A shaped cutter for a ball is an example of designing. Design of shaped cutters
Shaped cutters are used for processing both internal and external shaped surfaces and there are various varieties. They are used in mass, serial, and even in single production.
According to the principle of operation: radial and tangential. By design, radial shaped cutters are of three types: disk, or round; prismatic and rod. For core and prismatic cutters, the working tool is often made of high-speed steel, and the holder is made of structural steel. In addition, to save high-speed steel, the cutting part is welded.
The widespread use of round shaped cutters is explained by the relative simplicity of their manufacture and durability (it is allowed a large number of regrinding).
Recently, in the processing of hard-to-cut materials, carbide cutters have been used, despite the complexity of their sharpening, especially complex profiles.
The dimensions of the working part and the height of the profile of the cutting part of the tools will be equal to the corresponding dimensions and height of the profile of the machined part, if the angles α And γ are equal to zero. However, such geometric parameters are practically not used, because cutting in this case is almost impossible. Shaped cutters are sharpened and set so as to provide a positive front and back angle. The rake angle, both for the prismatic and for the round cutter, is provided by sharpening. The back angle of a round one is created by shifting the center of the cutter by an amount h p, while the prismatic one has its slope. See fig.
In practice, cutters with a parallel axis relative to the workpiece have become widespread. The inclined arrangement of the axis is used in cases where the configuration of the part in certain sections of the profile does not provide the minimum required clearance angles in a parallel arrangement.
Part profile measured along the axis ( l 1 , l 2 , …l n), exactly corresponds to the profile of the cutter, with the axis parallel to the workpiece. To fulfill the required height and shape of the profile, the corresponding correction calculations of the profile of the tools are made.
There are two ways: graphical and analytical. Graphic - is performed according to the rules of projection drawing and is described in [ Nefedov N. A. Tasks for the design of cutting tools / N. A. Nefedov, K. A. Osipov. - L .: Mashinostroenie, 1990. - 328 p.]. Then you can also use KOMPAS.
STAGES OF DESIGNING SHAPED CUTTER
The design of shaped cutters consists of the following main stages:
1) preparation of a drawing of a part for the calculation of a shaped cutter;
2) choice of cutter type;
3) determination of the angles of the cutting part and the angles of installation of the cutter;
4) determination of the overall and connecting dimensions of the cutter;
5) calculation of cutter profile dimensions (cutter correction calculation);
6) calculation of tolerances for profile dimensions, sharpening angles and cutter installation;
7) registration of the working drawing of the cutter;
8) designing a template to control the profile of the cutter during its manufacture and a counter-template to check the template;
9) designing a holder for mounting the cutter on the machine.
Preparation of a detail drawing for the calculation of a shaped cutter. To calculate the dimensions of the cutter profile, you must specify the calculated or theoretical dimensions of the part. In order to make it easier to obtain each size within its tolerance field when processing a part, its average dimensions are taken as the theoretical dimensions of the part. For example, given a shaft with a diameter 
. Then the average size of the shaft diameter in the tolerance field will be 49.934, and the calculated value of the radius will be 24.967. If the size is on the drawing without a tolerance, then it is taken according to 10 ... 11 qualifications of accuracy; the deviation sign in this case is "+" for female dimensions, "-" for male ones, "+" for other dimensions. As a rule, the longitudinal dimensions of the profile and the radii of the arc sections are taken with deviations "±", therefore, their nominal values can be taken as the calculated dimensions.
The greatest difficulty is the determination of the radii of the intermediate points of the arc sections. In this case, according to the given theoretical dimensions D 1 , D 2 , L, R, and lengths l 2 , l 3 , …l 6 , (Fig.) find the radii of points 2...6, i.e. r 2 , r 3 , … r 6. In some cases, it is also necessary to determine the smallest radius r min point M. To solve these questions, you first need to find the coordinates of the center of the circle l 0 and r 0 , which is produced by trigonometric dependencies.
In the event that high precision machining of the part is not required, the determination of such dimensions can be carried out graphically (by drawing a profile on a sufficiently large scale). It is also recommended to check the results graphically during the analytical calculation in order to avoid gross errors.
The solution to the issue of additional blades of the shaped cutter is due to the fact that often shaped cutters, in addition to processing a given profile, also chamfer the end of the part and cut a groove to facilitate the work of the cutting cutter (Fig. 3.10). Groove diameter D must not be less than the smallest diameter of the part D min and depends on the rigidity of the part and its configuration. In other words, the cutting edge for parting off should not protrude beyond the working profile of the cutter. Size b is made somewhat larger or equal to the width of the cutting tool, the angle φ = 15...20°. In the future, when designing the cutter, the entire profile is taken into account along with additional blades. To avoid rubbing the back surface of the cutting blade, its “C” point should be located below all points of the cutter profile.
Selecting the type of shaped cutter. In production conditions, usually when designing shaped cutters, the drawing of the part is the initial data. When choosing the type of shaped cutter for its processing, the following considerations are guided.
Prismatic shaped cutters are used only for external processing. The high rigidity of their fastening in holders with the help of a dovetail allows you to work with high feeds or process longer profiles with increased requirements for dimensional accuracy and the profile of the machined part.
Core cutters are used in single-piece and small-scale production of parts, as they allow a small number of regrindings and require adjustment in height with the help of linings after each regrinding. In other cases, round (disk) cutters are used. They allow a greater number of regrindings and are more technologically advanced in manufacturing. In addition, round shaped cutters process internal shaped surfaces.
More often, radial type cutters are used, since most machines have calipers with the cutter set along the height of the part axis. Tangential type cutters can be used with a small depth of the shaped profile of the part (t max< 0,12D), однако, надо учитывать возможности размещения и закрепления такого резца на суппорте станка. Важным достоинством тангенциального резца является возможность обработки деталей разного диаметра с одинаковыми фасонными профилями и постепенное врезание и выход резца, что ведет к уменьшению усилий резания и позволяет обрабатывать нежесткие детали, с точностью до 0,03 мм на диаметр. Однако производительность обработки при их использовании ниже, чем при работе резцов радиального типа.
