Round shaped cutter for processing parts. Calculation and analysis of basic elements. Design of a shaped disk cutter Manufacturing technology of a round shaped cutter
cutter lathe turret
Initial data: Figure 1.28. Option 9.
Rod material grade Brass L62: .
The cutter type is round.
Figure 1.1 Sketch of the part being manufactured
Figure 1.2 Sketch of a part with profile nodal points
We calculate the height dimensions of the profile at nodal points on the part using the formulas:
where d 1 is the smallest diameter of machined surfaces on the part, mm;
d i - diameters of machined surfaces on the part, mm.
Let's choose the overall and design dimensions of the cutter according to Table 2, the values of the front r and rear angles of the cutter according to Table 3.
Table 1.1
Overall and design dimensions
Table 1.2
The values of the front and rear angles
Let us determine the sharpening height of the cutter H and the installation height of the cutter h:
where is the radius of the largest circle of the cutter, mm.
Let us determine for each nodal point the height dimensions of the cutter profile, measured along the front surface:
where is the radius of the nodal point on the part profile, mm;
The value of the rake angle at the design point on the profile of the cutting edge of the cutter.
Let us determine the height dimensions of the cutter profile in the axial section necessary for manufacturing and control:
where is the radius of the circle passing through the nodal point of the cutter profile, mm.
We will enter the calculation results into Table 1.3.
Table 1.3
Calculation results
Figure 1.3 Diagram of the relative position of the part and the tool
Let's check the results of the analytical calculation of the values using formula (1.6) and graphically plotting the cutter profile.
Graphic construction sequence:
- 1) Draw the part in two projections on the coordinate planes V and H. The V plane is vertical, runs perpendicular to the axis of the part, the H plane is horizontal, coincides with the direction of feed of the cutter.
- 2) Let us designate the profile nodal points on the projections of the part with the numbers 1;2;3;4;5.
3) Draw on plane V the contours of the projections of the front and rear surfaces of the cutter. The projection of the front surface of a round cutter is a straight line drawn from a point at an angle z to the horizontal centerline of the part. The projection of the back surface of a circular cutter, circles of radii drawn from the center lie on a line from a point at an angle to the horizontal center line of the part at a distance equal to the radius ().
4) Draw the cutter profile in a normal section on the coordinate plane H, for which:
- a) choose arbitrarily the center of intersection of the traces of the planes N and H;
- b) from the center we draw a straight line NN, radially directed;
- c) transfer the height dimensions of the profile from plane V to plane H;
d) measure the height dimensions of each nodal point of the cutter profile in the drawing and divide the resulting values by the accepted scale of graphic profiling of the cutter, enter the results into Table 1.4 and compare them with the results of the analytical calculation.
Table 1.4
Height dimensions of cutter profile nodal points
Determine the dimensions of additional cutting edges.
Additional cutting edges prepare the part for cutting from the rod. The height of the edges should not be greater than the height of the working profile of the cutter, the width is equal to the width of the cutting edge of the cutting cutter.
b = t max + (5…12), mm (1.8)
L р = l d + b + c 1 + c 2 + f, mm (1.9)
Structurally, we take the following dimensions: b = 5 mm, c 1 = 1.5 mm, c 2 = 2 mm, f = 3 mm.
b =10+10= 25 mm
L р = 50 + 5 + 1.5 + 2 + 3 = 61.5 mm
To reduce the friction of the cutter on the workpiece, in sections of the profile perpendicular to the axis of the part, we sharpen an angle equal to 3?.
We develop a drawing of a template and a counter template to check the cutter profile for clearance.
The profile of the template is a negative profile of the cutter. The height dimensions of the template profile are equal to the corresponding height dimensions of the cutter profile. The axial dimensions between the nodal points of the template profile are equal to the corresponding axial dimensions of the cutter profile. To construct a template profile, it is necessary to draw a coordinate horizontal line through the nodal base point 1, from which, in directions perpendicular to it, plot the height dimensions of the cutter profile. Tolerance for the manufacture of vertical dimensions of the template profile ±0.01, linear dimensions ±0.02...0.03.
Template width
L w = L P + 2 f, mm (1.10)
where L P is the width of the cutter; f = 2 mm.
L w =61.5 + 2 2 = 65.5 mm
Figure 1.4 Template and counter-template
hob cutter cutting
Initial data: Figure 54, option 9
Figure 1.1 Sketch of the part being manufactured.
