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.
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 intersection point 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. 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 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 = 4.36mm
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. four
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.
Moscow State Technical University
them. N.E. Bauman
Kaluga branch
Department M4-KF
Course work
"Metal cutting and cutting tools"
Kaluga, 2008
1. Calculation of a shaped cutter
1.1. Preparing a part drawing for cutter calculation
1.2. Selecting the type of shaped cutter
1.3. Determining the angles of the cutting part
1.4. Determination of the overall and connecting dimensions of the cutter
1.5. The general part of the correction calculation of shaped cutters
1.6. Determination of the dimensions of the profile of a round cutter of a conventional installation with an angle λ 0 =0
1.7. Calculation of profile height deviations of a shaped cutter
1.8. Calculation of tolerances for the parameters of sharpening and setting the cutter
1.9. Making a working drawing of the cutter
1.10 Designing a template to control the profile of the cutter during its manufacture
1.11 Designing a tool holder
2. Calculation of broach
3.1 Initial data
3.2. Choice of the profile of the teeth of the worm cutter
3.3 The procedure for calculating the main structural elements of the worm cutter
INTRODUCTION
Shaped cutters are used for processing surfaces of complex profiles on lathes and less often on planing (grooving) machines in serial and mass production. As a rule, they are special tools designed for processing one part. The advantages of shaped cutters - strict identity of machined parts, long service life, high overall and dimensional stability, combination of preliminary and final processing, ease of installation and adjustment on the machine - make them indispensable in automated production, especially on automatic lathes.
Shaped cutters are classified according to several criteria:
By type of machine - turning, automatic, planing (grooving);
According to the shape of the body of the cutter - round (disk), prismatic, rod. Screw and snail cutters are used less frequently;
According to the position of the front plane of the cutter - with conventional sharpening (angle λ 0 = 0) and with lateral sharpening (angle λ 0 0) - fig. 2;
According to the position of the base surface of the cutter (the axis of the landing hole for round ones or the reference plane for prismatic ones) relative to the axis of the part - cutters of a conventional installation and cutters of a special installation. The latter, in turn, can be with a base turned in a horizontal plane at an angle ψ, and with a lateral inclination of the body (usually prismatic cutters) - Fig. 3;
According to the type of surface to be treated - external, internal, end. The latter can strike as external ones with a base turned at an angle ψ = 90°;
In the direction of feed - with radial and tangential feed (radial and tangential cutters, respectively) - fig. 1-3 - radial, fig. 4 - tangential cutters;
According to the design, the method of connecting the cutting part and the body, the material of the cutting part: mounted and tail (round); solid, welded, soldered; high-speed and hard-alloy.
1. Designing a shaped cutter
1.1. Preparation of a detail drawing for the calculation of a shaped cutter.
According to the dimensions of the part, we draw its profile on an enlarged scale of 2: 1, which is used later to graphically determine the dimensions of the cutter. Drawing a part profile is necessary to solve two issues:
1) Setting intermediate points of the profile, which is necessary if there are curved sections on the profile, as well as to improve the accuracy of processing conical, and in some cases, cylindrical sections. The greatest difficulty is the determination of the radii of the intermediate points of the arc sections. In this case, they are usually set by the axial dimensions of the profile:
l 2 =7 mm;
l 3 =11.5 mm;
l 4 =15.7 mm;
l 5 =21.4mm;
l 6 =27 mm;
l 7 =32 mm;
l 8 =35 mm;
According to the given theoretical dimensions and lengths, the radii of the points are found:
r 1 =35 mm;
r 2 =38 mm;
r 3 =37.5mm;
r 4= 37.6 mm;
r 5 =38.7mm;
r 6 =41 mm;
r 7 =41 mm;
r 8 =43 mm;
1.2. Selecting the type of shaped cutter
We use a shaped cutter of a round type, because. it has a long service life, so it is cost-effective. For processing internal surfaces, round cutters are almost always used. More often, radial type cutters are used, because. most machines have calipers with the cutter set to the height of the part axis. Tangential type cutters can be used with a small depth of the shaped profile of the part, however, it is necessary to take into account the possibility of placing and fixing such a cutter on the machine support. A valuable property of a tangential cutter is the ability to process parts of different diameters with the same shaped profiles and gradual insertion and exit of the cutter, which leads to a decrease in cutting forces and allows processing non-rigid parts. Round incisors are more often mounted; with small dimensions of the cutter, tail cutters are used. Round cutters, as a rule, are made in one piece from high speed steel.
1.3. Determining the angles of the cutting part
Front angle of cutter γ and rear corner α are set at the most protruding (base) point of the cutter. Angles α and γ it is recommended to choose from a number of values: 5, 8, 10, 15, 20, 25. We accept γ =20 degrees. For round incisors, the following back angles are most often taken: α =815 degrees. Accept α =10 degrees. It should be borne in mind that the back angles are variable at different points of the blade, moreover, in a section normal to the projection of the blade onto the main plane, they can be much less than the nominal value in some parts of the blade. Therefore, it is necessary to check the minimum value of the back angle according to the formula:
, where
α T- back angle at a given point in the end section;
φ - the angle between the tangent to the profile of the part at a given point and the end plane of the part.
1.4. Determination of the overall and connecting dimensions of the cutter
Usually, the overall and connecting dimensions are determined from design considerations, depending on the depth of the shaped profile of the product. tmax and profile length L, because the amount of resulting chips and the load on the cutter during its operation depend on them.
The overall radius of the disc cutters is determined by the formula:
The maximum diameter of the workpiece.
The largest diameter of the cutter, mm, is rounded up to values from the normal range of linear dimensions according to GOST 6636-60. Accept D=60 mm. The length of the cutter is determined depending on the size of the profile of the part, taking into account additional blades, and it is rounded up. Accept L=35 mm.
1.5. Corrective calculation of the profile of a round shaped cutter
General part of the calculation.
The purpose of the general part of the correction calculation is to determine the height dimensions of the shaped blade profile, which lie in the front plane of the cutter, in the direction perpendicular to the base of the cutter.
Mm, we accept h=5.5 mm;
Correcting the angle α
: 
;
Correcting the angle γ
: 
;
γ =30-α =30-10,56=19.44;
1. mm;
3.
;
4.
;
5.
;
6.
;
7.
;
8. γ8 =γ7 =16.43;
A 8 =A 7 =39.33mm;
C 8 =C 7 =6.33mm,
9.
;
Where r 1 - radius at the base point on the part; r 2 =r 9 - radii of the part profile in v.2-9; γ - front angle of the cutter at the base point; γ i- front angle i- that point of the incisor; FROM i- desired size i-th stage of the calculation.
1.6. Determination of the dimensions of the profile of prismatic and round shaped cutters of a conventional installation with an angle λ 0 = 0
When calculating the dimensions of the profile of a prismatic shaped cutter in a normal section, the initial data are the angles α and γ , as well as dimensions From 2,3,…, i found in the general part of the correction calculation. Desired profile dimensions R i are determined by the formula
When calculating round shaped cutters, the given values are the angles α and γ , the outer radius of the cutter corresponding to base point 1, and the dimensions C 2..i, lying in the front plane and found in the general part of the calculation. As a result of the calculation, the cutter radii corresponding to other points of the part profile are determined, as well as the height dimensions of the profile in the axial section of the cutter Pi.
The size H is also the radius of the control risk ρ to control the correct sharpening of the cutter.
1.7. Calculation of tolerances for the height dimensions of the cutter profile
This stage is very important, since the accuracy of the resulting diameters of the part depends on the accuracy of the height dimensions. For a reasonable assignment of tolerances for the height dimensions of the cutter, the following considerations should be followed.
When setting up a cutter on a machine slide during part processing, one of the most accurate of all the diameters of the shaped part is usually measured. The corresponding section of the shaped profile of the part and its diameter is called the base for measurement. If it turns out that this area is inconvenient for measurement, then another one is taken as the base area for measurement; at the same time, its tolerance is tightened compared to that specified in the drawing, doing this for technological reasons (the calculated value of the diameter is left the same).