Double rake cutters when λ and γ ≠ 0 are used in the processing of profiles with a conical section of increased accuracy.
Cutters with a special setting (with a deployed mounting base or an inclined body) serve to improve the conditions for processing the end sections of the part profile, since this increases the clearance angle α N . The rotation of the base by the angle ψ is applied to all incisors; lateral inclination of the body at an angle α b - usually for prismatic incisors. Lateral tilt is more profitable than base reversal, as it reduces the dimensions of the holder and increases its rigidity compared to the holder at ψ ≠ 0. When internal processing to increase the corners α N screw cutters are also used on end blades.
Round incisors are often made mounted; with small dimensions of the cutter (usually for internal processing), tail cutters are used. Round cutters, as a rule, are made of solid high-speed steel, and large prismatic cutters are made brazed or welded. The material of the cutting part of the cutter is selected taking into account the conditions of its operation (material of the part, expected cutting conditions, rigidity of the technological system).
Determining the angles of the cutting part. The cutter angles γ and α are set at the most protruding (base) point, which is set for radial cutters at the height of the part axis, in the section by a plane perpendicular to the base of the cutter attachment. For a cutter with a lateral inclination of the body (α b ≠ 0), these angles are set in a section perpendicular to the axis of the workpiece. According to the recommendations, the following values of the front angles of the shaped cutters are taken (Table 3.3).
The rear angle of prismatic incisors can be made larger than that of round incisors. Usually α = 8...12° for round and 10...15° for prismatic incisors. It should be borne in mind that the back angles are variable at different points on the edge. In a section normal to the projection of the cutting edge onto the main plane, they can be much less than the nominal value in some areas. Therefore, it is necessary to check the minimum value of the back angle according to the formula:
where α T is the rear angle at a given point in the end section; φ is the angle between the tangent to the profile of the part at a given point and the end plane of the part; D And Dx - respectively, the largest diameter and diameter of the cutter at the point x; for prismatic cutters D/D x = 1. The angle α N must not be less than 3°.
On sections of the blades perpendicular to the base of the cutter, undercuts are usually made at an angle φ 1 to 3...4° (fig.3.11).
In the case of designing a cutter with an angle λ ≠ 0, the angle of the lateral inclination of the front surface, λ 0 is calculated depending on the selected position of the base line (blade section, set along the height of the part axis) by the formula: tgλ 0 = tgσ sin γ,
where σ is the angle between the baseline and the axis of the part. The formula is only suitable for conventional cutters.
Determination of the overall and connecting dimensions of the cutter. Usually, the overall and connecting dimensions of the cutters are determined from design considerations, depending on the depth of the shaped profile of the product tmax and the length of the profile L.
The overall radius of the disc cutters is determined by the formula:
,
Where e - the depth of sharpening along the front surface, necessary for the placement of chips; TO - the thickness of the body of the cutter, necessary to ensure its strength, K = 8... 10 mm: d0 - bore diameter.
Quantities e And d0 are chosen depending on t max according to the table. 3.4.
Largest cutter diameter D H = 2R rounded up to values from the normal series of linear dimensions according to GOST 6636-69.
The design dimensions of the cutter (Figure 3.12) can be selected depending on the depth of the product profile. Diameter D H usually 6...8 times the depth of the profile. Such data are shown in Table 3.5.
On the right side of the cutter, a flange with corrugations is made to transmit torque and to rotate the cutter by 1/z after its regrinding and setting its top at a distance h p (Fig. 3.13) from the horizontal axis of the cutter. If the removed layer during regrinding does not correspond to the rotation of one corrugation, then the cutter receives an additional rotation using the holder's adjusting worm. The number of corrugated teeth z = 32...34. Their profile angle in normal section is 90°. For the constancy of the length of the platform at the top of the teeth, the bottom of the depressions between the teeth is placed to the end of the bead at an angle β: tgβ = π/z (see Fig. 3.12). Detailed information about the end teeth of the corrugations is given in.
To simplify the manufacture of round shaped cutters, its right side is made without a collar, but on this side a hole is drilled for a cylindrical pin belonging to a corrugated washer, corresponding in size and purpose to the cutter collar described above.
Overall and connecting dimensions of prismatic shaped cutters (see Fig. 3.11) are presented in Table. 3.6.
The length of the cutter profile is determined depending on the dimensions of the part profile, taking into account additional blades and is rounded up in accordance with the normal series standard sizes according to GOST 6636-69.
With a width L exceeding 2.5 A, it is allowed to use larger shanks from the table. 3.6.
In the absence of rollers with diameters d shown in the table, use the available rollers, size M while it is calculated according to the formula:
M \u003d A + d (1 + ctg λ / 2) - 2E ctg λ, Where λ \u003d 60 ° (Fig. 3.11, a).
Determination of the shape and dimensions of the profile of the working part of a prismatic shaped cutter. Let the contour of the shaped part be given by the nodal points 1 , 2 , 3 , 4 and one of the intermediate points - 5 , and the axial distances between them l 1,l 2,l 3,l 4, and the radii r1,r2,r3,r4, are specified by the drawing (see Fig. ↓). Based on the properties of the material being processed, we assign the value of the front angle γ (see Table 3.3) and draw from the point 1 at this angle, the trace of the front surface, which will intersect the profile of the part at points 1, 2/3, 4 And 5.
Let us take for an arbitrary coordinate axis a straight line passing through the first nodal point 1 (usually the first number indicates the point corresponding to the smallest radius of the part r1) at an angle α to the cutting plane at that point. Then the purpose of correction calculations is to calculate the distance from the rectilinear generatrix of the point 1 to parallel to it rectilinear generators of the back surface of the cutter, drawn through the nodal points 2/3, 4 and 5, i.e. sizing R 2/3, R 4 And R 5. To do this, we carry out some additional constructions.
