is a quadrangular rectangle, which is a figure with equal angles and sides to each other. Word " square" comes from the Greek word " quadratus", which translated means - " quadrangular».

In technical drawings It is not uncommon to see parts or parts thereof that have a square cross-section. To reduce the total number of dimension lines in the drawing, in this case, a special sign “ ” is used, which means that this size is one of the sides of the square, and the size is indicated only here. The height of the sign is selected according to the height of the dimensional numbers.

Designation of a square section of a product

Parts areas, having a square cross-section, can often be found on the fastening elements of auxiliary and cutting tools. Installation bolts, used in this case, take on significant mechanical impacts at intervals determined by the technological process.

Machine vice, intended for installation on metal-cutting machines, are equipped with a power screw, at one end of which there is a square cross-section. This was done so that the cap handle, which accordingly has a hole with a square cross-section, can be freely removed and put on, and it becomes possible to change its angular position. The load applied to the vice mechanisms is also quite significant.

As you know, a significant part of rotating parts is manufactured on turning machines. In order to clamp a part or workpiece for subsequent machining, special self-centering chucks are used. The most common of them are three-jaw chucks, but there are also four-jaw chucks in which, by the way, you can clamp square parts or blanks from the corresponding rolled products. The square can also be clamped in two jaw chucks, and, as in four jaw chucks, the movement of the jaws, depending on the type, can be carried out independently or using a special mechanism based on “ Archimedean spiral", which allows you to move the clamping elements synchronously. There are even six-jaw chucks, all of them are united by the fact that to clamp the part, a key with a square head is used.

The design of a traditional type faucet includes a water supply control element, such as a rod. At one end of the rod there is a square section onto which a handle with a square hole is installed. The efforts here are not too great, but, nevertheless, the use of a hexagon is not appropriate here (during operation, the angles between the edges may simply collapse).

Square holes, unlike round holes, are the most labor-intensive to manufacture. Usually they are milled, drawn, special firmware is used, accelerated on a slotting machine, etc. Technologies such as - laser cutting or electrical discharge machining, allow hollow elements of this type to be processed more or less quickly.

There is, however, another, exotic way. We are talking about drilling using a special tool. This method is based on the trajectory of movement " Reuleaux triangle", named after the German inventor and mechanical engineer Franz Relo, who lived in the nineteenth and early twentieth centuries, who was a long-time lecturer at the Berlin Royal Academy of Technology and eventually became its president. The cross-section of the drill is similar to the so-called " Reuleaux triangle", the sides of which are not straight segments, like a regular one, but arcs of the same size and radius. If, during the drilling process, using a special device, you move the axis of this tool along a special path, you will end up with a square hole with slightly rounded corners.

The simplest figure of the hundred-yang shi-ri-na will help us in drilling square holes. If you move the center of this “triangle” along a certain trajectory, then its vertices are drawn almost like a square, and the he will sweep the entire area inside the radiant figure.

The edges of the best figure, except for small pieces in the corners, will be strictly straight ! And if you continue to live from the cutting, then you will see the corners, then the result will be exactly a square.

In order to be described above, the center of the triangular Re-lo needs to be moved along the trajectory, clearly la-yu-shchey-glue-coy from four one-to-one arcs of el-lip-owls. The centers of the el-lips are located at the tops of the square, and along the axis, at an angle of $45^\circ$ from-but-si-tel-but the sides of the square are equal to $k\cdot(1+1/\sqrt3)/2$ and $k\cdot(1-1/\sqrt3)/ 2$, where $k$ is the length of a hundred square meters.

Curved, rounded corners also appear as du-ga-mi el-lip-sovs with centers in the corners of squares , their half-axis is at an angle of $45^\circ$ from the sides of the square and is equal to $k\cdot(\sqrt3+ 1)/2$ and $k\cdot(1/\sqrt3-1)/2$.

The area of ​​the invisible corners is only about 2% of the area of ​​the entire square!

Now, if you make a drill in the form of a triangular Re-lo, then you can drill square holes with a little -go-round-the-corner-of-me, but ab-so-lyut-but straight-we-a-hundred-on-mi!