Rod material grade Brass L62: uv = 380 MPa;
The cutter type is round.
We calculate the height dimensions of the profile at nodal points on the part using the formulas:
t2 = (d2 - d1)/2; (1.1)
t3 = (d3 - d1)/2; (1.2)
t4 = (d4 - d1)/2; (1.3)
where d1, d2, d3, d4 are the diameters of the machined surfaces on the part.
t2 = (24-20)/2 = 2 mm;
t3 = (28-20)/2 = 4 mm;
t4 = (36-20)/2 = 8 mm;
tmax = t4, mm.
Let's choose the overall and design dimensions of the cutter according to Table 1, the values of the front and rear angles of the cutter according to Table 3.
Table 1.1 Overall and design dimensions
Table 1.2 Values of front and rear angles
|
Brass L62 |
Let us calculate for each nodal point the height dimensions of the cutter profile, measured along the front surface.
xi = (ri·cos(r - gi) - r1)/cos g; (1.4)
where ri are the radii of nodal points on the part profile;
r - the value of the front angle at base point 1;
gi - the values of the rake angles for the design points on the profile of the cutting edge of the cutter.
sin gi = (ri-1/ri) sin g; (1.5)
sin r2 = (r1/r2) sin r = (10/12) sin3 = 0.04361;
r2 = 2.5? = 2?30ґ;
sin r3 = (r1/r3) sin r = (10/14) sin3 = 0.03738;
r3 = 2.14? = 19?8ґ;
sin r4 = (r1/r4) sin r = (10/18) sin3 = 0.02908;
r3 = 1.67? = 19?40ґ;
x2 = (r2·cos(r-r2)-r1)/cosг = (12·cos(3-2.5)-10)/cos3 = 2.0023 mm;
x3 = (r3·cos(r-r3)-r1)/cosг = (14·cos(3-2.14)-10)/cos3 = 4.004 mm;
x4 = (r4·cos(r-r4)-r1)/cosг = (18·cos(3-1.67)-10)/cos3 = 8.0061 mm;
Let us calculate the height dimensions of the cutter profile necessary for its manufacture and control.
The height dimensions of the profile for each nodal point are set in a radial section.
Тi = R1 - Ri; (1.6)
Where R1,Ri are the radii of circles passing through the nodal points of the cutter profile
Ri= (R12+xi2-2 R1xicos(b+ g))1/2 (1.7)
R2= (R12+x22-2 R1x2cos(b+ g))1/2=(252+2.00232-2 25 2.0023 cos(10+3))1/2=23.0534 mm;
R3= (R12+x32-2 R1x3cos(b+ g))1/2=(252+4.0042-2 25 4.004 cos(10+3))1/2=21.118 mm;
R4= (R12+x42-2 R1x4cos(b+ g))1/2=(252+8.0061 2-2 25 8.0061 cos(10+3))1/2=17.293 mm;
T2 = R1 - R2 = 25-23.0534 = 1.9466;
T3 = R1 - R3 = 25-21.118 = 3.882;
T4 = R1 - R4 = 25-17.293 = 7.707;
Let's check the results of the analytical calculation of the values T2, T3, T4 by graphically plotting the cutter profile.
- 1) Draw the part in two projections on the coordinate planes V and H. The V plane is vertical, runs perpendicular to the axis of the part, the H plane is horizontal, coincides with the direction of feed of the cutter.
- 2) Let us designate the profile nodal points on the projections of the part with the numbers 1,2,3,4.
- 3) Draw on plane V the contours of the projections of the front and rear surfaces of the cutter. The projection of the front surface of a round cutter is a straight line 1`P drawn from point 1` at an angle z to the horizontal center line of the part. Projection of the rear surface of a round cutter - circles of radii R1, R2, R3, R4 drawn from the center Or through the intersection points of line 1`P with the contour circles of the part profile. The center of the cutter Or lies on the line 1'O drawn from point 1' at an angle b to the horizontal center line of the part at a distance equal to the radius R1, i.e. 1`O = R1.
- 4) Draw the cutter profile in a normal section on the coordinate plane H, for which:
- a) choose arbitrarily the center O1 of the intersection of the traces of the planes N and H;
- b) from the center O1 we draw a straight line NN, radially directed;
- c) using a compass, transfer the height dimensions of the cutter profile from plane V to plane H.
