The geometric parameters of the cutting part of shaped cutters are selected depending on the material being processed. The rake angle of shaped cutters is obtained by sharpening the front surface. For aluminum and red copper rake angle = 20...25°, for bronze, lead brass = 0...5°, for steel with
up to 500 MPa (NV up to 150 units) = 20...25° s
= 500...800 MPa (NV 150...235) = 15...20° s
= 800...1000 MPa (NV 235...290) = 10...15°, for cast iron with NV up to 150 units. = 15° with NV over 150 units. = 10...12°. Back angle
is selected equal to 8...15° depending on the profile configuration and type of cutter.

To form the back angle of a round shaped cutter, its apex must be located below the axis of the base h. Offset amount:
, Where
– largest cutter diameter (selected according to Table 2.1).

The clearance angle of the prismatic cutter is obtained by appropriate installation in the holder. Front size and rear
angles is selected for the outer sections of the cutting edges of shaped cutters that process the minimum diameter of the part profile. For all other points of the cutting edge, the value of the rake angle decreases with increasing diameter being processed, and the rear angle increases.

Sections of the cutter profile perpendicular to the axis of the part have an angle
, equal to zero. To avoid strong friction and improve cutting conditions in the corresponding areas of the cutting edges of the shaped cutter, an undercut is made with an additional leading angle
or leave ribbons on a small section of the cutter profile (see Fig. 2.2).

Rice. 2.2. Improving cutting conditions is unfavorable

located sections of the cutting edge of the shaped cutter

Back angle
at an arbitrary point X in the section N-N, perpendicular to the cutting plane of the cutter, is determined by the formula

Where
– the angle between the tangent to the cutter profile of the point under consideration and a straight line perpendicular to the axis of the part. Corner
determined analytically or graphically.

2.1.6. Corrective calculation of profile of shaped cutter

Corrective calculation of the profile of a shaped cutter is considered using the example of a cutter with
And
. The purpose of the correction calculation is to determine the distances of the nodal points to the base surface. The procedure for calculations for a round shaped cutter, implemented on a computer, is as follows (Fig. 2.3).

The distance of nodal points to the base surface (the surface corresponding to nodal point 1 is conventionally taken as the base surface) (Fig. 2.4) is defined as:

Rice. 2.3. Scheme of correction calculation of a round shaped cutter

Rice. 2.4. Corrective calculation scheme for prismatic

shaped cutter

For any profile point X:

Procedure for calculating values ...
And
when corrective calculation of prismatic shaped cutters is similar. Next, the distances are determined
(Fig. 2.5) from the nodal points to the back surface corresponding to the 0 point, and back corners:
;
;
;
;
. The distance of the nodal points to the base surface (surface 1 is conventionally taken as the base surface) is determined by the formula

Rice. 2.5. Scheme for calculating the distances of nodal points

from the base surface

2.1.7. Assignment of tolerances on the profile dimensions of the shaped cutter, template and counter template

When assigning tolerances to the profile dimensions of a shaped cutter, it should be remembered that the values
are the closing links of the dimensional chain. The tolerance for these dimensions is taken equal to 1/2....1/3 of the tolerance for the corresponding closing links of the part profile. For example, the base surface is taken to be the surface of a cutter that processes the surface of a part with
mm. Height of the part profile corresponding to nodal point 2, s
mm is equal to;
mm. Distance tolerance nodal point 2 of the cutter from the base surface will be equal to (1/2....1/3) of the value ±0.12, i.e. 0.06...0.04 mm.

Templates and counter templates for comprehensive checking of the profile of shaped cutters are designed as profile gauges that control the transmission.

When checking through transmission, a template having a negative cutter profile is applied to it so that the base surfaces of the template and cutter profile fit tightly to each other, and a gap should form on the remaining surfaces. Its value should not exceed the tolerance for the size of the corresponding element of the cutter profile.

If in any section of the profile the clearance value is greater than the tolerance or equal to zero (the template profile touches the cutter profile), this indicates that in this section the cutter profile is made with an unacceptable deviation and the size of the profile in this section must be checked on a microscope or other universal -measuring instrument.

Tolerances on linear dimensions for templates are set in the body of the template, and for counter-templates symmetrically. The value of these tolerances is assumed to be equal for templates from 1/2...1/3 of the tolerance field of the corresponding dimensions of the cutter profile and, accordingly, for counter templates from 1/2...1/3 of the tolerance field of the corresponding dimensions of the template profile. However, taking into account the capabilities of tool production, they should not be less than the tolerances indicated in table. 2.2.

Shaped cutters are tools whose cutting edges are determined by the profile of the part and work using the copying method. They are widely used in serial, large-scale and mass production when processing rotating bodies with external or internal shaped surfaces. Processing is carried out from the rod on turret machines, automatic machines, and semi-automatic machines. Precisely calculated and manufactured shaped cutters for processing a specific part provide high productivity, identical part shapes and dimensional accuracy that do not depend on the qualifications of the worker. Dimensional accuracy of machined parts according to IT8-IT12 and surface roughness RA=0.63-2.5 microns.

The most common are round and prismatic cutters, working with radial and tangential (tangentially directed) feed.

Prismatic cutters are used for processing external surfaces. Compared to round cutters, they have increased rigidity, high processing accuracy, and ease of installation on machines.

Round cutters are used for processing external and internal surfaces. They are more technologically advanced to manufacture than prismatic ones, provide a greater number of regrinds, but are inferior to the latter in terms of rigidity and precision of processing.

When choosing the type of shaped cutter, the decisive factors are its cost, the accuracy of the shape and linear dimensions of the profile, which guarantee the receipt of a suitable part.

3.2.Methodology for designing shaped cutters

Designing a shaped cutter of any type for processing a given part consists of a number of general and mandatory steps for all types of cutters. Thus, the assignment of tool material, the choice of front and rear angles and the assignment of a number of design parameters are carried out absolutely the same for all shaped cutters.

3.2.1.Characteristic points

Before designing, characteristic (nodal) points 1, 2, 3, etc. are sequentially marked on the part profile. These include the start and end points of the profile; nodal, in which one section of the profile passes into another; additional midpoint on the conical section; two or three additional points equidistant from each other on a curved section. Simple chamfers are not coordinated. The cutter drawing indicates the same angle and chamfer size as on the part.

