Fig. 1995

Fig. 1995.

A not uncommon error is to place the gauge g against the tooth in front of that which is being ground, as in Fig. 1995, the gauge being against tooth c while tooth b is the one being ground. In this case the truth of the grinding depends upon the accuracy of the tooth spacing. Suppose, for example, that teeth b and c are too widely spaced, tooth c being too far ahead, and this error of spacing would cause tooth b to be too near the centre of the emery wheel and its cutting edge to be ground too low.

The object of feeding the cutter by hand along the arbor h is twofold: first, the amount of cut must be very light and the feed very delicate, for if the grinding proceeds too fast the cutting edge will be what is termed burned, that is to say, enough heat will be generated to soften the extreme cutting edge, which may be discovered by holding the front face of the tooth to the light, when a fine blue tint will be found along the cutting edge, showing that it has been softened in the grinding, and this will cause it to dull very rapidly.

Fig. 1996

Fig. 1996.

The second object is to insure parallelism in the cutter. Suppose, for example, that the cutter c was fast upon arbor h and was fed to the wheel by moving slide f, and if the arbor h stood at an angle, as in Fig. 1996, to the slide upon which f moved, the cutter would be ground taper, whereas if the cutter is fed along the arbor it will be ground parallel whether the arbor is true or not with the slideway of f, the only essential being that the arbor h be parallel and straight, which is much easier to test and to maintain than it is in the slideway (d, Fig. 1992). Here it may be noted that oil should not be applied either to arbor h or to the cutter bore or slideway d, as lubrication only increases the wear of the parts, causing the fine emery particles that inevitably fall upon them to cut more freely.

Fig. 1997

Fig. 1997.

As thin cutters would not have sufficient length of bore to steady them upon the arbor and insure parallelism, the cutter sleeve shown in Fig. 1997, which is from The American Machinist, is employed to hold them. It is provided with a collar, is threaded at t for the nut n to hold the cutter against collar c, and is bored to fit the cutter arbor h, which corresponds to h in Fig. 1993.

This device also affords an excellent means of holding two or more thin cutters requiring to be ground of exactly equal diameters.

Fig. 1998

Fig. 1998.

It follows from what has been said that taper tools, such as taper reamers, must be held with their upper face parallel to the line of their motion in being fed to the wheel, as in Fig. 1998, in which line m represents this line of motion, line n the axis of the reamer, and line o the line on which the fixture that holds the reamer must move, o being parallel to m.

Fig. 1999

Fig. 1999.

Fig. 1999 represents Slate’s fixture for this class of work. a is a stand that bolts upon the slideway d in Fig. 1992. Upon a is fixed a rectangular bar b, upon which (a sliding fit) is the shoe c. Upon c fits the piece d, which is pivoted to shoe c by the pin at e. At the other end of d is a lug, against which abuts the end of screw g, which is threaded through the end of c, so that by operating the screw g, d may be set to any required angle upon c, and at f is a set-screw threaded through d and abutting against c, so as to lock d in its adjusted position. At p is a pointer for the graduations on c, which are marked to correspond with the graduations upon the taper turning attachment of a lathe.

The work is held between centres, the head h fitting to a slideway on the top of d, and being secured in its adjusted position by the screw i. The work should obviously be set so that its upper face lies horizontal, and is fed to the wheel by moving shoe c by hand along bar b, the long bearing keeping c steady, and the lightness of the moving parts making the feeding more sensitive than it would be were it required to move bar b.

The tooth being ground is held by hand against the gauge g in Fig. 1994, as was described with reference to that figure, and the reamer, therefore, in the case of having spiral grooves, revolves upon its centre while being fed to the emery wheel.

Fig. 2000

Fig. 2000.

Fig. 2001

Fig. 2001.

For tapers that are beyond the capacity of this device, and also for holding cutters to have their face teeth ground, the device shown in Fig. 2000 is employed. Upon the slide f is fixed knee k (the corresponding parts to which are seen in the general view, Fig. 1992), whose disk face at r is graduated as shown. Piece s is pivoted by a pin passing through the hub of k and having a nut t to secure it in its adjusted position. s is bored to receive the cutter arbor h, and is split through so that by means of the screw at v the arbor may be gripped and locked in s. The stud w for holding the gauge g passes into a bore in the bracket x, and is secured therein by the screw at y, the lugs through which y passes being split through into the bore for w. As shown in the figure, the arbor h is set for grinding the side teeth of the cutter, but it is obvious that s being pivoted to k may be swung out of the vertical and to any required angle, so as to bring the face of the tooth that is to be ground horizontally beneath the emery wheel, as shown in Fig. 2001, which represents an angular cutter in position. We have now to consider the adjustment of the cutter to the emery wheel, necessary in order that the cutting edges may be given the necessary clearance.

