means a Gerotor motor appeared to be ineffective.

A seal 74' prevents leakage.

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Pipe connections 28 and. 29 (Fig. V) connect with ports. In Fig. I the pipe connection 29 connects with a discharge port when as a pump the rotors run clockwise. In the same way the pipe connection 28 connects with the intake port in Fig. I. Ports in a sidewall in Fig. I, being on the other side of section line U—H, are not shown in solid lines. Their positions relative to the rotors are indicated in this figure in dotted lines.

Ports in the wall surrounding the rotors are also indicated in dotted lines at 29, 30 and 31 in part; and in Fig. II in solid lines at 30. Outer wall ports 29a and 31, being optional, are indicated in Fig. I in dotted lines. All ports are referred to later.

Figs. IX, X and XI show both pinion and outer rotor mounted on antifriction bearings, while the outer rotor in Figs. I and II is mounted, to resist thrusts of fluid pressure in rotor chambers, both endwise and radial. Fig. IX shows rotors having the tooth ratio of 11 to 9. A number of factors may be observed. The space between the rotors along the crescent space 97a in effect is a continuation of the port ίθί extending from 97b to 97c, where the outline follows the rotor tooth contours in the position shown. Owing to back lash there is no actual contact on the right side of Fig. IX between the teeth along the contact pathway from 97d up to full mesh. The same is true in Fig. I, the pathway of actual tooth contacts between closing teeth being indicated from 41a to 43 where the pathway ends.

As compared to the liquid port abutment area 54 in Fig. I, the abutment area in Fig. IX is lengthened, extending from the said end 97a (along the rotor tooth contours in the position shown) to the lower edge of the discharge port 97 shown in dotted (not broken) lines which coincide (except for overlap) with rotor contours in the rotor position shown.

The chamber 98, containing its oil pool, closes until its outermost middle point 97p reaches the center line CL at full mesh, splashing oil into the crevices between the ends of the rotors and the side walls between which the rotors run, sealing the crevices against escape of pressure gases. This oil seal performs the functions of piston rings in cylinders with no loss due to wear or mechanical pressure.

The contact 100 is about to open, after which the contact 99a at full mesh separates the ports 97 and 101. The contact at 97e, just closed, seals the chamber 97/ from the crescent space and intake port, and as the rotors turn, compress air in the chamber until it reaches the discharge port 97. Successive chambers 97/, 97p, and 99 are sealed from each other, so that rising pressure cannot escape backward into chambers containing lower pressures, thus constituting staged compression.

The contacts between the teeth occur along a pathway from a point 97e to 100. The pathway of contact between opening rotor chambers is from full mesh to 97cZ. When the rotors have back lash there are no actual contacts along this pathway.

In Fig. I the pathway of actual contacts is indicated at 41a, extending from 42 to 43. The pathway of contacts of opening chambers is the same as 41a reversed. The term “pathway of contact” indicates the path along which tooth contours provide drive and pressure holding engagements when “worn in” by running, tho it also includes the similar path where actual opening contacts are absent due to back lash in a pump or motor.

The teeth of these rotary devices differ from those of prior patents. In patent No. 2,091,317 to M. F. Hill, teeth of the gears were proportionally shorter and displacement surprisingly less compared to the teeth of our present rotor mechanism, so that for a given displacement rotors would have to be larger and would cost more to make. Fig. XIII illustrates the difference with 11 to 9 toothed rotors, in which the principle is the same.

Moreover the teeth of the patent had even numbers, 4 to 6, 6 to 8, etc. This meant multiple settings and machining operations. For a difference of two teeth, two settings and two machining operations were essential. The indexing of the pinion blank had to be done with exact precision to avoid rattling of teeth, and was difficult and expensive. Merely machining the teeth cost nearly double.

Adding one tooth to both rotors eliminated this difficulty. The entire contour is now generated at one setting. The taller teeth with pointed crowns in Fig. ΧΠΙ and increased displacement also resulted.