Then the calculated dimensions of the characteristic points are determined, taking into account the size and location of the tolerance fields. The calculated nominal diameters are set in the middle of the tolerance field, with an accuracy of 0.001 mm. The results are recorded in a summary table.

The coordinates of the average intermediate point of the cone are determined by the following formulas:

,

Where
diameters of the initial, middle intermediate and final points of the cone;
linear dimensions of the cone and the average intermediate point.

The coordinates of the average intermediate point of the curved section (quadrant) are determined using the following formulas:

,

Where
diameters of the middle, intermediate and starting points of the quadrant, which is part of the curved section;
arc radius;
linear dimensions of the center of the arc and the middle intermediate point.

3.2.2. Purpose of the material of shaped cutters

Round shaped cutters are mainly designed and manufactured as one piece, and prismatic ones, in order to save tool material, are made as composite cutters. High-speed steel R6M5 is most often used as the material for the working part of cutters. When manufacturing parts from difficult-to-process materials, it is economically profitable to use cutters made from high-speed steels R10K5F5, R9K10, R18K5F2, R9K5 and hard alloys VK10-M, VK8, T15K6. When designing composite cutters, steel 45 GOST 1050-74 is used as a holder material.

General instructions for the implementation of the project (work).

The design of the graphic part of the project (format size, lettering, fonts, shading, etc.) must be done in accordance with the ESKD.

The main images on 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 geometric parameters of the cutting part, the shape of the shaped contour, etc., can be made on an enlarged scale, sufficient for a clearer implementation of the design features of the depicted elements.

Calculation schemes and graphical construction of profiles are carried out on an enlarged scale, the size of which is set depending on the required construction accuracy.

Working drawings of the designed tools, in addition to images of the main projections, sections and sections, must have the necessary dimensions, dimensional tolerances, designations of surface cleanliness 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.

An explanatory note of up to 30-40 pages is typewritten. It should be concise, written and presented in good literary language.

Calculations must contain initial formulas, substitution of corresponding digital values, intermediate actions and transformations sufficient for verification without additional calculations.

All decisions made regarding the choice of design parameters of the designed tool and cutting part material must be accompanied by justification.

Accepted normative, tabular and other data must be accompanied by links to the sources used. It is recommended to use official reference materials for this purpose.

For each tool being designed, it is necessary to develop technical specifications based on the requirements for the product being processed and the technical specifications for similar tool designs.

When developing a new tool, you need to keep in mind the requirements for precision and manufacturability, sharpening features and its productivity. It is necessary to provide for the saving of expensive tool materials, using prefabricated, welded structures, etc. for this purpose.

The fastening and mounting parts of the designed tools must be calculated and brought into accordance with the dimensions of the standardized mountings of existing machines or devices.

Design of shaped cutters

Shaped cutters are used to process parts with a shaped profile. The task of the designer designing a shaped cutter is to determine the dimensions and shapes of its profile that, at the designed sharpening and installation angles, would create on the workpiece the profile specified by its drawing. The calculations associated with this are usually called correction or simply correction of the profile of shaped cutters.

Preparation of as-built drawings of parts.

During the correction 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 points.

Based on these considerations, before proceeding with correction calculations, it is necessary to first check whether all the coordinate dimensions from the base surfaces to the nodal points are available on the as-built drawings of the shaped parts, and if they are not indicated, then it is necessary to determine the missing coordinate dimensions to all selected points. The drawings of shaped parts always contain dimensions that allow you to determine the missing coordinate dimensions. Basic and additional correction calculations for 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 section profiles are determined (without taking into account the radii of curvature of the transition surface).

When calculating round shaped cutters, radii R1, R2, R3, etc. are determined. circles passing through 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. This initial coordinate axis is usually drawn through a point or through a baseline that is at the height of the center of rotation of the part.

Methodology for calculating the profile of shaped cutters.

The initial data for designing a cutter are data on the workpiece (material and hardness, shape and dimensions of the shaped profile, cleanliness and accuracy classes).

Selection of design of shaped cutters.

The following considerations are taken into account when selecting the design of a high-speed steel shaped cutter.

Rod shaped cutters are the most primitive design of this type of cutters; They are cheap to make but allow for a small number of regrinds. Therefore, it is advisable to use rod 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 production. Often, rod shaped cutters are used as a second-order tool, i.e. for the manufacture of cutting tools with complex profiles.

Prismatic shaped cutters are more expensive to manufacture than rod cutters, but allow a significantly larger number of regrinds. All other things being equal, 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 shaped cutters is their high rigidity of attachment, due to which they provide higher machining accuracy compared to round shaped cutters.

Round shaped cutters as bodies of revolution are convenient and cheap to manufacture, and the number of regrinds they allow is large; Thus, the costs per manufactured part are the lowest when processing with round shaped cutters. As a result, shaped cutters have become most widespread in large-scale and mass production. Another important advantage of round shaped cutters is their ease of processing internal surfaces.

Their disadvantages include:

· a sharp decrease in the sharpening angle as the cutting edges approach the axis;

· curvature of cutting edges that occurs when the conical sections of the cutter profile intersect with the front plane.

Shaped cutters with soldered carbide plates allow multiple use of the body. However, they have not become widespread due to technological difficulties.

The selection of design parameters of shaped cutters is made according to the tables (Appendices 1 and 2) depending on the dimensions of the shaped profile of the workpiece. In this case, the main parameter influencing 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~ the largest and smallest radii, respectively

shaped profile of the part.

When assigning the cutter diameter, the following considerations are used. To reduce the consumption of cutter material per processed

It is always advantageous to work a part with a cutter of the smallest diameter. From all other points of view, it is advisable to work with a cutter of the largest possible diameter, since:

· heat dissipation improves and it becomes possible to increase
cutting speed;

· the complexity of manufacturing a cutter per part is reduced due to an increase in service life due to an increase in the number of regrinds.

At the same time, the manufacture and operation of shaped cutters with a diameter that is too large 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 permissible values ​​of 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 advisable to set the length of prismatic cutters to the maximum in order to increase the number of allowed regrinds; 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 shaped cutters depend mainly on the depth and width of the profile being processed.