Fig. 2002

Fig. 2002.

First, then, suppose in Fig. 2002 that the line a a represents the line of centres of the emery-wheel spindle and the cutter arbor, and if the front face b of the tooth be set coincident with this line, as in the figure, then the top of the tooth partaking of the curvature of the wheel that grinds it would have its heel c the highest; hence the edge at b could not cut.

Fig. 2003

Fig. 2003.

If, however, the line a a in Fig. 2003, still representing the line of centres, we so set the gauge (g, Fig. 1994) that the heel c of the tooth comes up to line a a, then the curvature of the emery wheel would give clearance to the heel c, and therefore a cutting edge to face b of the tooth.

Fig. 2004

Fig. 2004.

The amount of clearance that may be given in this way is limited by the spacing of the teeth and the diameter of the emery wheel, as is seen from Fig. 2004, it being obvious that when tooth a is being ground the emery wheel must clear the rear tooth b or it will grind its edge off, and it is obvious that the smaller the emery-wheel diameter the more the tooth to be ground may be set in advance of the line of centres of the wheel and spindle. It may be pointed out, however, that there are two methods of adjusting the cutter to the wheel.

Fig. 2005

Fig. 2005.

Fig. 2006

Fig. 2006.

In Fig. 2005, for example, let a a represent the line of centres of the cutter and the wheel, and line b the plane of the front face of the tooth being ground; and in Fig. 2006 let line a represent a vertical line from the axis of the wheel, and b a vertical line passing through the axis of the cutter, the tooth edge c occupying the same position in both figures. Now suppose we employ cutting edge c as a centre and swing the cutter until its axis or centre moves along the arc d to the dot e, and it is evident that during this motion the heel of the tooth will have approached the axis of the emery wheel and that more clearance will therefore have been given to the cutting edge c.

Fig. 2007

Fig. 2007.

The actual curve of the top face, as c, Fig. 2007, of the tooth t will remain the same in either case, but its position with relation to the front face will be altered. As this curve is greater in proportion as the diameter of the emery wheel is diminished, and as the curvature weakens the cutting edge of the tooth, it is obviously desirable to employ a wheel of as large a diameter as possible.

Fig. 2008

Fig. 2008.

Fig. 2009

Fig. 2009.

To eliminate this curvature it would appear that the position of the emery wheel might be reversed, as in Fig. 2008, but as the emery wheel would wear only where in contact with the tooth, it would gradually assume the shape in Fig. 2009, there being a shoulder at s that would destroy the cutting edge of the tooth.

Fig. 2010

Fig. 2010.

Fig. 2011

Fig. 2011.

This may to a great extent be remedied by presenting the cutter diagonally to the wheel, as in Fig. 2010, employing a wheel so thin that the whole of its face will cross the tooth top during a revolution. Or if the side faces of the wheel be recessed, leaving only a narrow annular grinding ring at the circumference, the wheel might be mounted as in Fig. 2011, thus making the top of the tooth quite flat. It may be observed, however, that the usual plan is to revolve the wheel at a right angle to the work axis, as was shown in Fig. 1994.

In grinding cutters having their teeth a right-hand spiral, care must be taken that in grinding one tooth the emery wheel does not touch the cutting edge of the next tooth.

Fig. 2012

Fig. 2012.

Fig. 2013

Fig. 2013.

Thus in Fig. 2013 it is seen that the corner c of the emery wheel is closer than corner d, and being at the back of the wheel and out of sight it is apt to touch at c unless a thin emery wheel be used.

In a left-hand spiral, Fig. 2012, it is the corner d that is apt to touch the next tooth, the liability obviously being greatest in cutters of large diameter.

The emery wheel should be of a grade of not less than 60 or more than 70. If it is too coarse it leaves a rough edge, which may, however, be smoothed with an oilstone slip. If the wheel is too fine it is apt to burn the cutter, or in other words, to soften the cutting edge, which may be known by a fine blue burr that may be seen on the front face of the tooth, the metal along this line being softened.

