US1797460A

US1797460A - Method of forming gears

Info

Publication number: US1797460A
Application number: US275142A
Authority: US
Inventors: Wildhaber Ernest
Original assignee: Individual
Current assignee: Individual
Priority date: 1928-05-04
Filing date: 1928-05-04
Publication date: 1931-03-24
Anticipated expiration: 1948-03-24

Description

March 24, 1931. E. WILDHABER METHOD OF FORMING GEARS 4 Sheets-Shet 1 Filed May 4, 1928 FIG-6 INVENTOR March 24, 1931. E. WILDHABER 1,797,460

METHOD OF FORMING GEARS FiledMay 4, 1928 4 Sheets-Sheet 2 FIG-Z2 INVENTOR {m EM WM March 24, 1931. E, WILDHABER 1,797,460

Filed May 4, 1928 4 Sheets-Sheet 3 r 99 y x INVENTOR 98 March 1931- E. WILDHABER 1,797,460

METHOD OF FORMING GEARS Filed May 4, 1928 4 Sheets-Sheet 4 I 36 I INVENTOR FI 6-18 881' E Ms willful-W Patented Mar. 24, 1931 PATENT OFFICE ERNEST WILDHAJBER, OF, BROOKLYN, NEW YORK METHOD OF FORMING GEARS Application filed May 4, 1928. Serial No. 275,142.

The present invention relates to methods of forming gears, and particularly to such methods in which a gear blank and a forming member or tool are continuously rotated on their axes, in engagement with each other and in timed relation to. each other.

One object of the present invention is to provide a method of forming ears in a s mple operation, which is capa le oi. a high rate of production. Another ob ect is to provide a method of forming gears in a continuous operation, which permits the use of a comparatively large and strong form ng member or tool while maintaining a high rate of production. A still other object is to provide a method of hobbing gears with a hob of comparatively large diameter and eat strength, without incurring such drawacks as increased distance ofv feed. A further aim is to provide a novel method of hobbing gears with a distance of feed.

The present invention is particularlv adapted to the production of gears having a comparatively small width of face. It is devised to make full use of the advantages afforded through .such specific application. A purpose of the present invention is to provide a novel method of hobbing gears, in

which a gear may be completely finished in a single position of relative feed between a gear blank and a forming member ortool,

and a method which permits roughing and fine finishing the tooth sides of a gear blank in a single and continuous operation. Another object-is to provide a method of roughing and finishing the teeth of a gear blank in a single operation and with a changing rate of feed.

Various other objects will appear in the course of the specification and from recital of the appended claims.

The present invention is applicable to forming gears by cutting, by grinding, by 45 lapping, by burnishing, in short it is applicable to any manner of forming. It may furthermore be applied to all kinds of gears.

It is here particularly explained in its application to gears suited to run on parallel axes or on intersecting axes, and to gears of constant profile, that is to say to gears having either helical or straight teeth. The adapta-' tion to worm gearing and to other gears having angularly disposed and offset axes is more specifically disclosed in a separate application for patent, filed on even date herewith, namely on'May 4, 1928, Serial No.

Embodiments of my invention are illustrated in the accompanying drawings, in which a Fig. 1 is a plan view of a gear blank and an axial section of a hob or forming member engaging said gear blank in accordance with the present invention.

Fig. 2 is a diagrammatic front corresponding to Fig.1.

Fig. 3 is a diagrammatic plan view of a simplified device for cai rying out a method in accordance with the present invention.

Fig. 4 is a front elevational view corresponding to Fig. 3, partly in section along lines 11 of Fig. 3.

Fig. 5 is an axial section through the rim of a gear, for diagrammatically illustrating a modification of the teeth allowing for miselevation alignment, and such as may be readily produced in accordance with the present invention.

Fig. 6 is a diagrammatic plan view illustrative of the use of two hobs for cutting opposite tooth sides of a gear blank respectively.

Fig. 7 is an elevational view corresponding to Fig. 6.

Fig. 8 and Fig. 9 are a plan view and a corresponding front elevation illustrative of a way of determining the accurate shape of the thread of a forming member or hob.

Fig. 10 is an end view of a relieving tool in engagement with a hob, the latter being shown in section.

Fig. 11 is a. front elevation of the hob and of the relieving tool also shown in Fig. 10.

.The thread of the hob is shown continuous,

for convenience. Fig. 10 and Fig-11 illustrate a way of making a hob for use in accordance with the present invention.

Fig. 12 is a partial section of a hob, the section being taken along its thread.

Fig. 13 is a normal section through a portion of a gear and an axial section through a hob or forming member conjugate to a rack of reduced pressure angle, and illustrative of another embodiment of the present invention.

Fig. 14 is a diagram illustrative of an embodiment of the present invention using a single forming member or hob for forming a plurality of gears in a sin le cycle.

Fig. 15 is a diagram re erring to the application of the invention to bevel gears.

Fig. 16 and Fig. 17 are corresponding diagrams, shown in front elevation and plan view, and illustrative of a method of locating the mesh between an involute spur gear and a forming member or hob, for determining the angular setting of the hob in accordance with the present invention.

Fig. 18 is an axial section through the rim of a spur gear for further explaining. said mesh.

Fig. 19 and Fig. 20 are corresponding diagrams, shown in plan view and front elevation, illustrative of a method of locating the mesh between a helical involute gear and a forming member, for determining the angular setting of the forming member.

Fig. 21 is a plane section of a hob constructed in accordance with the present invention, illustrative of certain features of a specific hob thread.

Fig. 22 is a diagrammatic plan view of a forming member, or of a hob, having forming portions or cutting teeth disposed in a spiral thread on a plane face.

Fig. 23 is a partial plan view at an enlarged scale of the forming member shown in Fig. 22, illustrative also of relative positions of gear blanks.