- 5) We measure the height dimensions of each nodal point of the cutter profile T2, T3, T4 in the drawing and divide the resulting values by the accepted scale of graphic profiling of the cutter, enter the results into a table and compare them with the results of the analytical calculation.
Table 1.3
Determine the dimensions of additional cutting edges.
Additional cutting edges prepare the part for cutting from the rod. The height of the edges should not be greater than the height of the working profile of the cutter, the width is equal to the width of the cutting edge of the cutting cutter.
b = tmax + (5…12) = 5 + 12 = 17 mm
Lр = lд + b1 + c1 + c2 + f = 55 + 3 + 2 + 2 + 2 = 64 mm
dimensions: b1?2 mm, c1 = 2 mm, c2 = 2 mm, f = 2 mm.
We take b = 6 mm, b1 = 3 mm, c1 = 2 mm, c2 = 2 mm, f = 2 mm.
To reduce the friction of the cutter on the workpiece, in sections of the profile perpendicular to the axis of the part, we sharpen an angle equal to 3?.
We develop a drawing of a template and a counter template to check the cutter profile for clearance.
The profile of the template is a negative profile of the cutter. The height dimensions of the template profile are equal to the corresponding height dimensions of the cutter profile. Axial dimensions between the nodal points of the part profile. To construct a template, it is necessary to draw a coordinate horizontal line through the nodal base point 1, from which the height dimensions of the cutter profile are plotted in directions perpendicular to it. Tolerance for the manufacture of vertical dimensions of the template profile ±0.01, linear dimensions +0.02…0.03.
Template width
Lsh = LP + 2·f = 64 + 2·2 = 68 mm; (1.17)
where: LP - cutter width; f = 2 mm.
Figure 1.2. Additional cutting edges of shaped cutters
Figure 1.3 Pattern and counter-pattern
Figure 1.4 Prismatic shaped cutter
3.1. BASIC CONCEPTS AND CLASSIFICATION OF INCISERS
Cutters with a shaped cutting edge are used to form the surfaces of bodies of rotation and prismatic parts, surfaces that have a line as a generator, representing a combination of straight and curved sections.
Obtaining a shaped surface of a part is possible by separately processing each of the sections of its generatrix using cutters, milling cutters, grinding wheels, but under the indispensable condition of their (sections) relative arrangement, which ensures obtaining a given profile of the generatrix of the surface of the part with the required accuracy. This processing option has a number of disadvantages: reduced process productivity, difficulty in obtaining the required location of treated areas, i.e. the accuracy of the profile of the generatrix of the processed part, and, finally, the need to use the labor of a highly qualified worker. This limits its use: it is used in conditions of single production of parts or in cases where it is impossible to obtain a profile at the same time due to its complexity, increased perimeter and other reasons.
The shaped surfaces of prismatic parts can be processed simultaneously along the entire profile of their generatrix by milling, broaching, grinding, and planing with a shaped cutter. The latter method, as it is low-productive, is rarely used. Some of its features make it possible to successfully use planing shaped cutters when producing simple shaped surfaces of considerable length.
Obtaining a generatrix shaped surface of bodies of rotation simultaneously along the entire perimeter is used in serial and mass production. This option of profiling provides, in comparison with the option of profiling by sections, an increase in processing productivity, an increase in the accuracy of the profile of parts and their identity in profile, which is carried out using shaped tools: cutters, broaches, grinding wheels, shaped cutters. Each of these methods has its own characteristics and indicators of productivity, accuracy, cost and other data, depending on the conditions in which they are used.
In mechanical engineering, there are parts of such sizes and such processes for their production that the use of milling, broaching and grinding is inappropriate and the use of shaped cutters is preferable. Precisely manufactured shaped cutters with correct installation them on machines provide high productivity, accuracy of shape and size of processed parts according to IT8...IT12 and surface with = 0.63…2.5 µm. They also have such advantages as: low metal consumption of the structure, long service life, ease of sharpening and regrinding, manufacturability of the design, relatively low cost, they do not require highly qualified workers for operation. Shaped cutters are used on lathes, turrets and automatic machines, i.e. on the same machines on which such parts are preprocessed. The presence of grinding machines for profiling shaped cutters increases the manufacturability of their manufacture and contributes to their wider use.