The diameter of the wheel may be larger for small cutters than for large ones, since the teeth of small cutters clear the wheel better. The larger the wheel the less the curvature on the top of the tooth.

For general work a diameter of 212 inches will serve well, the thickness being about 516 inch or 38 inch. The speed of a wheel of this diameter varies in practice from 3,000 to 4,500 revolutions per minute, but either too fast or too slow a speed will cause the wheel to burn the cutter, and the same thing will occur if the cutter is fed too fast to the wheel, or if too deep a cut is taken. The finishing cut should obviously be very small in amount, especially in cutters of large diameter, for otherwise the wear in the diameter of the wheel will sensibly affect the teeth height, those last ground being the highest.


Chapter XXIII.—EMERY WHEELS AND GRINDING MACHINERY.

Emery Wheels and Grinding.—Emery grinding operations may be divided into four classes as follow:—

1st. Tool or cutter grinding, in which the emery wheel is used to sharpen tools which, from their shape, were formerly softened and sharpened by the file, already largely treated in the preceding chapter.

2nd. Cylindrical grinding, in which both the work and the emery wheel are revolved, as has been explained with reference to grinding-lathes.

3rd. Flat surface grinding, in which the emery wheel takes the place of the ordinary steel cutting tool; and

4th. Surface grinding, in which the object is to remove metal or to smoothen surfaces.

The distinctive feature of the various makes of solid emery wheels lies in the material used to cement the emery together, and much thought and experiment are now directed to the end of discovering some cementing substance which will completely meet all the requisite qualifications. Such a material must bind the emery together with sufficient strength to withstand the centrifugal force due to the high speeds at which these wheels must be run to work economically; and it must neither soften by heat nor become brittle by cold. It must not be so hard as to project above the surface of the wheel; or in other words, it should wear away about as fast as does the emery. It must be capable of being mixed uniformly throughout the emery, so that the wheel may be uniform in strength, texture, and density. It must be of a nature that will not spread over the surface of the emery, or combine with the cuttings and form a glaze on the wheel, which will prevent it from cutting. This glazing is, in fact, one of the most serious difficulties to be encountered in the use of emery wheels for grinding purposes, while it is a requisite for polishing uses, as will be explained farther on. Many of the experiments to prevent glazing have been in the direction of discovering a cement which would wear away under about the same amount of duty as is necessary to wear away the cutting angles of the grains of emery, thus allowing the emery to become detached from the wheel, rather than to remain upon it in a glazed condition.

With the same grade of emery the wheel will cut more freely and glaze less in proportion as the cementing material leaves the wheel softer, but the softer the wheel the more rapidly it will wear away; indeed it is the dislodgement of the emery points as soon as they have become dulled that produces freedom from glazing. It may be remarked, however, that the nature of the material operated upon has a good deal to do with the glazing; thus wrought iron will glaze a wheel more quickly than hardened steel, and brass more quickly than wrought iron, while on the other hand soft cast iron has less tendency than either of them to glaze. Glazing occurs more readily in all cases upon fine than upon coarse wheels. Glazing is more apt to occur as the work is pressed more firmly to the wheel, and with broad and flat surfaces rather than with cylindrical ones. An excellent material for removing the glaze from an emery wheel is a piece of ordinary pumice stone.

The principal cements used in the manufacture of emery wheels are as follows, each representing the cement for one make of wheel:—

1. Hard rubber. 2. Chemical charcoal (leather cut down by acid and used to prevent shrinkage), and glue. 3. Oxychloride of zinc. 4. Shellac. 5. Linseed oil and litharge. 6. Silicate of soda and chloride of calcium. 7. Celluloid. 8. Oxychloride of magnesium. 9. Infusoria. 10. Ordinary glue.

The vitrified emery wheel is made with a cement which contracts slightly while cooling, leaving small pores or cells through which water, introduced at the centre, is thrown (by centrifugal force) to the surface. This causes, when the wheel is rotating, a constant flow of water from the centre to the surface, carrying off the cuttings and the detached emery.

