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General information about cones
The conical surface is characterized by the following parameters (Fig. 4.31): smaller d and larger D diameters and the distance l between the planes in which the circles with diameters D and d are located. Angle a is called the angle of inclination of the cone, and angle 2α is called the angle of the cone.
The ratio K= (D - d)/l is called taper and is usually indicated with a division sign (for example, 1:20 or 1:50), and in some cases with a decimal fraction (for example, 0.05 or 0.02).
The ratio Y= (D - d)/(2l) = tgα is called slope.
Methods for processing conical surfaces
When processing shafts, transitions between surfaces that have a conical shape are often encountered. If the length of the cone does not exceed 50 mm, then it can be processed by plunging wide cutter. The angle of inclination of the cutting edge of the cutter in the plan must correspond to the angle of inclination of the cone on the machined part. The cutter is given a transverse feed motion.
To reduce the distortion of the generatrix of the conical surface and reduce the deviation of the angle of inclination of the cone, it is necessary to set the cutting edge of the cutter along the axis of rotation of the workpiece.
It should be borne in mind that when processing a cone with a cutter with cutting edge with a length of more than 15 mm, vibrations can occur, the level of which is higher, the longer the workpiece is, the smaller its diameter, the smaller the angle of inclination of the cone, the closer the cone is to the middle of the part, the greater the overhang of the cutter and the lower the strength of its fastening. As a result of vibrations, traces appear on the treated surface and its quality deteriorates. When machining hard parts with a wide cutter, there may be no vibration, but at the same time, the cutter may be displaced under the action of the radial component of the cutting force, which leads to a misconfiguration of the cutter to the required angle of inclination. (Cutter offset depends on the machining mode and feed direction.)
Conical surfaces with large slopes can be processed by turning the upper slide of the caliper with a tool holder (Fig. 4.32) by an angle α, equal to the angle inclination of the processed cone. The cutter is fed manually (with the handle for moving the upper slide), which is a disadvantage of this method, since the uneven manual feed leads to an increase in the roughness of the machined surface. In this way, conical surfaces are processed, the length of which is commensurate with the stroke length of the upper slide.
A conical surface of great length with an angle α= 8 ... 10° can be machined when the tailstock is displaced (Fig. 4.33)
At small angles sinα ≈ tgα
h≈L(D-d)/(2l),
where L is the distance between the centers; D - larger diameter; d - smaller diameter; l is the distance between the planes.
If L = l, then h = (D-d)/2.
The displacement of the tailstock is determined by the scale printed on the end face of the base plate from the flywheel side, and the risk on the end face of the tailstock housing. The division value on the scale is usually 1 mm. In the absence of a scale on the base plate, the offset of the tailstock is measured using a ruler attached to the base plate.
To ensure the same taper of a batch of parts processed in this way, it is necessary that the dimensions of the workpieces and their center holes had minor deviations. Since misalignment of the machine centers causes wear of the center holes of the workpieces, it is recommended to machine the conical surfaces first, then correct the center holes, and then finish finishing. To reduce the breakdown of the center holes and the wear of the centers, it is advisable to carry out the latter with rounded tops.
Quite common is the processing of conical surfaces using copiers. A plate 7 is attached to the machine frame (Fig. 4.34, a) with a copy ruler 6, along which the slider 4 moves, connected to the caliper 1 of the machine by a rod 2 using a clamp 5. For free movement of the caliper in the transverse direction, it is necessary to disconnect the screw of the transverse feed movement. With the longitudinal movement of the caliper 1, the cutter receives two movements: longitudinal from the caliper and transverse from the copier ruler 6. The transverse movement depends on the angle of rotation of the copier ruler 6 relative to the axis 5 of rotation. The angle of rotation of the ruler is determined by the divisions on the plate 7, fixing the ruler with bolts 8. The movement of the cutter to the cutting depth is performed by the handle for moving the upper caliper slide. The outer conical surfaces are machined with through cutters.
Methods for processing internal conical surfaces
The processing of the inner conical surface 4 of the workpiece (Fig. 4.34, b) is carried out according to the copier 2 installed in the tailstock quill or in the turret of the machine. In the tool holder of the transverse caliper, fixture 1 is installed with a copy roller 3 and a pointed through cutter. With the transverse movement of the support, the cam roller 3, in accordance with the profile of the cam 2, receives a longitudinal movement, which is transmitted to the cutter through the device 1. Internal conical surfaces are machined with boring cutters.