All that's left is to make that drill... Or rather, it's not difficult to make the drill itself, you just need it to fit in this is the triangle of Re-lo, and the cutting edges of the owls are with its tops.

The difficulty lies in the fact that, as already mentioned above, the tra-ek-to-ria of the center of the drill must be -one hundred of four arcs of el-lip-owls. Vi-zu-al-but this curve is very similar to a circle and even ma-te-ma-ti-che-ski close to it, but still it is not a circle ness. And all the ex-cen-tri-ki (a circle placed on a circle of another ra-di-u-sa with a shifted center), use-use- They are in tech, they move strictly in a circle.

In 1914, the English engineer Harry James Watts figured out how to arrange such a drilling. On the surface he places a right-handed template with a pro-cut in the form of a square, in which a drill moves, inserted into a socket with a “free-floating drill in it.” A patent for such a pa-tron was issued to a company that started manufacturing Watts drills in 1916.

Je-ro-la-mo CARDANO (1501 - 1576). When, in 1541, im-per-ra-tor Charles V tri-um-fal-no entered the Za-vo-e-van-ny Milan, rector of the College of Vra -whose Kar-da-no was walking next to the bal-da-khin. In response to the honor, he offered to equip the royal crew with the weight of two shafts, which were not you-ve-det ka-re-tu from go-ri-zon-tal-no-go po-lo-zhe-niya […]. Justice demands to note that the idea of ​​such a system goes back to antiquity and that at the very least in the “At-lan-ti-che-sky codex” Leo-nar-do da Vin-chi has a ri-su-nok su-do-vo-go com-pa-sa with kar -given under the weight. Such com-pa-sys in the first half of the 16th century, apparently, without influence -I-niya Kar-da-no.

S. G. Gin-di-kin. Talk about physics and ma-te-ma-ti-kah.

We are using another known structure. We attach the drill rigidly to the triangular re-lo, placing it in a square on the right-hand frame . Sam-ma ram-ka fi-si-ru-et-sya on the drill. All that remains now is to transfer the rotation of the drill to the tri-corner of Re-lo.

Almost everyone knows how to drill a round hole, but not everyone knows about a drill for square holes. Meanwhile, you can drill a square-shaped hole both in soft wood products and in harder metal parts. To solve this problem, special tools and devices are used, the operating principle of which is based on the properties of the simplest geometric shapes.

Operating principles and design

In order to drill a square hole, a Watts drill is usually used, the design of which is based on a geometric figure such as the Reuleaux triangle. One of the most important features of such a figure, which represents the area of ​​intersection of three equal circles, is the following: if a pair of parallel reference lines are drawn to such a triangle, then the distance between them will always be constant. Thus, if you move the center of the Reuleaux triangle along a trajectory described by four ellipsoidal arcs, its vertices will draw an almost perfect square, with only slightly rounded vertices.

The unique properties of the Reuleaux triangle made it possible to create drills for square holes. The peculiarity of using such a tool is that the axis of its rotation should not remain in place, but move along the trajectory described above. Naturally, this movement should not be hindered by the equipment cartridge. When using such a drill and the appropriate equipment, a square hole is obtained with perfectly straight and parallel sides, but with slightly rounded corners. The area of ​​such corners not processed with tools is only 2% of the area of ​​the entire square.

Making a device for drilling square holes

Using Watts drills, which work on the principle of the Reuleaux triangle, you can drill square holes in metal workpieces even on a regular machine that is not equipped with special attachments. To create a square hole in a wooden part, you can use a regular drill, but for this it must be equipped with additional devices.

You can make a simple device that allows you to drill square holes in wooden blanks using the following recommendations.

• To begin with, using a sheet of plywood or a wooden board of small thickness, you need to make the Reuleaux triangle itself, the geometric parameters of which must correspond to the diameter of the Watts drill used.
• The drill must be firmly fixed on the surface of the manufactured triangle.
• In order for the Reuleaux triangle and the drill attached to it to move along the required trajectory, it is necessary to make a wooden guide frame. In the inside of the frame, you should cut out a square with geometric parameters that fully correspond to the dimensions of the hole that you are going to drill.
• The frame is fixed to the drill using a special strip, and the center of the Reuleaux triangle placed in the guide frame must coincide with the axis of rotation of the power tool chuck.
• In order to impart torque to the drill for making a square hole, but at the same time not create restrictions on the movement of the tool in the transverse direction, the shank is connected to the drill chuck through a transmission mechanism that operates on the principle of a truck drive shaft.
• The wooden workpiece in which it is necessary to drill a square hole should be securely fixed, and it should be positioned so that the center of the future hole strictly coincides with the axis of rotation of the drill used for processing.