The pinion tooth curve 32 in broken lines illustrates the relative form of teeth in the patent. It has a generative relation with the space curve 33 shown in broken lines. Such teeth left a long crescent range at open mesh between the teeth, between the arcs 34 and 35 of circles, one passing thru the tips of the pinion teeth and the other thru the tips of the outer rotor teeth, intersecting at about 38 and 37. Said crescent range is the area in which there is no contact between the teeth of one rotor relative to the teeth of the other rotor. Increasing the radial height of the teeth at 38 and 39 shortened the crescent range to 40-41, the points where the corresponding two circles thru the tips of teeth intersect.

Rotor chambers between the teeth cannot be sealed of course in the open mesh region along the crescent. They can only be sealed from each other away from the crescent. The rapid change in capacity of a rotor chamber passing along this region necessitates a crescent as short as possible. With the pinion drive in the earlier case, 659,098, the sealing region in a pump is where the chambers open. In this case it is where the chambers are closing. Since the teeth while travelling clockwise re-engage to the left of the crescent, the path of contact (see 41a in Fig. I) between the teeth begins at this point 49, and continues thru tooth contacts to full mesh.

The area of any rotor chamber between the teeth, as it is sealed off at 36 or 49 determines its maximum displacement. In Fig. XIII the chamber, sealed when its rear tooth contact reached the point 40, is not far from twice the size of a next chamber beyond. The differences between chambers 40a, 40b and 40c illustrate the rapid reduction in area of successive chambers. If the mass of a rotor mechanism has to be increased to compensate small displacement area, its cost of manufacture soars. The importance of a shorter crescent can therefore be realized.

By means of the geometry devised by the inventors, set forth in Figs. XV and XVI, called by some the Hill theorem, the new curves were developed. The crowns 39 of the pinion teeth mate with the tooth spaces 38 of the outer rotor.

The greater tooth height also contributes to displacement area which varies, inter alia, as

2,601,397 the square, of- the- radial tooth* dimension.. In Figs. IX, X: and:: χΐΐτ used: as: a. pump the- rotor chambers, as; they close: are sealed from each: other by contacts between the:· teeth,, similar to. those in Fig. I along the pathway of contact 41 a,. at 42, 45 and: 59, The: contacts travel along a path and around· a: loop similar to 51, Fig. I. Used as a motor the opening, chambers, are, sealed.

If actual: contacts: fail: due: to inaccuracies of tolerances of manufacture;they may nevertheless be so close as: to maintain fluid pressure: holding: engagements, made possible: only - by- our system of tooth contours and· generation, , and suitable· for many fluid’ pressures.

In: Fig; XIII back, lash- is omitted, the teeth making; pressure.· holding, engagements, sealing rotor chambers during both opening and closing until, they wear enough, to create back lash. In a pump: driving, the- outer rotor maintains: the the contacts between the; teeth ef closing chambers, in. spite of: wear.

In motors, the. opening chambers, are kept· tight by the, work done; the outer rotor driving the work shaft.

In pumps, what is called, “overlap” is necessary for speed of rotation.. If in-passing between the crescent: space: 2-4. to- a discharge port a closing chamber is, not connected to. the discharge port soon enough, its rotation is blocked- or retarded, (depending on the degree of end looseness-of the rotors).. So- a. chamber does not disconnect from the- suction, port , until, its has, connected with the discharge port, just enough to. avoid· blocking or retarding, rotation.. This relation, shown in Fig.. I is. termed the. “overlap” and is common and necessary to precision continuous contact liquid pumps.. For slow speeds it. is small, and for higher, speeds it. is larger.

When. the. ball, bearing, wears enough for the back plate to r.ub against the wall 2.5 it takesmore power, to operate. A shim 67 is. then inserted: between the. thrust, collar 5a and the back plate to free the. rotors.