We continue the trace of the front surface of the cutter beyond the point 1 to the left and lower it from the center of the part ABOUT perpendicular OK. In addition, we connect the center ABOUT with dots 1, 2/3, 4 And 5. From the same points we draw straight lines parallel to the segment OK. The distances from these lines to the segment OK denote by the letter A with the corresponding index of each anchor point. After that, from the points 2/3, 4 And 5 we draw perpendiculars to the back surface of the cutter, as a result of which we obtain a series of right-angled triangles.
From a triangle 1 2/3 A we have: P 2 \u003d C 2 / 3 cos ( α +γ),
Where C2/3 = A 2 – A 1.
From a triangle 2/3 C O leg A 2 = r2 cos ε 2, and the angle ε 2= arc sin ( h/ r 2), Where h = OK.
the value h And A 1 determine from triangle OK1:
h = r1 sinγ; A 1 \u003d r 1 cos γ.
In exactly the same way, one can define the quantities R 4 And R 5 and others for other points of the cutter profile.
In general, all calculation formulas can be represented as:
P n = C n cos(α + γ);
C n \u003d A n - A 1;
A p \u003d r n cosε n;
ε p \u003d arc sin (h / r n).
At λ=0 axial dimensions l 1,l 2,l 3,l 4, the details are not distorted, i.e., they are equal to the distance between the nodal points of the cutter profile.
Thus, according to the dimensions of the detail drawing and the found values R 2/3, R 4 And R 5 ... , R p we build a normal cutter profile.
Initial data:
Part profile, for the processing of which it is required to design a shaped cutter (Fig. 1);
Allowance for processing (indicated in the drawing);
Detail profile tolerance ±0.05 mm;
- material of a detail - steel35.
1.1. Calculation of the average dimensions of the part profile
The average profile dimensions in this example coincide with the nominal dimensions of the part profile, since the profile tolerance is set to b + u, i.e. located symmetrically. Therefore, it is not required to determine the average profile dimensions.
1.2. Selecting the position of the baseline
The specified profile of the part has a relatively small height: h = 4 mm. The cutter edge profile mainly consists of sections parallel to the axis of the part.
The section of the edge, which is the easiest to install the cutter at the level of the machine center line, i.e. in the axial plane of the part, are sections 1-2 and 5-6. Therefore, for a given part profile, the base line of the cutter is taken to be located on the edge sections 1-2 and 5-6 (Fig. 2).
1.3. Calculation of the overall dimensions of the cutter
The width of the cutter L = L children + 2n is calculated (Table 2.5, 2.6, 2.7):
L = 24 + 2 × 3 = 30 mm.
The height (depth) of the part profile q in the direction perpendicular to the axis of the cutter is calculated or determined graphically on an enlarged scale:
The diameter of the mounting hole d 0 is determined.
According to table 2.3 feed S=0.02 mm/rev and cutting force
P z (L \u003d 1mm) \u003d 110H \u003d 11 daN * (Table 2.2).
Then the cutting force P z \u003d P z (L \u003d 1mm) × L \u003d 11 × 30 \u003d 330 daN.
Given the width of the cutter and the fact that the cutting force is small, we accept the cantilever mounting of the mandrel. According to Table 2.1, the bore diameter d0= 27 mm.
The smallest allowable value of the outer diameter of the cutter is calculated
D>d0+2(q+l+m)
Assuming l = 4mm and m = 8mm,
we get
D>27 + 2 (4 + 4 + 8)> 59.
Rounding up to the nearest value according to the standard range of cutter diameters, we accept D = 60 mm.
1.4. Correction calculation of the cutter profile
The geometric parameters of the cutter are selected for sections of the cutting edge
1-2, 5-6, through which the base line passes (Fig. 4).
For the designed cutter, according to Table 2.4, we take the rake angle j = 18° (steel 35; Gb = 85daN/mm^). rear angle L = 12*.
The size of the sheet is calculated, which determines the position of the axis of the cutter relative to the axis of the part (Fig. 5):
hset \u003d R1 sinL;
hset \u003d 30 * sin 12 ° \u003d 30 X 0.20791 \u003d 6.237.
We accept husm = 6.2.
The profile of the cutter in the front plane is calculated. To do this, the profile of the workpiece is drawn. The numbers I, 2, 3, 4, etc. characteristic points of the profile are marked.
The coordinates of the design points of the part profile are calculated based on the performance dimensions of the part:
r1=r2=r5=r6=10 mm; l2=6 mm;
r3=11.4142 mm; l3=6.5858 mm;
r4= 12 mm; l4= 8 mm;
r7 = r8 = 14 mm; l5 = 10 mm;
For calculations, it is more convenient to write down all the equations in the calculation table. 1.1.
Table 1.1,
Note to table. 1.1.
Cz \u003d A3-A1 \u003d 10.96793 - 9.5106 \u003d= 1.47733; C3= 1.477;
C4 \u003d A4-A1 \u003d 11.59536 - 9.5106 \u003d 2.08476; C4 = 2.085;
C7.8 \u003d A7.8-A \u003d 13.65476 - 9.5106 \u003d 4.14416; C7.8 = 4.144.
The cutter profile is calculated in the axial plane (Fig. 6). The calculation is carried out according to the calculation table 1.2.
Table 1.2.
Continuation of Table 1.2,
Note.
Hc \u003d R1 - Rc \u003d 30 - 28.7305 \u003d 1.2695;
H4 \u003d R1 - R4 \u003d 30 - 28.214 \u003d I, 786;
H7.8= R1- R7 = 30 - 26.492 = 3.508.
1.5 Analysis of the front and back angles of the cutting part of the cutter
The calculation of the values of the front angles gx and rear angles ax at various points of the cutting edge of the cutter in a plane perpendicular to and osd of the cutter is made in the calculation table. 1.3.