In order that an emery wheel shall run true with its bore it must fit the driving spindle, and in order that it may do this closely the wheel bore is sometimes filled with lead, the latter being bored out to fit the spindle. If the bore of the emery wheel itself were made a tight fit to the spindle it would abrade the spindle in being put on, and the pressure of the fit if any would tend to split the wheel. A common method of securing emery wheels to their spindles is to fill the bore of the wheel with lead, and bore it out to fit the spindle of the emery grinding machine. The flanges between which the wheel is held are recessed so as to grip the wheel at and near their perimeters only. Between the flange and the wheel a thin disk of sheet-rubber is sometimes used to afford a good bedding for the flange.

The forms of the perimeters of emery wheels are conformed to suit the form of the work to be ground, and it is found that from the great strength of the emery wheel it can be used to a degree of thinness that cannot be approached in any kind of grinding stone. For instance, vulcanite emery wheels 18 inches in diameter and having 316 inch thickness, or face as it is commonly termed, are not unfrequently used at a speed of some 5,000 feet of circumferential feet per minute, whereas it would be altogether impracticable to use a grindstone of such size and shape, because the side pressure would break it, no matter at what speed it were run. Indeed, in the superior strength of the emery wheels of the smaller sizes lies their main advantage, because they can be made to suit narrow curvatures, sweeps, recesses, &c., and run at any requisite speed under 5,000 feet per minute, and with considerable pressure upon either their circumferential or radial faces.

Grades of Coarseness or Fineness of Emery Wheels.—Emery is found in the form of rock, and is crushed into the various grades of fineness. The crushing is done either between rollers or by means of stamps, the latter, however, leaves the corners of the grains the sharpest, and hence the best for cutting, though not for polishing purposes. The grades of emery are determined by passing the crushed rock through sieves or wire cloths having from eight to ninety wires to the inch; thus, emery that will pass through a sieve of sixty wires to the inch is called No. 60 grade.

The finest grade obtained from the manufactory is that which floats in the atmosphere of the stamping room, and is deposited on the beams and shelves, from where it is occasionally collected. Washed emery is used by plate-glass workers, opticians, and others that require a greater degree of fineness than can be obtained by the sieve.

The numbers representing the grades of emery run from 8 to 120, and the degree of smoothness of surface they leave may be compared to that left by files as follows:

8  and  10  represent the  cut of a  wood rasp
16 20 coarse rough file
24 30 ordinary rough file
36 40 bastard
46 60 second cut
70 80 smooth
90 100 superfine
120, F & FF dead smooth

The f and ff emery is flour emery which has been washed to purify it.

The following are the kinds of wheel suitable for the respective purposes named:—

Kind of work.   Kind of wheel.
For rough grinding, such as on the edges of iron or steel plates, for removing the protuberances on castings or on narrow surfaces where rough grinding is sufficient.  }  Coarse grain and hard texture.
For narrow surfaces, such as moulding knives, lathe tools, saw gumming, &c.  }  Medium grain and hard texture.
For free cutting without gumming on broad surfaces on iron, steel, or brass.  }  Medium grain and soft texture.
For grinding fine tools, such as milling machine cutters, or for work in which the duty is not great while the wheel requires to keep its shape and keep true.  }  Fine grain and soft texture.
For smooth grinding on soft metals, as cast iron and brass.  }  Fine grain and hard texture.
Fig. 2014

Fig. 2014.

When the work is presented to the wheel unguided, the wheel wears out of true, because the work can follow the wheel, hence it becomes necessary to true the wheel occasionally. This can be done by a tool such as in Fig. 2014, which is applied by hand on the hand rest, and corresponds to the tool shown in Fig. 2061 for grindstones, or by the use of a diamond set in a tool to be held by hand or in a slide rest. The diamond produces the most true and smooth work, but the cut of the wheel is at first impaired by the action of the diamond, which is not the case with the tool in Fig. 2014.

Corundum is a mineral similar to emery, and corundum wheels are made and used in the same manner as emery wheels. Their cutting qualifications are, however, superior to those of the emery wheel, both cutting more freely and being more durable with less liability to glaze.