Fig. VII illustrates, the travelling positions of an outer tooth curve like 22 in Fig. I. along a pinion tooth curve 25'. The. center of. the outer rotor tooth, curve is shown at 53, and as this center travels along, the circroid 62,, the tooth curve; as at 64; rolls in successive positions 65 along-a pinion tooth curve as at 63, until following teeth take their places. It doesn’t, slide along as is usual, between a gear tooth entering a tooth space at full. mesh, but has an. almost frictionless rolling drive, ideal for high speedoperation.

Assuming, that a cutting tool, takes, the place, of the outer rotor tooth curve, in successive positions it. cuts or machines the teeth- and spaces in the rotor, blank having a contour 66· until the other rotor is produced.

The hydraulic motor in Figs. X and XI is in many respects similar in: construction to the pump in Figs. I and II. It has pipe connections 69: and 70 in the. cover plate 7i for the ports(Fig. XIV). The balls 72 run similarly between collars endwise and: race rings radially, as the outer rotor drives the keyed shaft 73. Incidentally the pinion helps- the outer rotor along. The fluid pressure in the rotor chambers delivers a torque to both rotors, the outer rotor prevented from running wild by the work of the shaft, and the. pinion by its teeth engaging and pressing against the, teeth of the outer rotor to help· it along as the: chambers: open.

The seal 74 on the hub 75 of the: back driving: plate 76 of the. outer rotor prevents leakage.

The pinion 77 is; journalled on the stub: shaft 77a on a: roller or needle bearing 77b.

The shaft 77a may be molded, into a cover plate of plastic·, or of poured metal, or otherwise applied. The ports as at 77 c upon the inner face of the cover 71 may also be formed by molding or casting. The key 78 fixed in the. casing 79 10: prevents mounting the c.over in a. wrong position.

The plate 71. rests· against a shoulder 60 (with, gasket: if desired). It. should leave: barely enough room for the rotors-to run freely. The hollow nut 81: screwed into the casing 79 holds the cover 15 against its shoulder: 86. The outer rotor may he a. ring 82: with: the teeth: formed, upon: its inside. It. is fastened to the back driving plate 76, by rivets ,as: at 7 6a. Such a rotor may be of: hardened steel, preferably- case hardened; It may be ma20: chined while in. a. softer state, to within, a. few thousandths of an inch , smaller than its final diameter..

A plug. 84: (Fig; XII) is made , of: hardened: Rex AA tool steel preferably, with slots 84a accurately 25 ground and indexed: to. correct: the size and indexing of; the ring and: teeth.

Lt.is: connected to., a·, pipe. 8:5., having; a shut-off: valve 86. Vent holes 8.7 are drilled in each slot to. connect with, the ,pipe; The ring: 8,2: is heated 30 to about 1550^s F., and while expanded: from heat is slipped: over the plug. At the same time the valve: 8:6 is: opened, to admit- a chilling fluid against the inside-of: the ring,, shrinking, the inside, of: the ring onto the plug.

The- inside- of: the. heated: rotor ring, shrinks first and is sized and indexed while the rest of the ring is-still hot-and pliable. The rest of the ring cools and: is: stretched in the process. The valve is closed when there is not enough heat left 4()- in the- ring, to anneal: it. The. ring then may be lifted: off - from, the- plug easily.

The: inside, thus- hardened, is durable and correctly indexed, and. the pinion, in running wears to a perfect fit.

The: same idea, may be applied to pump· as. well: ⁰ as motor mechanisms.