Table 1.3.
The calculation of the values of the rear angles axn at the points of the cutting edge of the cutter in a plane perpendicular to the section of the edge under consideration is carried out according to the calculated tya.1.4.
Table 1.4
| N design point | tg ax | g°x | sin gx | tgaxn = tgax singx | axn |
| 0,212557 | 0,212557 | 12° | |||
| 0,212557 | 0,212557 | 12° | |||
| 2¢ | 0,212557 | 0° | |||
| 0,282317 | 0,707107 | tgasn = 0.282317 * * 0.707107 = = 0.199628 | 11°17¢42² | ||
| 0,309456 | 0,309456 | 17°11¢42² | |||
| 0,309456 | 0,212557 | 12° | |||
| 5¢ | 0,212557 | 0° | |||
| 0,212557 | 0,212557 | 12° | |||
| 6¢ | 0,707007 | tga6¢n = 0.212557 * * 0.707107 = = 0.151301 | 8°36¢13² | ||
| 7¢ | 0,39862 | 0,707107 | tga7¢n = 0.39862 * * 0.707107 = = 0.281867 | 15°44¢29² | |
| 0,39862 | 0,39862 | 21°44¢09² | |||
| 0,39862 | 0,39862 | 21°44¢09² |
The calculation of the values of the limiting angles gxn at the points of the cutting edge of the cutter in a plane perpendicular to the considered section of the edge is made according to the calculation table 1.5.
Table 1.5.
| N design point | gx | tg gx | sin jx | tg gXN = tg gxsin jx | gXN |
| 18° | 0,32490 | 0,32490 | 18° | ||
| 18° | 0,32490 | 0,32490 | 18° | ||
| 2¢ | 18° | 0,32490 | 0° | 0° | |
| 15°42¢28² | 0,281234 | 0,707107 | tgg3N = 0.281234 * * 0.717101 = = 0.198862 | 11°14¢50² | |
| 14°55¢22² | 0,266505 | 0,266505 | 14°55¢22² | ||
| 18° | 0,324920 | 0,324920 | 18° | ||
| 5¢ | 18° | 0,324920 | 0° | ||
| 18° | 0,324920 | 0,324920 | 18° | ||
| 6¢ | 18° | 0,324920 | 0,707107 | tg gGN = 0.32492 * * 0.707107 = = 0.229753 | 12°56¢22² |
| 7¢ | 12°45¢01² | 0,226282 | 0,707107 | tg giN = 0.226282 * 0.707107 = = 0.160006 | 9°05¢38² |
| 12°45¢07² | 0,226282 | 0,226282 | 12°45¢01² | ||
| 12°45¢01² | 0,226282 | 0, 226282 | 12°45¢01² |
For clarity, graphs of the values of the rear and front angles of each section of the cutting edge are plotted. Axial dimensions are plotted along the abscissa axis, and angle values are plotted along the ordinate axis.
On the charts rie. 7 and 8, the angles do not have negative values. Their minimum values correspond to the conditions for satisfactory operation of the cutting edges, except for points 2¢ to 5¢.
The cutting part of the cutter has points 2 and 5, which are the intersection points of the edge sections 1-2 and 5-6 with the radius edge 2-5. These points need to be considered separately. If we consider them related to straight sections 1-2 and 5-6, then they will have the front and rear angles accepted? for these sections, for which the radial plane coincides with the plane normal to the edge.
For a curved section of radius t, these planes do not coincide. The plane tangent to the circle at points 2 and 5 is normal to the axis of the cutter. As a result, the anterior and posterior angles in the plane perpendicular to the curve at these points are zero. The existing recommendations for the possibility of introducing undercuts, undercuts, turning the cutter, inserting, sections of the mitt back surface in the area of such points cannot be used, because the profile is symmetrical, the radius is small, and there are only points operating at zero angles. As a result of this, the greatest wear of the cutter will be located at these points. In such cases, it is required to decide on the advisability of using a shaped cutter or, if its use is necessary, to establish the appropriate conditions for its operation.
The strength of the cutting part in the zones of the maximum value of one of the angles does not decrease, because compensated by a corresponding decrease in the value of the other angle.
Thus, the choice of the position of the base line, the diameter of the cutter and its geometry satisfies the basic requirements for cutters, and can be finally adopted.
In case of insufficient value of one of the angles, it is necessary to change the initial value of the corresponding angle and carry out a corrective calculation of the dimensions of the cutter profile, the angles of the cutting part and their analysis.
1.6. Appointment of constructive dimensions of the cutter.
The dimensions of the corrugations and the constructive size l2 of the cutter are assigned according to Table 2.9 and Fig. 15.
The length of the undercut for the screw head l1 is assigned depending on the width of the cutter.
l1=(1/4 ... 1/2)L
The diameter of the undercut for the screw head d1 is assigned depending on the diameter of the cutter bore d0.
For a hole with a length of l>15.mm, the length of the ground belts is taken
For the designed cutter, we accept:
L = 30 + 5 = 35 mm;
The size of the outer diameter of the cutter D is made according to h / 2.
Bore diameter d0 is done according to H7 . The remaining design dimensions of the cutter are made 14-16th to the valencies.
Cutter design indicating elements, dimensions, tolerances and requirements
specifications are given in fig. 16.