Fig. 24 is a section along lines 2-2 or along 3-3 of Fig. 23.

Fig. 25 and Fig. 26 are partial sections through the periphery of gear blanks and views of gear teet illustrative of the general form of chips removed with conventional methods and with the method in accordance with the present invention.

In Fig. 1 and Fi 2, the numeral 11 denotes a spur gear b ank having teeth 12 extending m the direction of its axis 13 and containing convex tooth profiles. 'A forming member 14 is shown in engagement with the gear blank. Forming member 14 ma be embodied as a hob or as a grinding 0! apping member, and in all these cases contains forming portions disposed in a thread or in threads 15. When embodied as a hob, the

hob contains also flutes or gashes forming cutting ed s in known manner. The per-- tions of a t read intermediate adjacent flutes project then from the body portion of the hob in the form of cutting teeth, which are relieved back of the cutting edges in known manner.

In accordance with thepresent invention,

conjugate to a gear blank 11 in a degree so as to mesh with line contact with finished tooth sides of said gear blank, the lines of contact covering the whole tooth surfaces of the gear blank in asingle position of the axes of the hob and of the gear blank. In contradistinction thereto hobs of conventional type have cutting edgesdisposed in threads which mesh with a gear blank with point contact only, so that mathematically a single line is covered on a tooth surface of the gear blank, when the hob and the gear blank are rotated in a single relative posltion of their axes.

The character of a hob thread, formed in accordance with the present invention, will be further explained hereafter.

The hob 14 and the gear blank 11 are turned on the

respective axes

16, 13 at a ratio inversely proportional to the respective number of threads 15 and teeth 12. Hob 14'may be fed towards gear blank 11 in direction of arrow 17, to approach the

axes

16, 13 relatively to each other. Feed in this direction continues until final cutting depth is reached,

such as in the position Fig. 1, in which a hob thread 15 sweeps the entire surface of the teeth 12. In this position the finishing cut is applied to the gear blank. Before attaining this finishing position, the hob does only roughing work, and does not reach the final surface of the teeth. The feed, in the direction of arrow 17, may be adapted to the stage of the process. Preferably a larger rate of feed is used for roughing, that is to say for removing the bulk of material, and the feed is then gradually slowed up as the finishing position is approached. It is particularly noted that with the present arrangement it is possible to combine a heavy roughing cut with a fine finishing cut in a single cycle, without such repetitions as are customary and necessary in the usual methods of hobbing, that is to say without resorting to a lurality of cycles or cutting -o erations.

requentl it 1s desirable to pro uce gears having modified tooth surfaces to allow for misaliirlilment. Such modification is especially own in spiral bevel gearing and in hy oid gearing, and consists in relieving the ends of the teeth, so that on a rigidly and accurately mounted gear air the plortions of the teeth immediately a jaoent t e lengthwise ends do not carry load, at least as long as the tooth load is moderate. To produce spur gears and helical gears having such tooth modification is a complicated problem for known hobbing processes, but-can be accomplished without complication with the present method, as will be further described ereafter. A' tooth 18 (Fig. 5) can be made to contact inside of the dotted area 19 or inside of any other suitable area, and the ends 20 of the teeth can be suitably relieved.

The present method can be carried out on existing machines, if so desired. -Moreover a simple device for carrying out the said method will now be described with reference .to the Figures 3 and 4. These figures also tatably mounted on a shaft 23, which receives motion through a gear 24. Shaft 23 is set at an angle 25 which is preferably in excess of ten degrees, also when the method is applied to the production of spur gears with straight teeth, (Fig. 1 and Fig. 2). I have found that the width of face which may be covered and completely finished by a hob increases with the settingangle (25), as will be more fully described hereafter. In cutting spur gears, an angle (25) in excess of 10 degrees can only be attained with hobs having multiple threads, which are therefore preferred for cutting spur gears in accordance with the present invention. In cutting helical gears either single thread hobs or multiple thread hobs may be provided.

A gear blank 26 having helical teeth 27 is rotated on its axis 28 in timed relation to hob 22, by means of a worm 29 meshing with a worm gear 30, which is coaxial with gear blank 26. Worm 29 receives motion from shaft 31, to which it is slidably keyed, and which is geared to the shaft of the hub by means of a pair of hypoid miter gears 32. Worm gear 30 and worm 29 are mounted on a slide 33, which is movable on bed 34 along guides 35. During the cutting operation slide 33 with gear blank 26 is moved towards hob22, in direction of arrow 36, until the finishing position is reached as the final position; Thereafter the feed is reversed, and the finished gear is withdrawn from the hob 22 in a direction opposite to arrow 36.

The changing rate of feed permits to obtain maximum efliciency at every moment and at every phase of the cutting operation. It can be conveniently effected by means of a cam. In Fig. 3 and Fig. 4 a cam 38 of k barrel type is indicated, which is rotatably mounted on a shaft 39. It is driven from shaft 31 by means of change gears 40, which are chosen to impart a full revolution to cam 38 during the period selected for a full working cycle. Cam 38 contains a groove 41 cf changing inclination, with which engagesa conical projection 42 secured to slide 33. As

the camturns around, it moves said conical projection, and with it the slide 33.

The hobs (14, 22) are preferably of the hour glass type, having an outside surface 43 of curved lengthwise profile. An outside surface of this character, set at an angle 25, can

be made "to contact with the cylindrical root surface 44 of a gear blankalong a line extending over the. whole widthof face. In other words an hour glass hob is suited to cover the teeth of a gear blank to their full depth on the whole length of the teeth.

- Cylindrical hobs, when operated in accordance with the present invention, apply a somewhat deeper cut in the center of the face than at the ends. Otherwise they are also suited for use without feed lengthwise of the teeth.

