Methods for obtaining conical surfaces. Manufacturing of cylindrical and conical parts using hand tools - Knowledge Hypermarket Processing of conical surfaces on a lathe
Machining of conical surfaces on lathes is carried out different ways: by turning the upper part of the caliper; displacement of the tailstock housing; turning the cone ruler; wide incisor. The use of one or another method depends on the length of the conical surface and the angle of inclination of the cone.
Processing the outer cone by rotating the upper slide of the caliper is advisable in cases where it is necessary to obtain a large inclination angle of the cone with a relatively short length. The maximum length of the cone generatrix should be slightly less than the stroke of the upper support carriage. Processing the outer cone by displacing the tailstock body is convenient for obtaining long flat cones with a small slope angle (3...5). To do this, the tailstock body is shifted transversely from the line of the machine centers along the guides of the headstock base. The workpiece being processed is fixed between the centers of the machine in a driving chuck with a clamp. Processing cones using a cone (copying) ruler attached to the rear side of the bed lathe on a slab, used to obtain a flat cone of considerable length. The workpiece is secured in centers or in a three-jaw self-centering chuck. The cutter, fixed in the tool holder of the machine support, receives simultaneous movement in the longitudinal and transverse directions, as a result of which it processes conical surface blanks.
Processing the outer cone with a wide cutter is used if it is necessary to obtain a short cone (l<25 мм) с большим углом уклона. Широкий проходной резец, режущая кромка которого длинней образующей конуса, устанавливают в резце держатель так, чтобы главная режущая кромка резца составляла с осью заготовки угол а, равный углу уклона конуса. Обработку можно вести как с продольной, так и с поперечной подачей. На чертежах деталей часто не указывают размеры, необходимые для обработки конус и их необходимо подсчитывать. Для подсчета неизвестных элементов конусов и их размеров (в мм) можно пользоваться следующими формулами
a) taper K= (D--d)/l=2tg
b) cone slope angle tg = (D--d)/(2l) = K/2
c) slope i = K/2=(D--d)/(2l) = tg
d) larger cone diameter D = Kl+d = 2ltg
e) smaller cone diameter d = D-- K1 = D--2ltg
e) cone length l = (D--d)К = (D--d)/2tg
Machining of internal conical surfaces on lathes is also carried out in various ways: with a wide cutter, turning the upper part (sled) of the caliper, turning a conical (copying) ruler. Internal conical surfaces up to 15 mm long are processed with a wide cutter, the main cutting edge of which is set at the required angle to the cone axis, carrying out longitudinal or transverse feed. This method is used when the cone slope angle is large, and high demands are not placed on the accuracy of the cone slope angle and surface roughness. Internal cones longer than 15 mm at any angle of inclination are processed by turning the upper slide of the caliper using manual feed.
§ 1. General information
1. Scope of application of cones. Along with cylindrical parts, parts with conical surfaces have become quite widespread in mechanical engineering. Examples of them include cones of centers, drill shanks, countersinks, and reamers. To fasten these tools, the front sections of the lathe spindle and quill holes are also conical in shape.
However, the use of cones is not limited to cutting tools. Many machine parts have conical surfaces.
The widespread use of conical joints is explained by a number of their advantages.
1. They provide high accuracy of centering of parts.
2. When flat cones come into close contact, a fixed connection is obtained.
3. By changing the axial position of the parts of the conical connection, you can adjust the size of the gap between them.
2. Cone and its elements. A cone is a geometric body, the surface of which is obtained by rotating a straight line (generative) inclined to the axis of rotation (Fig. 129, a).
The point of intersection of the generatrix with the axis is called the vertex of the cone.
The planes perpendicular to the axis of the cone are called bases.
There are full and truncated cones. The first is located between the base and the top, the second - between two bases (larger and smaller).
The cone is characterized by the following elements: the diameter of the larger base D; diameter of the smaller base d; length l; the slope angle a between the generatrix and the axis of the cone; cone angle 2a between opposite generatrices.