2. REFERENCE MATERIAL FOR DESIGNING SHAPED CUTTER
| Table 2.1. Minimum diameters of mandrels d0 for mounting round cutters, mm. | |||||||||||||||||||||||
| Cutting force Pz daN | Cutter width L, mm. | ||||||||||||||||||||||
| 10 to 13 | Wed 13 to 18 | St 18 to 25 | St 25 to 34 | St 34 to 45 | St 45 to 60 | St 60 to 80 | |||||||||||||||||
| Cantilever mandrel mounts | |||||||||||||||||||||||
| Up to 100 Sv100 up to 130 Sv130 up to 170 Sv170 up to 220 Sv220 up to 290 Sv290 up to 380 Sv380 up to 500 Sv500 up to 650 Sv650 up to 850 Sv 850 to 1100 | - - - - - - - - - - | - - - - - - - - - - | |||||||||||||||||||||
| Double-sided fastening of the mandrel. | |||||||||||||||||||||||
| Up to 100 Sv100 up to 130 Sv130 up to 170 Sv170 up to 220 Sv220 up to 290 Sv290 up to 380 Sv380 up to 500 Sv500 up to 650 Sv650 up to 850 Sv 850 up to | - - - - - - - - - - | - - - - - - - - - - | - - - - - - - - - - | ||||||||||||||||||||
Note. The numbers in columns 1 refer to incisors with D< 3L , в граф 2 – к
incisors D > 3L.
Table 2.2
Cutting conditions (shaped turning)
Notes: 1. Cutting speeds V remain constant regardless of the width of cut.
2. Tabular values of the cutting force Rg. and elective power Ne are multiplied by the cutter width L.
| Cutter width L, mm | Processing diameter, mm | |||||||
| 60-100 | ||||||||
| Feed S mm / rev | ||||||||
| 0,02-0,04 | 0,02-0,06 | 0,03-0,08 | 0,04-0,09 | 0,04-0,09 | 0.04-0,09 | 0,04-0,09 | 0,04-0,09 | |
| 0.015-0,035 | 0,02-,052 | 0,03-0,07 | 0,04-0,088 | 0,04-,0088 | 0,04-0,088 | 0,04-.088 | 0,04-0,088 | |
| 0.01-0,027 | 0,02-0,04 | 0,02-0,055 | 0,035-0,077 | 0,04-0,082 | 0,04-0,082 | 0,04-0,082 | 0,04-0,082 | |
| 0,01-0,024 | 0,015-0,035 | 0,02-,.048 | 0,03-0,059 | 0,035-0,072 | 0,04-0,08 | 0,04-0,08 | 0,04-0,08 | |
| 0,008-0,018 | 0,015-0,032 | 0,02-0,042 | 0.025-0,052 | 3.03-0,063 | 0,04-0,08 | 0,04-0,08 | 0.04-0,08 | |
| 0,008-0,018 | 0,01-0,027 | 0,02-0,037 | 0,025-0,046 | 3,02-0,055 | 0,035-0,07 | 0,035-0,07 | 0,035-0,07 | |
| - | 0,01-0,025 | 0,015-0,034 | 0,02-0,043 | 0,025-0,05 | 0,03-0,065 | 0,03-0,065 | 0,03-0,065 | |
| - | 0,01-0,023 | 0,01-5-0,031 | 0,02-0,039 | 0,03-0,046 | 0,03-0,06 | 0,03-0,06 | 0,03-0,06 | |
| - | - | 0,01-0,027 | 0,015-0,034 | 0,02-0,04 | 0,025-0,055 | 0,025-0,055 | 0,025-0,055 | |
| - | - | 0.01-0.025 | 0,015-0.031 | 0,02-0,037 | 0.025-0,05 | 0.025-0,05 | 0,025-0,05 | |
| - | - | - | - | 0.015-0,031 | 0,02-0,042 | 0,025-0,046 | 0,025-0,05 | |
| - | - | - | - | 0,01-0.028 | 0,015-0,038 | 0,02-0.048 | 0,025-0,05 | |
| - | - | - | - | 0,01-0,025 | 0,015- 0,034 | 0,02- 0,042 | 0,025- 0,05 |
Note. Smaller feed rates - for complex profiles and hard materials; large - for simple profiles and soft metals.
Explanations for fig. 9-14.
I. In the presence of extreme sections of the profile parallel to the axis of the cutter (Fig. 9,10,11,13,14) or in the presence of concave profiles of the product, the amount of overlap h per side is taken depending on the width L of the product according to Table 2.5.
Table 2.5.
At the same time, if the height of the protrusion is not limited by the height of the product profile, the protrusion should overlap the product profile at a height of 1 - 3 mm (Fig. 11.12)
4. For cutters for products with the exact dimensions of the profile width l1 (Fig. 13,14), mounting protrusions are made with a height Bo depending on the width of the protrusion m1 (Table 2.7)
Table 2.7.
Table 2.9
The size of the corrugations (Fig. 15)
METHOD OF CALCULATION OF DISC SHAPED CUTTER
1.1.1. Initial data:
Detail: type of workpiece; brand of material; hardness and tensile strength; dimensions, accuracy and roughness of the machined surfaces of the part.
Equipment: machine model.
Selecting a base point on the part profile.
The base point lies on the smallest part radius.
1.1.3. Selection of the number of nodal points N on the part profile
Nodal points are determined by the intersections of the linear sections of the part profile.
Choice of tool material
Disk shaped cutters are made in one piece from high-speed steels or prefabricated with a cutting part made of hard alloy. When processing workpieces made of structural and alloyed steels, cutters made of high-speed steels of the R6M5 type and hard alloys of the TI5K6 type are used; for processing workpieces made of cast iron and non-ferrous alloys, cutters made of hard alloys of the VK8 type are used.
Selection of the main parameters of the disk shaped cutter
The main design parameters of the disk shaped cutter is the outer diameter D, mandrel hole diameter d, cutter width L, cutter attachment elements α2 And l 2(fig.1.1.1).
The design dimensions of the cutters (Fig. 1.1.1) are selected according to Table 1.1.1, depending on the maximum profile depth of the workpiece
tmax = Rmax – Rmax, mm, (1.1.1)
Where Rmax And Rmax- respectively, the maximum and minimum radii of the part, mm.