The main requirement that must be met when assigning tolerances to the cutting dimensions of the cutter, the angles of its installation and sharpening, is as follows:
If, during the processing of the part, the base measuring diameter is obtained as valid (it lies in the tolerance field), then all other diameter sizes must be within their tolerance fields, i.e. also be valid.
This requirement is due to the fact that the cutter is a monolithic tool and does not allow for separate adjustment of each size (diameter) of the part when setting up its installation on the machine.
A section or point of the cutter profile in the technological section, processing the base diameter, we will call the base (section or point) for counting the effective heights of the cutter profile. In the general case, they do not coincide with the base section or point adopted for the correction calculation of the cutter profile. In this case, it is necessary to set the height dimensions of the profile from the newly selected base. The same is done on the part profile.
1.8. Calculation of tolerances for the parameters of sharpening and setting the cutter
For all angles that determine the sharpening and installation of the cutter (, ), tolerances in arc minutes are accepted, numerically equal to the smallest tolerance for the height dimension of the cutter profile, expressed in micrometers. The corner tolerance is ±76'.
The tolerance for the installation height of the axis of the round cutter above the axis of the part is determined by differentiating the formula
In the same way, the tolerance for the sharpening height of the cutter or the radius of the control risk is found (H or )
1.9. Making a working drawing of the cutter
On the working drawing of the cutter, the number of projections, additional cuts, sections, and views necessary for the full disclosure of the structure and setting all dimensions should be placed. The profile of the cutter is set by height and longitudinal dimensions, affixed from the selected bases. Dimensions are affixed with the allowable deviations obtained as a result of the calculation. Connecting dimensions must be selected in accordance with the standards. Overall and other dimensions without tolerances are made according to 5 or 7 accuracy classes. The drawing should contain dimensions characterizing the sharpening of the cutter - angles and for a prismatic and - the radius of the control risk of a round cutter.
The technical requirements should contain indications of the grade of the material of the cutter, the hardness of its cutting part and holder, the quality of the material and other requirements depending on the specific conditions for the manufacture and operation of the cutter, as well as data for marking. On the drawing of the cutter, the place of marking should be indicated.
1.10 Designing a template to control the profile of the cutter during its manufacture
Often, to control the profile of shaped cutters during their manufacture, templates are used that are applied to the shaped rear surface of the cutter. The size of the clearance is used to judge the accuracy of the cutter profile.
The template has the same nominal profile dimensions as the shaped cutter, however, the tolerances for the dimensions of the template profile must be 1.5 ... 2 times tighter than the corresponding tolerances of the cutter.
To control the template during its operation, we use the counter-template. Its profile is the same as the profile of the cutter, but the tolerances for the dimensions of the profile are 1.5 ... 2 times tighter than the tolerances for the dimensions of the template.
Template W and counter-template KSh are made of sheet material 3 mm thick. To increase wear resistance, we harden them to a hardness of 56...64 HRC. To reduce warping, we use alloyed tool steel KhVG. We make measuring edges along the entire shaped contour thinner than the main plate (0.5 mm.) To facilitate the processing of precise profile dimensions and ease of control of the cutter.
1.11 Designing a tool holder
The fastening of the shaped cutter is carried out by means of a finger holder. This toolholder consists of the following parts: toolholder body, pin, driver and support washers, bushing, two adjusting screws, nut and guide pin.
Holder assembly procedure: install a shaped cutter on pin 2, then install support washer 5, put drive washer 4 on it, insert this entire assembly unit into bushing 3, previously installed in holder body 1, fix the pin in the bushing using a guide pin, carry out the final fixing of the pin, tightening the nut 8 on it, install the adjusting screws 7 and 6 into the body of the holder.
The cutter position can be adjusted in two ways:
1. By means of adjusting screw 6.
2. by means of 50 teeth notched on the support and drive washers. This is done by loosening the fixing of the cutter and then turning the support washer, then the cutter is fixed by screwing the nut 8.
2. Calculation of a flat keyway broach
It is required to machine the 8H8 groove with a keyway in a hole with a diameter of 30H7 and a length of 65mm
The size t is Z3.3H12 mm. Workpiece material - Steel 45KhN with hardness HB -207. Broach material R6M5K5 steel; broach with a welded shank. The broaching is carried out without cutting fluid on a horizontally broaching machine tool type 751.
We accept a broach with a thickened body and a shank. Total broach lift
∑h=t-D+ f Q =33.05-30+0.55=3.6mm;
accept 3.6 mm; f Q =0.55 mm .
Body Width
B≈L+(2..6)=8+(2..6)=10..14mm
accept H=12.mm.
Tooth width b n = b max - ∂ = 8.027-0=8.027 mm.
Feed per tooth s : =0.06mm(Table 10). Tooth pitch t =12 mm(Table 10). Number of simultaneously working teeth z t = 6 (Table 8).
flute dimensions(Table 9):
h 0 = 5 mm, r= 2.5 mm, F a = 19.6 mm
Cavity fill factor
Front and rear corners according to the table 12 and 13:
y \u003d 15 °; α \u003d 4 °.
cutting height (4) h " o = 1.25 h 0 = 1.25 5 = 6.25mm; rounded up to 9 mm according to the table. 4. what is more
t - D = 33.05 -30 =3.05mm.
Pulling force
Section height on the first tooth, at [a] = 20 kg mm 2 for broaching high speed steel
accept according to table 4 h =18mm
Height of last cutting tooth
Number of cutting teeth
accept 62 teeth.
Cutting length .
The shank is flat according to the table. 6 with dimensions : H,= h 1 = mm
Tensile stress in the shank material
Calibrating part: tooth height H 5= h, = mm; number of teeth (Table 15) = 4; step t K= t = 12mm;
Length l=t(z+0.5) =12(4+0.5)=54~50mm; the chip groove is the same as that of the cutting teeth; chamfer f K=0.2mm;
The length of the smooth part, taking into account that the broach will work with disconnection from the machine, is
l = l ,- l 3 + lc + l a + l 6 + l .+ l " 4 Given that 1 3 = 0;
1 C = 70 (Attachment 1); 1 a = 20mm; 1 4 = L +10mm=65+10=75~75mm;
1= 70 + 20 + 8 + 75 =183mm; accept 185mm.
total length
Lm = I +1 5 +1 6 = 185 +744+0 = 929 mm;
round up to 950 mm; tolerance ±2 mm.
Groove depth in guide mandrel
H = h ,+ fo =18 + 0.59 = 18.59 mm.
Checking the thickness of the body of the mandrel according to the condition :
3. Calculation of a worm cutter for cylindrical gears with an involute profile
3.1 Initial data
The module is normal ( m) - 7.0 mm; engagement angle ( α w) - twenty; tooth head and root height ratio ( f) – 1.0; radial clearance factor ( With) - 0.25; number of teeth ( z) - eighteen; teeth inclination angle - 10; the direction of the teeth is left; correction factor normal 0; degree of accuracy - 7 - C; material - Steel 40X; σv– 900 mm/mg; type of milling with a worm cutter - final.
3.2 Selecting the tooth profile of the hobbing cutter
Our class A cutter is profiled on the basis of the Archimedean worm. This profiling method is based on replacing the curvilinear profile of the side in the axial section of the involute worm with a rectilinear one close to it. In this case of approximate profiling of worm cutters for cylindrical gears with an involute profile, the involute main worm is replaced with an Archimedean worm. Worm cutters, profiled approximately on the basis of Archimedean worm, form, in comparison with other methods of approximate profiling, the smallest errors in the profile of the teeth of the cut wheels in the form of a small undercut of the stem and cut of the head, which favorably affect the engagement condition of the mating pair of gears. In addition, such worm cutters have the following advantages:
1. The sides of the teeth of Archimedean hobs can be hemmed in the radial direction.
2. For the final inspection of the profile of the flank of the teeth of Archimedean hobs, special devices have been developed and used to ensure high and stable measurement accuracy.
When designing finishing hobs for spur gears with an involute profile, approximate profiling based on the Archimedean worm is preferred.