In addition, the concepts of taper and slope are often used in working drawings of conical parts.
Taper is the ratio of the difference in diameters of two transverse sections of a cone to the distance between them. It is determined by the formula
The slope is the ratio of the difference between the radii of two cross sections of a cone to the distance between them. It is determined by the formula
From formulas (9) and (10) it is clear that the slope is equal to half the taper. 
Trigonometrically, the slope is equal to the tangent of the slope angle (see Fig. 129, b, triangle ABC), i.e.
In the drawing (Fig. 130) the taper is indicated by the sign<, а уклон -, острие которых направляется в сторону вершины конуса. После знака указывается отношение двух цифр. Первая из них соответствует разности диаметров в двух принятых сечениях конуса, вторая для конусности- расстояние между сечениями, для уклона - удвоенной величине этого расстояния.
Taper and slope are sometimes written as decimal numbers: 6.02; 0.04; 0.1, etc. For taper, these numbers correspond to the difference in cone diameters over a length of 1 mm, for slope - the difference in radii over the same length.
To process a full cone, it is enough to know two elements: the diameter of the base and the length; for a truncated cone - three elements: the diameters of the larger and smaller bases and the length. Instead of one of these elements, the angle of inclination a, slope or taper can be specified. In this case, to determine the missing dimensions, the above formulas (9), (10) and (11) are used. 
Example 1. Given a cone with d=30 mm, /=500 mm, K=1: 20. Determine the larger diameter of the cone.
Solution. From formula (9)
Example 2. Given a cone with D=40 mm, l = 100 mm, a=5, Determine the smaller diameter of the cone.
Solution. From formula (11)
Using the table of tangents we find tan5°=0.087. Therefore, d=40-2*100X X0.87=22.6 mm.
Example 3. Determine the slope angle a, if the cone dimensions are indicated in the drawing: D-50 mm, d=30 mm, /=200 mm.
Solution. According to formula (11)
From the table of tangents we find a = 2 50.
Example 4. Given a cone with D=60 mm, /=150 mm, K=1: 50. Determine the slope angle a.
Solution. Since the slope is equal to half the taper, we can write:
Using the table of tangents we find a=0 30.
3. Normal cones. Cones whose dimensions are standardized are called normal. These include Morse tapers, metric tapers, cones for mounted reamers and countersinks with a taper of 1:50 0, for conical pins - with a taper of 1:50, for conical threads with a taper of 1:16, etc.
The most widely used in mechanical engineering are Morse and metric tool cones, the main dimensions of which are given in table. 13. 
The sizes of Morse cones are expressed in fractional numbers. This is explained by the fact that for the first time the standard for them was adopted in the inch measurement system, which has been preserved to this day. Morse tapers have different tapers (approximately 1:20), metric tapers are the same - 1:20. 
TO category:
Turning
Machining of external and internal conical surfaces
If you rotate a right triangle ABC around leg AB, then the resulting body is called a complete cone, leg AB is the height of the cone. The straight line AB is called the generator of the cone, and point A is its vertex. When the leg BV rotates around the AB axis, a surface called the base of the cone is formed. The angle between the generatrix AG and the axis AB is the angle a of the inclination of the cone. The angle VAG between the generatrices AB and AG of the cone is called the cone angle; it is equal to 2a. If you cut off its upper part from a complete cone with a plane parallel to the base, then the resulting body will be a truncated cone (Fig. 206.6), which has two bases - an upper and a lower one. Distance 001 between the bases is the height of the truncated cone. The drawing usually indicates three main dimensions of the cone (Fig. 206, c): the larger diameter D, the smaller diameter d and the height of the cone.