Table 1.1.1
Design parameters of disk shaped cutters, mm
| Part Profile Depth tmax | Form cutter parameters | |||||||
| Diameters | Width bmax | Gap TO | Radius R | Diameter d2 | Length l 2 | |||
| Dh13 | αH8 | d1 | ||||||
| Up to 4 | - | - | ||||||
| 4 – 6 | ||||||||
| 6 – 8 | ||||||||
| 8 – 10 | ||||||||
| 10 – 12 | ||||||||
| 12 – 16 | ||||||||
| 16 – 18 | ||||||||
| 18 – 21 |
Fig 1.1.1.
Table 1.1.2
Geometrical parameters of disk shaped cutters
| Processed material | Tensile strength, σ b , MPa | Hardness, HB | Rake angle γ | Rear angle α | |
| cutting material | |||||
| high speed steel | Hard alloy | ||||
| Copper, aluminum | - | - | 25 – 30 | - | 8 – 15 |
| Steel | up to 500 | up to 150 | 20 – 35 | 10 – 15 | 10 – 12 |
| Steel | 500 – 800 | 150 – 235 | 10 – 20 | 10 – 15 | 10 – 12 |
| Steel | 800 – 1000 | 235 – 290 | 10 – 15 | 0 – 5 | 10 – 12 |
| Steel | 1000–1200 | 290 – 350 | 5 – 10 | 0 – 5 | 10 – 12 |
| Bronze, brass | - | - | 0 – 5 | - | 8 – 10 |
| Cast iron | - | up to 150 | 8 – 10 | ||
| Cast iron | - | 150 – 200 | 8 – 15 | ||
| Cast iron | - | 200 – 250 | 8 – 10 |
Notes: 1. It is allowed to use tabular values of non-wired diameters D for smaller values tmax
2. The length of the polished belts l 1 \u003d (0.5-1.0) d(see Fig. 4); recesses for the bolt head l 3 \u003d 0.8 d 1(see fig. 4)
3. Cutter width L determined by the calculation below.
4. Unspecified limit deviations of the dimensions of holes according to the quality H14, shafts - according to the quality h14,
the rest by qualification ±IT14/2.
The choice of geometric parameters of the cutting part of the cutter
Front γ and rear α the angles of the cutter at the peripheral point are selected depending on the grade and physical and mechanical properties of the material being processed and the grade of the tool material according to Table. 1.1.2.
Determining the cutting height
Relative to machine center line
h p = R sind 0, mm, (1.1.2)
Where R– outer radius of the cutter, mm; d0- back angle of the cutter at the peripheral point of the profile, degrees (see Fig. 1.1.1)
Determination of distance
From the axis of the cutter to the plane of the front surface
H p \u003d R sin (γ 0 + α 0), mm, (1.1.3)
Where γ 0 - front angle of the cutter at the peripheral point of the profile, degrees (see Fig. 1.1.1)
1.1.9. Determining the length of the cutter (see Fig.1.1.4)
When processing blanks from forgings and castings
L = log+ (4..6), mm. (1.1.4)
When processing blanks from a bar
L \u003d lg + S 1 + 2S 2 + S 3, mm. (1.1.5)
Where S1– additional cutting edge for cutting off the part from the bar ( S1 0.5 - 1.0 mm more than the width of the cut-off tool); S2– cutting edge overlap equal to 2..3 mm; S3- hardening part of the cutter, equal to 2..5 mm.
Flute sizing
For unhindered chip flow, it is necessary to provide a sufficient sharpening depth along the front surface of the cutter (see Fig. 1.1.1). Size TO depends on the maximum profile depth of the part tmax is selected according to Table 1.1.1.
Corrective calculation of the cutter profile
The work of a round shaped cutter is possible with a positive clearance angle. The day the formation of such an angle, the front surface of the cutter must be displaced below the center by an amount hp(see fig. 1.1.1). From formula (1.1.2) it follows that the clearance angle α is not the same along the entire length of the cutting edge, but varies depending on the distance of the cutting edge to the center of the cutter: the closer any point of the cutting edge is to the center of the cutter, the greater the clearance angle. In practice, the values of the rear angles for different points of the cutting edge of a disk shaped cutter can vary within 6..15 0 .
Due to the displacement of the center of the disk shaped cutter relative to the center of the part and the presence of a positive rake angle, only the point (see Fig. 1.1.1) of the cutter profile will lie on the axis of the part, and all the rest below it. This indicates that the cutter profile is not identical to the part profile. To obtain an accurate profile of the part, the profile of the disk shaped cutter is subjected to graphical or analytical correction.
The graphical method for correcting shaped cutters is less accurate, and it is used in cases where high requirements are not imposed on the calculation of cutters. The analytical correction method described below gives more accurate results.
Appointment of tolerances and specifications
Roughness parameters of the front and rear surfaces of the cutter Ra= 0.4..0.2 µm; mounting hole Ra= 0.3..0.4 µm ; hardness of the cutting part of high-speed cutters HRC 62..65.
On the overall dimensions of the cutters D And L tolerances are assigned according to 12..13 qualifications, and for the landing diameter of the cutter d- for 7..8 qualifications.
Tolerances for the linear and diametrical dimensions of the profile of a shaped cutter are taken equal to 1/3 of the tolerances for the corresponding dimensions of the machined part. Tolerances for diametrical dimensions are usually 0.02..0.06 mm.
NUMERICAL EXAMPLE OF CALCULATION
DISC SHAPED CUTTER
Initial data
Rice. 1.1.2
Detail - fitting; blank - hexagonal bar B = 14 mm; material grade - steel 45; hardness - I80 HB; tensile strength - σ in= 650 MPa; dimensions, accuracy and roughness of the machined surfaces - Fig.2.
It is necessary to design a shaped cutter for processing the part shown in the sketch.