As a, compressor, to avoid, pressure loss, oil is caused- to: fill· crevices, between the ends - of the rotors and the casing walls. Also oil: is sprayed into the-compressor: air intake-to absorb the heat of compression, reducing the power required to compress. Oil is removed from the air-by centrifugal force. The- air is discharged into a pipe 8.8 (Fig; VIII) with: a, vent 89 (Fig. Villa) tan_r_ gential' to the inside of: a, cylinder 90 where it creates, a, whirlwind and throws the particles of oil mist out by centrifugal force to the cylinder wall. The oil. then drains down into a pool 91 at the bottom of the cylinder. The oil is cooled by • the, cylinder wall. The height of the cylinder is ^υ adjusted to the temperature drop desired. The air, separated from oil is drawn off from the middle of the cylinder by a, pipe 93. The pipe is fitted with usual equipment for service including _C5 a blow-off valve. 94. If air at 70° F. is, compressed ^υ to 100 lbs. its adiabatic, rise of temperature as already related is, some 400 degrees F. The oil is sprayed into, the: incoming air at the intake 28 to, absorb the heat of compression. The valve 05 70 is adjusted to, keep, the top temperature down to near 105°- F: with. as. small a flow as possible. Chilled oil in the. cylinder 90- lowers discharge temperature. Oil spray gathers dust and has to be renewed* A non-foaming cutting oil, one part 75 to 20 parts of water is- efficient. Compression and

2,601,397 centrifugal force restore the mist to a liquid state for pools in the rotor chambers. (A variable pump at 95 adjusts oil for a gas motor spray.)

In Fig. I ports shown in dotted lines at 29, 39 and 31 in the outer wall surrounding the rotors for a hydraulic pump are not used in compressors lest the oil pools drain off.

Manufacturing cost of a given unit is affected by its displacement. The greater the displacement, the less the relative cost and selling price. In Fig. I rotor chamber displacement areas are somewhat evenly balanced inside and outside of the ratio circles. In Fig. XV, for example, the ratio circle passes thru the middle part of a pinion tooth. With the same numbers of teeth and the same eccentricity, the displacement areas in Fig. IX would be further out radially than in other figures. As displacement areas vary according to the radial distance, the advantage of the form in Fig. IX for displacement is evident. The centers of curvature of the outer rotor teeth are close to its ratio circle due to being small, so that the displacement area of each rotor is perhaps 90 % outside of its ratio circle.

Assuming that the mechanism in Fig. IX is a compressor rotating clockwise, that a discharge port 97 might hold say 105 lbs. of air pressure, and a chamber 99 might have air compressed to seven atmospheres, the port 97 is located to receive the compressed air during rotation at the same pressure without drop or loss. Oil being splashed into the crevices from the next chamber 98 prevents escape of air into the intake port 10 1, and there being no clearance space (thanks to the oil pool), all the air is delivered out thru the port 97. Liquid might lock the rotors from turning unless the port 97 is extended to the abutment between the dotted lines 97 a and. the left end of port 101.

Assuming that the rotors in Figs. IX, or X and XI, act as gas expansion motors, compressed air from the cylinder 90 and pipe 93 may enter successive rotor chambers thru the port 97, Fig. IX, or 97b in Fig. X, causing both rotors to rotate anticlockwise. Part of the oil sprayed by a pump into the intake 97 travels round and round in pools in the rotor chambers and at full mesh is splashed into crevices to prevent air leakage to the low pressure port, now an exhaust port. Oil entering a motor as mist gives up its latent heat to gases as temperature lowers adding to their power of expansion.

The pinion 102 in Fig. IX may be mounted on a roller bearing 103 running on the hardened, ground and polished steel shaft 104, similar to the shaft 73 in Figs. X and XI. The rollers run in a race ring 105 mounted in the cast iron pinion i 02. The outside of rotor 106 is also of hardened steel, ground and polished. It may rotate in a roller bearing 107 in the casing 108, and have a connection to a ball bearing shaft as in Figs. II and XI, in which case the balls 8 are loose radially between the rings 5c and 5d.

In fluid mechanisms even the best tooth forms and rolling contacts are useless without correct port relations to match. It requires ports located and shaped to provide continuous traveling fluid pressure-holding engagements between the teeth, and abutments located to cooperate with the continuous contacts to prevent escape of fluid pressures thru the teeth or around abutments.

In Fig. I as a pump or compressor, escape of fluid pressure from a high pressure port 52 to a low pressure port 53, both shown in dotted lines, is prevented by abutment areas and by continu16 ous driving contacts and fluid pressure-holding tooth engagements traveling along said abutment areas. One abutment area is at full mesh and the other is between the port 52 and the open crescent space 24.

