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1 MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION federal state budgetary educational institution higher vocational education ULYANOVSK STATE TECHNICAL UNIVERSITY M. Yu. Smirnov, G. I. Kireev, V. V. Demidov Tutorial Ulyanovsk UlGTU 011
2 UDC 61.9 (075) BBK 34.6 y7 C 50 Reviewers: Ph.D. tech. Sci., Associate Professor of the Department "Mathematical Modeling of Technical Systems" UlGU Evseev A. N., Department "Materials Science and Engineering Technology" UlGSKhA. Approved by the editorial and publishing council of the university as a textbook C 50 Smirnov, M. Yu. Calculation and design of shaped cutters: a textbook / M. Yu. Smirnov, GI Kireev, VV Demidov. Ulyanovsk: UlGTU, p. ISBN The method of calculation and design of round and prismatic shaped cutters is given. Examples of calculations of shaped cutters and execution of working drawings are presented. The manual is intended for students of higher educational institutions students in the direction of "Design and technological support of machine-building industries." UDC 61.9 (075) LBC 34.6 y7 Smirnov M. Yu., Kireev G. I., Demidov V. V., 011 ISBN Design. UlGTU, 011
3 3 CONTENTS INTRODUCTION METHODOLOGY FOR CALCULATION OF ROUND SHAPED CUTTER WITH RADIAL FEED Determination of structural and geometrical parameters of a round shaped cutter Profiling of a round shaped cutter with a lateral inclination of the front surface (λ 0) dimensions of the profile of a part having a curved section in the form of an arc of a circle METHODOLOGY FOR CALCULATION OF PRISMATIC SHAPED CUTTER WITH RADIAL FEED Determination of the structural and geometric parameters of a prismatic shaped cutter Profiling a prismatic shaped cutter without a lateral inclination of the front surface (λ=0) (λ 0) METHODOLOGICAL INSTRUCTIONS FOR THE DEVELOPMENT OF WORKING DRAWINGS OF A SHAPED CUTTER AND A TEMPLATE WITH A COUNTER-TEMPLATE TO IT ... 8 CONCLUSION REFERENCES APPENDIX ... 3
4 4 INTRODUCTION Shaped cutters are single-edged cutting tools that are used to process bodies of revolution with various form generatrix. Compared to conventional cutters, shaped cutters provide the identity of the shape, the accuracy of the dimensions of the parts, since they depend mainly on the accuracy of the manufacture of the cutter. In addition, shaped cutters provide high performance processing of workpieces due to the simultaneous processing of all sections of the shaped profile of the part and ease of regrinding. Shaped cutters are used on lathes and turrets, automatic and semi-automatic machines in large-scale and mass production. Shaped cutters can be rod, prismatic and round. The last two types of incisors are most widely used. Round shaped cutters are used for turning external and internal surfaces, and prismatic ones are used only for external ones. The main advantages of round shaped cutters are the ease of their manufacture, a large number of regrinding compared to prismatic cutters. At the same time, prismatic shaped cutters have a higher accuracy and reliability of fastening. In the direction of feed, shaped cutters are divided into radial and tangential. When working with radial cutters, a transverse feed is provided along the radius of the workpiece. For prismatic cutters, a tangential feed direction is carried out to the processed shaped surface. When designing a shaped cutter, the problem of its profiling is solved. To profile a shaped cutter means to determine its profile in a plane normal to its back surface according to the known axial profile of the part. 1. METHOD OF CALCULATION OF ROUND SHAPED CUTTERS WITH RADIAL FEED 1.1. Determination of structural and geometric parameters of a round shaped cutter Determination of the outer diameter of the cutter and the diameter of the hole for the mandrel details; e rake distance required for chip formation and curling: e 3 10mm; f wall thickness: f 0, r a ; d 0 bore diameter; d 0 \u003d 0.3 d a \u003d 0.6 r a, where d a is the outer diameter of the cutter. After substituting f and d 0 into formula (1), we get:
5 5 r a (t e) or d a preliminary = 4 (t + e). () Standard values d a and d 0 can be selected from the table. 1 or by the profile depth t, or by the calculated value d 0 (see formulas (4) and (5)). Fig.1. Scheme for calculating the outer diameter of a round shaped cutter the strength of the mandrel is checked. One-sided and two-sided fastening of incisors are used. One-sided fastening is used for cutters up to 30 mm wide along the part axis. In this case, from the side of the part segment in the cutter, a groove is made for the head of the mandrel with a diameter of d in =1.4 d 0 +1 and a length of l in =5 8 mm. With a cutter width of more than 30 mm, double-sided fastening is used, in which the mandrel for installing the cutter has two supports.