3.3 The procedure for calculating the main structural elements of the worm cutter
3.3.1. Number of visits ( Z zah. )
The number of starts of a worm cutter is one of the factors affecting productivity when cutting cylindrical wheels. The choice of the number of starts of worm cutters is influenced by the degree of accuracy of the wheels being cut and their dimensions (number of teeth and module). Worm cutters, especially finishing ones, are designed as single-threaded cutters. Accept Z zah. =1.
3.3.2. The angle of elevation of the helix along the dividing cylinder ( γ mo )
The tooth profile errors of cut wheels with an involute profile, associated with the approximate profiling of worm cutters, largely depend on the helix angle along the indexing cylinder of the cutters. With an increase in the angle of elevation of the helix along the dividing cylinder, the value of the error in the profile of the teeth of the cut wheels increases. As a result, for finishing hobs, the angle of helix elevation along the dividing cylinder is assumed to be no higher than 6 degrees 30 minutes. Accept γ mo=4.45 degrees.
The choice of the direction of the helical comb of the worm cutter depends on the direction of the teeth of the wheels being cut. . We accept the direction of the helix along the dividing cylinder - left.
3.3.4. Outside diameter ( Dao )
The approximate value of the outer diameter of the worm modular cutter is determined by the formula:
In accordance with GOST 9324-80 E, we accept Dao=124 mm.
3.3.5. Tooth shape
We use the so-called form b). It is characterized by the following features: it has two sections of a backed back surface formed along the Archimedean spiral: the first section with a decline To and the second with a decline K1. The first (main) section of the back surface is formed finally after heat treatment by grinding. The second section is designed to provide a free exit of the grinding wheel during the processing of the first one and is formed by a backing cutter before heat treatment. Worm cutters with teeth in the form b) are characterized by increased accuracy of profile dimensions and durability. The shape b) of the teeth is used in the designs of worm cutters for finishing and finishing the teeth of the cut wheels up to the 8th degree of accuracy.
3.3.6. The number of cutter teeth in the end section ( Zo )
The number of cutter teeth in the end section affects the number of cuts that form the side of the teeth of the cut wheels. To improve the accuracy of the profile of the teeth of the cut wheels and the processing performance, it is preferable to take the maximum allowable number of teeth.
The approximate number of teeth in the end section of backed hobs for spur gears with an involute profile is determined by the formula:
;
Accept Zo =9.
3.3.7. The amount of recession of the back surface of the teeth of the cutters To and K1
The value of the recess of the back surface of the teeth of the cutter in the first section is determined by the formula:
; α
in- back angle at the top of the teeth (10-12 degrees). 
. Accept To
=8,0;
The value of the recession of the rear surface of the teeth in the second section is taken equal to:
Where β - correction factor.
For general purpose cutters β =1,2…1,5.
. Accept K1
=9;
3.3.8.Profile depth ( ho )
The value of the profile depth or the ground part of the teeth of the worm cutters is equal to:
3.3.9. Flute depth ( hk )
The size of the flute depth is determined depending on the shape of the teeth of the hobs.
For worm cutters with teeth in the form b):
3.3.10. Flute root radius
The value of the radius of the cavity of the flute is determined by the formula:
3.3.11. Flute root angle ( ε )
The value of the angle of the cavity of the flute is taken depending on the number of cutter teeth of the following values:
At Zo =9, e = 22.
3.3.12. Hole diameter ( d )
In order to increase the rigidity of the cutter mounting, the diameter of the hole for the mandrel should be taken as the maximum allowable. The approximate value of the size of the hole diameter is determined by the formula:
According to the final size of the hole diameter, the thickness of the cutter body in the dangerous section is checked according to the formula:
; where t
1
- the size,
determining the depth of the keyway from the wall of the hole. Accept t 1 =4 mm.
- right.
3.3.13. Total cutter length ( Lo )
The approximate value of the length of the working part of the worm cutter is determined by the formula:
mm; accept L =115;
The value of the total length of the cutter is determined by the formula:
where l 1 - the length of the cylindrical beads, l 1 =4 mm;
χ - coefficient selected according to the table χ =3;
3.3.14. Collar diameter ( d 1 )
The cylindrical surface of the shoulders is used to control the installation of the cutter on the machine. The diameter of the beads is taken equal to:
3.3.15. Estimated diameter of the dividing cylinder ( D calc. )
The calculated diameter of the dividing cylinder takes into account the change in a number of geometric parameters (helix angle, inclination angle of the front surface, etc.) of the worm cutter during its regrinding during operation. To reduce the deviation of the operational values of the parameters from the calculated ones, the value of the calculated diameter of the dividing cylinder is determined for the section located at a distance of (0.15-0.25) of the circumferential step from the front surface of the cutter. In accordance with this, the calculated diameter of the dividing cylinder is determined by the formula:
Accept D calc.= 103.3 mm.
3.3.16. Estimated helix angle along the dividing cylinder ( γmo )
The value of the calculated angle of elevation of the helix along the dividing cylinder is determined by the formula:
;
Accept γmo\u003d 3.59 degrees, that is, 3 ° 35 '
Chip grooves to ensure the same rake angle on the side cutting blades of the teeth of the cutter are located normally to the helical ridge and are helical. The angle of inclination of the flutes is assumed to be equal to the angle of helix rise along the dividing cylinder, i.e.
βk =γmo\u003d 3.59 degrees.
3.3.18. flute pitch ( Tk)
The pitch value of the chip grooves is included in the marking marks of the cutter and is determined by the formula:
mm;
3.3.19. Axial pitch of cutter teeth ( That)
The step size in the axial section of the cutter is determined by the formula:
mm.
3.3.20. Normal tooth pitch of the cutter ( T n )
The step size in the normal section of the cutter is determined by the formula:
3.3.21. Helical cutter tooth profile dimensions in normal section
A) Tooth thickness along the dividing cylinder:
mm;
∆S- allowance for the thickness of the teeth of the cut wheels for further processing. Equal to 0, because final processing.
b) Tooth head height: mm
C) Tooth pedicle height: 
, where Xi- coefficient of radial clearance between the tooth head of the cut wheel and the cavity of the cutter tooth. Value Xi can be taken equal to With
.
h 2 =h 1 =8.75 mm.
D) Radius of the fillet on the tooth head: mm.
E) Radius of the fillet at the root of the tooth: mm
The value of the angles of the profile of the right and left side back surfaces of the teeth of the worm cutter in the axial section is determined by the formulas:
for right: ;
We accept αop=20.11
Task 1. Building a parametric model of a shaped cutter in the APM GRAPH module
1. Type of cutter - prismatic shaped cutter (option No. 10).
2. Detail drawing.
3. Material of the workpiece - Steel 40XC (σ in = 1200 MPa).
4. Special processing conditions - the presence of a groove for the subsequent cut
Fig.1. Detail sketch
A task 2. Building a solid model in a module ARM STUDIO
A task 3. Designing a Cutter in a Module ARM GRAPH
The initial data are presented in task 1. The construction of the model is based on the results obtained in solving problem 1.
Date of issue, signature
Teacher ._____
SEQUENCE OF EXECUTION ANDGUIDELINES
Task 1
1) According to a given part, a shaped cutter is designed and a correction calculation of the profile depth is performed.
2) An analysis of the input data required to build the model is carried out. The data are divided into original (independent) and derived (depend on the original).
3) Input data, in the form of variables, is entered in the dialog box Variables(rice.) , moreover, for the original data, only the value is specified, and for the derivatives, also an expression that is a function of the original and already declared derived data. So, the dimensions of the front surface are determined using the expression. There is a single rule: a variable that is used in subsequent expressions must be declared in advance.
4) A sequence of commands leading to the construction of the desired model is set graphically.
5) Listed parametric commands specify, if necessary, parameters for commands. In this case, in the calculation expressions, the variables specified in clause 3 or auxiliary variables created in the process of building the model are used.
6) The conformity of the model formed in this way with the required one is analyzed, and, if necessary, the parameters of the commands are corrected or the method of constructing the entire model or its part is changed.
7) The correctness of the constructed model is analyzed for various values of the initial data.