Fig.1
Job option - 5234
Workpiece reference data
Part dimensions
D1=69mm D2= 55.5mm D3= 13mm L1=5mm L2= 10mm
L3=13mm R1=28mm D4=62.5mm D5=58.5mm D6=55.5mm
D7=53.5mm D8=52.5mm L4=13mm L5=3mm L6=6mm
L7=9.5mm D9=49mm D10=44mm L8=12mm L9=10mm
Part material - Steel 50
The hardness of the material of the part HB, MPa - 2364
The workpiece is a body of revolution and has cylindrical, conical, spherical sections and a section specified by coordinates.
Graphical and mathematical expression of the shaped profile of the workpiece
shaped cutter worm cutter
The graphical and mathematical expression of the shaped profile of the workpiece is determined relative to the X and Y coordinate axes. The center of the 0 coordinate axes is at the point of intersection of the left edge of the workpiece and its axis of rotation. The Y coordinate axis is drawn from the center of the 0 coordinate axes perpendicular to the X axis. The shaped profile of the part in some areas in most cases consists of a combination of straight line segments and circular arcs. Using the coordinate method, you can set the shaped profile of a part, the forming surface of which is described by curved lines. The shaped profile of the workpiece is conditionally divided into separate elementary sections (straight line segments, circular arcs, etc.), for each of which a mathematical expression is determined.
The graphical expression of the shaped profile is shown in Figure 1.
Fig.2
Mathematical expression of a shaped profile:
In the interval 0?X?5, the profile is a line segment parallel to the axis of the part (axis X), and is expressed by the formula Y = 27.75.
In the interval 5? X?13 profile is a line segment defined along a circle, and is expressed by the formula
In the interval 13? X? 26 the profile is a line segment defined by the coordinate method and is expressed by the formulas:
Y \u003d 31.25 X \u003d 13
Y = 29.25 X = 16
Y = 27.75 X = 19
Y = 26.75 X = 22.5
Y = 26.25 X = 26
In the interval 26? X?38 profile is a line segment inclined to the axis of the part (X axis), passing through two points 1 and 2 with coordinates: point 1 - 26, 24.5; point 2 - 38, 22 - and is expressed by the formula
Y \u003d + 22- \u003d -0.1875X + 22.1875 \u003d -0.188X + 22.188
The choice of overall dimensions of the shaped cutter
The overall dimensions of the shaped cutter are selected depending on the maximum depth Tmax of the shaped profile of the workpiece and the coefficient K, which are determined by the formulas:
Tmax = ,
where Dmax and Dmin - the maximum and minimum diameter of the shaped profile of the workpiece
L is the total length of the shaped profile of the workpiece (along the X axis).
Tmax = = 12.5 mm
The choice of overall dimensions of the prismatic shaped cutter
The overall dimensions of the prismatic shaped cutter (Fig. 3) are selected from table 2. [ 6, p. 10]
For Tmax \u003d 12.5 and K \u003d 3.84, the overall dimensions of the shaped cutter are as follows
The width Lp is determined after the design of the shaped profile of the cutting part of the cutter; the angle φ of the elements of the fastening part of the shaped cutter is assumed to be 60°; the angle in is determined by the formula
c \u003d 90o - (b + d)
where b and d are the front and rear corners of the shaped cutter, depending on the material of the workpiece and tool material.
Rice. 3.
Choice of front and back corners of the shaped cutter
The front and back angles are selected from table 4 depending on the material of the workpiece.
When processing steel 50 HB = 2364 MPa
r=12°; b=8°.
at=90°-12°-8°=70°.
Calculation of the depth of the shaped profile of a prismatic shaped cutter
To process a section of a part whose profile is a segment of a straight line parallel to the axis of the part, the depth of the shaped profile of the cutter is constant for all values of X and is calculated by the formula
Cp = M),
where M is the coefficient characterizing the segment of a straight line, is taken equal to b0
In the interval 0?X?5 M = 27.75 mm
Ср = 27.75*) = 27.75*) = 27.75* *4.519 = 27.75*0.0436*4.5199 = 5.46 mm.
To process a section of a part whose profile is a segment of a straight line inclined to the axis of the part, the depth of the shaped profile of the cutter for each value from X1 to X2 is calculated by the formula
Ср = (NX +Q) ],
where the coefficients N and Q characterize a segment of a straight line and are taken equal to
Wed \u003d (-0.188 * 26 + 22.188)] \u003d
17,3*) = 17,3* = 17,3*(-
0.0523)*4.519 = 4.09 mm
Wed \u003d (-0.188 * 38 + 14.875)] \u003d
7,731*) = 7,731* =
7.731*(-0.1074)*4.519 = 3.75mm
To process a section of a part whose profile is a segment of a line defined along a circle, the depth of the shaped profile of the cutter for each value from X1 to X2 is calculated by the formula
where the coefficients S, G, B and W characterize the line segment and are taken equal to:
Cp=(1*6.5)*sin
= (1* +6.5)*sin (12- =
34.0499*sin(12-7°40?)*4.5199 = 34.099*0.0756*4.5199=11.64mm
Cp=(1*6.5)*sin
34.3388*sin(12-7°40?)*4.5199 = 34.338*0.0756*4.5199=11.74mm
To process a section of a part whose profile is a segment of a line specified by a coordinate method, the depth of the shaped profile of the cutter for each X value is calculated by the formula
Wed \u003d 31.25 *) * \u003d 31.25 * sin (12-
*=31.25* sin(12-*4.5199=31.25*0.0640*4.5199= 9.04mm
Wed \u003d 29.25 *) * \u003d 29.25 * sin (12-
*=29.25* sin (12-*4.5199 = 29.25*0.0523*4.5199 = 6.92 mm
Wed \u003d 27.25 *) * \u003d 27.25 * sin (12-
*=27.25* sin (12-*4.5199 =27.25*0.0436*4.5199 = 5.37 mm
For X = 22.5
Wed = 26.75*)* = 26.75*
26.75*0.0378*4.5199 = 4.57mm
For X = 26.0
Wed \u003d 26.25 *) * \u003d 26.25 * sin (12-
*= 23.25*sin (12- *4.5199 = 26.25*0.0349*4.5199 = 4.36 mm
Structural design of the shaped cutter
The construction of the shaped profile of the cutter is carried out in a coordinate way. For a prismatic shaped cutter, the coordinates are the depth Cp of the cutter shaped profile and the X dimension along the axis of the workpiece.