Fig. 6 and Fig. 7 diagrammatically illustrate an embodiment in which two hobs 46, 7 are provided for finishing the two sides of the teeth of a gear blank 48. Two separate hobs permit the use of different flutes on the two hobs, the flutes being preferably made to form acute angles with the thread on the side of the cutting edges. Such flutes effect keen cutting angles by providing what is known as side rake, and enable the hob to apply a very smooth finish also intough steel. When two hobs are used, they are moreover preferably set apart in axial direction of the gear, away from the central position, so that each hob is positioned somewhat nearer to one end of the teeth. The

points

49, 49, in which the axes 46', 47' of the two hobs come closest to the axis 48' of the blank 48, are then displaced in the direction of the axis 48 by an amount 49 (Fig. 7). The reason for this different setting will be evident from the formulas to be derived hereafter, which indicate that a larger width of face can be covered on a single side of the teeth, when the hob is somewhat offset from the center of the face. Narrow face gears do however not necessitate different hob positions.

The surface of a thread of a hob or forming member may be accurately determined in a. manner, as will now be explained with reference .to Fig. 8 and Fig. 9. A tool 50 of gear form' is provided, having

cutting edges

51, 52 forming part of the final tooth surfaces of a gear to be formed on a quantity basis. In the instance illustrated, tool 50.corresponds to a helical gear. The teeth of tool 50 are relieved back of the cutting edges 51, 52 in own manner. A hob blank 53 is mounted on an axis 23, which is set to an angle 25 relatively to a plane perpendicular to the axis 28, the angular settings being exactly the same as those to be used for gear cutting. The two

axes

23, 28 are oifset by a distance equal to the offset between the respective axes in the finish cutting position. To generate the proper thread on the hob blank 53, the latter is first set out of engagement with tool 50, and is then gradually fed towards and past the tool in the direction of the axis 28 of said tool 50 of gear form, while hob blank 53 and tool 50 are rotated in timed relation to each other, as if the hob blank were to cut a helical gear like the cutter 50 in a standard hobbing operation. The tool 50 moves then relatively to the hob blank to a position indicated in dotted lines 50' (Fig. 9) and proceeds to the position 50 shown in full lines. The feed should be long enough that the

edges

51, 52 coverfthe whole :widthof face of of the tool 50 or of the hob blank 53, to represent in known manner the helical shape of the gear teeth with the cuttin edges 51, 52. When lengthwise tooth modi cation is desired (Fig. 5), the said angular motion .is silightly modified to conform to the desired s ape. I

The thread 54 generated on the hob blank contains profiles of changing inclination in any axial plane and is in all cases truly conjugate to the gear represented by tool 50. The conditions under which mesh between the thread 54 and the finished tooth sides of a gear blank covers the whole width of face will be analyzed hereafter.

Instead of providing

cutting edges

51 and 52 of equal axial position on tool 50, cutting edges of variousaxial positions may be pro vided on the different teeth of a tool, in a .manner that the various cutting edges cover essof' using a tool of hob form for generating the hob thread is also applicable to bevel gears and to any other gears.

Frequently it is' unnecessary to generate the hob thread, as its shape can be accurately computed, at least when applying the process to spur gears or helical gears.

hob blank 53 After the thread 54 of the has been generated, flutes or ashes are pro vided, which are equal to the utes to be used on the actual hob. The gashes may be made of the conventional helical type, or they may be made planes; for instance planes extending along lines perpendicular to the average direction of the thread 54.

Thelatter case is particularly suited for making a hob in accordance with an experimentally generated thread 54, andeither case is equally suited for mathematical computation.

A relieving tool is then fitted to the thread along the side of the flute which embodies the cutting face of the hob. The relieving tool is provided with one or more teeth fitting one or a plurality ofspaces intermediate adjacent coils of the thread or threads 54. The

profile of the relievin tool equals or very closely approximates t e shape of a gear of larger tooth number than the gear blank to be cut. as will be further described. When turned on the center of said gear the profile taining a hob of hardened or bar 54, when the latter is turned on its axis in timed relation to the rotation of said relieving tool.

In Fig. 10 and Fig. 11, the relieving tool 56 is shown in engagement with a hob blank 57, which after hardening constitutes a hob to be used in accordance with the present invention for cutting gears. Relieving tool 56 is understood to be hardened and providedwith suitable relief back of its cutting teeth 58, so that it is fit to cut blank 57. The cutting teeth 58 are preferably made all alike, and aside of their relief, are equal to the teeth of a straight spur gear having an axis 60. Preferably the axis 60 of the tool 56 is inclined in such manner, that the face of the relieving tool follows the cutting face of the hob. The hob blank 57 is then relieved by of the relieving tool gradually sweeps over I the entire surface of, the generated thread rotating it and the relieving tool 56 on the

respective axes

61 and 60 in timed relation to each other and by simultaneously providing relieving motion. Relieving motion between hob blank 57 and relieving tool 56 may be provided in any known manner, such as by moving the tool 56 in the direction of arrow 62 radially towards the hob blank'in addition to its rotary motion, or, when relieving one side of the teeth at a time, by moving tool 56 in the direction of the hobaxis, or in any other direction inwardly to the thread surface. A still other form ofrelief may beprovided by moving the relieving tool 56 in the manner of an oscillation superimposed to the continuous rotation of the relieving tool, the tool being so oscillated on its axis that it cuts inwardly of the continuous thread back of the cuttin edges. As the relieving. motion goes on, t e relieving tool is slowly fed to final depth of cut in the direction of arrow 62.

The face 63 of a relieving tool is preferably made a plane. When the cutting faces of a hob are planes which may be either inclined to or parallel to the hob axis, the face of the relieving tool is made to coincide with a cutting face, in one position of the hob, and the profile ofthe relieving tool equals the profile of the above said thread in said plane.