6 6 To check the strength of the mandrel, first of all, it is necessary to calculate the cutting force according to the formula: " P p l, (3) z N / mm; l "and the projection of the length of the cutting edge on the axis of the cutter, mm. When processing other materials, the ore should be multiplied by the coefficient k, equal to the ratio of the allowable tensile stresses of the material in question and steel 45 (40X). beats Table Specific cutting force of structural steel blanks and Feed, S, mm/rev 0.03 0.04 0.05 0.06 (recommended in the calculation) 0.08 0.09 0.1 Specific cutting force, r ud., N/mm Strength calculation is made according to the formulas of resistance of materials. For one-sided fixing of the cutter, the strength of the mandrel is calculated based on the scheme of operation of the beam, fixed at one end in the support. For double-sided fastening based on the scheme of operation of a two-support beam. Mandrels made of steel 45 or 40X are usually used, the allowable bending stresses of which can be taken equal to MPa (N/mm). Formulas are given in which it is possible to determine the diameter of the fitting hole of a shaped cutter: 0.33 0.38 d 0 0.6 L d Pz, (4) for two-sided fixing of the cutter: 0.33 0.5 d 0 0.78 L d Pz, (5) where L d is the length of the part, mm. After calculating d 0, formulas (4) and (5) should take the standard value d 0 and the corresponding value according to the table Purpose of the front and rear corners of the cutter Approximate values of the angles α 1 and γ 1 for shaped cutters made of high-speed steel R5M5 according to GOST, depending on the image
7 7 of the material used are given in table. 3 (front and back angles are assigned to the base point of the incisor). The value of the geometric parameters of the shaped cutter Table 3 Workpiece material Mechanical properties The value of the angles (at the base point) σ in, MPa HB γ 1, degree α 1, degree Red copper, aluminum Bronze, lead brass 0 5 to 500 up to Steel Cast iron up to Depending on profile configuration α = 8 15º 1.. Profiling a round shaped cutter with a lateral inclination of the front surface (λ 0) Profiling a round shaped cutter (KFR) means determining its profile in a section normal to the back surface (axial section) according to the known profile of the part. The CFR profile in the normal section must be known for its manufacture (to know the profile of the cutting tool for the manufacture of the CFR) and to control the accuracy of the profile with a template or on a universal measuring tool. CFR profiling can be performed graphically and analytically. Graphical CFR Profiling Graphical CFR profiling will be shown in the following example. Let a shaped part of a body of revolution be given, which has a conical section, which must be made with a minimum shape error (Fig.).
8 8 Fig. Scheme of processing a part with a shaped cutter In this case, it is necessary to use a CFR with a lateral inclination of the front surface (λ 0). Next, perform the following actions: 1. Set the width of the CFR, taking into account the need for overlapping by processing the length of the part: from the end of the bar (from which the shaped part is made on semi-automatic bar lathes), to compensate for the possible non-perpendicularity of the end of the part axis, the overlap is 1 mm; and on the other side of the part, for the subsequent cutting of the part with a cutting cutter, the overlap is 5 mm. we take into account the extreme points of the KFR profile (points 4 and 7). 3. We depict in the selected scale (depending on the required accuracy of profiling) the workpiece with additional points of overlap by processing (p. 4 and 7) in two projections (Fig. 3). The characteristic points of the part profile lying on the straight line segments (points 3 and 6) can not be profiled, since their profiling in this case is provided by profiling the ends of the straight line segments (points and 4 for point 3; points 5 and 7 for t .6). 4. We calculate the excess of the CFR axis over the axis of the part h R 1 sin 1, where R 1 is the radius of the outer surface of the CFR at the base point 1 (see p) R1 r a, α 1 is the rear angle at the base point 1 of the part (see clause 1.1. ). By known values h and R 1 with the help of a compass and a ruler, we find the center of the KFR point O and draw the contour of the KFR.