There are various ways to secure prismatic shaped cutters. The book recommends sizes for prismatic dovetail shaped cutters. The dovetail sizes indicated in the table (Appendix 2) are used by domestic factories that produce multi-spindle automatic lathes.

Choice of front and back angles.

The angle corresponding to the section of the shaped profile furthest from the cutter axis is selected in accordance with the mechanical properties of the material being processed according to the table (Appendix 3). It is generally accepted to select an 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 at sections of the shaped profile at different distances from the axis of the part; As the sections of the profile under consideration move away from the axis of the part, the front angles decrease.

When external machining with shaped cutters with >0, in order to avoid vibrations, the cutting edges should not be allowed to be excessively reduced in relation to the axis of the workpiece; as established by practice, this reduction should not exceed (0.1-0.2) the largest radius of the workpiece being machined. Therefore, the angle selected from the table must be checked using the formula:

On machines, as a rule, normalized holders are installed that have a standard design, therefore, the clearance angle is taken within the range of 8-15°.

It should be noted that for shaped cutters, as the profile points in question move away from the axis of the workpiece, the rear angles increase.

To create satisfactory cutting conditions, in all areas of the cutting profile perpendicular to the projection of the cutting edge onto 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 clearance angles are refined in all areas.

Corrective calculation of the profile of a shaped cutter.

Profile correction can be done graphically and graphically. The last method is the simplest and most obvious, so it is recommended for use.

To calculate the cutter profile, it is necessary to select a number of nodal points on the part profile, which, as a rule, correspond to the connection points of elementary sections of the profile.

Calculation of round and prismatic cutters is performed using various formulas.

a) The procedure for calculating the profile of a round shaped cutter (Figure 1).

Through nodal point 1, draw rays at angles and connect the resulting intersection points 2 and 3 with the center of part O1.

In right triangle 1a01, determine 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 - Graphic 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)

B1 = R1 * cos, (1.8)

where R1 is the outer radius of the cutter.

Determine the lengths using the formula

(1.9)

Calculate the value of the cutter radii corresponding to nodal point 2

Calculate the sharpening angles at the nodal points of the cutter

(1.12)

The minimum acceptable angle values ​​for round cutters are: 40° when processing copper and aluminum; 50° - when processing automatic steel; 60° - when processing alloy steels; 55° - when processing cast iron.

Check the clearance angles to the minimum permissible value (4-5°) in normal sections to the projections of the cutting edges onto the main plane. The calculation is performed using 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 ; 3 n, etc.

b) Features of calculating the profile of a prismatic shaped cutter (see Figure 2).

Figure 2 - Graphical profile definition

prismatic shaped cutter.

The calculation of a prismatic cutter is performed in the same sequence as a circular cutter. After calculating the value of Ci, it is necessary to determine the dimensions of Pi, which are the legs of right 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

Profiles of shaped parts usually consist of straight sections located at different angles to their axis and sections outlined by circular arcs. 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 circular arcs turn into curved lines, the exact outlines of which can only be specified by the location of a series of sufficiently close spaced friend points.

The angular dimensions of the cutter profile (Figure 3) are determined by the formula:

Figure 3 - Calculation of the angular dimensions of the shaped cutter profile.

where is the cutter profile angle;

The distance between the nodal points measured perpendicular to the lateral planes of the cutter.

The need to determine the shape of curved sections of a cutter profile from the position of a number of its points arises relatively rarely, since in most cases, with sufficient accuracy for practice, a selected replacement circular arc is drawn on the calculated section of the cutter profile.

The radius and position of the center of such an arc are 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 parallel to the axis of the part, and the Y axis is perpendicular to it. The coordinates X 0 and Y 0 of the center of the “replacing” arc of a circle are determined by the formulas:

(1.19)

Where: x 1- smaller, a x 2- 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 using the formula

With the common symmetrical arrangement of the replacement arch

the calculation of these quantities is greatly simplified (Figure 4):

circle, the calculation of these quantities is greatly simplified:

It remains only to determine

The above dependencies are often replaced by 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 outlines of the workpiece (Figure 5), the shaped cutter in most cases has additional cutting edges S 1 parts preparing for cutting from the rod, and S 2, processing a chamfer or part of a part that is cut off during trimming.

Figure 5 - Additional cutting edges of shaped cutters.

When processing chamfers, the corresponding cutting edges must overlap S 3, equal to 1-2 mm, and the cutter should end with a reinforcing part S 4 up to 5-8 mm wide. Cutting width S 5 must be greater than the width of the cutting edge of the cutting tool. The following requirements apply to additional cutting edges of a shaped cutter:

1) 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 the scoring cutter at the inflection point of the profile, and the cutting cutter at the point, as a result of which the finished part will have the length specified in the drawing.

Thus, the total width of the cutter is determined by the formula:

(1.23)

3) The cutting edge preparing the cut should not protrude beyond the working profile of the cutter, i.e.

Ways to reduce friction in sections of the profile,

perpendicular to the axis of the part.

A significant disadvantage of shaped cutters of the basic type is their lack of the necessary clearance angles in 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 area of ​​the side plane of the cutter profile.

Since cutting does not occur in such areas and the edges on them are only auxiliary, working in these conditions at shallow depths and processing brittle metals is possible, but is always accompanied by increased wear of the cutter and deterioration in the quality of the machined surface. As the depth of the profile increases and the viscosity of the material increases, processing sections of the profile perpendicular to the axis of the part becomes impossible.

In order to reduce friction and wear of sections of the cutter perpendicular to the axis, an undercut is used at an angle of 2-3° or a narrow strip is left on the cutting edge (Figure 7).

Figure 7 - Methods for reducing friction in sections of the profile,

perpendicular to the axis of the part.

Due to these design changes, the lateral plane of the cutter profile occupies a position (plan view) at which it comes 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 rotating the cutter axis relative to the axis of the part.

Instructions for choosing 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).

There are internal and external bases. The position of the internal bases relative to the external ones is determined by the machine settings. The external bases are the axis and the end of the part. The internal bases are those surfaces of the part whose dimensions or distances are specified from the external bases with the highest accuracy.

As shown in Figure 8, from the position of the base surface of the BR, connected by 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 processed surfaces

shaped cutter, internal and external processing bases.