When the cutting faces of a hob are helicoidal surfaces, the face of the relieving tool is set to coincide with a mean or average tangential plane so as to follow the eneral direction 0 a cutting face. Aside 0 being capable of accurate computation, the sha e of the relieving tool can also in this case determined by actual generation. The relieving operation can namely be reversed to genhaving been determined in the aforesaid way.

Such operation differs from the actual relieving operation of the hob merely by coner mate rial than the tool to be generated, so that the said hob cuts the tool.

In any case, whether plane cutting faces or helicoidal cutting faces are provided, the cutting faces are preferably so positioned as to effect a front rake, so that the profile of the cutting faces is nonradial, as indicated at 64 in Fig. 12. In principle the front rake has nothing to do with the shape of the generated surfaces, but provides a good cutting action in steel.

Fig. 13 illustrates a modification of the present invention. According to this modification a hob 66 is provided with a rack section of reduced pressure angle. The rack embodied by the hob meshes with a gear blank 67 along lines of

action

68, 68 which intersect inside of the pitch circle 69 of the gear blank. The latter meshes with said rack by rolling on a circle 70 which is smaller than the pitch circle 69. The hob is preferably made single threaded and of very largediameter, so that in the narrow face of a gear blank thesurface of the hob thread is almost identical with the surface of the rack teeth. The cutting operation consists in rotating the hob and a gear blank in timed relation to'each other, and in providing feeding motion between said hob and said gear blank in the direction of a radius of the gear blank. Although strictl no theoretically accurate gears can be pro uced accordin to this modification of my invention, with obs of finite diameter, the arrangement reduces the error obtained with a hob having a pressure angle equal to the pressure angle of the gear blank, and being fed in the manner described relatively to the gear blank. The thread of hob 66 recedes on'the sides from the plane tooth surfaces of the rack in the same manner as a conical surface would recede having an axis parallel to the axis of the hob and located near the axis of the hob. With a reduction of the pressure angle, the said conical surface, and the thread surface of the hob assume more nearly the shape of the plane rack surface, so that for instance a hob having a pressure angle of 5 degrees'reduces to about one third the error incurred with a hob of equal diameter and having a pressure angle of 15 ldiag'rleges equal to the pressure angle of the gear A hob thread constructed according to the first described embodiments contains portions corresponding to many pressure angles and especiall also portions of reduced pressure angle. Iii any case the reduction of the pressure angle is found to be an asset on hobs for use with radial feed.

Fig. 14 illustrates an'embodiment of the present invention, in which a single hob 22 of large diameter acts simultaneously on a plurality of gear blanks 26. In such cases the hob 22 is fed in preference to the blanks 26. It may be fed on a circle 65, indicated in crown gear having teeth extending dotted lines. The center 71 of the hob'assumes then gradually all the positions along said circle 65, such as position 72. The hob finishes the blanks 26 successively, and the finished gears can be removed and blanks mounted in their place in the interval between successive cuts. Instead of feeding the hob along a circle 65, it may also be fed in a different 'manner, if so desired; for instance along a series of straight lines 65', forming a square. 7 2 denotes a position of the center of a hob thus fed.

Fig. 15 diagrammatically illustrates an application of the present invention to hobbing bevel gears. In such cases preferably hobs 73 of tapered form or face hobs are provided. One type of spiral bevel gears which can be most easily produced in accordance with the present invention, is the type which corresponds accurately or approximately to a lengthwise along involutes 7 4. In other words the developed pitch lines of such spiral bevelgears are identical with the said involutes 74. The base circle of these involutes is indicated at 75, and the center of the crown gear and also the apex of the bevel gear blank is shown at 76. A mean line of action 77 between a gear blank and its crown gear is preferably made the basis of computation, which will be further explained hereafter as ap lied to gears cut from c lindrical blanks. ine of action 77 is found to be a straight line of constant pitch, when referring to the above said type of spiral bevel gears.

An analysis of the mesh between the thread of a forming member or hob and an involute spur car will now be described, referring to the igures 16. 17, 18. With this novel analysis the angular settingof a hob relatively to a gear blank may be determined in a manner that the whole widh of face of the gear blank is actually covered by the hob thread. Another-use of the analysis is to make sure, that.a hob thread generated for an assumed position of the hob actually makes contact withthe whole tooth surfaces of the gear blank, during its mesh with the gear blank. A further object of the analysis is to determine'the best possible relative positions of hob and gear blank.

In the drawings, the spur gear 79 is indicated by its base circle 78 and its axis 80, and the hob is indicated b its eneral contour 81 and its axis 82; n Fig. 16

tooth normals

83, 83! are indicated. They are tangent to base circle 78 at points 84, 84' and include variable angles a with the plane X. which passes through the axis 82 of the hob and is parallel to the axis of the gear. The normals 83, 83' intersect plane X in points ,85, 85' which are offset from the axis 82 of the hob.

For convenience the followin symbols are introduced: Let E be the set between the two

axes

80, 82. E equals the root radius of the gear blank plus the outside radius of the hob at its orge circle. Let N and n be the number 0% teeth of the gear and the number of threads of the hob respectively.

Let s be the setting angle of the hob, see.

Fig. 17. Let rbe the radius of the base circle of the gear. Let further the distance of any point 85 from the central plane 86 of the gear be (9'. Inasmuch as a normal 83 is parallel to the plane-86, distance y also constitutes the distance of a considered normal from the said plane 86.

Any point of the tooth surface of a gear comes into mesh or contact with a mating tooth surface or thread surface in the position, whena force acting in the direction of the normal at said point of contact efl'ects turning moments on said gear and on its mating member proportional to the numbers of teeth or threads of the respective gear or member. It can be readily demonstrated, that a deviation from this relation would violate the law'of the conservation of energy.