9 Fig. 3. Graphic profiling of a round shaped cutter (CFR): D a is the actual outer diameter of the CFR (at λ 0, a deviation of the value of D a from the standard value is allowed) 9
10 10 5. Using the methods of descriptive geometry, we find points 1", ", 4", 5", 7" of the intersection of the front surface of the KFR with characteristic circles (circles passing through characteristic points 1, 4, 5, 7). At λ 0 m. 1" and " lie on the generatrix of the cone, and the remaining m. 4", 5" and 7" are found using additional constructions. For example, to find point 4 "it is necessary to extend the generatrix of the cone to the intersection with the plane of the characteristic circle of point 4, we get point 4". We find the projection of point 4 "on another projection of the part and draw a line through it at an angle γ 1 until it intersects with the characteristic circle of point 4, this will be the desired point 4". Similarly, constructions are performed for other points 5 "and 7". Connecting t. 1", ", 4", 5" and 7" with straight line segments, we obtain the corresponding projection of the KFR profile. О 1. Otherwise, it is necessary either to abandon the profiling of the entire part with one CFR, or to increase the value of α 1 at the base point. 7. The angle λ is determined in view A (see Fig. 3). 8. The distances from the center O and CFR to points 1", ", 4", 5" and 7" are the radii of the CFR corresponding to characteristic points 1, 4, 5 and 7. Putting these radii from the axis of the CFR in its axial section on the corresponding axial distances from each other, we obtain the profiled points of the KFR.Connecting the profiled points with line segments, we obtain the desired profile of the cutter in normal section.On sections of the profile of the KFR perpendicular to its axis (with the exception of sections that are not involved in cutting), undercuts of 3º are performed. sharp edges, it is recommended to make a cylindrical section 3 mm long to reinforce the edge 9. Graphically, taking into account the scale, the differences between the profiled points are determined and put down on the working drawing of the CFR Analytical profiling of the CFR 1. Enter the coordinate system YO 1 X centered on the axis of the part (see Fig. Fig. 3. The coordinates of the center of the KFR point O and will be: yo and h R1 sin1; x and R1 cos1 r1.. Find the coordinates of points 1", ", 4", 5" and 7". For t. 1": y 1" = 0; x 1 "= r 1. For t.": y "= 0; x" = r. For t. 4 ": y 4" and x 4 "we find as a solution to a system of two equations: one equation of a straight line passing through t. 4" at an angle γ 1 to the X axis; the second equation of the circumference of the part passing through point 4. y tg1 x1 r "tg 4 1, y x r4
11 where 11 r r1 r 4 "r l4 tgk, tg k. l1 . sin 1 r 4 cos + sign for r 4" r 4 and for r 4"< r 4. Для точек 5" и 7" координаты y 5", x 5" и y 7", x 7" определяют аналогично точке 4" с соответствующей заменой в формуле r 4" на r 5" и r 7", а r 4 на r 5 и r 7. Радиусы КФР определяем как расстояние между центром КФР т. О и и точками 1", ", 4", 5", 7". Радиус КФР до точки 1" R 1" известен как радиус наружной поверхности КФР (см. п), т.е. R 1" = R 1 = r a. Радиус КФР до точки " находим по известной формуле: R "" oи "" (y y) (x x), Радиусы КФР до остальных точек 4", 5", 7" КФР находим аналогично т. ". С соответствующей заменой в формуле y " и x " на координаты точек 4", 5" и 7" получаем R 4", R 5", R 7". 4. По найденным радиусам КФР R 1", R ", R 4", R 5", R 7" рассчитываем соответствующие перепады профиля резца: oи; 1 R "" R 1 "" 14 R 4 "" R 1 "" 15 R 5 "" R 1 "" 17 R 7 "" R 1 "" ; ;. Перепады могут быть представлены в виде углового размера: 1 arctg[ 1 / l1], где l 1 проекция расстояния между точками 1" и " на ось КФР. Аналогично могут быть рассчитаны углы остальных перепадов 14, 15, Рассчитываем задние и передние углы в плоскости вращения детали (в плоскости рис. 3). Для т. 1": углы α 1" и γ 1" заданы: "" 1, "" 1. Для т. ": "" arctg [(yoи y "") /(xoи x "")] arctg(y "" / x "") arctg (y / x). "" 1 1 Для остальных точек 4", 5" и 7" значения углов рассчитываются аналогично т. " с соответствующей заменой в формуле координат y " и x " на координаты точек 4", 5" и 7". "" 1 "" "" 1
12 1 6. Calculate the values of the rear and front angles in the normal section (perpendicular to the projection of the cutting edge on the main plane), on the value of which the tool life depends. "" arctg , ni i i arctg , ni "" where α i" and γ i" are the corresponding rear and front angles at the i"-th point of the KFR profile in the plane of rotation of the part; α ni" and γ ni" respectively the rear and front angles in i "-th point of the KFR profile in a normal section; φ i" plan angle (the angle between the tangent to the cutter profile and the feed direction) at the i"-th point of the KFR profile. The value can be determined by the formula: i "" i "" i "" arctg , i "" i "" where l i" is the projection of the distance between two adjacent points of the CFR profile, one of which is i "-th, onto the CFR axis; R i" KFR radius to point i"; R is the radius "" of the KFR to the point adjacent to the i-th point. When R R i "" To ensure cutting, it is necessary that α ni">3º and γ ni">0º. Otherwise, it is necessary either to take large values of α i and γ i or to abandon the profiling of the part with one shaped cutter. Fig. 7. The angle of the lateral inclination of the front surface λ (see view A in Fig. 3) and the front angle in the transverse plane γ pop (see section B-B in fig. 3): arctg ; pop. arctg. i "" i "" 1.3. Features of profiling a round shaped cutter without a lateral inclination of the front surface (λ=0) Profiling a KFR with λ=0 is carried out basically similarly to profiling a KFR with λ 0. Features of profiling (both graphical and analytical) are as follows. 1. For the base point of the part, take the characteristic point located on its smaller diameter. KFR lie on the same straight line passing through point 1 at an angle γ 1 to the X axis. Therefore, for graphical finding of points ", 4", 5", 7" additional constructions are not required (see item 1..1) and their projections on a plane perpendicular to the KFR axis are found as the points of intersection of the corresponding characteristic circles with a straight line passing through point 1 at an angle γ 1 to the X axis.