Rice. 198. Use of drills for processing holes
Rice. 199. Devices for fastening drills
Using the formula tga = =(D- d)/(2l), you can determine the angle a of the cone, which is set on a lathe by turning the upper slide or shifting the tailstock. Sometimes the taper is specified as follows: K = (D - d)/l, i.e. the taper is the ratio of the difference in diameters to the length. In Fig. 206, d shows a cone in which K = = (100 -90)/100 = 1/10, i.e., over a length of 10 mm, the diameter of the cone decreases by 1 mm. The taper and diameter of the cone are related by the equation d = = D - Kl, whence D = d + Kl.
If we take the ratio of the half-difference of the diameters of the cone to its length, we obtain a value called the slope of the cone M = (D - d)/(2l) (Fig. 206, e). Cone slope and taper are usually expressed in ratios of 1:10, 1:50 or 0.1:0.05, etc. In practice, the formula is used
Rice. 200. Drilling blind and deep holes
Rice. 201. Boring holes
Morse cones and metric cones are common in mechanical engineering. The Morse cone (Fig. 207) has seven numbers: 0, 1, 2, 3, 4, 5 and 6. Each number corresponds to a certain angle of inclination: the smallest 0, the largest 6. The angles of all cones are different. Metric cones have a taper of 4; 6; 80; 100; 120; 160 and 200; they have the same slope angle (Fig. 208).
The processing of conical surfaces differs from the processing of cylindrical ones only by the feed angle of the cutter (Fig. 209), which is achieved by setting the machine. When the workpiece rotates, the tip of the cutter moves at an angle a (cone angle). On a lathe, cones are processed in several ways. Machining a cone using a wide cutter is shown in Fig. 210, a. In this case, the height of the cone should be no more than 20 mm. In addition, the cutting edge of the cutter is set at an angle a to the axis of rotation of the part exactly at the height of the centers (Fig. 210.6).
The simplest way to obtain conical surfaces is to shift the center line. This method is used only when processing surfaces in the centers by displacing the tailstock housing. When the tailstock body is shifted towards the worker (towards the tool holder), a conical surface is formed, in which the larger base of the part is directed towards the headstock (Fig. 211, a). When the tailstock body is displaced from the working one, the larger base is located towards the tailstock (Fig. 211.6). Transverse displacement of the tailstock body H = L - sina. With a slight shift in the angle of inclination of the cone a, we can assume that sinaa;tga, then H = L(D - d)/(2l). The displacement of the tailstock body is measured with a ruler (Fig. 211, c), the alignment of the centers can also be checked with a ruler (Fig. 211, d). However, when shifting the tailstock body, it should be taken into account that the shift is allowed by no more than 1/50 of the length of the part (Fig. 211, d). With a larger displacement, an incomplete fit between the center holes of the part and the centers is formed, which reduces the accuracy of the machined surface.
Rice. 203. Indicator bore gauge for measuring the depth of holes: 1 - centering bridge; 2-measuring tip; 3-double arm; 4-adjustable stop; 5-spring, eliminating the gap in the transmission elements; 6-Measurement Rod Indicator
Rice. 204. Solid and mounted zenners
Rice. 205. Unfold
It is advisable to handle cones with a large angle a and a small height by turning the upper caliper. This method is used when processing the outer (Fig. 212, a) and internal (Fig. 212,6) cone. In this case, manual feed is carried out by turning the handle of the upper support. To rotate the upper caliper to the required angle during mechanical feed, markings are used on the flange of the rotating part of the caliper. If angle a is not specified in the drawing, it is calculated using the formula tga = (D - d)/(2l). The cutter is installed strictly in the center. Deviation from the straightness of the generatrix of the processed cone occurs when the cutter is installed above (Fig. 213.6) or below (Fig. 213.c) the center line.
To obtain conical surfaces with a^ 10...12°, use a copy ruler (Fig. 214). A ruler 2 is installed on the plate 1, which is rotated to the required angle a around pin 3 and secured with a screw 6. The slider 4 is rigidly connected to the transverse part of the support 8 using a rod 7 and a clamp 5. The copying ruler must be installed parallel to the generatrix of the cone that needs to be obtained . The angle of rotation of the copy ruler is determined from the expression tga = (Z) - d)/(2l). If the divisions on the plate are indicated in millimeters, then the number of divisions C is H(D - d)/(2l), where R is the distance from the axis of rotation of the ruler to its end.