In the present case, a force P acting in the direction of any normal 83 (or 83') effects a turning moment equal to Pm on the involute gear. The same force P effects a turning moment on the threaded member 81 equal to the distance of point 85 of the normal from axis 82 multiplied by (P.sin a) The force P can namely be considered acting at point 85,

' and can be dissolved into a component (P.sin a) perpendicular to plane X and passing through point and into another component lying in lane X. The latter component does not e ect a turning moment relatively to axis 82, as it intersects the said axis. The distance D of point 85 from axis 82 can be expressed in terms of y and an le (1.

According to the above, the ratio ,0 the said turning moments (Pm) and (P.sin a.-

distance D) is equal to the ratio of the numbers N and n. From this the following formula may be derived after transformation: tan 8 'n, s-n7 T, E

In involute gearing, namely in involute spur gears and involute helical gears, a tooth normal 83 remains. perpendicular to the involute tooth surface also when the gear 79 assumes different angular positions while point of tooth contact, but it is the joint normal of all the points of an involute tooth surface, which during the rotation of the gear successively intersect said normal 83 and thereby enter into mesh. In other words in involute gearing a normal 83 defines not only a single point of mesh, but it is a whole line of action, action between gear 7 9 and-the thread of thehob 81 taking place along normal 83, while a thread surface of a hob of conventional type meshes with the gear blank along a single line of action, mesh takes place along a great number of lines of action 83 in the present case. In all such lines.'action takes place at the same constant rate, a point of contact moving along a line of action at a constant ratio. The location of the individual lines of action is indicated by the above formula. constitute a surface of action, which is composed of straight lines.

Each line of action corresponds to a tooth profile of the gear 79. Line of action 83 corresponds to the involute tooth profile 87, shown as a straight line in the view Fig. 18; and line of action 83' corresponds to the involute tooth profile 87', v The said profiles have a distance 2 fromthecentral plane 86.

Ordinarily a hob is set to the center (88) of the face of the gear blank, as indicated in Fig. 17. The hob thread contains normals (83) of constant pitch and of a great number of pressure angles, which usually include increased pressure angles as well as reducedpressure angles. In. cases where separate hobs are used for cutting the two sides of the gear-teeth (Fig: 6 and Fig. 7 a hob is preferably offset from the'center of the gear face in such manner that it covers a maximum width of face on the sin le side on which it acts. The most, desirable amount of offset can be computed with the above formula. A hob of this character frequently contains only normals or lines of action of reduced pressure angle. v

The diagrams Fig. 19 and Fig. 20 illustrate an analysis relating to helical involute gears. The axis 80 of the gear blank and the axis 82 of the hob are ofiset by a distance again denoted E. The symbols used in this analysis are the same as the ones used before, namely when referring to involute spur gears having teeth parallel to their axes. In addition angle H denotes the inclination angle of the tooth normals with respect to a plane perpendicular to the axis 80 of the gear blan This angle is the same for tooth normals, as well Thetotalitv of the lines of action The formula indicates that known, and can alsobe considered as the helix angle at the radius r of the base circle 7 8.

The analysis can be carried out in the manner described with reference to involute spur gears, and is found to furnish the following equation:

l n-r tan a,

Ordinate 3 refers here to the point of tangency 84 between normal 83 and base cylinder 78, and denotes the distance of said point from a central plane 86. The normal lines of action 83 again correspond to lines of the tooth surface of the gear blank. The said lines of the tooth surfaces can be located with the known means ofthe art, and are found to be inclined to the tooth profiles of a circumferential plane. Proportions and setting angle 8 are so selected, with the help of the above formula, that the said lines of the tooth surfaces cover the whole toothsurfaces inside of the given width of face.

While I have indicated here only analyses referring to involute gearing, it is understood that the described general procedure can also be applied to any other type of gearing. In addition to the mathematical investigation of the mesh between a gear blank and a thread of novel form, an experimental investigation could also be carried out, by using thread forms generated in the manner described, and by determining the mesh between the generated thread surface and a gear by experiment, for instance by covering the mating surfaces with a thin coat of red 1ead,-and by running the thus covered surfaces together. The contacting port on w1ll then rub off the red lead and thus indicate the area of conjugate contact. When the coat is rubbed oif from the whole width Ff face of the gear, then the generated thread surface is suited to form the basis of a hob or forming member. Otherwise a new thread a surface is generated after assuming a dif ferent setting, and the o eration is repeated until the whole width 0 face is covered by a generated thread surface.

- Fig. 21 refers to a hob for cuttmg involute gears and is a plane section through the thread of a hob, taken along a line of action 90. v The plane of Fig. 21 is suited to constitute a plane cutting face extending either parallel to or at an angle to axis 91 of the hob. It can also be considered as a plane extending in the general direction of a helicalcutting face. According to the above analysis the hob thread contains a. constant. pitch along line of action 90, as well as along any other line of action. Distance 92-93 equals therefore distance 9394. We will consider now a mean point 93 located about at the .center of the tooth heightand suited to cut (E-tan s+r-tan H) 95 is located at 96 and may be either mathematically or experimentally determined by measurement of the generated profile 95.