Width Lr of the shaped profile of the workpiece (along the axis of the workpiece); T1 and T2 - dimensions that determine additional reinforcing edges of the shaped profile of the cutter. Since our part is made from a piece blank, then T1 = T2.
where T3 - the size is taken equal to 1 ... 2 mm, T4 is taken equal to 2 ... 3 mm.
We take T3 and T4 equal to 2 mm.
Lp = 48+2*4 = 54 mm
Size T5 is selected from the ratio
where Tmax is the maximum depth of the shaped profile of the workpiece
We accept T5 = 12 mm
The size T6 is taken equal to T5 with an overlap of 2 ... 3 mm.
T6 \u003d 12.5 + 3 \u003d 15 mm
The angle is assumed to be 15°.
Rice. 4
Shaped cutters with width Lp? 15 mm are made composite. In a compound prismatic cutter, in a compound shaped cutter, the cutting part has the following dimensions:
height - (0.5 ... 0.6) H \u003d 0.5 * 90 \u003d 45 mm;
width - Lр= 52 mm
thickness - (0.6 ... 0.7) V \u003d 0.7 * 25 \u003d 17.5 mm
Hardness of the shaped cutter:
a) cutting part made of high-speed steel - HRC, 62…65;
b) fastening part - HRC, 40…45.
Surface roughness parameters of the shaped cutter:
a) front surface and shaped rear surface - Ra? 0.32 microns;
b) mounting surfaces of the fastener - Ra? 1.25 microns;
c) other surfaces - Ra? 2.5 microns.
The maximum deviations of the depth of the shaped profile are taken to be ± 0.01 mm, the width of the shaped profile of the cutter is taken depending on its tolerance, i.e. ±1/2Tr.
The tolerance for the width of the shaped profile of the cutter is determined by the formula
Тр=(0.5…0.7)Тs,
where Ts is the tolerance on the width of the shaped profile of the workpiece.
Limit deviations of other dimensions of the shaped cutter are accepted:
a) for the shaft - h12;
b) for the hole - H12;
c) for the rest - ±1/2IT12.
Limit deviations of angles:
a) front r and rear b angles ± 1 °;
b) angle of the fastening part φ=±30?;
c) other angles ±1.5°.
A comprehensive check of the fastening part of the shaped cutter is carried out according to the size P (with an accuracy of 0.05 mm)
where d is the diameter of the calibrated roller, d=E=10 mm.
Shaped cutters are tools whose cutting edges are determined by the profile of the part and work according to the copying method. They are widely used in serial, large-scale and mass production in the processing of bodies of revolution with external or internal shaped surfaces. Processing is carried out from a bar on turret machines, automatic machines, semi-automatic machines. Precisely calculated and manufactured for processing a specific part, shaped cutters provide high productivity, the identity of the part shape and dimensional accuracy, regardless of the skill of the worker. Workpiece dimensional accuracy according to IT8-IT12 and surface roughness RA=0.63-2.5 µm.
The most common are round and prismatic cutters, working with radial and tangential (tangentially directed) feed.
Prismatic cutters are used for processing external surfaces. Compared to round cutters, they have increased rigidity, high processing accuracy, and ease of installation on machine tools.
Round cutters are used for processing external and internal surfaces. They are more manufacturable than prismatic ones, provide a greater number of regrindings, but are inferior to the latter in terms of the rigidity of processing accuracy.
When choosing the type of shaped cutter, its cost, the accuracy of the shape and linear dimensions of the profile, which guarantee the receipt of a suitable part, are of decisive importance.
3.2. Methodology for designing shaped cutters
Designing a shaped cutter of any type for processing a given part consists of a number of common and mandatory steps for all types of cutters. So, the assignment of the material of the tool, the choice of front and rear angles and the assignment of a number of design parameters are carried out in exactly the same way for all shaped cutters.
3.2.1 Characteristic points
Before designing, characteristic (nodal) points 1, 2, 3, etc. are sequentially marked on the part profile. These include the start and end points of the profile; nodal, in which one section of the profile passes into another; additional midpoint on the conical section; two or three additional points equidistant from each other on a curved section. Simple chamfers are not coordinated. The cutter drawing indicates the same angle and chamfer size as on the part.
Then the calculated dimensions of the characteristic points are determined, taking into account the size and location of the tolerance fields. The calculated nominal diameters are set in the middle of the tolerance field, with an accuracy of 0.001 mm. The results are recorded in a summary table.
The coordinates of the middle intermediate point of the cone are determined by the following formulas:
,
Where 
diameters of the initial, middle intermediate and end points of the cone; 
linear dimensions of the cone and the middle intermediate point.
The coordinates of the middle intermediate point of the curved section (quadrant) are determined by the following formulas:
,
Where 
diameters of the middle, intermediate and starting point of the quadrant, which is part of the curved section; 
arc radius; 
linear dimensions of the center of the arc and the middle intermediate point.
3.2.2. Designation of the material of shaped cutters
Round shaped cutters are mainly designed and manufactured in one piece, and prismatic cutters, in order to save tool material, are composite. High-speed steel R6M5 is most often used as the material of the working part of the cutters. When manufacturing parts from hard-to-machine materials, it is economically beneficial to use cutters made of high-speed steels R10K5F5, R9K10, R18K5F2, R9K5 and hard alloys VK10-M, VK8, T15K6. When designing composite cutters, steel 45 GOST 1050-74 is used as the holder material.