For getting tapered bore in a solid material, the workpiece is first pre-treated (drilled, bored), and then finally (deployed). Deployment is performed sequentially with a set conical reamers. Pre-diameter drilled hole 0.5 ... 1 mm less than the lead diameter of the reamer.
If a tapered bore is required high precision, then it is processed with a conical countersink before deployment, for which a hole with a diameter of 0.5 mm less than the diameter of the cone is drilled in a solid material, and then a countersink is used. To reduce the allowance for countersinking, step drills of different diameters are sometimes used.
Center hole machining
In parts such as shafts, center holes are often made, which are used for subsequent turning and grinding of the part and for restoring it during operation. Based on this, the centering is performed especially carefully.
The center holes of the shaft must be on the same axis and have the same conical holes at both ends, regardless of the diameters of the end journals of the shaft. If these requirements are not met, the machining accuracy decreases and the wear of centers and center holes increases.
The designs of the center holes are shown in fig. 4.35. Most widespread have center holes with a cone angle of 60°. Sometimes in heavy shafts this angle is increased to 75 or 90°. In order for the top of the center not to rest against the workpiece, cylindrical recesses with a diameter d are made in the center holes.
To protect against damage, reusable center holes are made with a safety chamfer at an angle of 120 ° (Fig. 4.35, b).
Various methods are used to machine center holes in small workpieces. The workpiece is fixed in a self-centering chuck, and a drilling chuck with a centering tool is inserted into the tailstock quill. Center holes large sizes they are processed first with a cylindrical drill (Fig. 4.36, a), and then with a single-toothed (Fig. 4.36, b) or multi-toothed (Fig. 4.36, c) countersink. Center holes with a diameter of 1.5 ... 5 mm are processed with combined drills without a safety chamfer (Fig. 4.36, d) and with a safety chamfer (Fig. 4.36, e).
Center holes are processed with a rotating workpiece; the feed movement of the centering tool is carried out manually (from the tailstock flywheel). The end, in which the center hole is processed, is pre-cut with a cutter.
Required size The center hole is determined by the deepening of the centering tool, using the tailstock flywheel dial or the quill scale. To ensure the alignment of the center holes, the part is pre-marked, and long parts are supported with a steady rest during centering.
Center holes are marked with a square.
After marking, the center hole is punched. If the diameter of the shaft neck does not exceed 40 mm, then it is possible to punch the center hole without preliminary marking using the device shown in fig. 4.37. The body 1 of the fixture is installed with the left hand on the end of the shaft 3 and the center of the hole is marked with a hammer blow on the center punch 2.
If during operation the conical surfaces of the center holes were damaged or unevenly worn, then they can be corrected with a cutter. In this case, the upper carriage of the caliper is rotated by the angle of the cone.
Control of conical surfaces
The taper of the outer surfaces is measured with a template or universal goniometer. For more accurate measurements, sleeve gauges are used (Fig. 4.38), with the help of which not only the angle of the cone is checked, but also its diameters. Two or three risks are applied to the machined surface of the cone with a pencil, then a gauge-sleeve is put on the measured cone, slightly pressing on it and turning it along the axis. With a correctly executed cone, all risks are erased, and the end of the conical part is between marks A and B.
When measuring conical holes, a plug gauge is used. The correctness of the processing of a conical hole is determined (as in the measurement of external cones) by the mutual fit of the surfaces of the part and the plug gauge. If a thin layer paint applied to the plug gauge will be erased at a small diameter, then the cone angle in the part is large, and if large diameter- the angle is small.
Center hole machining. Control of conical surfaces
Center hole machining. In parts such as shafts, it is often necessary to make center holes, which are used for subsequent processing of the part and for restoring it during operation. Therefore, the alignment is carried out especially carefully. The center holes of the shaft must be on the same axis and have the same dimensions at both ends, regardless of the diameters of the shaft end journals. If these requirements are not met, the machining accuracy decreases and the wear of centers and center holes increases. The designs of the center holes are shown in Figure 40, their dimensions are in the table below. The most common are center holes with a cone angle of 60 degrees. Sometimes in heavy shafts this angle is increased to 75 or 90 degrees. In order for the top of the center not to rest against the workpiece, cylindrical recesses with a diameter d are made in the center holes. To protect against damage, reusable center holes are made with a safety chamfer at an angle of 120 degrees (Figure 40 b).