Like other metal-cutting tools, shaped cutters are characterized by a number of features that are used to classify them. Shaped cutters can be divided into the following groups: by shape - rod, prismatic and round cutters; by type of surface being treated - external and internal; by installation relative to the workpiece and the direction of feed movement - radial and tangential; according to the location of the cutter relative to the part - with parallel and angled axes or the measurement base; according to the location of the front surface - without tilt ( λ = 0) or angled λ ; according to the shape of the forming shaped surfaces - ring and screw.
Initial data:
Part profile for processing of which it is necessary to design a shaped cutter (Fig. 1);
Allowance for processing (indicated in the drawing);
Part profile tolerance ±0.05 mm;
- part material - steel35.
1.1. Calculation of average dimensions of a part profile
The average profile dimensions in the example under consideration coincide with nominal sizes part profile, since the profile tolerance is specified by b+u, i.e. located symmetrically. Therefore, it is not necessary to determine the average profile dimensions.
1.2. Selecting the Baseline Position
The given profile of the part has a relatively small height: h = 4 mm. The cutter edge profile mainly consists of sections located parallel to the axis of the part.
The section of the edge that makes it 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, we take the base line of the cutter to be located in edge sections 1-2 and 5-6 (Fig. 2).
1.3. Calculation of the overall dimensions of the cutter
The width of the cutter is calculated L = L parts + 2n (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 cutter axis 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 =1mm) =110H=11 daN * (Table 2.2).
Then the cutting force P z =P z (L =1mm) ×L=11 × 30=330 daN.
Taking into account the width of the cutter and the fact that the cutting force is small, we accept a cantilever mounting of the mandrel. According to Table 2.1, the diameter of the mounting hole is d0 = 27 mm.
The smallest permissible value of the outer diameter of the cutter is calculated
D>d0+2(q+l+m)
Taking l = 4mm and m = 8mm,
we get
D>27 + 2 (4 + 4 + 8)> 59.
Rounding to the nearest value according to the standard series of cutter diameters, we take D = 60 mm.
1.4. Correction calculation of 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, we take according to Table 2.4 the rake angle j = 18° (steel 35; Gb = 85 daN/mm^). clearance angle L = 12*.
The size of the blade is calculated, which determines the position of the cutter axis relative to the axis of the part (Fig. 5):
hust =R1 sinL;
hust = 30 *sin 12° = 30 X 0.20791 = 6.237.
We accept hcm =6.2.
The cutter profile in the front plane is calculated. To do this, a profile of the workpiece is drawn. 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 as-built 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 all equations in a calculation table. 1.1.
Table 1.1
Note to table 1.1.
Сз =A3-A1 = 10.96793 - 9.5106 == 1.47733; C3= 1.477;
C4 =A4-A1= 11.59536 - 9.5106 = 2.08476; C4 = 2.085;
C7.8=A7.8-A= 13.65476 - 9.5106 = 4.14416; C7.8 = 4.144.
The cutter profile in the axial plane is calculated (Fig. 6). The calculation is carried out according to calculation table 1.2.
Table 1.2.
Continuation of Table 1.2,
Note.
Нз = R1 - Rз = 30 - 28.7305 = 1.2695;
H4 = R1 – R4 = 30 - 28.214 = I, 786;
H7.8= R1- R7 = 30 - 26.492 = 3.508.
1.5 Analysis of the values of the front and rear angles of the cutting part of the cutter
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 axis of the cutter is carried out in the calculation table. 1.3.
Table 1.3.
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 calculation method.1.4.
Table 1.4
| N of 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 |
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 section of the edge under consideration is carried out according to the calculation table 1.5.
Table 1.5.
| N of 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. The abscissa axis shows the axial dimensions, and the ordinate axis shows the angle values.
On the graphs rie. 7 and 8 angle values 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 edge sections 1-2 and 5-6 with radius edge 2-5. These points need to be considered specially. If we consider them to belong to straight sections 1-2 and 5-6, then they will have front and back 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 located normal to the cutter axis. As a result, the front and rear angles in the plane perpendicular to the curve at these points are equal to zero. Existing recommendations for the possibility of introducing undercuts, undercuts, turning the cutter, inserting sections of the in-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 that operate at zero angles. As a result, the greatest wear on the cutter will be located at these points. In such cases, it is necessary 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 is 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 accepted.