As one tooth engagement reaches the end 43 of its active range, its path of contact, it is followed by others. The tooth contacts by which the outer rotor drives the pinion perform the pressure holding contact function. Elsewhere along the path of tooth engagement, the teeth lap each other as a valve to a valve seat, until they cease mechanical pressure and slide over each other with no substantial friction. Between this region and open mesh, to prevent closing rotor chambers from driving fluid back into the crescent range 24, an abutment area is needed at 54 between the port 52 and the crescent range

24. It is so located and of such a size and form that at about the time when the teeth engage at 42 the rotor chamber ahead disconnects from the crescent range 24 and connects with the port 52, with enough overlap of port and crescent range, depending on speed and fluid viscosity, to soften fluid pressure variations during the transit of the rotor chamber over the abutment. Inertia and momentum of fast-travelling liquids is relied upon to carry them past the overlap without substantial loss.

The travelling contact at full mesh and the abutment 54 at the end of the crescent range 24, leave no other outlet from closing chambers except the discharge port 52.

If on the other hand, in a pump, the rotors are reversed and travel anti-clockwise, the travelling tooth contacts follow along a similar path of contact on the right side of the figure. An abutment area 55, a duplicate in reverse of 54, leaves only the port 53 as the outlet from closing chambers. The teeth along the abutment area 54 are then out of contact due to back lash. Considering again clockwise rotation, the filling of chambers would be limited by the abutment 55, were the teeth not out of contact due to back lash as at 56.

This opening at 56 connects fluid pressure, the intake port fluid pressure, extending from 53 to 55, to the open crescent area 24. So that for all practical purposes the intake port fluid pressure area extends from 53 to the abutment 54. These abutment areas, 54 and 55, are the areas between the ports outlined by dotted (not broken) lines. The abutment 54 registers with a rotor chamber as it becomes sealed by the contacts at 42, except for a jog along the path of contact 41a across the next tooth to the contact 45. Without this jog very little pressure could be developed in running clockwise. The reversed abutment 55 follows a similar outline. In clockwise rotation in a pump the teeth that form the chambers draw apart from full mesh to the middle of the crescent range 24 and then approach each othei· again until they reach the point 42 where they seal the rotor chambers, and then close until an outer rotor tooth reaches the middle of full mesh, meanwhile discharging fluid out of the discharge port 52. (The term fluid, by the way, is intended to include liquids and gases that flow.)

This not only affords chambers traveling at high speeds to fill more completely but the teeth approaching each other beyond the middle point of the crescent tend to eliminate cavitation in liquids, and to slightly raise pressure with gases.

If now the pump is reversed again to run anticlockwise, the port 52 is connected to the crescent

2,601,397 area thru contacts open at 42 and with the same characteristics as in clockwise rotation.

While the edges of abutments 54 and 55 except for overlap and with the exception along the path of contact 41a to 45, register with the contours of rotor chambers, the edges may extend beyond the contours. In compressors the abutment 54 extends as far as the shortened high compression port 50a. The same is true of the abutment 55 running anti-clockwise. No overlap here is employed in compressors or gas expansion motors.

Liquid ports working with pressure gases, are most uneconomical at the speeds usually employed. Economical gas ports prevent operation on incompressible liquids. With a long discharge port (50a in Fig. I) high discharge port pressure would instantly fill a chamber as it passed an abutment 54, only to be driven out of the chamber again into the discharge port at a considerable waste of power.

Assuming a high predetermined pressure in the discharge port 50a the closing rotor chamber should not connect with it until its compression equals the pressure in the discharge port. This discharge port is therefore located with respect to the rotor chambers at a point where they have correspondingly compressed air. This gives the most efficient cycle so far as ports are concerned. (A small pair of rotors, watch size, have compressed air to 400 lbs. pressure, most of the heat of compression being absorbed by the rotors and side walls.)