Task 2
1. The initial stage of solving the 2nd problem is the construction sketch cutter (working plane in 3D space in which plane curves are built).
2. To obtain a solid model of a shaped cutter, graphic operations are used - extrusion, rotation and torsion.
Task 3
1. The resulting parametric model (task 1) is inserted as a block into the APM GRAPH drawing field. To do this, use the BLOCK / INSERT BLOCK command.
2. You can insert a parametric object into the drawing from Database. Before pasting, you can change the value of the main parameters in the list of variables.
1. Darmanchev S.K. Shaped cutters. - M .: Mashinostroenie, 1968. -166 p.
2. Semenchenko I.I., Matyushin V.M., Sakharov G.N. Design of metal-cutting tools. - M .: Publishing house of machine-building literature, 1962. - 952 p.
3. Freifeld I.A. Calculations and designs of special metal-cutting tools.- M.-L.: Mashgiz, 1957.- 196 p.
4. Methodical instructions and a set of control tasks for the course project "Design of a metal-cutting tool" / V.N. Kisilev and others - Voroshilovgrad: VMSI, 1987. - 48 p.
5. Guidelines "Computer-aided design of shaped cutters using the SM-2M computer" / Kisilev V.N., Androsov P.M. . - Lugansk: LMSI, 1991. - 20 p.
6. Shelofast V.V. Fundamentals of machine design. - M .: APM Publishing House, 2005. - 472 p.
7. Shelofast V.V., Chugunova T.B. Fundamentals of machine design. Examples of problem solving. – M.: APM Publishing House, 2004.- 240 p.
Research Method and Computing Tools : the method of constructing parametric models based on the Parasolid parametric geometric kernel was applied; computer technologies for computer-aided design of prismatic and round shaped cutters were used. When solving design problems, various modules were used: APM Saft, APM Bear, APM Joint, APM Trans and the APM WinMachine database toolkit.
Efficiency The use of the proposed toolkit makes it possible to drastically reduce the cutter design time and improve the technical level of the design decisions made.
Application area The proposed parametric modeling tools can be used as part of the courses "Machine parts", "Design of metal-cutting machines" and "Design, calculation and CAD of machine tools".
Introduction
1 Designing a shaped cutter
1.1 Initial data and calculation algorithm:
1.2 Determination of the geometric parameters of the cutting part and the main design dimensions of the shaped cutters of the cutter.
1.3 Pattern and counter-pattern design
2 Building a parametric model of a prismatic shaped cutter
2.1 Initial data:
2.2 Entering initial data to create a parametric model
2.3 Building a parametric model.
2.4 Saving a parametric model
Literature
Introduction
In modern mechanical engineering, there is a large range of products with shaped surfaces. These surfaces can be processed on CNC lathes for this a program is set to obtain a shaped profile) or with a special shaped cutter, which
is a copy tool. The profile of the cutting edge of the cutter corresponds to the surface profile of the part.
Shaped cutters provide the identity of the shape and the necessary accuracy of parts, high processing performance and have a long service life due to a significant number of allowable regrinds. They are used in small-scale, serial and mass production for processing external and internal surfaces on automatic lathes, semi-automatic machines and turret machines.
The most widespread are radial round and prismatic incisors.
Processing of shaped surfaces with a shaped cutter.
Cutters, the cutting edge of which coincides with the curvilinear or stepped profile of the machined surface, are called shaped.
The advantage of the incisors under consideration is simplicity, and therefore the relatively low cost of their manufacture. A significant drawback of such cutters is that after several, and sometimes two or three regrindings along the front surface (and to maintain the profile, they can only be reground along the front surface), the plate is ground, the height in the center decreases during installation and the cutter becomes unusable for further work. . Therefore, rod shaped cutters are used mainly in cases where the work is not of a massive nature and the profile of the cutters is simple (for example, for processing fillets).
To obtain the correct profile of the workpiece, the shaped cutter must be installed so that its cutting edge is exactly at the height of the machine centers. The position of the shaped cutter, when viewed from above, should be checked using a small square. If one edge of such a square is applied to the cylindrical surface of the part (along its axis), and the other is brought to the side surface of an ordinary or prismatic cutter, or to the end surface of a disk cutter, then there should be no uneven clearance between the square and the cutter.
When fixing shaped cutters, it is necessary to carefully follow the general rules for fixing cutters.
The feed of the shaped cutter is in most cases carried out manually. It should be uniform and not exceed 0.05 mm / rev with a cutter width of 10-20 mm and 0.03 mm / rev with a width of more than 20 mm. The feed should be the smaller, the smaller the diameter of the workpiece. When machining an area of a part located close to the chuck (or tailstock), the feed can be taken more than when machining an area located relatively far from the chuck (or tailstock).
When processing shaped surfaces of steel parts, oil cooling should be used. The surface of the part is smooth and even shiny. Shaped surfaces of cast iron, bronze and brass parts are machined without cooling.
The correctness of the shaped surface is checked by a template. There should be no gap between the treated surface and the template.
If the workpiece surface has large differences in the diameters of different sections, then when working with a shaped cutter, you have to remove a lot of metal. In order to avoid rapid wear of the cutter, the preliminary processing of such a surface must be carried out with a peeling cutter, the profile of which is similar to the profile of the final shaped cutter, but much simpler than it.
Processing of shaped surfaces with the simultaneous action of the longitudinal and transverse feeds of the cutter. The processing of shaped surfaces with the simultaneous action of the longitudinal and transverse manual feeds of the cutter is carried out with a small number of workpieces or with relatively large sizes of shaped surfaces. In the first case, the manufacture of even an ordinary shaped cutter is impractical, in the second, a very wide cutter would be required, the work of which would inevitably cause vibrations of the part.
The allowance is removed with a sharp-nosed finishing or through-cutting cutter. To do this, move (manually) the longitudinal slide to the left and at the same time the cross slide of the caliper back and forth. When processing relatively small shaped surfaces, the longitudinal feed is carried out using the upper slide of the caliper, installed so that their guides are parallel to the center line of the machine; for cross feed, the cross slide of the caliper is used. In both cases, the tip of the cutter will move along the curve. After several passes of the cutter and with the correct ratio of feed values (longitudinal and transverse), the machined surface will receive the required shape. It takes a lot of skill to do this job. Experienced turners, processing shaped surfaces in this way, use automatic longitudinal feed, while simultaneously moving the transverse support manually.
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 line of centers of the machine, 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)
General instructions for the implementation of the project (work).
The design of the graphic part of the project (format size, letters, fonts, shading, etc.) must be done in accordance with ESKD.
The main images on the working and assembly drawings are made in full size, because this allows you to most fully represent the actual dimensions and shape of the designed tool.
Tools and their sections, explaining the shape and geometrical parameters of the cutting part, the shape of the shaped contour, etc., can be made on an enlarged scale, sufficient to more clearly fulfill the design features of the depicted elements.
Calculation schemes and graphic constructions of profiles are carried out on an enlarged scale, the value of which is set depending on the required accuracy of construction.
Working drawings of the designed tools, in addition to images of the main projections, cuts and sections, must have the necessary dimensions, dimensional tolerances, designations of surface finish classes, data on the material and hardness of individual parts of the tool, as well as technical requirements for the finished tool for control, adjustment, regrinding , tests.
A settlement and explanatory note up to 30-40 pages is typewritten. It should be short, written and presented in good literary language.
Calculations must contain the original formulas, substitution of the corresponding digital values, intermediate actions and transformations sufficient for verification without additional calculations.
All decisions made on the issue of choosing the design parameters of the designed tool and the material of the cutting part must be accompanied by justifications.
Accepted normative, tabular and other data should be accompanied by references to the sources used. It is recommended to use official reference materials for this purpose.
For each designed tool, it is necessary to develop specifications based on the requirements for the workpiece and the specifications for similar tool designs.
When developing a new tool, you need to keep in mind the requirements for accuracy and manufacturability, sharpening features and its performance. It is necessary to provide for the economy of expensive tool materials, by practicing prefabricated, welded structures, etc. for this.