In determining a gear profile which could be used for relieving a hob, it is seen that any involute gear .would be suited to mesh with the hob thread. along line of action 90, pro vided that its pitch along said line of action equals the pitch 92-93 of the hob thread. Certain of these gears have profiles with the same curvature at point 93 as profile 95, that is to say their profiles contain curvature centers located at 96. The base circles of these gears contact with line of action 90 in the said center of curvature 96; and the turning centers of these gears lie therefore on a perpendicular 97 to line of action 90. 98, 99 are two such centers. When it is desired to relieve both sides of the teeth ofthe hob simultaneously, the center of the gear to be embodied as a relieving tool is preferably chosen at 98,

on the central line 100 of the hob. A still higher accuracy may be obtained by relieving the two sides of the hob teeth in two operations. The center of the relieving tool is then selected in a point (99) of line 97 in such manner, that the involute tooth curve matches curve 95 on the whole length as closely as might ever be desirable. In extreme cases moreover a single relieving tooth maybeemployed, and the center of the relieving! tool is fed on a line (101) parallel to line of ac-- tion 90, in proportion to the turning angle of the relieving tool. The turning center of the contains cutting teeth 105 projecting from aplane 106, and which is therefore of theface hob type. The cutting teeth are disposed along a spiral 107, which is completely shown in Fig. 22. For cutting gears from cylindrical blanks, the spiral 107 is preferably an involute, having a base circle 108. An involute is known to have a constant pitch along any line (109) which is tangent to the base circle (108). The cutting teeth 105 of a segment 110 are preferably integral with each other and constitute a rack. The cutting teeth 105 adjacent one end of the zone of teeth may be made of tapering height, if so desired. The various segments are rigidly secured to a cutter body 111, which is rotatable on an axis 112.

point of the pitch circle of a gear blank. 4 The center of curvature of the thread profile A spur gear 113, indicated in'dotted lines in Fig. 23, may be cut by setting the spur gear and the hob in such a relative position that the central plane of the gear contains a line 109. The hob 104 and the gear blank 113 are then rotated on their

axes

112, 115 in. timed relation, and the hob is fed in the direction of its axis 112 to full cutting depth. This feed is preferably effected at a changing rate.

During the rotation of the hob the rack section adjacent the central plane of the gear blank seemingly travels at a uniform rate along line 109 and the thread surface of the hob remains constantly at right angles to line 109. Adjacent line 109 the hob 10 1 embodies therefore accurately a rack. Considering

lines

116, 117 which are parallel to line 10%, it is seen that the hob thread moves in the direction of these lines only approximately uniformly, and that it changes its inclination slightly relatively to the two lines, considering a point moving through the zone of mesh along a

line

116 or 117. The hob thread therefore does not embody a mathematical rack along lines parallel to line 109, that is to say along

lines

116, 117, but embodies a rack only approximately. This feature is made use of for producin gears having slightly modified tooth sur aces, as described with respect to Fig. 5. Tooth surfaces of a pair of gears produced in the manner described from a pair of complementary hobs transmit true uniform motion, namely with the profiles corresponding to section 109. They mesh theoretically with point contact, which is the ver feature aimed at in a moderate degree. T he deviation from line contact is found to be very slight, and

just sufficient to relieve the ends of the teeth from pressure when the gears are very rigidly mounted.

Two hobs which are fully complementary are necessarily of opposite hand. When a hob is provided with but a single thread, like the one indicated in Fig. 22, it is found that satisfactory results are also obtained when the same hob is used for cutting both gears of a air.

A gear blank 120 (Fig. 23) may be provided with teeth inclined to its axis 121, by setting the blank at a suitable angle to a line 109' of the hob. In'this case too a pair of gears may be roduced from a pair of complementary ho s, so that they transmit true uniform motion while containin slightly modified tooth-surfaces capable o standing misalignment.

Fig. 25 diagrammatically illustrates successive positions of the periphery of a hob which is fed in customar known manner in the direction of the axis 0 a gear blank. The

area intermediate adjacent positions 122 corresponds to the chips removed in the cutting operation. The chips are seen to be of changing thickness, starting from zero to a maximum reached adjacent the top 123 of the tion havea substantially constant thickness,

as is shown in Fig. 26, where 124-. denotes successive positions of the periphery of a hob. The positions 124 correspond to a radial feed between the hob and a machine more uniformly than the cut according to Fig. 25, and permits therefore also for this reason a coarser out without chatter.

In most of the illustrated examples the feed between a hob and a gear blank is in a direction at right angles to the pitch surface of the gear blank, or alon a radius of the ear blank. The feed may owever, also be e ected in a direction inclined to the pitch surface of the gear blank at any other angle or at changing angles, without departing in the least from the spirit of the present invention. For instance relative feed may be effected in a manner, that the central point of the hob axis moves along any suitable line contained in a plane perpendicular to the axis of the gear blank.

Numerous other modifications may be made in my invention without altering its principle. For definition of its scope it is relied upon the appended claims.

What I claim is:

car blank. Acut of I this character may be e ected with increased efiiciency. Moreover it strains the cutting 1. The method of forming gears having constant tooth profiles in planes perpe n.

dicular to their axes, which consists in providing a hob having cutting teeth disposed in a thread, the profiles of an axial section of said thread having a changing inclination to the axis of said hob, in setting said hob at anangle in excess of ten degrees to a plane perpendicular to the axis of a rotating said hob and said gear Ian]: on their respective axes in timed relation, and in providing feeding motion between said hob and said gear blank in a direction inclined to the pitch surface of the gear blank.

3. The method" of forming gears having constant tooth profiles in planes perpendicular to their axes, which consists in providing gear blank, in

a hob having cutting teeth disposed in a thread, the profiles of an axial section of said thread having a changing inclination to the axis of said hob, in rotatlng sald hob and a gear blank in timed relation on axes angudisposed to and offset from each other, and in.

roviding feeding motion between said memher and said gear blank in a direction inclined to the pitch surface of said gear blank.