If operated in one direction only as a pump, the abutment on the side of opening chambers may be omitted as useless.

Rotating in the opposite direction the port 53 is shortened the same as at 50a in reverse, and the abutment 55 becomes active instead of 54, in which the case the foregoing description would apply.

Rotors of the prior art differing by two or more teeth in which the tooth contours have no continuous contact contours between their ports, require a solid insert between the teeth in the crescent range 24 which with the teeth are supposed to seal one port from the other, but with our continuous tooth engagement no insert whatever is needed. In fact that crescent area is put to better use in filling chambers and reducing cavitation.

As a motor, both rotors are preferably mounted on antifriction bearings as at 72, Fig. XI, 77b in Fig. X and ί 07 in Fig. IX.

The ports in the side walls, or in the surrounding wall, or both, may be used, in which case the motor is reversible.

The motor may operate under liquid pressure with the liquid pump ports (Fig. I) in either direction, or with but one abutment, 54 or 55, in one direction.

The air compressor ports used in a motor permit expansion of high pressure gases. Back lash and the crescent area of course permit expansion under heat conditions.

In both cases suitable antifriction bearings may be used. These bearings locate the rotors between the side walls and centered in a surrounding wall without contact with either. If there is contact, pressure fluids entering rotor chambers cause them to hug the walls like an old auto clutch and often prevent rotation.

In Fig. X the pinion 77 is mounted on needle or roller bearings 77b on the stub shaft 77a fixed in the cover plate 71. The outer rotor back driving plate 76 is thrust by internal fluid pres18 sure against the balls 72. These balls run between collars and rings the same as the balls 8 in Fig. H, and center the outer rotor in housing 79.

Our liquid pumps and gas compressors, and our Ratoid hydraulic and gas motors operate with greater efficiency than with our earlier types of rotors, whether with even numbers of teeth differing by two, or with numbers of teeth differing toy one. This is owing to greater displacement for a given size, superior pressure driving angles at full mesh producing a rolling drive suitable for high speeds, easier manufacturing methods, and quicker delivery after machining, to users.

Drawings cannot represent the actual sizes and shapes of rotor teeth. A discrepancy equal to the thickness of a line on this printed page might render them so tight as to toe inoperative, or so loose as to permit gas to flow between the teeth freely.

Rotors are made with precision, with tolerances down to lowest commercial limits. This keeps losses of defective units down to a reasonable degree. Back lash suits conditions from a few to many thousandths of an inch.

Mathematics may toe resorted to, in order to determine the inward limits of generation for a given set of conditions. The equations are intricate.

Equations for curves generated by circular master forms may be within the reach of some engineers, but equations for variable forms, other than circles, ellipses or cycloids, would be difficult even for an Einstein. Enlarged geometrical drawings on a chart suffice to determine diameters, tooth curves, and displacements.

The Hill theorem

There are six geometrical stages involved in arriving at continuous contact contours.

1. Describing a cycloid with a point in a ratio circle of one of the rotors as it rolls on the ratio circle of the other rotor.

2. Scribing a trochoid, using a point on an extended radius of the outer ratio circle as it rolls on the inner ratio circle, to do the scribing. This curve is termed a “circroid.”

3. Finding the limits within which the inner rotor contour must lie.

4. Outlining an envelope within the limits, for tooth contours.

5. Selecting a portion of the envelope for a side of a tooth, thereby determining the size of the pinion.

6. Locating and limiting the contour of outer rotor teeth to cooperate with the pinion teeth.

Fig. XV illustrates the first two stages, and Fig. XVI illustrates the last four stages.

It is understood that when one side of each tooth is arrived at, the other side may (not must) be the same curve reversed.