Rice. 40. Center holes
| Workpiece diameter | The smallest diameter of the end neck of the shaft Do, mm | Nominal center hole diameter d | D no more | l at least | a |
| Over 6 to 10 | 6,5 | 1,5 | 1,8 | 0,6 | |
| Over 10 to 18 | 2,0 | 2,4 | 0,8 | ||
| Over 18 to 30 | 2,5 | 0,8 | |||
| Over 30 to 50 | 7,5 | 3,6 | 1,0 | ||
| Over 50 to 80 | 4,8 | 1,2 | |||
| Over 80 to 120 | 12,5 | 1,5 |
Figure 41 shows how the rear center of the machine wears out when the center hole is not made correctly in the workpiece. With misalignment (a) of the center hole and misalignment (b) of the centers, the part is based with a misalignment during processing, which causes significant errors in the shape of the outer surface of the part. Center holes in small workpieces are machined various methods. The workpiece is fixed in a self-centering chuck, and a drilling chuck with a centering tool is inserted into the tailstock quill.
Rice. 41. Wear of the rear center of the machine
Center holes with a diameter of 1.5-5 mm are processed with combined center drills without a safety chamfer (Figure 42d) and with a safety chamfer (Figure 41d on the right).
Center holes of large sizes are processed first with a cylindrical drill (Figure 41a on the right), and then with a single-toothed (Figure 41b) or multi-toothed (Figure 41c) countersink. Center holes are processed with a rotating workpiece; the centering tool is fed manually (from the tailstock flywheel). The end face in which the center hole is processed is pre-cut with a cutter. The required size of the center hole is determined by the deepening of the centering tool, using the tailstock flywheel dial or the quill scale. To ensure the alignment of the center holes, the part is pre-marked, and during centering it is supported with a steady rest.
Rice. 41. Drills for the formation of center holes
Center holes are marked with a marking square (Figure 42a). Pins 1 and 2 are located at an equal distance from the edge of the AA elbow. Putting a square on the end and pressing the pins to the neck of the shaft, along the edge of the AA, draw a risk on the end of the shaft, and then, turning the square by 60-90 degrees, draw the next risk, etc. The intersection of several scratches will determine the position of the center hole on the end of the shaft. For marking, you can also use the square shown in Figure 42b. After marking, the center hole is punched. If the diameter of the shaft neck does not exceed 40 mm, then it is possible to punch the center hole without preliminary marking using the device shown in Figure 42c. The body 1 of the fixture is installed with the left hand on the end of the shaft 3 and the center of the hole is marked with a hammer blow on the center punch 2. If during operation the conical surfaces of the center holes were damaged or unevenly worn, then it is allowed to correct them with a cutter; in this case, the upper carriage of the caliper is rotated by the angle of the cone.
Rice. 42. Marking the center holes
Control of conical surfaces. The taper of the outer conical surfaces is measured with a template or a universal goniometer. For more accurate measurements, sleeve gauges are used, Figure d) and e) on the left, with the help of which not only the angle of the cone is checked, but also its diameters. 2-3 risks are applied to the treated surface of the cone with a pencil, then a gauge-sleeve is put on the measuring cone, slightly pressing on it and turning it along the axis. With a correctly made cone, all risks are erased, and the end of the conical part is between marks A and B of the sleeve gauge. When measuring conical holes, a plug gauge is used. The correctness of the processing of a conical hole is determined (as in the measurement of external cones) by the mutual contact of the surfaces of the part and the plug gauge. If the risks drawn with a pencil on the plug gauge are erased at a small diameter, then the angle of the cone in the part is large, and if at a large diameter, the angle is small.
Tapered surfaces can be processed in several ways: with a wide cutter, with the upper slide of the caliper turned, with the tailstock body displaced, with the help of a tapered ruler and with the help of special copying devices.