5. The method of forming gears of convex,

tooth profile, which consists 1n providin a rotar member having forming portions ispose in a thread, said thread 'havin a concave rofile in an axial plane, in'rotatmg said mem r and a ear blank on axes angularly disposed to an offset from each other, in providing feedin motion between said member and said gear lank in a direction inclined to the pitch surface of said gear blank-to approach said member and said gear blank, and in discontinuing feed in said direction while said member is in engagement with the finished tooth surfaces of the gear blank. 7

6. The method of forming gears of convex tooth profile, which consists in providin a rota member having forming portions 'spose d in a thread, the profile of an axial section of said thread being concave and having a changing inclination relatively to the axis of said thread, in rotating said member and a gear blank on axes angularly disposed to and offset from each other, and in providing feeding motion between said member and said gear blank in a direction inclined to the pitch surface of the ear blank, to approach said mgmber and said gear blank relatively to each ot er. 7. The methodof forminggearshaving con- .stant tooth profiles in planes perpendicular to their axes, which consists in providing a hob having curved cutting teeth disposed in a thread, said thread being conjugate to the desired constant tooth profiles of the entire face of a gear blank, in rotating said hob and said gearblank in engagement with each other on angularly disposed and offset axes, the angle between the directions of said axes differing at leastthirty degrees (30) from the angle between the directions of the axis of the gear blank and the axis of its mating gear, and in providing feeding motion between said hob and said gear blank in the hob and the gear a plane nperpendicular to the axis of said gear bla 8. The method of forming gears running on parallel axes, which consists in providing a rotary member having forming portions disposed in a thread,said threadcontaining parts suited to mesh at a reduced pressure angle with the desired tooth surfaces of a gear blank, in rotating said member and said gear blank in engagement with each other on angularly disposed and offset axes, the an le between the directions of said axes diflfermg at least thirty degrees (30) from the zero angle between the directions of the axis of the gear blank and the axis of its mating gear, and in providing feeding motion between said member and said gear blank in a direction inclined to the pitch surface of said gear blank, to approach said member and said gear blank relatively to each other.

9. The method of forming gears running on parallel axes, which consists in providing a rotary member having forming portions disposed in a thread, said thread containing parts suited to mesh at a reduced pressure angle-with the desired tooth surfaces of a,

gear blank, in rotating said'member and said gear blank in engagement with each other on angularly disposed and offset axes, the

ing a rotary member having forming por-.

tions disposed in a thread, said thread containing parts suited to mesh at a reduced pressure angle with a gear blank, in rotating said member in engagement with a rotating gear blank, in providing feeding motion between said member and said gear blank in a direction inclined to the pitch surface of the gear blank to approach said 'member and said gear blank relatively to each other, and in discontinuing feed in said direction while said member is in en agemen't with the finished tooth surfaces of the gear blank.

.11. The method of forming gears, which consists in providing a hob having cutting, teeth disposed in a thread, in rotating said hob and a gear blank on angularly disposed and offset axes, in providing, feeding motion between said hob and said gear blank at av changing. rate in adirection"inclined to the pitch'surface of said gear blank, to approach other, and in finishing the entire tooth surfaces of said gear blank-exclusively in the position of closest approach.

12. The method of forming gears, which not ank relatively to each consists in providing a hob having curved cutting teeth disposed in a thread, in rotating said hob and a gear blank on angularly disposed and offset axes, in providing feeding motion at a changing rate between the hob and the gear blank in adirection at right angles to the pitch surface of the gear blank, to approach the hob and the gear blank relatively to each other, and in finishin the entire tooth surfaces of said gear blan exclusively in the position of closest approach.

13. The method of forming gear pairs having modified tooth surfaces suited to contact on part of their length only while relieving the ends of the teeth, which consists in forming each gear of said pair by providing a v rotary member having forming portions disposed in a thread, by rotating said'member and a gear blank in engagement with each other on angularly disposed and offset axes, and by providing feeding motion between said member and said gear blank.

14. The method of forming gears having modified tooth surfaces suited to contact on part of their length only while relieving the ends of the teeth, which consists in providing a hob having cutting teeth arranged in the form of a thread, in rotating said hob and a gear blank on angularly disposed and offset axes, in providing feeding motion between said hob and said gear blank in a direction inclined to the pitch surface of said gear blank to approach said hob and said gear blank relatively to each other, and in discontinuing feed in said direction while said hob is in engagement with the finished tooth surfaces of the gear blank.

15. The method of forming gears running on parallel axes, which consists in providing a hob of hour glass form having cutting edges disposed in a thread, in rotating saidhob and a gear blank inengagement with each other on angularly disposed and offset axes, said axes having an angular relation differing at least thirty degrees (30) from the parallel relation of the axes .of said gear blank and its mating gear, and in providing feeding motion between said hob and said ar blank in a manner to approachthe axes of said hob and of said gear blank relatively to each other.

16. The methodof forming gears running on parallel axes, which consists in providing 0. bob of hour glass-form having curved cutting edges disposed in a thread, in rotating said hob and a gear blank in engagement with with respect to a plane perpendicular to the axis of a gear blank, in rotating said hob in engagement with a rotating gear blank,

and in providing feeding motion in-a manner to approach the axis of the hob and the axis of the gear blank relatively to each other. 18. The method of forming gears having straight teeth extending parallel to the axes of said gears, which consists in providing a hob having cutting edges disposed in multiple threads, in setting the axis of said hob at an angle exceeding ten degrees (10) with respect to a plane perpendicular, to the axis of a gear blank, in rotating said hob adjacent said gear blank, in rotating the gear blank in timed relation to the rotation of said hob, and in providing feeding motion between hob and gear blank in a manner to reduce the distance between the axis of the hob and the axis of the gear blank.

19. The methodof forming gears having straight teeth extending parallel to the axes of said gears, which consists in providing a hob of hour glass form having curved cutting edges disposed in multiple threads, said cutting edges having different inclinations with respect to the axis of said hob, in setting the axis of said hob at an angle exceeding ten degrees 10) with respect to a plane perpendicular to the axis of a gear blank, in rotating said hob, in rotating said gear blank in timed relation to the rotation of said hob, and in providing feeding motion between hob and gear blank in a manner to reduce the distance between. the axis of the hob and the axis of the gear blank; 1

20. The method of forming a gear, which .consistsin providing a hob for each of the two sides of the teeth of said gear, each hob containing flutes effecting a side rake adia- Ill motion between said hobs and said gear blank.