Speeds for Emery Wheels.—The speed at which an emery wheel may be run without danger of bursting varies according to the thickness or breadth of face of the wheel, as well as according to the quality of the cementing material and excellence of manufacture. Hence, although a majority of manufacturers recommend a speed of about 5,000 circumferential feet per minute, that speed may be largely exceeded in some cases, while it would be positively dangerous in others. It is, in fact, impracticable in the operations of the workshop to maintain a stated circumferential speed, because that would entail a constant increase of revolutions to compensate for the wear in the diameter of the wheel. Suppose, for example, that a wheel when new is a foot in diameter: a speed of about 1,600 revolutions per minute would equal about 5,000 circumferential feet; whereas, when worn down to 2 inches in diameter, the revolutions would require, to maintain the same circumferential speed, to be about 9,500 per minute, entailing so many changes of pulleys and counter-shafting as to be impracticable. In practice, therefore, a uniform circumferential speed does not exist, the usual plan adopted being to run the large-sized wheels, when new, at about the speed recommended by the manufacturer of the kind of wheel used, and to make such changes in the speed of the wheel during wear as can be accomplished by changing the belt upon a three-stepped cone pulley, and perhaps one, or at most two, changes of pulley upon the counter-shaft. It is sometimes practicable to use wheels of a certain diameter upon machines speeded to suit that diameter, and to transfer them to faster speeded machines as they diminish in diameter. Even by this plan, however, only an approximation to a uniform speed can in most cases be obtained, because as a rule certain machines are adapted to certain work, and the breadth of face and form of the edge of the emery wheel are very often made to suit that particular work. Furthermore, a new wheel is generally purchased of such a size, form, and grade of emery as are demanded by the work it is intended at first to perform. Neither is it, as a rule, practicable to transfer the work with the diametrically reduced wheel to the lighter and faster-speeded grinding machine. So that, while it is desirable to run all emery wheels as fast as their composition will with safety admit, yet there are practical objections to running small wheels at a rate of speed sufficient to make their circumferential velocities equal to those of large wheels. The speeds recommended for the various kinds of wheels now in use vary from about 2,700 to 5,600 circumferential feet per minute; but the speeds obtaining in workshops average between 2,000 and 4,000 feet for wheels 3 inches and less in diameter, and from about 3,000 to 5,600 feet for wheels above 12 inches in diameter. Wheels above 15 inches in diameter, and of ample breadth of face, are not unfrequently run at much greater velocities.

On account of the high velocity at which emery wheels operate, it is necessary that they be very accurately balanced, otherwise the unequal centrifugal motion causes them to vibrate very rapidly, every vibration leaving its mark upon the work.

The method of balancing adopted by one firm is as follows: The arbors are of cast iron, and are cast standing vertical so as to induce equal density in the metal, it having been found that if the arbors were cast horizontally the lower part of the metal would from the weight of the molten metal be more dense than that at the top of the casting. In casting the arbors upright, the difference in the density of metal simply causes one end of the arbor to be more dense than the other, and the difference being at a right angle to the plane of revolution has no tendency to cause vibration. The driving pulleys are cast horizontal to obtain equal density, and after being turned are carefully balanced. The driving pulleys are held to the arbors by being bored a driving fit, and are driven on so as to avoid the use of keys, which would throw the wheels out of balance.

The centrepiece and flange to hold the wheel to the arbor are turned and balanced. The nut to hold the wheel is a round one, which is easier to balance than a hexagon nut. After the centrepiece is put on the arbor, the whole is tried for balance, and corrected if necessary. The pulley is then put on and the whole is again balanced, and so on, the arbor being balanced after each piece is added, so that while each piece is balanced of itself the whole is balanced after the addition of each separate piece.

Fig. 2015

Fig. 2015.

Fig. 2016

Fig. 2016.

The emery or corundum wheel is then put on the arbor and tried for being in balance. The method of correcting the balance of the wheel is as follows: The arbor with the wheel on is placed in the lathe, the wheel turned true with a diamond tool (the wheel revolving at a comparatively slow speed). The arbor is then revolved at its proper speed (5,000 circumferential feet per minute), and a point applied to just meet the circumference will touch the wheel where it is heaviest, leaving a line as shown in Fig. 2015 at a. The centre of the arbor is then moved over towards this line as shown in Fig. 2016, in which w is the wheel, the location of the line a (marked as above) being as denoted by the arc a, and c represents the arbor whose centre is moved over towards the arc a. When therefore the arbor is again put in the lathe, it will run out of true by reason of the centre at one end having been altered. A cut is taken down that radial face of the wheel which faces the end of the arbor that has had its centre moved so that the wheel is turned thinner where the mark (a, Fig. 2016) is. The amount of cut to be taken off is a matter of judgment and trial, since it must be just sufficient to compensate for the greater density of the wheel on that side. This greater density, be it noted, occurs from the difficulty in mixing the corundum or other abrasive grains with the cementing material with entire uniformity throughout the mass.