Basic ratio circles A and B proportional to the numbers of teeth are settled upon, and the inner one scribed in both figures. Next, in Fig. XV the path of the center of the outer circle as it rolls tangentially on the inner ratio circle is scribed. This circle E is termed the circle of eccentricity. A radius of B from a point in the circumference of E, thru the center of E and thru the ratio circle A is drawn, preferably at an angle to a perpendicular P (through the eccentric axes) equal to one half of a pinion tooth division. Starting from this angular radius line the ratio circle A and the circle of eccentricity '2,601,397 safely outside of N. If to the left, inside of N, the arcs would cross each other and a theoretically true generated curve would fail to be realized.

More specifically, the arcs Bl indicate successive locations of the ratio circle B, rolling on A and pivoting on the trangential contacts between B and A so that the end of the radicroid scribing the circroid CR corresponds to a straight line radius from the circroid to the ratio circle A, which is therefore the normal to the circroid.

The successive points of the circroid therefore are connected by normals, which are instant radii, to successive points on A, such as 000 to 00; 209 to 22; 250 to 25; 300 to 33 etc. Some of these radii diverge, but some converge and therefore intersect each other. When we locate the nearest intersection N to the circroid CR, we locate the limit within which, between the intersection and the circroid, the rotor curve must lie. The instant radii are not shown in Fig. XVI as they might confuse the diagram. But a straight edge applied from points on the circroid to corresponding points on A will verify the location of N. While drawings are not accurate as to points, a drawing on a scale of 10 to 1, accurately laid off may come so close that with an allowance for aberrations, the rotor curve may be determined with safety, subject to mechanical verification. If the rotor curve by mischance lies to the left of N in Fig. XVI, the cutting tool that generates will cut a correct curve then to loop back and undercut it. If not serious enough, little harm might result in some applications; but it may be corrected by shifting the cutting tool further from the ratio circle axes until undercutting disappears.

To· put this another way, the radius M may be shortened, or the radicroid lengthened so that the circroid CR will be farther away. If the tooth curve is exactly at N, a sharp corner results, usually of no benefit. By shifting the tool outward, the sharp corner disappears and a rounded corner results, much better for wear and for driving.

Having arrived at a tooth curve T, the next stage is to select the portion suitable for a tooth. Let the arms of a protractor, centered at Y lie at angle of one half of 360° divided by the number of pinion teeth. The angle therefore is 36°.

Let this protractor swing the center Y to right and left until the portion of T enclosed between the arms is the desired curve. In Fig. , XVI it extends from H to G, and establishes onehalf of a pinion tooth. By swinging the protractor clockwise the width and strength of the tooth suffer. In the other direction the radial height is less and that means less displacement. The mean position is adopted.

The other side of the pinion tooth may have the same curve in reverse, starting at T. If it should have a different tooth curve, it would require different generative curves on the other rotor.

Next the tooth curve of the outer rotor is to be found. The curve M generated the pinion curve HG, therefore it is the curve for a corresponding side of an outer rotor tooth. In generat70 ing the pinion curve HG this master or tool curve M, or rather its center COO travelled along the circroid CR. Its center lies in a norm, or radius of M, from a point in CR normal to M, at .H, therefore the tooth curve of the outer rotor

E are divided into an equal number of divisions. Ten divisions are convenient, one of them being subdivided for. reasons later recited. The divisions on E start at C, and the divisions on A start at CO, both numbered anticlockwise for convenience.

It will be noted that its radius line R extends beyond ratio circles. It is called a radicroid, a condensation of “radius of a circroid”. As the outer ratio circle B rolls on A it carries along its radicroid R, The outer end of R describes a curve. The location of this end R is found by trial and error until an acceptable tooth curve is produced. The location of point OOB is convenient for illustration.

While the inner end of the radicroid is travelling around the eccentric circle E, there is nothing to determine its changing angles until we discover that it also intersected a zero point in B, and curiously that zero point was the one that scribed the cycloid Cy. Therefore the radicroid followed that point along the cycloid, while its center traveled around E. If the center advanced anticlockwise one division, or rath of the eccentric circle E, the point 000 in B advanced anticlockwise, one division on the cycloid to Cy IO; that is, the point on the cycloid marked I0. When on E, the radicroid is advanced another 10th to “2” on E—it swings angularly to intersect the point 20 on the cycloid; and so on until the cycloid veered back toward the ratio circle A again.