The cone, in which the length of the generatrix is greater than the stroke length of the upper carriage of the caliper, is ground by using longitudinal and transverse feeds (Fig. 215). In this case, the upper carriage must be rotated at an angle p relative to the center line: sinp = tga(Snp/S„+ 1), where oPr and S„ are the longitudinal and transverse feeds. To obtain the taper of the required shape, the cutter is installed strictly in the center.
The conical hole is processed in the following sequence. Drill a hole with a slightly smaller diameter than the diameter of the smaller base of the cone (Fig. 216), then drill out the hole with a drill. After this, the stepped hole is bored with a cutter. Another way to obtain a conical hole is by drilling a hole (Fig. 217, a), rough reaming (Fig. 217.6), semi-finishing (Fig. 217, c), finishing (Fig. 217, d).
Rice. 206. Geometric parameters of the nonus
Conical surfaces are controlled with inclinometers (Fig. 218, a), gauges (Fig. 218, b, c) and templates (Fig. 218, d). Conical holes are checked by the ledges and marks marked on the gauges (Fig. 219). If the end of the conical hole of the part coincides with the left end of the ledge, and the outer diameter coincides with one of the marks or is located between them, then the dimensions of the cone correspond to the specified ones.
Rice. 207. Morse taper
Rice. 208. Metrical nonus
Rice. 209. Scheme for processing cylindrical and nonical surfaces: a-the tip of the cutter moves parallel to the axis of the centers; b-the tip of the cutter moves at an angle to the center axis
Machining of conical surfaces on lathes is carried out three ways.
First way
The first method is that the tailstock body is shifted in the transverse direction by an amount h (Fig. 15, a). As a result, the axis of the workpiece forms a certain angle a with the axis of the centers, and the cutter, during its movement, grinds the conical surface. From the diagrams it is clear that
h = L sin a; (14)
tgα=(D-d)/2l; (15)
Solving both equations together, we get
h=L((D-d)/2l)cosα. (16)
This method is unsuitable for the manufacture of precise cones due to the incorrect position of the center holes relative to the centers.
Second and third way
The second method (Fig. 15, b) is that the cutting slide is rotated by an angle a, determined by equation (15). Since feeding in this case is usually carried out manually, this method is used when processing cones of short length. The third method is based on the use of special devices that have a copying ruler 1, mounted on the back side of the frame on brackets 2 (Fig. 15, c). It can be installed at the required angle to the center line. A slider 3 slides along the ruler, connected through a pin 4 and a bracket 5 with a transverse carriage 6 of the caliper. The carriage cross feed screw is separated from the nut. When the entire support is moved longitudinally, the slider 3 will move along the fixed ruler 1, communicating one
Rice. 15. Schemes for processing conical surfaces
temporary transverse displacement of carriage 6 of the caliper. As a result of two movements, the cutter forms a conical surface, the taper of which will depend on the angle of installation of the copy ruler, determined by equation (15). This method provides accurate cones of any length.
Processing of shaped surfaces
If in the previous copying device a shaped ruler is installed instead of a conical ruler, the cutter will move along a curved path, processing the shaped surface. For processing shaped and stepped shafts, lathes are sometimes equipped with hydraulic copy supports, which are most often located on the rear side of the machine support. The lower slide of the support has special guides, usually located at an angle of 45° to the axis of the machine spindle, in which the copying support moves. In Fig. 6, b showed a schematic diagram explaining the operation of the hydraulic copying support. Oil from pump 10 enters the cylinder, rigidly connected to the longitudinal support 5, on which there is a transverse support 2. The latter is connected to the cylinder rod. Oil from the lower cavity of the cylinder, through the slot 7 located in the piston, enters the upper cavity of the cylinder, and then into the follower spool 9 and to the drain. The follower spool is structurally connected to the caliper. Probe 4 of spool 9 is pressed against copier 3 (in area ab) using a spring (not shown in the diagram).