Mounting and seating parts of the designed tools must be calculated and brought into line with the dimensions of the standardized seats of existing machines or fixtures.
Design of shaped cutters
Shaped cutters are used for processing parts with a shaped profile. The task of the designer who designs the shaped cutter is to determine such dimensions and shapes of its profile, which, at the designed angles of its sharpening and installation, would create a profile on the workpiece specified by its drawing. The calculations associated with this are usually called correction or simply correction of the profile of shaped cutters.
Preparation of executive drawings of details.
When corrective calculation, it is necessary to determine the coordinates of all points that make up the profile line of the shaped cutting blade of the cutter. To do this, calculate the coordinates of the nodal points of a given shaped profile and, in some cases, when there are curved sections, also the coordinates of individual points located between the nodal ones.
Based on these considerations, before proceeding with correction calculations, it is necessary to first check whether the as-built drawings of shaped parts have all the coordinate dimensions from the base surfaces to the nodal points, and if they are not indicated, then it is necessary to determine the missing coordinate dimensions to all selected points. On the drawings of shaped parts there are always dimensions that allow you to determine the missing coordinate dimensions. Basic and additional correction calculations of shaped cutting blades of incisors are made according to nominal sizes.
If there are radius transitions on the shaped profile, the distances to the nodal points formed by the intersection of the conjugate profiles of the sections are determined (without taking into account the radii of curvature of the transition surface).
When calculating round shaped cutters, the radii R1, R2, R3, etc. are determined. circles passing through the nodal design points. When calculating prismatic shaped cutters, the distances from the nodal points of the normal shaped cutter profile to some arbitrarily chosen coordinate axis are determined. Such an initial coordinate axis is usually drawn through a point or through a baseline that is at the height of the part's center of rotation.
Method for calculating the profile of shaped cutters.
The initial data for the design of the cutter are data on the workpiece (material and hardness, shape and dimensions of the shaped profile, cleanliness and accuracy classes).
The choice of the design of shaped cutters.
The following considerations are taken into account when selecting a HSS shaped cutter design.
Rod shaped cutters are the most primitive design of this type of cutters; they are cheap to manufacture, but allow a small number of regrinds. Therefore, it is advisable to use core cutters for the manufacture of small batches of parts, provided that the savings due to the use of shaped cutters exceed the cost of their manufacture. Often, rod shaped cutters are used as a second-order tool, i.e. for the manufacture of cutting tools with a complex profile.
Prismatic shaped cutters are more expensive to manufacture than rod cutters, but allow a much larger number of regrinds. Ceteris paribus, the cost of processing one part with a prismatic shaped cutter is lower than with a rod cutter; this is possible in conditions of large-scale and mass production.
The great advantage of prismatic dovetail cutters is their high clamping rigidity, which makes them more accurate than round cutters.
Round shaped cutters as bodies of revolution are convenient and cheap to manufacture, and the number of regrindings they allow is large; thus, the costs per manufactured part when machining with round shaped cutters are the lowest. As a result, shaped cutters in the conditions of large-scale and mass production are most widely used. Another important advantage of round shaped cutters is the convenience of processing their internal surfaces.
Their disadvantages include:
a sharp decrease in the angle of sharpening as the cutting edges approach the axis;
curvature of the cutting edges that occur when the conical sections of the cutter profile are crossed by the front plane.
Shaped cutters with soldered carbide blades allow multiple use of the body. However, they are not widely used due to technological difficulties.
The choice of design parameters of shaped cutters is made according to the tables (Appendix 1 and 2) depending on the dimensions of the shaped profile of the workpiece. In this case, the main parameter affecting the dimensions of the cutters is the depth of the shaped profile, which is determined by the formula:
t max = r max - r min, (1.1)
where t max , r min~ respectively, the largest and smallest radii
shaped profile of the part.
When assigning the diameter of the cutter, the following considerations are guided. To reduce the consumption of cutter material per machined
the detail is always advantageous to work with a cutter of the smallest diameter. From all other points of view, it is desirable to work with a cutter of the largest possible diameter, since:
Improves heat dissipation and makes it possible to increase
cutting speed;
· the labor intensity of manufacturing a cutter per one part is reduced, due to an increase in the service life due to an increase in the number of regrindings.
At the same time, the manufacture and operation of shaped cutters with a too large diameter causes a number of inconveniences, as a result of which cutters with a diameter of more than 120 mm are not used.
The table (Appendix 1) shows the minimum allowable values of the cutter radii, which are determined by the depth of the processed profile and the minimum required diameter of the mandrel or shank to secure it.
It is desirable to assign the length of prismatic cutters to the maximum in order to increase the number of allowable regrindings; the maximum length is limited by the possibility of fixing the cutters in holders and the difficulty of manufacturing long shaped surfaces. The remaining dimensions of the shaped cutters depend mainly on the depth and width of the processed profile.
There are various ways to secure prismatic shaped incisors. The book recommends sizes for prismatic dovetail chisels. The sizes of dovetails indicated in the table (Appendix 2) are used by domestic factories producing multi-spindle automatic lathes.
Choice of front and rear corners.
Angle corresponding to the section of the shaped profile furthest from the axis of the cutter is selected in accordance with the mechanical properties of the material being processed according to the table (Appendix 3). It is generally accepted to choose the angle from the standard range: 5, 8, 10, 12, 15, 20 and 25 degrees.
It should be borne in mind that the rake angle is not constant in sections of the shaped profile at various distances from the axis of the part; as the considered sections of the profile move away from the axis of the part, the front angles decrease.
When external processing with shaped cutters with > 0, in order to avoid vibrations, excessive reduction of the cutting edges with respect to the axis of the workpiece should not be allowed, as established by practice, this reduction should not exceed (0.1-0.2) the largest radius of the workpiece. Therefore, the angle selected from the table must be checked by the formula:
On machines, as a rule, normalized holders are installed, which have a standard design, therefore, the clearance angle is taken within 8-15 °.
It should be noted that for shaped cutters, as the considered points of the profile move away from the axis of the workpiece, the rear angles increase.
To create satisfactory cutting conditions, in all sections of the cutting profile perpendicular to the projection of the cutting edge on the main plane, clearance angles of at least 4-5° must be provided. Therefore, in the process of corrective calculation of the cutter profile, the rear angles are refined in all areas.
Corrective calculation of the profile of a shaped cutter.
Profile correction can be done by graphical and graphic-analytical methods. The last method is the simplest and most visual, so it is recommended for use.
To calculate the profile of the cutter, it is necessary to select a number of nodal points on the profile of the part, which, as a rule, correspond to the connection points of the elementary sections of the profile.
The calculation of round and prismatic incisors is carried out according to various formulas.
a) The procedure for calculating the profile of a round shaped cutter (Figure 1).
Through the nodal point 1, draw the rays at angles and and connect the resulting intersection points 2 and 3 to the center of the part O1.
In a right triangle 1a01, determine the leg aO1 using the formula:
Calculate the angle values for the remaining points according to the dependence:
From triangles 1a01 and 2a01 determine the sides (A1 and A2)
Figure 1 - Graphical definition of the profile of a round shaped cutter.
Calculate the lengths of the segments Ci
Сi+1 = Ai+1 – A1 (1.6)
hp = R1 * sin; (1.7)
В1 = R1 * cos , (1.8)
where R1 is the outer radius of the cutter.
Determine the lengths by the formula
(1.9)
Calculate the value of the cutter radii corresponding to anchor point 2
Calculate taper angles at nodal points of the cutter
(1.12)
The minimum allowable angles for round cutters are: 40° when machining copper and aluminum; 50 ° - when processing free-cutting steel; 60 ° - when processing alloyed steels; 55 ° - when processing cast iron.
Check the rear angles for the minimum allowable value (4-5°) in normal sections to the projections of the cutting edges on the main plane. The calculation is performed according to the formula:
Define values as differences
(1.14)
Construct a profile of a shaped cutter in a normal section N-N, taking point 1 as the origin of coordinates. The coordinates of the cutter profile points correspond to: 2 n ; 3n etc.
b) Features of calculating the profile of a prismatic shaped cutter (see Figure 2).