Surfaces I and P are connected to surface Br by the dimensions of the profile depth. The internal axial base B0 is here one of the surface joints, connected to the external base (end of the part) by the axial base dimension l B; the axial position of nodal points I and 2 (l1 and l2) relative to the end of the part depends on the size l B and dimensions transmitted by the cutter to the part, 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 basic 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 carried out according to the base size (internal base).

Obtaining the basic size of a part can be done with a certain accuracy, which is limited by the adjustment tolerance. It can be taken equal to .

The dimensions of the depth and width of the part profile are calculated using the formulas:

(1.24)

The depth dimensions of the cutter profile differ from the corresponding dimensions of the part profile and are calculated using similar formulas with an accuracy of 0.01 mm, and the width dimensions of individual sections of the profile coincide with the dimensions of the corresponding sections of the part profile.

The depth tolerance of the part profile is determined by the formula:

To select tolerances for cutter profile depths, use the formula

where is the tolerance for the corresponding depth of the part profile;

Distortion factor.

When determining tolerances for profile width dimensions, it is assumed that the cutter profile widths are equal to the part profile widths. In addition, deviations from the calculated dimensions of the geometric parameters do not affect the profile width. Therefore, taking into account only compensation for operational errors, we can accept:

(1.27)

where is the tolerance for the width of the cutter profile;

Tolerance for the width of the product profile.

Tolerances of the rake and clearance angles affect the deviations in the depth of the cutter profile. It has been established that with equal deviations of the angles and ,

the rear angle causes larger profile depth errors than the front angle. Therefore, it is recommended to choose angle tolerance values ​​that are equal in value, but different in sign. In addition, the tolerance sign of the front angle should be taken positive, and the rear angle - negative.

Tolerances for cutter diameters are assigned according to the formula

Construction of templates for control of cutter profiles.

Based on the results of correction calculations, it is possible to construct profiles of templates to control the accuracy of grinding of 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 laid in perpendicular directions that determine the relative position of all points of the shaped profile. The location of 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 to calculate and indicate the inclination angles of the contour sections, as well as the lengths of all blades, on the as-built drawings of the templates, in addition to the coordinate dimensions.

Tolerances for the manufacturing accuracy of the linear dimensions of the template shaped profile specified in 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 accuracy of manufacturing the counter-pattern are taken equal to 50% of the tolerances for manufacturing the template.

Since control of the cutter profile with a template and the template profile with a counter template is carried out “through the light”, the working areas of the template and counter template are made in the form of a narrow strip 0.5-1.0 mm wide. At the internal interface points of sections of the shaped profile without fastenings, holes or rectangular slots are made for the purpose of tight contact with the surface being measured.

Development and execution of as-built drawings of shaped cutters.

On working as-built drawings, shaped cutters should be shown in two projections. The exact dimensions of the cutters are specified in the template drawings and therefore re-dimensions of the shaped profile on the cutter drawings are not necessary.

For the correct orientation of the shaped cutter profile during the grinding process, the as-built drawings must indicate the diameters or distances to the base surfaces from the extreme nodal points of the shaped cutter profile.

The main dimensions that must be indicated on the as-built drawings of shaped cutters are: overall dimensions, dimensions of the base holes or surfaces, depth and angle of sharpening, diameter of the control circle at the end of the round cutters, if it is provided for in the calculation, dimensions of the fastening crown.

To eliminate the possibility of rotating round shaped cutters on mandrels during operation, either annular bands with corrugations of rectangular cross-section 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 second versions, come into contact with the corrugated belt of the posts in which the cutters are fixed. The pitch of the corrugation teeth is 3-4 mm. There is a method of securing using wedge grooves.

On round cutters of small diameters that cut chips of small cross-section, no constructive measures are taken to prevent rotation of the cutters; the cutters are attached only due to friction forces.

The length of prismatic cutters should be 75-100 mm so that the cutter can be sharpened many times. However, the final length of the cutter must be coordinated with its installation location on the machine. To accurately install 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.

Design of broaches

General instructions

When starting to develop a broach design, the designer must have a clear idea of ​​what requirements the designed broach must satisfy. Depending on the specific production conditions, the requirements vary. In some cases it is required that the broach has the greatest durability, in others it is required that it provide the least roughness and the greatest accuracy, in others it is necessary that the broach have 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 processing particularly precise holes with a high class of surface finish must have a large number of finishing teeth and work with low feeds. Often the finishing part of the broach in this case turns out to be longer than the rough part. Therefore, such broaches cannot be short.

By using the methodology outlined below, broaches can be designed to meet various requirements. However, depending on the specific production conditions and requirements for the part, the designer, using these recommendations, can supplement or change the original values ​​​​given in the tables.

Thus, in the case of high requirements for 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, avoid 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, durability, and other performance qualities of the tool largely depend on the adopted cutting pattern.

The method for calculating broaches of various types is largely similar, with the exception of the calculation of some structural elements.

Methodology for designing round broaches.

The initial data for designing a broach are:

a) data on the workpiece (material and hardness, hole dimensions before and after broaching, processing length, cleanliness class and processing accuracy, as well as other technical requirements for the part);

b) characteristics of the machine (type, model, traction and drive power, speed range, rod stroke length, chuck type);

c) the nature of production;

d) the degree of automation and mechanization of production.

Selection of broach material.

Designing a broach begins with choosing the broach material. In this case, it is necessary to take into account:

properties of the processed material,

· type of broach,

nature of production,

· class of cleanliness and accuracy of the surface of the part (Appendix 6).

For steel, guided by Appendix 5, it is first established which machinability group the steel of a given grade belongs to. If there is no steel of a given grade in Appendix 5, then it belongs to the machinability group in which the steel grade that is closest to it in chemical composition and hardness, or in physical and mechanical properties is located.

Choosing a method for connecting the broach body and the shank

According to their design, broaches can be: solid, welded and prefabricated. All broaches made of HVG steel are manufactured in one piece, regardless of their diameter.

Figure 11 - Cutting part of the broach with a lift for 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 made of high-speed steel grades P6M5, P9, P18 must be made in one piece when their diameter is ; welded with a shank, made of steel 45X if ; welded or with a screw made of steel 45X, 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 Cutting part of variable cutting broach.

a) general view of the cutting part (I - rough teeth; P - transition teeth; W - finishing teeth; IV - calibrating teeth);

b) longitudinal profile of the teeth;

c) transverse profile of roughing and transition teeth (1-slotted tooth; 2-cleaning tooth);

d) transverse profile of finishing section teeth;

e) transverse profile of 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. The dimensions of the shanks are given in Appendix 7.