13 13 In analytical profiling, the coordinates of the points ", 4", 5", 7" are found by the formulas, for example, for t. ": x "" r sin (r sin y "" 1) r 1 "" r x. sin 1 r cos For the remaining points 4", 5", 7" the coordinates x i" and y i" are found similarly to t. "with the radius r replaced in the above formula by the radius of the corresponding characteristic point of the part profile r i. 1; 1.4. Determination of the missing dimensions of the part profile, having a curved section in the form of an arc of a circle The curved section of the profile of the part, as a rule, is set by an arc of a circle.The options for setting this arc of a circle can be different.Suppose that for the profile of the part according to Fig. 4, a, the diameters d 3 and d 4, and the length L. It is also known that the section of the profile between points 3 and 4 is outlined by an arc of a circle of radius R. To determine the profile of a shaped cutter between points 3 and 4, it is necessary to determine additional parameters of a given section of the profile of the part: the coordinates of the center of the circle of radius R (x 0, y 0) and the coordinates of the lowest (upper) points of the curvilinear profile of the part (x 6, y 6) determining the maximum (minimum) diameter of the part in the area between points 3 and 4 (Fig. 4b). Based on the graphic diagram in Fig. 4b the system of equations is compiled: x0 y0 R (y6 y0) R (6) (x 4 x0) (y4 y0) R b; c; x x 1 b 4 4 ab d ; y 0 d d c ; 1 b x0 a by 0 ; y6 R y0. (7)
14 14 a) b) Fig. 4. The specified curved section of the profile of the part (a) and the scheme for determining its missing parameters (b) d 3, d 4, d 6, L can also be set and the drawing shows the section of the profile specified by points 3-6-4, the arc circles. It is required to determine the coordinates of the center of the circle x 0 and y 0 and the value of the radius of this circle R. The calculation can be performed using the formulas: y6(x 4 y4 y4y6) x 4y6 A ; B; y y x 4 0 B B A ; 4 0 R x 0 y ; (8) x 4 y4 x 4 y0 x0. y4 y4 After calculating the radii of the profile points of the cutter R 3, R 4, R 6, you can determine the coordinates of the profile points relative to the selected coordinate system, on-
15 15 example, as shown in the graphic diagram of fig. 5. Based on the diagram, you can compose a system of equations: "" 0 6 "0 6" "0 4" 0 4 "" 0 "0) (R) y (y) x (x) (R) y (y) x ( x) (R) (y) (x (9) The solution of the system of equations allows you to determine the coordinates of the center of the circle that replaces the curved section of the theoretical profile of the cutter, x "0 and y" 0 and the value of its radius R ":) y x y (x y6 y y x y y y x x " 0 ;) y x y (x x6 y x x x y x x y " 0 ; (10) " 0 " 0 ") (y) (x R.
16 16 a) b) c) d) e) Fig. Fig. 6. Curvilinear profiles (a, d) and their replacement for processing with a shaped cutter (b, c, e) It should also be noted that not any curved profile can be processed with a shaped cutter. If there are sections with a profile angle φ d = 90 on the curvilinear profile of the part, then at these points of the task cutter the angle in the normal plane will be 0, and near these points it will be insufficient. For example, at point A (Fig. 6, a) the rear angle in the plane normal to the cutting edge of the cutter is equal to zero, regardless of the angle α 1 ; on a curved section approaching point A, the relief angle will also be insufficient.