Figure 2 - Graphical definition of a profile
prismatic shaped cutter.
The calculation of the prismatic cutter is performed in the same sequence as the round cutter. After calculating the value of Ci, it is necessary to determine the dimensions of Pi, which are the legs of right-angled triangles 1a2
Thus, the generalized formula for calculating the radius of an arbitrary point in the profile of a round shaped cutter is:
When calculating prismatic cutters, the dependence is used
Outlines of corner and radius sections
The profiles of shaped parts usually consist of straight sections located at different angles to their axis and sections outlined by arcs of circles. Due to the fact that the depth dimensions of the cutter profile are distorted in comparison with the corresponding dimensions of the part profile, the angular dimensions of its profile also change accordingly, and the arcs of circles turn into curved lines, the exact outlines of which can only be specified by arranging a row of sufficiently close spaced other points.
The angular dimensions of the cutter profile (Figure 3) are determined by the formula:
Figure 3 - Calculation of the angular dimensions of the profile of the shaped cutter.
where is the cutter profile angle;
Measured perpendicular to the side planes of the cutter, the distance between the nodal points.
The need to determine the shape of the curved sections of the cutter profile by the position of a number of its points arises relatively rarely, since in most cases, with sufficient accuracy for practice, a selected replacing arc of a circle is carried out on the calculated section of the cutter profile.
The radius and position of the center of such an arc is determined when solving a well-known problem - drawing a circle through three given points. The necessary calculations are performed as follows (Figure 4).
Figure 4 - Determination of the replacement radius of the cutter profile.
One of the three nodal points located on the curved section of the cutter profile is taken as the origin of coordinates 0. The X axis is drawn parallel to the part axis, and the Y axis is perpendicular to it. The X 0 and Y 0 coordinates of the center of the "replacing" circular arc are determined by the formulas:
(1.19)
where: x 1- smaller, a x2- large coordinates of the two used
when calculating points;
y 1 and y 2 - coordinates of points I and 2;
(1.20)
The radius of this arc is calculated by the formula
With the often occurring symmetrical arrangement of the replacement arc
the calculation of these quantities is greatly simplified (Figure 4):
circumference, the calculation of these quantities is greatly simplified:
It remains only to determine
The above dependencies are often replaced by the corresponding graphical constructions. Provided that such constructions are carried out on an enlarged scale and with sufficient accuracy, they lead to results that are satisfactory for most cases.
Additional cutting edges of shaped cutters.
In addition to the main cutting part, which creates the shaped outline of the workpiece (Figure 5), the shaped cutter in most cases has additional cutting edges S1 parts preparing the cut from the bar, and S2, processing a chamfer or a part of a part that is cut off during trimming.
Figure 5 - Additional cutting edges of shaped cutters.
When chamfering, the corresponding cutting edges must have an overlap S3, equal to 1-2 mm, and the cutter should end with a hardening part S4 up to 5-8 mm wide. Cutting Width S5 must be greater than the width of the cutting edge of the cutting tool. The following requirements apply to the additional cutting edges of the shaped cutter:
1) In order to avoid friction of the rear surfaces of the cutter on the part, additional cutting edges should not have sections perpendicular to the axis of the part, but should be inclined to it at an angle of at least 15 °.
2) In order to facilitate the installation of scoring or parting cutters, it is desirable that additional cutting edges mark the exact position of the end contour points on the workpiece. For example, after processing the part shown in Figure 5 with a shaped cutter, it is easy to install a trimming cutter at the profile inflection point, and a cutting cutter at the point, as a result of which the finished part will have the length specified by the drawing.
Thus, the total width of the cutter is determined by the formula:
(1.23)
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Ways to reduce friction in sections of the profile,
perpendicular to the axis of the part.
A significant disadvantage of shaped cutters of the main type is that they do not have the necessary rear corners in the sections of the profile perpendicular to the axis of the part (Figure 6).
Figure 6 - Friction between the part and the cutter in areas
perpendicular to the axis of the part.
In such areas, friction occurs between the end plane of the part, limited by radii and , and the platform of the side plane of the cutter profile.
Since cutting does not occur in such areas and the edges on them are only auxiliary, then work under these conditions at shallow depths and processing of brittle metals is possible, but is always accompanied by increased wear of the cutter and deterioration in the quality of the machined surface. With an increase in the depth of the profile and an increase in the viscosity of the material, the processing of sections of the profile perpendicular to the axis of the part becomes impossible.
In order to reduce friction and wear of the cutter sections perpendicular to the axis, an undercut is used at an angle of 2-3 ° or a narrow ribbon is left on the cutting edge (Figure 7).
Figure 7 - Ways to reduce friction in sections of the profile,
perpendicular to the axis of the part.
Due to these design changes, the side plane of the cutter profile takes a position (plan view), in which it goes out of contact with the part.
There are other ways to improve cutting conditions in sections of the profile perpendicular to the axis. These include: sharpening additional angles on the cutters or turning the cutter axis relative to the part axis.
Instructions on the choice of tolerances for the manufacture of shaped cutters.
When assigning tolerances for the manufacture of a shaped cutter, it is necessary, first of all, to select the base surfaces of the part (radial and axial).
Distinguish between internal and external bases. The position of the internal bases relative to the external ones is determined by the machine settings. The axis and end face of the part serve as external bases. For internal bases, those surfaces of the part are taken, the dimensions or distances of which are specified from external bases with the highest accuracy.
As shown in Figure 8, from the position of the base surface of the BR associated with the radial base dimension r B with the axis of the part, which is the external processing base for it, only the diameter directly depends d B.
Figure 8 - Technological complex of surfaces processed
shaped cutter, internal and external processing bases.
Surfaces I and P are connected with the surface Br by the dimensions of the profile depth. The internal axial base B0 here is one of the joints of the surfaces associated with the external base (the end of the part) by the axial base dimension l B; the axial position of the nodal points I and 2 (l1 and l2) relative to the end face of the part depends on the size l B and transmitted by the cutter to the part dimensions, profile width l 01 and l 02
It is convenient to divide the dimensions used in the design and operation of shaped cutters as follows:
radial basic dimensions;
profile depth dimensions;
axial base dimensions;
profile width dimensions;
dimensions characterizing the shape of surfaces.
The adjustment of the shaped cutter in the radial direction for processing a given part is performed according to the base size (internal base).
Obtaining the basic size of the part can be performed with a certain accuracy, which is limited by the setup tolerance. It can be taken equal to .
The dimensions of the depth and width of the part profile are calculated by the formulas:
(1.24)
The dimensions of the depth of the cutter profile differ from the corresponding dimensions of the profile of the part and are calculated using similar formulas with an accuracy of 0.01 mm, and the dimensions of the width of individual sections of the profile coincide with the dimensions of the corresponding sections of the profile of the part.
The depth tolerance of the part profile is determined by the formula:
To select tolerances for the depth of the cutter profile, the formula is usedwhere is the tolerance for the corresponding depth of the part profile;
Distortion factor.
When determining the tolerances for the dimensions of the profile width, it is assumed that the width of the cutter profile is equal to the width of the part profile. In addition, deviations from the calculated dimensions of the geometric parameters do not affect the width of the profile. Therefore, taking into account only the compensation of operational errors, we can accept:
(1.27)
where is the tolerance for the width of the cutter profile;
Tolerance on the width of the product profile.
The rake and clearance tolerances affect the depth deviations of the cutter profile. It is established that with equal deviations of the angles and ,
the rear corner causes larger profile depth errors than the front corner. Therefore, it is recommended to choose the values of the tolerances of the angles and the same in magnitude, but different in sign. In addition, the sign of the tolerance of the front angle should be taken positive, and the rear - negative.
Tolerances for cutter diameters are assigned by the formula
Construction of templates to control the profile of cutters.
Based on the results of correction calculations, it is possible to build template profiles to control the accuracy of grinding the shaped surfaces of cutters. To do this, a coordinate line is drawn through the base surfaces or points parallel and perpendicular to the axis or base of the cutter attachment, from which distances are plotted in perpendicular directions that determine the relative position of all points of the shaped profile. The location of the nodal points along the depth of the shaped profile of the template is determined by calculation, and the axial distances are equal to the axial distances between the same nodal points of the shaped profile of the part.