If one of the angles is insufficient, it is necessary to change the initial value of the corresponding angle and carry out a correction calculation of the dimensions of the cutter profile, the angles of the cutting part and their analysis.
1.6. Designation of cutter design dimensions.
The dimensions of the corrugations and the design size l2 of the cutter are assigned according to Table 2.9 and Fig. 15.
The length of the recess for the screw head l1 is determined depending on the width of the cutter.
l1=(1/4 … 1/2)L
The diameter of the recess for the screw head d1 is assigned depending on the diameter of the cutter mounting hole d0.
For a hole with a length of l>15.mm, the length of the polished 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.
The diameter of the mounting hole d0 is made according to H7. The remaining design dimensions of the cutter are made to 14-16th to valets.
Cutter design indicating elements, dimensions, tolerances and requirements
technical specifications shown in Fig. 16.
2. REFERENCE MATERIAL FOR DESIGNING SHAPED CUTTERS
| Table 2.1. | |||||||||||||||||||||||
| Minimum diameters of mandrels d0 for fastening round cutters, mm. | Cutting force Pz daN | ||||||||||||||||||||||
| Cutter width L, mm. | From 10 to 13 | Sat 13 to 18 | Sat 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 up to 1100 | |||||||||||||||||||||||
| Double-sided mandrel mounting. | - - - - - - - - - - | - - - - - - - - - - | - - - - - - - - - - | ||||||||||||||||||||
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< 3L , в граф 2 – к
Note. The numbers in column 1 refer to cutters with D
cutters D > 3L.
Table 2.2
Cutting modes (shaped turning)
Notes: 1. Cutting speeds V remain constant regardless of cutting width.
| 2. Tabular values of cutting force Pr. and elective power Ne are multiplied by the cutter width L. | Cutter width L, mm | |||||||
| 60-100 | ||||||||
| Processing diameter, mm | ||||||||
| 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 |
Feed S mm/rev
Note. Lower feed rates - for complex profiles and hard materials; large - for simple profiles and soft metals.
Explanations for Fig. 9-14.
I. If there are extreme sections of the profile parallel to the axis of the cutter (Fig. 9, 10, 11, 13, 14) or if there are 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.
Moreover, if the height of the protrusion is not limited by the dimensions of 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 dimensions l1 exact in profile width (Fig. 13, 14), mounting projections of height B are made depending on the width of the projection m1 (Table 2.7)
Table 2.7.
Table 2.9
Size of corrugations (Fig. 15)
It is necessary to design a shaped cutter to process the part shown in the sketch.
Fig.1
Task option - 5234
Initial data about the workpiece
Part dimensions
D1 =69mm D2= 55.5 mm D3= 13 mm L1=5 mm L2= 10 mm
L3 = 13 mm R1=28 mm D4=62.5 mm D5=58.5 mm D6=55.5 mm
D7=53.5 mm D8=52.5 mm L4=13 mm L5=3 mm L6=6 mm
L7=9.5 mm D9=49 mm D10=44 mm L8=12 mm L9=10 mm
Part material - Steel 50
The workpiece is a body of rotation 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 hob 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 located at the intersection of the left edge of the part and its axis of rotation. The Y coordinate axis is drawn from the center of the coordinate axes 0 perpendicular to the X axis. The shaped profile of a part in certain areas in most cases consists of a combination of straight line segments and circular arcs. Using the coordinate method, you can define a shaped profile of a part, the forming surface of which is described by curved lines. The shaped profile of the workpiece is conventionally divided into separate elementary sections (segments of straight lines, 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 for shaped profile:
In the interval 0? X? 5, the profile is a line segment parallel to the axis of the part (X axis), 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 range of 13? X? 26 profile is a segment of a line specified by a coordinate method, and is expressed by the formulas:
Y = 31.25 X = 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= + 22- = -0.1875X+22.1875 = -0.188X+22.188
Selection of overall dimensions of a 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:
Тmax = ,
where Dmax and Dmin are 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
Selection of overall dimensions of a prismatic shaped cutter
Overall dimensions of the prismatic shaped cutter (Fig. 3) are selected from table 2. [6, p.10]
For Tmax = 12.5 and K = 3.84, the overall dimensions of the shaped cutter are as follows
The width Lр is determined after the design of the shaped profile of the cutting part of the cutter; the angle f of the elements of the fastening part of the shaped cutter is taken equal to 60°; angle b is determined by the formula
c = 90o - (b+g)
where b and d are the front and rear angles of the shaped cutter, depending on the material of the workpiece and the tool material.