Having assembled such a simple device and securely fixed all the elements of its design and the workpiece being processed, you can turn on the electric drill and begin the drilling process.

As mentioned above, a square hole drilled using such a device will have absolutely straight and parallel sides, but its corner sections will be slightly rounded. Solving the problem with rounded corners is not difficult: you can refine them using a regular needle file.

It should be borne in mind that the device described above, which is not very rigid, is used for drilling square-shaped holes in wooden pieces of small thickness.

Watts drill and a square hole made with it in a metal workpiece

In some cases it is necessary to obtain square-shaped holes. Conventional methods are inefficient and cumbersome. The most primitive of them comes down to preliminary drilling a hole with a diameter equal to the circle inscribed in a square, and gradually punching it out. You will need a tool that can work without rotating the tool head, as well as a special adapter. It’s easier to use a so-called “square” drill (Watts drill), or, more precisely, a cutter.

A little history with geometry

Back in the 15th century, the legendary Leonardo da Vinci, while studying the properties of geometric figures, drew attention to the so-called geometric objects with equal thickness. There are an infinite number of such figures, but the simplest - besides a circle - is a rounded triangle, which can be formed as follows. An equilateral triangle is drawn, each of the corners of which is connected by an arc of a circle drawn from the center of the opposite side. The peculiarity of such a triangle will be that all its sides will have a constant width, which is equal to the length of the side of the original equilateral triangle.

L. Euler drew practical benefit from this fact, who three centuries later demonstrated the rotation of such a rounded triangle: first around its own axis, and then with some eccentricity, since the cardan mechanism was already known to science and technology of that time.

The German engineer F. Relo went even further in the practical use of this figure, who drew attention to the fact that the trajectory of the corners of a moving triangle with certain methods of its rotation is very close to a square. Only directly at the corners of the square does the outer surface describe an arc, however, of a small radius. In modern technical literature, such a triangle is called the Reuleaux triangle, although this figure actually no longer has any angles.

A few more decades will pass, and the Englishman G. Watts will come up with a device that can provide a guaranteed square trajectory for a metal-cutting tool. The technical solution for the Watts drill was patented in 1916, and a year later mass production of such tools began.

Drill or cutter?

The majority of the technical community believes that it is still a milling cutter. However, manufacturers stubbornly continue to call this tool a drill for square holes, a Watts drill, or a drill whose profile corresponds to the Reuleaux triangle.

Which is more correct? If we turn to the kinematics of movement of such a cutting tool (for clarity, you can use the diagram shown in Fig. 1), you will find that metal removal will be carried out only by the side surface, and there will be not one cutting plane, like a conventional drill, but four, which more typical for cutters.

However, a single rotating motion will not be enough to obtain a square hole. Simple mathematical calculations (not given in this article) show: in order for a “drill” for a square hole to perform its function, during operation it must describe not only the basic rotational movement of the cutting edge, but also the rocking movement of the drill/cutter around a certain axis. Both movements must be made in mutually opposite directions.

Figure 1 – Reuleaux Triangle: a) – construction; b) rotation sequence to obtain a square-shaped hole.

The angular velocity of both rotations is determined quite simply. If we take the rotation frequency of the drill shaft (or hammer drill) as the parameter f, then a speed of 0.625f is sufficient for oscillatory rotations of the spindle around its own axis. In this case, the spindle axis is, as it were, clamped between the working shaft and the drive wheel, causing the drill/cutter to oscillate in the clamping device with a residual speed

(1 – 0.625)f = 0.375f.

The resulting rotation speed of the cutter can be more accurately determined using the technical characteristics of the drill/hammer, but it is clear that it will be much lower than that for which the tool was originally designed. Therefore, obtaining a square hole will occur with less productivity.