In order for the shank to pass freely through the hole previously prepared in the part, and so that at the same time it is strong enough, its diameter is selected according to the tables that is closest to the diameter of the part hole before broaching. If the selected shank diameter corresponds to a pulling force that is permissible under the conditions of its strength, significantly greater than the traction force of the machine Q, then the shank diameter can be reduced for design reasons.

Choice of front and back angles. The rake angle (Appendix 8) is assigned depending on the material being processed and the type of teeth (roughing and transition, finishing and calibrating).

The allowance for broaching is determined using the formula:

(2.1)

where is the largest size of the hole being machined,

(2.2)

where is the smallest size of the previously prepared hole; hole diameter tolerance.

Determination of tooth lift.

For broaches operating according to a profile cutting pattern, the lift 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 calibrating teeth.

For variable cutting broaches, the rise of rough teeth is determined by their durability. The durability of the broach is determined by the durability of its finishing part; the durability of the rough part should be equal to or should be slightly greater, but in no case less than the durability of the finishing part.

Typically, the lifts on the teeth of the finishing part are 0.01-0.02 mm per diameter. Smaller lifts are rarely used due to the difficulties 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 As you go up the diameter, the thickness turns out to be different.

Figure 14—Cut thickness of the finishing part of the variable cutting broach.

When lifting on each tooth, the thickness of the cut is equal to twice the lift on the side, i.e. . When constructing teeth in sections, it is equal to the lift, i.e. . Feed rates 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 cleanliness and accuracy of processing, are indicated in Appendix 11. Depending on the selected cutting speed, the nomograms (Appendix 12) determine the durability of the finishing part of the broach . If this durability turns out to be insufficient for specific conditions, it can be increased by reducing the previously selected cutting speed. Then, based on the durability found for the finishing teeth and the accepted cutting speed, the cut thickness of the rough teeth is found.

Determination of the flute depth, see figures 11, 12, 13.

produced according to the formula:

(2.3)

where is the pulling length;

The fill factor of the chip groove is selected according to Appendix 13.

To ensure sufficient rigidity of a broach having a cross-sectional diameter at the bottom of the chip flute of less than 40 mm, it is necessary that the depth of the chip flute does not exceed .

The profile parameters of the cutting teeth in the axial section are selected depending on the depth of the chip flutes 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

The largest number of simultaneously working teeth is calculated by the formula:

The fractional part obtained during the calculation is discarded.

Determination of the maximum permissible cutting force

The cutting force is limited by the traction force of the machine or the broaching strength in dangerous sections - along the shank or along the cavity in front of the first tooth. The least of these forces should be taken as the maximum permissible cutting force.

The values ​​of , and are defined as follows.

The calculated traction force of the machine, taking into account the efficiency of the machine, is usually taken equal to:

(2.5)

where is the traction force according to the machine’s passport data (Appendix 15).

The cutting force allowed by the tensile strength of the shank in the 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 Р6М5, Р9 and PI8- = 400 MPa for steels ХВГ and 45Х- = 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 P6M5, P9 and PI8 with a diameter of up to 15 mm, it is recommended

400...500 MPa;

with a diameter over 15 mm = 35О...400 MPa;

for broaches made of HVG steel (all diameters) = 250 MPa.

Determination of axial cutting force during broaching.

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 broach strength in the dangerous section and the strength of the shank.

When designing a group broach, the cutting force calculated using 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 diameter of the front guide part is determined by the diameter of the hole before broaching with deviations according to the fits f7 or e8.

Determining the size of cutting teeth.

For single broaches, the diameter of the first tooth is assumed to be equal to the diameter of the front guide part, the diameter of each subsequent tooth increases by SZ.

On the last cutting teeth, the lift per tooth gradually decreases. The diameters of these teeth are 1.2SZ and 0.8SZ, respectively.

In variable cutting broaches, the first teeth of the roughing and transition sections are called slotted, and the last are called stripping. Each of the teeth cuts a layer of material of the same width with the same SZ rise.

The cleaning tooth is made of a cylindrical shape with a diameter () mm less than the diameter of the slotted teeth. The tolerance for the diameter of the cutting teeth is assigned

The number of cutting teeth for single broaches is calculated using the formula:

(2.13)

The number of calibrating teeth is accepted.

The number of sections of rough teeth for variable cutting broaches is determined by the formula:

If the calculation results in a fractional number, it is rounded to the nearest smaller integer. In this case, 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 classified as a roughing, transition or finishing part. If half of the residual allowance exceeds the amount of tooth lift on the side of the first transition section, then one additional section of rough teeth is assigned to cut it off. The lift of the teeth on the transition part is selected from Appendix 10.

If half of the residual allowance is less than the rise on 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. A micron portion of the residual allowance is transferred to the last finishing teeth.

Thus, the number of rough teeth:

The numbers of transition, finishing and calibrating teeth are selected according to Appendix 10 and adjusted depending on the distribution of the residual allowance. Total number of broach teeth:

The pitch of the calibrating teeth for single cylindrical broaches is assumed to be equal to:

(t is determined according to the table in Appendix 13).

For variable cutting broaches, the average pitch values ​​of finishing and calibrating teeth are determined from the condition (Appendix 14):

. (2.19)

The resulting step values ​​are rounded to table values.

The first step of the finishing part (between the first and second teeth) is more important. The variable steps move 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 broached hole.

Note: For long and heavy broaches supported in operation by a steady rest, determine the diameter of the rear support pin.

Determining the distance to the first broach tooth using the formula:

where is the length of the shank (Appendix 7); , then they 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 to be equal to the diameter of the calibrating teeth of the broach of the previous pass.

The designation of structural elements of chip separating 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 chips cut by one section is divided into equal parts between the teeth of the section. For each tooth of the section there is a part of the perimeter equal to:

The number of cutting sectors, and therefore 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 (rounding the results obtained to the nearest even number):

On the last transition section and on all finishing teeth, to ensure that the fillets overlap with the cutting sectors of subsequent teeth, the width of the fillets is taken to be 2-3 mm less than on the first sections of the transition teeth, i.e.