To facilitate control measurements of the accuracy of manufacturing the shaped profile of the templates, it is advisable on the executive drawings of the templates, in addition to the coordinate dimensions, to calculate and indicate the angles of inclination of the contour sections, as well as the lengths of all blades.
Tolerances for the accuracy of manufacturing the linear dimensions of the shaped profile of the template specified by the drawing are 0.01 mm.
The counter-template is used to check the shaped profile of the template. The dimensions of its profile correspond to the dimensions of the template and differ in manufacturing accuracy. Tolerances for the manufacturing accuracy of the counter-template are taken equal to 50% of the tolerances for the manufacturing of the template.
Since the control of the cutter profile with a template and the profile of the template with a counter-template is carried out "through the light", the working sections of the template and the counter-template are made in the form of a narrow strip 0.5-1.0 mm wide. Holes or rectangular slots are made at the points of internal junctions of sections of the shaped profile without fastenings in order to make close contact with the measured surface.
Development and execution of executive drawings of shaped cutters.
On the working executive drawings, shaped cutters should be shown in two projections. The exact dimensions of the cutters are specified in the drawings of the templates, and therefore it is not necessary to re-set the dimensions of the shaped profile on the drawings of the cutters.
For the correct orientation of the shaped profile of the cutter during the grinding process, the diameters or distances to the base surfaces from the extreme nodal points of the shaped profile of the cutter must be indicated on the as-built drawings.
The main dimensions that should be indicated on the executive drawings of shaped cutters are: overall dimensions, dimensions of base holes or surfaces, depth and angle of sharpening, diameter of the control circle at the end of round cutters, if it is provided by the calculation, dimensions of the mounting crown.
To exclude the possibility of turning round shaped cutters on mandrels during operation, either annular corrugations with rectangular cross-section corrugations or holes for a pin are made at the ends of the cutters.
The pin is inserted into the hole of the cutter, and the corrugations, both in the first and in the second version, are in contact with the corrugated belt of the racks in which the cutters are fixed. The pitch of the teeth of the corrugations is 3-4 mm. There is a way to secure using wedge grooves.
On round cutters of small diameters that cut chips of small section, no constructive measures are taken to prevent the rotation of the cutters; incisors are attached only due to frictional forces.
The length of the prismatic cutters should be 75-100 mm so that the cutter can be reground many times. However, the final length of the cutter must be coordinated with the place of its installation on the machine. To accurately set the cutter at the height of the center of the part and increase the stability of the cutter in the working position, a hole for the adjusting pin is made in its lower part.
Broaches design
General instructions
When starting to develop a broach design, the designer must have a clear idea of what requirements the designed broach must meet. Depending on the specific production conditions, the requirements are different. In some cases, it is required that the broach has the greatest durability, in others - that it provides the least roughness and the greatest accuracy, in the third - it is necessary that the broach has the shortest length (sometimes even limited to a specific size). Broaches that satisfy one of these requirements may not satisfy others. For example, broaches for machining high-precision holes with a high surface finish class must have a large number of finishing teeth and operate at low feed rates. Often the finishing part of the broach in this case is longer than the draft part. Therefore, such broaches cannot be short.
Using the methodology outlined below, it is possible to design broaches that meet various requirements. However, depending on the specific production conditions and the requirements for the part, the designer, using these recommendations, can supplement or change the initial values \u200b\u200bgiven in the tables.
So, in case of high demands on the roughness of the part, the designer must increase the number of finishing teeth compared to the number of teeth given in the corresponding table. At the same time, do not allow large feeds on the roughing teeth, choosing from the calculated options one in which the feeds will be the smallest.
When designing broaches, great attention must be paid to choosing the optimal cutting pattern, since smooth operation, normal placement or removal of chips, tool life, and other performance qualities of the tool largely depend on the adopted cutting pattern.
The methodology for calculating broaches of various types is largely similar, with the exception of the calculation of some structural elements.
Technique for designing round broaches.
The initial data for the design of the broach are:
a) data on the workpiece (material and hardness, hole dimensions before and after broaching, machining length, cleanliness class and machining accuracy, as well as other technical requirements for the workpiece);
b) machine characteristics (type, model, pulling force and drive power, speed range, rod stroke, chuck type);
c) the nature of production;
d) the degree of automation and mechanization of production.
Choice of broach material.
Broach design begins with the choice of broach material. In this case, it is necessary to take into account:
properties of the processed material,
type of stretch
the nature of the production
class of cleanliness and accuracy of the surface of the part (Appendix 6).
For steel, guided by Appendix 5, it is preliminarily established to which machinability group the steel of a given grade belongs. If there is no steel of a given grade in Appendix 5, then it belongs to the machinability group in which the steel grade is located, which is closest to it in chemical composition and hardness, or in terms of physical and mechanical properties.
Selecting the method of connecting the broach body and the shank
Broaches by their design can be: solid, welded and prefabricated. All broaches made of HVG steel are made in one piece, regardless of their diameter.
Figure 11 - The cutting part of the broach with a rise on each tooth
a) general view; b) longitudinal profile of roughing and finishing teeth; c) longitudinal profile of the calibrating teeth; d) transverse profile of rough teeth; e) options for making grooves for chip separation.
Broaches from high-speed steel grades P6M5, P9, P18 must be made in one piece when their diameter is ; welded with a shank, from steel 45X if 
; welded or with a 45X steel screw, if D>40 mm. Welding of the shank with the broach rod is carried out along the neck at a distance of 15-25 mm from the beginning of the transition cone.
Figure 12 The cutting part of the variable cutting broach.
a) general view of the cutting part (I-roughing teeth; P-transitional teeth; Ш-finishing teeth; IV-calibrating teeth);
b) longitudinal profile of the teeth;
c) transverse profile of roughing and transitional teeth (1-cut tooth; 2-cleaning tooth);
d) transverse profile of finishing sectional teeth;
e) transverse profile of the finishing teeth (3-second tooth of the second section; 4-first tooth of the second section; 5-second tooth of the first section; 6-first tooth of the first section).
The type of shank is selected depending on the type of chuck available on the broaching machine. Shank dimensions are given in Appendix 7.
In order for the shank to pass freely through the hole previously prepared in the part, and at the same time to be strong enough, its diameter is chosen according to the tables as the closest smaller diameter to the diameter of the hole in the part before pulling. If the selected shank diameter corresponds to the pulling force allowed by the condition of its strength, which is much greater than the traction force of the machine Q, then the shank diameter can be reduced for design reasons.
Choice of front and rear corners. The front angle (Appendix 8) is assigned depending on the material being processed and the type of teeth (rough and transitional, finishing and calibrating).
The broaching allowance is determined by the formula:
(2.1)
where - the largest size of the machined hole,
(2.2)
where is the smallest size of the pre-prepared hole; hole diameter tolerance.
Definition of rise per tooth.
For broaches working according to the profile cutting scheme, the rise per tooth is made the same for all cutting teeth (Appendix 9). On the last two or three cutting teeth, the lift gradually decreases towards the gauge teeth.
For variable cutting broaches, the rise of the roughing teeth is determined by durability. The resistance of the broach is determined by the resistance of its finishing part; the hardness of the roughing part must be equal to or slightly greater, but in no case less than the hardness of the finishing part.
Typically, the rises on the teeth of the finishing part are 0.01-0.02 mm per diameter. Smaller lifts are rarely used due to the difficulty of their implementation and control. Due to the fact that the finishing part of the variable cutting broaches has two types of teeth: the first - with a rise on each tooth (Figure 14, a) and the second - (Figure 14,6) with a rise on a section of two teeth, with one and the same the same rise on the diameter of the thickness is different.
Figure 14-Slice thickness of the finishing part of the variable cutting broach.