Rice. 3.
Selecting the rake and back angles of the shaped cutter
The rake 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°.
в=90°-12°-8°=70°.
Calculation of the profile depth 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 cutter profile is constant for all X values and is calculated using the formula
Ср = М) ,
where M is the coefficient characterizing the straight line segment, taken equal to b0
In the interval 0? X? 5 M = 27.75 mm
Av = 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 cutter profile for each value from X1 to X2 is calculated by the formula
Ср = (NX +Q) ],
where the coefficients N and Q characterize a straight line segment and are taken equal
Avg = (-0.188*26+22.188)] =
17,3*) = 17,3* = 17,3*(-
0.0523)*4.519 = 4.09 mm
Avg = (-0.188*38+14.875)] =
7,731*) = 7,731* =
7.731*(-0.1074)*4.519 = 3.75 mm
To process a section of a part whose profile is a segment of a line defined along a circle, the depth of the shaped cutter profile 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:
Avg=(1*6.5)*sin
= (1* +6.5)*sin (12- =
34.0499*sin(12-7°40?)*4.5199 = 34.099*0.0756*4.5199=11.64 mm
Avg=(1*6.5)*sin
34.3388*sin(12-7°40?)*4.5199 = 34.338*0.0756*4.5199=11.74 mm
To process a section of a part whose profile is a segment of a line specified by the coordinate method, the depth of the cutter shaped profile for each X value is calculated using the formula
Avg = 31.25*)* = 31.25 * sin (12-
*=31.25* sin (12- *4.5199 =31.25*0.0640*4.5199= 9.04 mm
Av = 29.25*)* = 29.25 * sin (12-
*=29.25* sin (12- *4.5199 = 29.25*0.0523*4.5199 = 6.92 mm
Avg = 27.25*)* = 27.25 * sin (12-
*=27.25* sin (12- *4.5199 =27.25*0.0436*4.5199 = 5.37 mm
For X = 22.5
Avg = 26.75*)* = 26.75*
26.75*0.0378*4.5199 = 4.57mm
For X = 26.0
Avg = 26.25*)* = 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 cutter profile is carried out using the coordinate method. For a prismatic shaped cutter, the coordinates are the depth Cp of the shaped cutter profile and the dimension X along the axis of the workpiece.
Width Lр 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 cutter profile. Since our part is made from a piece blank, then T1 = T2.
where T3 - 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
We take size T6 equal to T5 with an overlap of 2...3 mm.
T6 = 12.5+3=15 mm
The angle is assumed to be 15°.
Rice. 4
Shaped cutters with width Lp? 15 mm are manufactured in composites. In a compound prismatic cutter, in a compound shaped cutter, the cutting part has the following dimensions:
height - (0.5…0.6)H = 0.5*90=45 mm;
width - Lр= 52 mm
thickness - (0.6…0.7)B = 0.7*25 = 17.5 mm
Shaped cutter hardness:
a) cutting part made of high-speed steel - HRC, 62…65;
b) fastening part - HRC, 40…45.
Roughness parameters of shaped cutter surfaces:
a) front surface and shaped rear surface - Ra? 0.32 microns;
b) mounting surfaces of the fastening part - Ra? 1.25 microns;
c) other surfaces - Ra? 2.5 microns.
The maximum deviations of the depth of the shaped profile are accepted as ±0.01 mm, the width of the shaped profile of the cutter is accepted depending on its tolerance, i.e. ±1/2Tr.
The tolerance for the width of the shaped cutter profile is determined by the formula
Tr=(0.5…0.7)Ts,
where Ts is the tolerance for the width of the shaped profile of the workpiece.
Maximum deviations of other sizes of shaped cutter are accepted:
a) for the shaft - h12;
b) for the hole - H12;
c) for the rest - ±1/2IT12.
Maximum angle deviations:
a) front d and rear b angles ±1°;
b) angle of the fastening part f=±30?;
c) other angles ±1.5°.
A comprehensive check of the fastening part of the shaped cutter is carried out according to dimension P (with an accuracy of 0.05 mm)
where d is the diameter of the calibrated roller, d=E=10 mm.