When constructing finishing teeth in sections, their diameters (within one section) are chosen to be the same. The same applies to the last section of transition teeth.

The radius of the fillets is assigned depending on the width of the fillet and the diameter of the broach (Appendix 18).

The 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.

Methodology for designing splined broaches.

There are three types of spline broaches: type A, type B and type C. For type A broaches, the teeth are arranged in the following order: round, chamfered, splined; for type B broaches: round, chamfered, splined; for type B broaches: chamfered, splined, and round ones are absent.

To calculate broaching, set (Figure 15): hole diameter before broaching D0, outer diameter of splines D, internal diameter of splines d, number of splines n, width of splines B, spline size m and chamfer angle at the inner diameter of the spline grooves (if not specified in the drawing, then the constructor assigns it himself). The nature of production, material of the part, hardness, broaching length l, required surface roughness and other technical requirements, as well as the model, traction force Q of the machine and stroke of the rod.

The calculation sequence is the same as when designing 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 chamfered, splined and round teeth.

The length of the cutting edges on shaped teeth is approximately determined by the formulas: for type A broaches

Figure 15 - Geometric parameters of the original profile of the spline part.

For broaches type B and B

Introduction

Shaped cutters are a tool whose cutting edges have a shape that depends on the profile shape of the workpiece.

Shaped cutters work in difficult conditions, since all cutting edges simultaneously engage in cutting and create high cutting forces. Their use does not require highly qualified workers, and the accuracy of the processed parts is ensured by the design of the cutter itself. Carefully calculated and precisely manufactured shaped cutters, when installed correctly on machines, ensure high productivity, accurate shape and dimensions of the processed parts.

The accuracy of manufacturing parts using shaped cutters can be achieved up to 9-12 accuracy grades.

Round shaped cutters are used for turning external and internal surfaces, and prismatic ones only for external ones. The main advantages of round shaped cutters are the ease of their manufacture and a large number of regrinds compared to prismatic cutters. The cutters are fixed on a mandrel and secured against rotation using corrugations made on one of the ends.

More often, corrugations are made on a special ring with a pin, which is part of the holder for attaching the cutter to the machine. In this case, a hole for the pin is drilled at the cutter.

The length of the profile of the shaped cutter is taken to be slightly greater than the length of the workpiece. The permissible length of the cutter profile L p when fastening the workpiece in the chuck is limited.

Round shape cutter design

Shaped cutters are an expensive and complex tool. For a round cutter, only the cutter itself is made of high-speed steel, and the holder on which it is mounted is made of structural steel. To prevent the cutter from turning on the holder, a serrated corrugated surface is made.

For the production of round cutters, it is advisable to use multi-purpose CNC machines.

When processing on these machines, the ease of manufacturing even the most complex shaped profiles is noted.

The main structural elements of a shaped round cutter that need to be determined are:

outer diameter of the cutter;

hole diameter;

shaped cutter profile;

cutter length.

The outer diameter of the cutter is set taking into account:

product profile height,

distance required for chip removal L,

minimum value of the cutter wall size M.

Figure 1. Standard size of shaped surface

Part dimensions: D - 42 mm; D 1 - 45 mm; l 1 = 3 mm; l 2 -- 18 mm; l 3 = 33 mm;

L =40 mm; f = 0.5 mm.

Processed material - steel 20XG

We take the length of the cutter to be increased by 4 mm compared to the length of the part to compensate for the inaccuracy of installing the rod relative to the cutter.

On the surface in contact with the bar, we make an undercut angle to prevent the side surface of the cutter from rubbing against the bar.

To facilitate precise installation of the cutter at the height of the center of the product, notches should be made on the body of the cutter. For ease of sharpening, it is recommended to place a control circular mark on the cutter, the radius of which is equal to hp.

Tolerances for the manufacturing accuracy of all linear dimensions of the cutter are not directly specified. Tolerances are usually set for the manufacture of all template sizes for a given cutter, and the profile of the cutter is measured by the template. Tolerances for template manufacturing are accepted in the range of 0.01-0.02mm.

Choice of material for cutting parts.

We choose high-speed steel R6M5.

Characteristics of R6M5.

R6M5 steel has mainly replaced steels R18, R12 and R9 and has found application in the processing of non-ferrous alloys, cast irons, carbon and alloy steels, as well as some heat-resistant and corrosion-resistant steels.

The strength of this material is satisfactory. Increased wear resistance at low and medium cutting speeds. This material has a wide range of quenching temperatures.

Sandability is satisfactory.

R6M5 steel is used for the production of all types of cutting tools when processing carbon alloy structural steels; Preferably for the manufacture of thread-cutting tools, as well as tools that work with shock loads.

Chemical composition of R6M5 steel:

The hardness of the P6M5 material after annealing is HB 10 -1 = 255 MPa.

Geometry of the shaped cutter.

A shaped cutter, just like any other cutter, must be equipped with appropriate rear and rake angles so that the chip removal process takes place under sufficiently favorable conditions.

The geometric parameters of the cutting part - angles b and d - are set at the base point (or on the base line) of the cutting edge in the n plane, perpendicular to the base of the cutter attachment. Point A, which is furthest from the mounting base, is taken as the base point.

Figure 2. Geometric parameters of the cutting part

The front angle of a radial round cutter is made during its manufacture, placing the front surface at a distance h from the cutter axis, and the rear angle is obtained by setting the cutter axis above the axis of the part by the value h p.:

h p = RХsin(b)

where R = D/2 is the radius of the cutter at the base point (D is the maximum diameter of the cutter).

The value of the anterior angles of radial incisors is assigned according to the table. 5 depending on the material being processed and the material of the cutter.

The clearance angle of the cutting edge of the cutter depends on the shape of the shaped cutter and its type; for round shaped cutters, the clearance angle is selected within the range of 10 0 -15 0. For calculations we will take 15 0.

The given values ​​of the back and front angles refer only to the outer points of the cutter profile. As the points under consideration approach the center of the round cutter, the rear angle continuously increases, and the rake angle decreases.

Calculation of shaped cutter

The profile of the shaped cutter, as a rule, does not coincide with the profile of the workpiece, which requires adjustment of the cutter profile.

To do this, determine the dimensions of the normal section for prismatic and axial sections for round cutters.