By this method of balancing, the wheel will remain in true balance notwithstanding its wear, because the balancing proceeds equally from the perimeter towards the centre of the wheel.

Fig. 2017

Fig. 2017.

Emery Grinding Machines. (For grinding-lathes and roll grinding, see article on Lathes.)—Fig. 2017 represents Brown & Sharpe’s grinding machine. The bed, the table, and the cross-feed motion of this machine closely resemble those of the planing machine, but its work is far more smoothly and accurately done than can be performed in a planing machine. The table traverses to and fro, accurately guided in ways, and the revolving emery wheel takes the place of the ordinary cutting tool, being carried in a sliding head upon a cross slide or cross bar. The drum for driving the emery wheel is at the back of the machine, as shown in the cut.

Fig. 2018

Fig. 2018.

The vertical feed motion for adjusting the depth of cut of the emery wheel is capable of very minute adjustment, thus avoiding a difficulty commonly experienced in iron planing machines on account of the coarseness of feed-screw pitch, which coarseness is necessary to insure their durability. The means by which this capability of minute adjustment is effected is shown in Fig. 2018, in which d is the cross head of the machine and c the sliding head having the arm c′, which provides at b a pivot for the wheel-carrying arm a. f is a stud fast in c and carrying e, which forms the nut for the feed screw. Outside this nut is the spiral spring s, whose force steadies the upper end of a.

Now suppose the feed wheel g be operated a full rotation, and the motion of that end of a will be that due to the pitch of the feed screw, but the motion at the centre h of the emery wheel will be the pitch of the screw divided by the difference between the length from the centre of h to the centre of the feed screw, and that from the centre of h to the centre of b. But even this diminished motion at h is still further reduced, so far as the depth of cut put on is concerned, because the motion of h is not directly vertical but an arc p, of which b is the centre.

The standards carrying the cross slide are segments of a circle struck from the centre of the driving drum, which is necessary to enable the raising and lowering of the cross slide, and maintain a uniform tension on the belt driving the emery wheel without employing an idler wheel or belt tightener.

Fig. 2019

Fig. 2019.

Fig. 2019 represents Wm. Sellers & Co.’s drill-grinding machine, in which the drill is held in a chuck operated by the hand wheel a. The jaws of the chuck grip the drill at the outer corners of the cutting edge as shown in Fig. 2020, and so as to grind the point of the drill central to those corners. In order to give to the cutting edges a suitable degree of clearance in their lengths, and to allow for the difference in thickness at their points between large and small drills, the following construction is employed.

Fig. 2020

Fig. 2020.

Fig. 2021

Fig. 2021.

Fig. 2022

Fig. 2022.

Fig. 2020 represents the jaws j j holding on the left a small, and on the right a large drill. The line of motion of the right-hand jaw in opening and closing to grip the drill is along the line r, while that of the left-hand is along the line p p, the centre upon which the chuck is revolved to grind the drill being denoted by the small circle at s. x′ represents the centre line of the large drill when held in the chuck, and it is seen that the action of the jaws in closing upon small drills is to lift the drill point closer to the centre s upon which the chuck revolves (the cutting edge being ground to be on the line y′ y′). The reason for this peculiar and simple but exceedingly ingenious construction is, as before remarked, to maintain the cutting edge in its proper relation to the thickness of the drill point (which thickness varies in different diameters of drills), and to maintain a proper degree of clearance at every point along the length of the cutting edge. In other drill grinding machines the drill when rotated to grind the clearance is moved on the axis a a in Fig. 2022 as a centre of motion, and as this line is parallel to the face of the emery wheel it follows that if the drill were given a full revolution its circumference would be ground to a cylinder as shown in Fig. 2021 by the dotted lines.

Fig. 2023

Fig. 2023.

Fig. 2024

Fig. 2024.

In this machine the drill is rocked on the line b, Fig. 2023, as a centre of motion, this line corresponding to the axis of the shaft of lever f in Fig. 2019 upon which the chuck swings, and to the line b in Fig. 2024. As a result the surface is ground to the form of a cone as denoted by the dotted lines in Fig. 2024. The results of the two systems are shown in Figs. 2025 and 2026, which represent the conical holes made by a drill.

Fig. 2025 top

Top View.

Fig. 2025 bottom

Section.
Fig. 2025.

Fig. 2026 top

Top View.