Design and principle of operation

It is impossible to directly use a cutter/drill for square holes with a Reuleaux triangle profile - grooves are needed to remove the resulting chips.

Therefore (see Fig. 2) the profile of the working part of the tool is the figure described above, from which three half-ellipses are cut out. In this case, three goals are realized: the moment of inertia of the drill and the load on the spindle are reduced, and the cutting ability of the cutter is increased.

Figure 2 – Actual profile of the working part of the tool

The design of the tool is as follows. Actually, the working part includes a working surface used to remove metal and grooves that remove chips. A cutter-drill for square holes is made from U8 steel and hardened to a hardness of HRC 52...56. Under particularly severe operating conditions, products made of X12 alloy steel with a hardness of HRC 56...60 are used. With normal coolant supply and due to relatively low temperatures in the processing zone, tool life is high.

The adapter spindle has a more complex design. It includes:

1. Frame.
2. Ring gear.
3. A seat for the main spindle (if the tool is installed in the tool head of a metal-cutting machine, then the adapter has the form of a Morse cone).
4. Drive gear.
5. Main spindle.
6. Meshing gears with a ring gear.
7. Oscillating bushing.

For household devices, manufacturers of cutters/drills for square holes offer overhead frames that are connected by a cardan drive to the chuck and impart eccentric movements to the cutting tool. The thickness of this frame determines the depth of the resulting hole.

To connect the device to the machine chuck, a special adapter is also required. It consists of:

1. Cases.
2. Floating shank.
3. Swinging ring.
4. Replaceable bushings for cartridges of various metalworking machines.
5. Mounting screws.
6. Support balls.

For the practical use of the tool in question, it is enough to give the spindle of the main equipment a feed in the required direction. Broaching milling machines and lathes are suitable for making square holes using such equipment.

Alternative Methods for Making Square Holes

The disadvantage of Watts drills is the presence of radius arcs in the corners of the square, which is not always acceptable. In addition, square hole drills made using the Reuleaux triangle cannot handle thick workpieces. In such cases, you can use electroerosive/laser technologies, and also, which is easier, use welding or stamping.

Sets of punches for square holes are produced in an assortment of transverse sizes up to 70×70 mm in metal with a thickness of up to 12...16 mm. The kit includes:

• Punch holder for punch.
• Guide bushing.
• Ring travel stop.
• Matrix.

A hydraulic jack can be used to exert force on the punch. The punched hole is distinguished by the cleanliness of the resulting edges, as well as the absence of burrs. A similar tool is produced, in particular, by the Veritas trademark (Canada).

If you have a welding inverter in your household, you can burn a square hole in a steel part. For this purpose, a round hole is pre-drilled (with a reserve) in the workpiece, then a square of graphite grades EEG or MPG of the required size is inserted into it, after which it is scalded along the contour. The graphite is removed, and a square hole remains in the product. If necessary, it can be cleaned and sanded.

Anyone can do it in a material of any density. But what if you need a square hole? Many people will find it implausible to be able to drill a square into soft, pliable wood or into a piece of durable metal. The Watts drill copes with this difficult task.

History with geometry

Even today, to obtain a square hole, craftsmen drill a round hole of the appropriate diameter and punch out the corners with special tools. This operation can be performed much faster and easier with a “square” Watts drill. The basis of its design is the Reuleaux triangle - a figure formed by the intersection of three identical circles. The radii of these circles are equal to the side of a regular triangle, and its vertices are the centers of the circles.

The figure bears the name of the German scientist Franz Reuleaux, since he was the first to study in detail the properties of the resulting triangle and apply them in his inventions. However, the geometry of the Reuleaux triangle was used in the shape of windows in the construction of the Church of Our Lady in Bruges back in the 13th century. At the beginning of the 16th century, Leonardo Da Vinci depicted a “map of the world” on four Reuleaux triangles. This figure appears in his manuscripts and the Madrid Codex. In the 18th century, a triangle made of equal arcs of three circles was demonstrated by the famous mathematician Leonhard Euler. In 1916, an English engineer working in the USA, Harry Watts, developed and patented a cutter for square holes in a “floating” chuck.