21. The method of forming gears. which consists in providing a hob and a. plurality of gear blanks, in setting said gear blanks adjacent the periphery of said hob. in rotating said hob and said gear blanks in timed relation, and in feeding said hob past said gear blanks in a manner to successively finish said gear blanks.

22. The method of forming gears, which consists in forming each gear o f.a ainby providing a rotary member .havmg ornnng ortions disposed in a thread, said threa being suited to mesh with line contact with providing a rotary member having forming portions disposed in a thread, said thread 7 being suited to mesh with line contact with accurately finished tooth surfaces of a gear blank, in rotating said member in engagement with a rotating gear blank, in providing feeding motion between said member and said gear blank in a dire'ction'inclinedto the pitch surface of said gear blank to approach saidmember and said gear blank relatively to each other, and in discontinuing feed in said direction while said member is in engagement with the finished tooth surfaces of the gearblank.

24. The method of forming a pair of gears having modified tooth surfaces suited to contact on part of their length only while relieving the ends of the teeth, which consists n forming each gear of said pair by providing a rotary member having forming port1ons disposed in a thread, said thread being suited to mesh with line contact with accurately finished tooth surfaces of the said character, in rotating said member in engagement with a rotating gear blank, and in providing feeding motion between said member and said gear blank in a direction inclined to the-pitch surface of said gear blank.

25, The method of forming gears, which consists in forming each-gear of a pair by providing a hob having cutting teeth arranged in a thread, said thread being suited to mesh with line contact with accurately finished tooth surfaces of a gear blank, in rotating said hob in engagement with a rotating gear blank, and in providing feeding motion between hob and blank at right angles to the pitch surface of said gear blank.

26. The method of forming gears, which consists in forming each gear ofa pair by providing a rotary member having forming portions disposed in a thread, said thread being suited to mesh with line contact with accurately finished tooth surfaces of a gear blank and projecting from a surface of revorofile 1n aplane at right angles to its axis, in rotatmg f lution having a convex circular said member in engagement with a rotating gear blank, and in providing feeding motion between said member and said blank 1n a direction inclined to the itch surface of said gear blank, to complete y. finish said tooth surfaces in a single position of feed.

27. The method of forming gears, which consists in forming each gear of a pair by providing a rotary member having forming portions disposed in a thread of concave profile, said profile being constant but having a changing inclination with respect to planes perpendicular to the axis of said member, in rotating said member in engagement with a rotating gear blank, and in providing feeding motion between said member and said gear blank in a direction inclined to the pitch surface of said gear blank.

28. The method of forming gears running on parallel axes, which consists in providing a gear blank and a rotary member having forming portions disposed in a thread, said thread being fully conjugate to said gear so as to mesh with line contact with accurate final tooth surfaces of said gear, in positioning said member and said gear in engagement with each other, and in rotating said member and said gear on axes angularly disposed to and offset from each other at the.

ratio of the respective number of threads and teeth, to completely finish the entire tooth surfaces of said gear in a single bodily position of said member and said gear.

29. The method of forming gears running on parallel axes, which consists in providing a gear blank and a rotary member having forming portions disposed in a plurality of threads, said threads having curved profiles in axial planes and being fully conjugate to said gear in a manner to mesh with line contact with accurate final tooth surfaces of said gear, in positioning said member and said gear in engagement with each other, and in rotating said member and said gear on axes angularly disposed to and offset from each other at the ratio of the respective number of threads and teeth.

30. The method of forming gears running on parallel axes, which consists inproviding a gear blank and a rotary member having forming portions disposed in threads,said threads having concavely curved profiles and being fully conjugate to said gear in a manner to mesh with line contact with accurate final tooth surfaces of said gear, in positioning said member and said gear in engagement with each other,and in rotating said member and said gear on axes angularly disposed to an oifset'from each other. at the ratifi of the respective number of threads and teet 31. The method of forming gears running on parallel axes, which consists in providing a gear blank and a forming member having orming portions disposed in a plurality of surfaces equally spaced about an axis, said surfaces containing concavely curved profiles, in positioning said member and said gear blank in enga ment with each other 1n a manner that t c axis .of said forming member includes an angle in excess of ten degrees with a plane perpendicular to the axis of said gear lank, and in effecting linear and angular relative motion between a said forming member and said gear blank. 32. The method of forming a pair of ears I having cylindrical or conical pitch sur aces 1 rolling on each other without sliding, which consists in providin a pair of forming members conjugate to t e tooth surfaces of said 10 members and suited to form substantially equal lines on said pitch surfaces, said lines being considered in development of said itch surfaces to a lane, at least one of said orming members having forming portions projecting externally from a surface of revolution, and in forming each gear of said pair by affecting engagement between a blank and the respective forming member and by rotating said blank and said forming member on angularly disposed and offset axes, for v finishing the entire tooth surfaces of at least one side of the teeth of said blank in a single relative position of the rotating bodies of said blank and said forming member.

5 33. The method of forming a gear having a pitch surface capable of rolling without sliding on the pitch surface of its mating gear; which consists in providing a forming member having formingportions disposed 0 in a thread conjugate to the desired tooth surfaces of a gear blank, said thread projecting externally from asurface of revolution and being conjugate to a surfacehaving a constant involute profile in parallelplanes;

in effecting engagement between said blank i and said forming member; and in rotating said blank and said forming member on angularly disposed and ofiset axes, for finishing the entire tooth surfaces of at least one side 40 of the teeth of said blank in a single relative position of the rotating bodies of said blank and said forming member, the axis of said formin member being inclined to a plane perpen icular to the axis of said blank.

' ERNEST 'WILDHABER.