The profile of a shaped cutter is adjusted in two ways:

graphic;

analytical;

Graphic methods provide the greatest accuracy; at the same time, they are simple and acceptable when adjusting the profile of cutters with simple configurations, with low accuracy requirements, and for approximate determination of the profile of complex and precise shaped cutters. All of them are based on finding the natural size of a flat figure, determined by the normal or axial section of the shaped cutter. In practice, the profile of a shaped cutter is adjusted using an analytical method that ensures high accuracy.

When the rear and rake angles are equal to 0, the profile of the cutter will exactly coincide with the profile of the part.

In our case, the angles do not equal 0, in this case you can notice that the profile of the cutter changes in comparison with the profile of the part, all dimensions of the profile, measured perpendicular to the axis of the part, change on the cutter.

Let us determine the cutting edge profile for our cutter in two ways and compare them.

First method: Graphic,

Second method: Analytical.

Graphic calculation of cutter profile

Profiling comes down to the following. Characteristic points 1, 2, 3... of the horizontal projection of the part are transferred to the horizontal axis of the vertical projection of the part, and then, with radii described from the center of the vertical projection of the part, are transferred to the mark of the front surface of the cutter. This achieves correction from the presence of the anterior angle. The resulting points are transferred from the mark of the front surface with radii described from the center of the cutter to the horizontal axis of its vertical projection. As a result of this transfer, a correction is made for the presence of a back angle. The resulting points are lowered down until they intersect with horizontal lines drawn from the characteristic points of the horizontal projection of the part.

In Fig. 4, in addition to profiling, additional cutting edges of the cutter are given, the dimensions of which can be taken into account when designing its design: S 1 - cutting edge that prepares for cutting the part from the workpiece (usually a rod); its top should not protrude beyond the working profile of the cutter, i.e. t - should be less than (or equal to) t max. In this case, the width of the groove for cutting should be 0.5... 1 mm wider than the length of the main cutting edge of the cutting tool. The angle q must be at least 15°.

An additional cutting edge S 2 is required for chamfering or trimming a part; S 5 = 1...2 mm - overlap; S 4 = 2...3 mm - strengthening part.

Thus, the length of the cutter

L R = l d + S 2 + S 4

where l d is the length of the part.

L p = 40 + 15 + 2 = 57 mm

Figure 4. Graphic method for profiling a cutter with sharpening at an angle r

The diameter of the round shaped cutter is determined graphically. Maximum depth of processed profile

d min, d max - the largest and smallest diameters of the profile of the workpiece.

According to the greatest depth of the processed profile according to the table. 3 we find

D = 60 mm, R 1 = 17 mm.

where, R= D/2 is the radius of the cutter at the base point (D is the maximum diameter of the cutter).

To obtain the rear angle of a round shaped cutter, its apex in operation is set below the axis of the cutter at a distance h.

Figure 5. Determining the clearance angles of the form cutter

We calculate the sharpening height of the shaped cutter with a base point relative to the axis of the part:

h p =17 * sin25=7.1 mm

The shaped contour is divided into separate sections, the base points characterizing the ends of the sections are designated by numbers and the coordinates of all base points are determined, i.e. Table 1 is compiled (see Figure 5).

It is advisable to arrange the base points so that they have the same radii r in pairs, which reduces the amount of correction calculations. Unknown coordinates of points are determined by solving right triangles. For example: the size l i is set, after that the radius of the point r 1 is determined, and then, having the radius, the size l i ” is obtained in a similar way. The accuracy of calculating the coordinates of the workpiece points is 0.01 mm.

Since a shaped cutter usually must be calculated over a number of nodal points, for convenience the calculations can be presented in the form of a table

Table 1

Analytical calculation of the profile of a shaped cutter

Solving elementary geometric problems, the number of characteristic points by which we determine the radii of the profile points of the part, as in the geometric method - 8.

Let us denote by numbers 1,2,...., i conditionally the points of a given profile, the radii r 1 , r 2 .... of nodal points and the distance along the axis between them l 21 .......l i1 are determined from the part drawing and are summarized in Table 1. Let point 1 be located at the height of the center of rotation of the part (base point). Through point 1 we draw the front surface of the cutter at an angle r 1. Due to the inclination of the front surface, the remaining nodal points (2, 3, ..., i) are located below the center of rotation of the part.

To calculate the profile of round and prismatic shaped cutters, it is necessary to determine the distances C i1 along the front face from point i to point 1.

Where r 1, r i are the radii of the base and i-th node points, respectively.

Consequently, the value of C i1 is not related to the structural shape of the cutters, i.e. the formula is valid for both prismatic and round cutters.

Determine the radius R i of the cutters for external processing:

where r 1, b 1 - front and rear angles for base point 1;

We determine the distance of the profile depth in the axial section of the round shaped cutter:

t 2 =30-29.5=0.5 mm

t 3 =30-29.5=0.5 mm

t 4 =30-26=4 mm

t 5 =30-24.8=5.2 mm

t 6 =30-26=4 mm

t 7 =30-29.5=0.5 mm

t 8 =30-29.5=0.5 mm

Let's compare the cutter sizes obtained by two methods:

Table 2.

Thus, the maximum discrepancy between the two methods was 1.163%. By comparing these two methods for calculating the profile of a shaped cutter, we determine that the analytical method is the most accurate.

The error is not large, so for small-scale production you can use the graphical method.

Designing a template and counter-pattern

Based on the results of the correction calculation, a template profile is constructed to control the accuracy of the profile of the shaped surface of the cutter after grinding, and a counter template to control the profiles of the grinding wheel for processing the cutter profile. To do this, a coordinate line is drawn through the base point parallel to the axis, from which the calculated values ​​of the cutter profile height at characteristic points DR i are plotted. The axial dimensions of the cutter profile with an axis parallel to the axis of the part are equal to the axial dimensions of the part.

Curvilinear sections of the profile are specified in the form of an arc of radius r, the value of which is determined using the coordinates of three characteristic points located on the curved section, or the coordinates of a number of points through which the curve passes.

Profile manufacturing accuracy ±0.01. To facilitate grinding along the profile, a chamfer is made at an angle of 30°. Template material - steel 20ХГ, hardness HRC 58...62.

hob cutter cutting

Initial data: Figure 54, option 9

Figure 1.1 Sketch of the part being manufactured.