Features of the Watts drill

A unique invention makes it possible to obtain holes of almost regular shape: the corners of the square are rounded with a small radius. The raw area of ​​a square hole does not exceed 2%. A distinctive feature of the Watts triangular drill is that when rotated, its center describes an arcuate ellipsoidal curve, rather than standing still like a traditional twist drill. With this movement, the vertices of the triangle draw a square with parallel, perfectly straight sides. The chuck for such a cutter has an original design that does not impede movement.

Drill structure for square holes

When chips are formed, the cutter must have grooves to remove them. The profile of the working part of the Watts drill is a Reuleaux triangle with three halves of ellipses cut out of it.

This design with grooves for chip removal solves 3 problems simultaneously:

1. The inertia of the drill is reduced.
2. The cutting ability of the drill is increased.

Typically, square holes are made on lathes or milling machines. The drill for square holes is fixed in the machine chuck with a special adapter. For household use of a square cutter, manufacturers offer overhead frames that connect to the cardan drive chuck and impart eccentric movements to the cutting tool. The depth of the hole corresponds to the thickness of the frame.

Drill steel

Today, high-quality drills that work quickly and for a long time are made from high-alloy steel grades. In their composition, such alloys contain more than 10% alloying additives, such as tungsten, chromium, vanadium and molybdenum. Different percentages of elements and various methods of hardening steel form alloys that differ in levels of hardness, toughness, impact load resistance, cost and other characteristics.

Metal drill bits are the most widely used electrical consumable for several reasons:

• Metal products most often require holes for fastening: threaded connections, rivets and other types of connections.
• Metal drills can also be used when working with softer materials, such as wood.
• The production technology for this type of product is similar to the principles for the production of drills for various applications.

In Russia and many other countries, the greatest demand is for drills made of high-speed steel grade R6M5, which contains tungsten and molybdenum. The strength and price of products significantly increases when cobalt is added to the alloy or drills are coated with cooling titanium-nitride sputtering.

for metal products

Metal drills are used to make holes in products made of bronze, cast iron, copper, steel of various grades, cermets and other materials. For drilling tough, difficult-to-cut steel, high-strength products with the addition of cobalt are used. During operation, chips are discharged along two longitudinal grooves. Based on the shape of the tail, such instruments are divided into three types:

• hexagonal,
• conical,
• cylindrical.

A metal drill with a conical shank is inserted directly into the machine when used. A special chuck is required for hex and cylindrical shanks.

Definitions of quality by color

The quality of a drill for any material is determined primarily by its color:

• Tools of increased wear resistance are black in color, since they are treated with steam at the final stage of production.
• Heat-treated products have no internal stress, are highly resistant to high temperatures and do not deform when working with carbide steels. These drills have a slightly golden tint.
• The highest quality and durable ones have a bright golden color. They are coated with friction-reducing titanium nitride.
• Regular untreated gray drills have the shortest service life and the lowest price.

Size range

The working sizes of metal drills are presented by modern manufacturers in a wide range. GOST provides for the division of such products into types in accordance with certain sizes.

Metal drills are divided into several categories:

GOSTs 4010-77, 886-77 and 10902-77 regulate the classification of drills by length and diameter.

How to choose a drill for glass or ceramics

Professional craftsmen in their collection have drills for every material: brick and concrete, metal and plastic, diamond drill for glass and ceramics. Glass is an extremely capricious material and requires the use of a high-quality and durable drill. Glass and ceramic surfaces can be machined with diamond-coated drill bits at the working end. The quality of such products is determined by the method of their manufacture. The thinnest and most inexpensive drills are made using the galvanic method. Stronger instruments are produced using the powder process. They are distinguished by durability and stability. Relatively inexpensive, high-strength drills with increased abrasiveness are produced using the modern vacuum method.

To drill a hole in a glass surface, you need to have good skills. This long and painstaking process is carried out smoothly and slowly at maximum speed without pressure, only with a diamond drill mounted strictly vertically. The hole must be constantly moistened with water to cool it. This action is more like scratching a hole with diamond grains.

If you have the necessary tools and drills of the right size on hand, any repair work will be completed quickly and efficiently.