Processing of cones with a wide cutter. Conical surfaces 20-25 mm long are processed with a wide cutter (Fig. 151, a). To obtain the required angle, an installation template is used, which is applied to the workpiece, and to its inclined working surface bring up the cutter. Then the template is removed and the cutter is brought to the workpiece (Fig. 151.6). Processing of cones with the upper slide of the caliper turned (Fig. 152, a, b). The rotary plate of the upper part of the caliper can be rotated relative to the cross slide of the caliper in both directions; To do this, you need to release Guy-
152 PROCESSING OF TAPERED AT - " SURFACES (CONES) WITH THE TOP CALIPER SLIDE TURNED:
Ki screws fixing the PLATE. The control of the angle of rotation with an accuracy of one degree is carried out according to the divisions of the rotary plate.
Advantages of the method: the possibility of processing cones with any angle of inclination; ease of machine setup. The disadvantages of the method: the impossibility of processing long conical surfaces, since the length of processing is limited by the stroke length of the upper support (for example, for a 1KG2 machine, the stroke length is 180 mm); turning is performed by manual feed, which reduces productivity and degrades the quality of processing.
When processing with the upper part of the caliper turned, the feed can be mechanized using a device with a flexible shaft (Fig. 153). Flexible shaft 2 receives rotation from the lead screw or from the machine shaft through bevel or helical gears.
(IK620M, 163, etc.) with a mechanism for transferring rotation to the screw of the upper part of the caliper. On such a machine, regardless of the angle of rotation of the upper caliper. you can get automatic feed.
If the outer conical surface of the shaft and the inner conical surface of the sleeve are to be mated, then the taper of the mating surfaces must be the same. To ensure the same taper, the processing of such surfaces is performed without readjusting the position of the upper part of the caliper (Fig. 154 a, b). At the same time, a boring cutter with a head bent to the right of the rod is used to process the taper hole, and the spindle is rotated in reverse.
Adjustment of the rotary plate of the upper part of the caliper to the desired angle of rotation is carried out using an indicator according to a pre-fabricated reference part. The indicator is fixed in the tool holder, and the tip of the indicator is set exactly in the center and brought to the conical surface of the standard near the smaller section, while the indicator needle is set to "zero"; then the caliper is moved so that the indicator pin touches the workpiece, and the needle is at zero all the time. The position of the caliper is fixed with clamping nuts.
Machining of conical surfaces by shifting the tailstock. Long external tapered surfaces are machined by offsetting the tailstock body. The workpiece is installed in the centers. The body of the tailstock with the help of a screw is displaced in the transverse direction so that the workpiece becomes “skewed”. When turned on
Feeding the carriage of the caliper, the cutter, moving parallel to the axis of the spindle, will grind the conical surface.
The displacement value H of the tailstock body is determined from the LAN triangle (Fig. 155, a):
H \u003d L sin a. It is known from trigonometry that for small angles (up to 10 °) the sine is practically equal to the tangent of the angle. For example, for an angle of 7°, the sine is 0.120 and the tangent is 0.123.
As a rule, workpieces with small slope angles are processed by the tailstock displacement method, so we can assume that sina = tga. Then
Ig. g D-d L D-d
And \u003d L tg a ~ L ------------- \u003d ----- MM.
Tailstock offset by ±15 mm is allowed.
Example. Determine the amount of displacement of the tailstock for turning the workpiece shown in fig. 155.6 if L=600 mm /=500 mm D=80 mm; d=60 mm.
I=600----===600 ■_______=12mm.
The amount of displacement of the body of the tailstock relative to the plate is controlled by divisions at the end of the plate or with the help of a limb cross feed. To do this, a bar is fixed on the tool holder, which is brought to the tailstock quill, while the position of the limb is fixed. Then the cross slide is retracted to calculated value limbo, and then tailstock displaced until it comes into contact with the bar.
The adjustment of the machine for turning cones by shifting the tailstock can be performed according to the reference part. To do this, the reference part is fixed in the centers and the tailstock is displaced, controlling the parallelism of the generatrix of the reference part to the feed direction with the indicator. For the same purpose, one can use
1 55 PROCESSING OF THE EXTERNAL CONIC - SURFACES (CONES) BY THE METHOD OF OFFSETTING THE TAILSTOCK:
Use a cutter and a strip of paper: the cutter is in contact with the conical surface along a smaller and then along a larger diameter so that a strip of paper is pulled between the cutter and this surface with some resistance (Fig. 156).
According to the law of conservation of energy, the energy expended on the cutting process cannot disappear: it turns into another form - into thermal energy. The heat of cutting occurs in the cutting zone. In the process of cutting more ...