Rod material grade Brass L62: uv = 380 MPa;

The cutter type is round.

We calculate the height dimensions of the profile at nodal points on the part using the formulas:

t2 = (d2 - d1)/2; (1.1)

t3 = (d3 - d1)/2; (1.2)

t4 = (d4 - d1)/2; (1.3)

where d1, d2, d3, d4 are the diameters of the machined surfaces on the part.

t2 = (24-20)/2 = 2 mm;

t3 = (28-20)/2 = 4 mm;

t4 = (36-20)/2 = 8 mm;

tmax = t4, mm.

Let's choose the overall and design dimensions of the cutter according to Table 1, the values ​​of the front and rear angles of the cutter according to Table 3.

Table 1.1 Overall and design dimensions

Table 1.2 Values ​​of front and rear angles

Brass L62

Let us calculate for each nodal point the height dimensions of the cutter profile, measured along the front surface.

xi = (ri·cos(r - gi) - r1)/cos g; (1.4)

where ri are the radii of nodal points on the part profile;

r - the value of the front angle at base point 1;

gi - the values ​​of the rake angles for the design points on the profile of the cutting edge of the cutter.

sin gi = (ri-1/ri) sin g; (1.5)

sin r2 = (r1/r2) sin r = (10/12) sin3 = 0.04361;

r2 = 2.5? = 2?30ґ;

sin r3 = (r1/r3) sin r = (10/14) sin3 = 0.03738;

r3 = 2.14? = 19?8ґ;

sin r4 = (r1/r4) sin r = (10/18) sin3 = 0.02908;

r3 = 1.67? = 19?40ґ;

x2 = (r2·cos(r-r2)-r1)/cosг = (12·cos(3-2.5)-10)/cos3 = 2.0023 mm;

x3 = (r3·cos(r-r3)-r1)/cosг = (14·cos(3-2.14)-10)/cos3 = 4.004 mm;

x4 = (r4·cos(r-r4)-r1)/cosг = (18·cos(3-1.67)-10)/cos3 = 8.0061 mm;

Let us calculate the height dimensions of the cutter profile necessary for its manufacture and control.

The height dimensions of the profile for each nodal point are set in a radial section.

Тi = R1 - Ri; (1.6)

Where R1,Ri are the radii of circles passing through the nodal points of the cutter profile

Ri= (R12+xi2-2 R1xicos(b+ g))1/2 (1.7)

R2= (R12+x22-2 R1x2cos(b+ g))1/2=(252+2.00232-2 25 2.0023 cos(10+3))1/2=23.0534 mm;

R3= (R12+x32-2 R1x3cos(b+ g))1/2=(252+4.0042-2 25 4.004 cos(10+3))1/2=21.118 mm;

R4= (R12+x42-2 R1x4cos(b+ g))1/2=(252+8.0061 2-2 25 8.0061 cos(10+3))1/2=17.293 mm;

T2 = R1 - R2 = 25-23.0534 = 1.9466;

T3 = R1 - R3 = 25-21.118 = 3.882;

T4 = R1 - R4 = 25-17.293 = 7.707;

Let's check the results of the analytical calculation of the values ​​T2, T3, T4 by graphically plotting the cutter profile.

• 1) Draw the part in two projections on the coordinate planes V and H. The V plane is vertical, runs perpendicular to the axis of the part, the H plane is horizontal, coincides with the direction of feed of the cutter.
• 2) Let us designate the profile nodal points on the projections of the part with the numbers 1,2,3,4.
• 3) Draw on plane V the contours of the projections of the front and rear surfaces of the cutter. The projection of the front surface of a round cutter is a straight line 1`P drawn from point 1` at an angle z to the horizontal center line of the part. Projection of the rear surface of a round cutter - circles of radii R1, R2, R3, R4 drawn from the center Or through the intersection points of line 1`P with the contour circles of the part profile. The center of the cutter Or lies on the line 1'O drawn from point 1' at an angle b to the horizontal center line of the part at a distance equal to the radius R1, i.e. 1`O = R1.
• 4) Draw the cutter profile in a normal section on the coordinate plane H, for which:
  • a) choose arbitrarily the center O1 of the intersection of the traces of the planes N and H;
  • b) from the center O1 we draw a straight line NN, radially directed;
  • c) using a compass, transfer the height dimensions of the cutter profile from plane V to plane H.
• 5) We measure the height dimensions of each nodal point of the cutter profile T2, T3, T4 in the drawing and divide the resulting values ​​by the accepted scale of graphic profiling of the cutter, enter the results into a table and compare them with the results of the analytical calculation.

Table 1.3

Determine the dimensions of additional cutting edges.

Additional cutting edges prepare the part for cutting from the rod. The height of the edges should not be greater than the height of the working profile of the cutter, the width is equal to the width of the cutting edge of the cutting cutter.

b = tmax + (5…12) = 5 + 12 = 17 mm

Lр = lд + b1 + c1 + c2 + f = 55 + 3 + 2 + 2 + 2 = 64 mm

dimensions: b1?2 mm, c1 = 2 mm, c2 = 2 mm, f = 2 mm.

We take b = 6 mm, b1 = 3 mm, c1 = 2 mm, c2 = 2 mm, f = 2 mm.

To reduce the friction of the cutter on the workpiece, in sections of the profile perpendicular to the axis of the part, we sharpen an angle equal to 3?.

We develop a drawing of a template and a counter template to check the cutter profile for clearance.

The profile of the template is a negative profile of the cutter. The height dimensions of the template profile are equal to the corresponding height dimensions of the cutter profile. Axial dimensions between nodal points of the part profile. To construct a template, it is necessary to draw a coordinate horizontal line through the nodal base point 1, from which the height dimensions of the cutter profile are plotted in directions perpendicular to it. Tolerance for the manufacture of vertical dimensions of the template profile ±0.01, linear dimensions +0.02…0.03.

Template width

Lsh = LP + 2·f = 64 + 2·2 = 68 mm; (1.17)

where: LP - cutter width; f = 2 mm.

Figure 1.2. Additional cutting edges of shaped cutters

Figure 1.3 Pattern and counter-pattern

Figure 1.4 Prismatic shaped cutter