When lifting per tooth, the thickness of the cut is equal to twice the amount of lifting per side, i.e. . With a sectional construction of the teeth, it is equal to the lift, i.e. . Feeds recommended for finishing teeth of variable cutting broaches are indicated in Appendix 10. Cutting speeds depending on the properties of the material being processed, the purity and accuracy of processing are indicated in Appendix 11. Depending on the selected cutting speed according to nomograms (Appendix 12), determines the resistance of the finishing part of the broach . If this tool life is insufficient for specific conditions, it can be increased by lowering the previously selected cutting speed. Then, according to the resistance found for the finishing teeth, and the accepted cutting speed, the thickness of the cut of the roughing teeth is found.
Determining flute depth, see figures 11, 12, 13.
produced by the formula:
(2.3)
where is the pulling length;
The filling factor of the chip groove is selected according to Appendix 13.
To ensure sufficient rigidity of a broach with a cross-sectional diameter at the bottom of the flute of less than 40 mm, it is necessary that the depth of the flute does not exceed 
.
The profile parameters of the cutting teeth in the axial section are selected depending on the depth of the chip grooves for single broaches in Appendix 13, and for variable cutting broaches in Appendix 14.
Since one profile in Appendix 14 corresponds to several step values, the smaller one is taken.
Note: In order to obtain the best quality of the machined surface, the pitch of the cutting teeth of single broaches is made variable and equal to
The largest number of simultaneously working teeth is calculated by the formula:
The fractional part obtained in the calculation is discarded.
Determining the maximum allowable cutting force
The cutting force is limited by the traction force of the machine or the strength of the broach in dangerous sections - along the shank or along the cavity in front of the first tooth. The smallest of these forces should be taken as the maximum allowable cutting force.
The values , and are defined as follows.
Estimated traction force of the machine, taking into account the efficiency of the machine, is usually taken equal to:
(2.5)
where - traction force according to the passport data of the machine (Appendix 15).
The cutting force allowed by the tensile strength of the shank in section (Appendix 7) is determined by the formula:
(2.6)
where is the area of the dangerous section.
The values are selected depending on the material of the shank: for steels R6M5, R9 and PI8- = 400 MPa for steels KhVG and 45X- = 300 MPa. The cutting force allowed by the strength of the dangerous section of the cutting part is determined by the formula:
(2.7)
where is the diameter of the dangerous section
For broaches made of steels R6M5, R9 and PI8 with a diameter of up to 15 mm, it is recommended
400...500 MPa;
diameter over 15 mm = 350...400 MPa;
for steel broaches ХВГ (all diameters) = 250 MPa.
Determination of the axial cutting force during pulling.
It is carried out according to the formula:
where 
- see appendix 16.
Hole diameter after broaching.
When designing a single broach, the obtained value is compared with the traction force of the machine, with the cutting forces allowed by the strength of the broach in the dangerous section and by the strength of the shank.
When designing a group broach, the cutting force calculated by formula (2.9) is used to calculate the number of teeth in the section:
And they are assigned only for group broaches according to Appendix 10.
The determination of the diameter of the front guide part is carried out by the diameter of the hole before pulling with deviations in fit f7 or e8.
Determining the size of the cutting teeth.
For single broaches, the diameter of the first tooth is taken equal to the diameter of the front guide part, the diameter of each subsequent tooth increases by SZ.
On the last cutting teeth, the rise per tooth gradually decreases. The diameters of these teeth are 1.2SZ and 0.8SZ, respectively.
For variable cutting broaches, the first teeth of the roughing and transition sections are called slotted, and the last are called cleaning. Each of the teeth cuts a layer of material of the same width with the same lift SZ.
The cleaning tooth is cylindrical in shape with a diameter of () mm less than the diameter of the slotted teeth. The tolerance for the diameter of the cutting teeth is assigned
The calculation of the number of cutting teeth for single broaches is performed by the formula:
(2.13)
The number of gauge teeth is taken .
The number of sections of roughing teeth for variable cutting broaches is determined by the formula:
If the calculation results in a fractional number, it is rounded down to the nearest lower whole number. In this case, a part of the allowance remains, which is called residual allowance, it is determined by the formula:
(2.15)
Depending on the size, the residual allowance can be attributed to the roughing, transitional or finishing part. If half of the residual allowance exceeds the amount of teeth lift to the side of the first transitional section, then one additional section of roughing teeth is assigned to cut it. The rise of the teeth on the transition part is selected from Appendix 10.
If half of the residual allowance is less than the rise to the side of the first transition section, but not less than 0.02-0.03 mm, then the residual allowance is transferred to the finishing teeth, the number of which increases accordingly. The micron part of the residual allowance is transferred to the last finishing teeth.
Thus, the number of roughing teeth:
The number of transitional, finishing and calibrating teeth is selected according to Appendix 10 and adjusted depending on the distribution of the residual allowance. Total number of broach teeth:
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The pitch of the calibrating teeth for single cylindrical broaches is taken equal to:
(t is determined from the table in Appendix 13).
For variable cutting broaches, the average values of the pitch of the finishing and calibrating teeth are determined from the condition (Appendix 14):
. (2.19)
The resulting step values are rounded to tabular values.
The first step of the finishing part (between the first and second teeth) is of greater importance. The variability of steps passes from the finishing to the calibrating part in any sequence.
Determination of the structural dimensions of the rear guide part.
For cylindrical broaches, the rear guide part has the shape of a cylinder with a diameter equal to the smallest diameter of the drawn hole.
Note: For long and heavy broaches supported by a steady rest, the diameter of the rear support pin is determined.
Determining the distance to the first broach tooth by the formula:
where - shank length (Appendix 7); , then make a set of broaches. The total number of cutting teeth is divided by the accepted number of passes so that the lengths of the broaches of each pass are equal. The diameter of the first cutting tooth of the broach of this pass is taken equal to the diameter of the calibrating teeth of the broach of the previous pass.
The designation of the structural elements of the chip separation grooves for single broaches is carried out according to Appendix 17, and for variable cutting broaches, the structural elements for chip separation are calculated in the following order.
The entire perimeter of the chip cut by one section is divided into equal parts between the teeth of the section. Each tooth of the section has a part of the perimeter equal to:
The number of cutting sectors, and hence the fillets, is determined by the formula:
where B is the width of the cutting sector, which is recommended
determined by the formula:
(2.27)
The width of the fillets is determined by the formula:
(2.28)
The number of fillets for finishing teeth can be calculated using the following formula (rounded to the nearest even number):
On the last transition section and on all finishing teeth, in order to ensure that the fillets are covered by the cutting sectors of subsequent teeth, the width of the fillets is taken 2-3 mm less than on the first sections of the transition teeth, i.e.
In the sectional construction of finishing teeth, their diameters (within one section) are chosen to be the same. The same applies to the last section of transition teeth.
The fillet radius is assigned depending on the width of the fillet and the diameter of the broach (Appendix 18).
Fillets on the finishing teeth and on the last section of the transition teeth are applied on each tooth and are staggered relative to the previous tooth. If the broach has one transition section, then it is built as the last transition section.
Method for designing slotted broaches.
There are three types of slotted broaches: type A, type B and type C. Type A broaches have teeth in the following order: round, chamfer, slotted; for type B broaches: round, chamfered, slotted; type B broaches: chamfered, splined, and round broaches are absent.
To calculate the broach, set (Figure 15): the diameter of the hole before pulling D0, the outer diameter of the splines D, the inner diameter of the splines d, the number of splines n, the width of the splines B, the size of the splines m and the angle of the chamfer at the inner diameter of the spline grooves (if the drawing is not specified, then the constructor assigns itself). The nature of production, the material of the part, the hardness, the pulling length l, the required surface roughness and other technical requirements, as well as the model, the pulling force Q of the machine and the stroke of the rod.
The calculation sequence is the same as for the design of round broaches. However, taking into account the design features of the spline profile, the following calculations are additionally performed.
Determination of the largest values of the cutting edges (Figure 16) of chamfer, spline and round teeth.
The length of the cutting edges on the shaped teeth is approximately determined by the formulas: for type A broaches
Figure 15 - Geometric parameters of the original profile of the splined part.
For broaches type B and B