A feature of modern technical progress is automation based on the achievements of electronic technology, hydraulics and pneumatics. The main directions of automation are the use of tracking (copier) devices, automation of machine control and control of parts. Automatic control …
>>Technology: Production of cylindrical and conical parts hand tool
Cylindrical parts, which in cross section have the shape of a circle of constant diameter, can be made from square bars. Bars are usually sawn out of boards (Fig. 22, a). The thickness and width of the bar should be 1 ... 2 mm more than the diameter of the future product, taking into account the allowance (reserve) for processing.
Before manufacturing a round part from a bar, it is marked out. To do this, at the ends of the workpiece, the center is found by crossing the diagonals and a circle is drawn around it with a compass with a radius equal to 0.5 of the diameter of the workpiece (Fig. 22, b). Tangent to the circle, from each end, with the help of a ruler, draw the sides of the octahedron and outline with a thickness gauge lines 1 of the cut edges of width B on the sides of the workpiece.
The workpiece is fixed on the cover of the workbench between the wedges or installed in special device(prism) (Fig. 22, e).
The edges of the octahedron are cut with a sherhebel or planer to the marking lines of the circle (Fig. 22, c). Once again, tangents to the circle are drawn, lines 2 are drawn along the ruler and the faces of the hexagon are cut off (Fig. 22, d).
Further processing is carried out across the fibers with a rounding of the shape, first with a rasp, and then with files with finer notches (Fig. 22, e).
The cylindrical surface is finished with sandpaper. In this case, one end of the workpiece is fixed in the clamp of the workbench, and the other is covered with sandpaper and rotated. Sometimes the workpiece is wrapped with sandpaper, clasped with the left hand, and rotated with the right hand and moved along its axis of rotation (Fig. 22, f). Similarly, the workpiece is ground from the other end.
The diameter of the part is measured with a caliper first on the part (Fig. 23, a), and then it is checked with a ruler (Fig. 23, b). 
The sequence of all these operations when obtaining a cylindrical billet from a square bar can be recorded in the route map. In this map, the sequence (route, path) of processing one part is recorded. Table 2 shows a route map for the manufacture of a handle for a shovel.
On fig. 24 shows a drawing of a handle for a shovel. 
Practical work
Product manufacturing cylindrical shape
1. Develop a drawing and draw up a route map for the manufacture of a cylindrical or conical product, for example, shown in fig. eleven.
2. Mark out and make a handle for a shovel according to (Fig. 24) and a route map (Table 2).
♦ Caliper, route map.
1. What is the sequence for manufacturing a cylindrical and conical part?
2. How to measure the diameter of a part with a caliper?
3. What is recorded in the route technological map?
Simonenko V.D., Samorodsky P.S., Tishchenko A.T., Technology Grade 6
Submitted by readers from the website
The processing of conical surfaces on lathes is performed different ways: by turning the upper part of the caliper; displacement of the tailstock body; turning the conical ruler; wide cutter. The use of one or another method depends on the length of the conical surface and the angle of the cone.
Machining the outer cone by turning the upper slide of the caliper is advisable in cases where it is necessary to obtain a large cone slope angle with a relatively small length. The largest length of the generatrix of the cone should be somewhat less than the stroke of the carriage of the upper caliper. Processing the outer cone by shifting the body of the tailstock is convenient for obtaining long gentle cones with a small slope angle (3 ... 5). To do this, the body of the tailstock is shifted in the transverse direction from the line of machine centers along the guides of the base of the headstock. The workpiece to be processed is fixed between the centers of the machine in a driving chuck with a collar. Processing of cones using a cone (copy) ruler, fixed on the back of the bed lathe on a plate, used to obtain a gentle cone of considerable length. The workpiece is fixed 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.
The processing of 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 \u003d K / 2 \u003d (D - d) / (2l) \u003d tg
d) larger cone diameter D = Kl + d = 2ltg
e) smaller cone diameter d = D-- K1 = D--2ltg
e) the length of the cone l \u003d (D - d) K \u003d (D - d) / 2tg
The processing of internal conical surfaces on lathes is also performed in various ways: with a wide cutter, turning the upper part (sled) of the caliper, turning the conical (copy) 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 requirements are not imposed 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.