Meanwhile the outer end of the radicroid has been outlining the circroid CR, a species of trochoid.

The different rolling positions of B are indicated by the arcs Bi, the points 00, 10, 20, 30 etc. being the corresponding points of the cycloid Cy, and the points 000, 100, 200 etc. being the corresponding points on the circroid.

The next stage is described with relation to Fig. XVI. The ratio circle A, with some of its division points, and the circroid with its corresponding points are shown in this figure.

The first objective is to find the intersection. of norms to the circroid, that lies closest to the circroid. A norm extends from a point in the circroid at the circle A, to a point where the circle B is tangent to it. If the outer end of the norm is swung to the right or left along the circroid, its inner end, the point of rolling contact of B on A, travels to right or left with it. The norm, for example, from the point G09 in the circroid extends inter alia to the point 09 of the ratio circle A. A norm from the next point 100 extends to the point 11 of the circle A because 100 is at the tip of the radicroid, the extended radius of B, when B has rolled on A one division to the next point II, the next instant center of the norm.

Likewise the norm from the point 238 of the circroid extends to the point 22 of the circle A, and the norm from 250 extends to 25.

If lines are drawn between these various points their intersection with each other is nearest the circroid at about the point N. As further norms from 300 etc. are explored, they intersect farther and farther away from the circroid and need no further consideration. The line M is shorter than the distance from N to CR.

Let us therefore adopt the arc Ml, having the radius M, centered at 000, as the start, and draw additional arcs M2, with the same radius from successive points along the circroid. Tlie tooth curve T is the envelope of the arcs, and it lies 75 -begins at the same point H and may extend outj

55c

2,601,397 ward to a circle M3 at the tip G of a tooth at full mesh, the center of M3 being at Y2 in line with Y and G and in the circle E to include the eccentricity.

The other side of the outer rotor tooth may be the same curve in reverse.

These are forms of teeth in Fig. I. The rounded variety of tooth space curve with a free running fit over the tops of the pinion teeth, have already been described.

Tlie radius of M may be shortened, and a new curve HG generated to match. Or a circroid CR may be nearer the circle A. In case of variations the point N has to toe located in order to locate a curve HG. Usually the theoretical sides of a tooth meet at G at a point, but variations may alter the relations.

Tips of the outer teeth in Fig. IX are modified by a small, circle 112 the center 113 of which is outside of the outer ratio circle 114 correspond- 20 ing to a circle B in Fig. XV. A tool of this circular form and in the relative position of an outer rotor tooth may generate the pinion tooth curve i(5. It also may generate a tool having the form of the pinion tooth, which then may generate the complete outer rotor tooth contours including the circular tips 112 that were used?in the first place. The large drawing is used for laying out such teeth, which have advantages in manufacture. Precision cast pinions may be finally trimmed by a large grinding wheel having a rim with the shape 112.

As the displacement areas are mostly outside of the ratio circles, they are about the maximum for rotors.

Compressor ports are shown, the discharge port at 97 and the intake port at 101, both mostly in dotted lines.

The system of hardening on a plug, Fig. XII, is ideal for this type of rotors for precision with low cost.

Our geometry may be applied to involute gear teeth, changing their curves so that the same continuous driving contact across full mesh at steady ratio speeds may be attained, which in that art is lacking, and is the cause of noise at high speeds and under loads.

While we have described specific curves and contours for teeth, it is understood that many variations may occur from those shown and specifically described without departing from the principle underlying our rotors and gears.

While we have described the several embodiments of our invention, it embraces combinations set forth in the claims, intended to include all systems of contours of rotors and ports characterized by the continuous contacts at steady ratio speeds not already covered in prior cases of ours or of either of us, regardless of curve interruptions or variations where such contacts are not needed.