In this position of the dipstick, oil flows through spool 9 to the drain, and transverse support 2, due to the difference in pressure in the lower and upper cavities, moves back. At the moment when the probe is in area be, it is recessed under the action of the copier, overcoming the resistance of the spring. In this case, the oil drain from spool 9 is gradually blocked. Since the cross-sectional area of the piston in the lower cavity is larger than in the upper cavity, oil pressure will force caliper 2 to move down. In practice, there are a variety of models of lathes and screw-cutting lathes, from tabletop to heavy-duty ones, with a wide range of sizes. The largest processing diameter on Soviet machines ranges from 85 to 5000 mm with a workpiece length from 125 to 24,000 mm.
Goal of the work
1. Introduction to methods of processing conical surfaces on lathes.
2. Analysis of the advantages and disadvantages of methods.
3. Choosing a method for manufacturing a conical surface.
Materials and equipment
1. Screw-cutting lathe model TV-01.
2. The necessary set of wrenches, cutting tools, protractors, calipers, blanks for manufactured parts.
Work order
1. Read carefully the basic information on the topic of work and understand the general information about conical surfaces, methods of processing them, taking into account the main advantages and disadvantages.
2. With the help of the training wizard, familiarize yourself with all the methods of processing conical surfaces on a screw-cutting lathe.
3. Complete the teacher’s individual assignment on choosing a method for manufacturing conical surfaces.
1. Title and purpose of the work.
2. Diagram of a straight cone indicating the main elements.
3. Description of the main methods of processing conical surfaces with diagrams.
4. Individual assignment with calculations and justification for the choice of one or another processing method.
Basic provisions
In technology, parts with external and internal conical surfaces are often used, for example, bevel gears, rollers of tapered bearings. Tools for making holes (drills, countersinks, reamers) have shanks with standard Morse tapers; machine spindles have a tapered boring for the shanks of tools or mandrels, etc.
Machining parts with a conical surface involves the formation of a cone of rotation or a truncated cone of rotation.
Cone is the body formed by all the segments connecting some fixed point with the points of the circle at the base of the cone.
The fixed point is called the top of the cone.
A segment connecting a vertex and any point on a circle is called forming a cone.
Cone axis, is called the perpendicular connecting the vertex of the cone with the base, and the resulting straight segment is cone height.
The cone is considered direct or cone of rotation, if the axis of the cone passes through the center of the circle at its base.
A plane perpendicular to the axis of a straight cone cuts off a smaller cone from it. The remaining part is called truncated cone of revolution.
A truncated cone is characterized by the following elements (Fig. 1):
1. D And d – diameters of both the larger and smaller bases of the cone;
2. l – height of the cone, distance between the bases of the cone;
3. cone angle 2a – the angle between two generatrices lying in the same plane passing through the axis of the cone;
4. cone angle a – the angle between the axis and the generatrix of the cone;
5. slope U– slope angle tangent Y = tg a = (D –d)/(2l) , which is indicated by a decimal fraction (for example: 0.05; 0.02);
6. taper – determined by the formula k = (D –d)/l , and is indicated using a division sign (for example, 1:20; 1:50, etc.).
The taper is numerically equal to twice the slope.
Before the dimensional number that determines the slope, the sign Р is applied , the acute angle of which is directed towards the slope. Before the number characterizing the taper, a sign is applied, the acute angle of which should be directed towards the top of the cone.
In mass production on automatic machines for turning conical surfaces, copy rulers are used for one constant angle of inclination of the cone, which can only change when the machine is readjusted with another copy ruler.
In single and small-scale production on CNC machines, turning of conical surfaces with any cone angle at the apex is carried out by selecting the ratio of longitudinal and transverse feed rates. On non-CNC machines, conical surfaces can be machined in four ways, listed below.