17 17 Therefore, in order to obtain satisfactory cutting conditions in terms of clearance angle in these places, it is necessary to change the profile of the part. And, if it is permissible by the purpose of the part (the issue of change should be agreed with the designer of the unit that includes the part), then the possible options for the changed profile of the part can be the options shown in Fig. 6b and c. In option b (Fig. 6), another profile is replaced by an arc and a straight profile associated with it. This reduces the size l 1 parts. In option c (Fig. 6), the dimension l 1 is retained, and a part of the arc profile is replaced by a chordal straight line. On fig. 6d shows another profile and possible variant its replacement (Fig. 6e). If any other similar profiles with φ d =90 appear, it is recommended to proceed by analogy. Determination of structural and geometric parameters of a prismatic shaped cutter.1.1. Determination of the overall dimensions and fastening elements of the cutter Prismatic shaped cutters (PFR) are made of high-speed steel. To save high-speed steel, they are made welded. The cutting part is welded end-to-end or into a rectangular socket of the holder made of steel grades 45 or 40X. In the mass production of shaped parts (for example, in the production of engine glow plug housing internal combustion) prismatic shaped cutters are equipped with a hard alloy welded to the cutter body. The shape and dimensions of the high-speed part of the cutter depend on the welding method and the dimensions of the cutter profile. In table. 4 shows the design dimensions of prismatic shaped cutters according to fig. 7. From the side of the open end of the workpiece, the profile cutter must overlap the part by 0.5 mm (i.e., it must have an overlap). From the end of the cutter, with which the cutter should be located to the machine chuck, an additional edge is made 4–5 mm long (straight or trapezoidal) for the subsequent cut of the finished part. Thus, the dimension L is the sum of the length of the workpiece, the overlap and the length of the profile for cutting off. With a workpiece length of up to 30 mm, the dimensions of the dovetail are determined only by the depth of the workpiece profile t. With a workpiece length of more than 30 mm, the strength of the dovetail should be checked in the weakest place. To do this, it is necessary to determine the cutting force when processing the part P z. The procedure for calculating P z for the PFR is similar to the calculation for the KFR, which is presented in paragraph 1 (formula 3 and table). The cross-sectional area of the material "dovetail", working on a cut,
18 18 can be calculated by the formula: Fav (A 1.15 E) (H B tg0), (1) where (see clause 1.). The shear stress is: Pz cf. (13) Fср The following condition must be met: ср Ср, (14) where τ Ср is the allowable shear stress for steel 45 (40Х); [τ cf ] = 10 N/mm. If condition (14) is not met, then one should proceed to the design of the cutter, the dimensions of which will correspond to a larger value of t. In order to increase the rigidity of the cutter, a threaded hole should be provided at the end opposite the front surface, into which, when using the tool, a screw will be screwed, providing additional support. If it turned out that size A60 mm, the design of the tool holder should be developed taking into account the specific equipment on which the designed prismatic shaped cutter will be used. Rice. 7. Structural dimensions of the prismatic shaped cutter
19 19 Dimensions of prismatic cutters Table 4 Profile depth t, mm Cutter dimensions, mm Shank dimensions in mm depending on the roller diameter, mm b=tmax+3 Welded dimensions. parts, mm B H E A F r d M d M b H ,5 4 1.5 6 9.5 6 34.54 55 In addition to fastening the cutter with a dovetail, other methods of fastening are also used. In this case, cutters are designed with excellent fastening elements adapted to the corresponding designs of tool holders. Equipping prismatic shaped cutters with a hard alloy increases the productivity of workpiece processing. However, the manufacture of carbide shaped cutters is associated with certain difficulties. In addition, due to the insufficient strength of the hard alloy, chipping of the cutting edges is quite possible. Therefore, the transition to the use of hard alloy to equip a prismatic shaped cutter requires a fundamentally new approach to design development. For example, it is undesirable to use a cutter to machine the full profile of a part. It is more expedient to process the shaped profile of the part using separate cutters. In this case, the failure of one of the cutters and its replacement become less noticeable in terms of tool costs compared to if a single full-profile cutter was used. In addition, the use of cutters for individual parts of the profile of the part allows you to put the cutters with optimal values of the rear angles along the profile of the cutting edge..1.. Appointment of the front and rear angles KFR according to the table. 3 (see clause 1.1.). For cutters equipped with hard alloy, on average, you can take α 1 = γ 1 =10º.
20 0.. Profiling a prismatic shaped cutter without lateral inclination of the front surface (face) ) and in a plane perpendicular to the back surface (in the normal plane) to produce a cutter profile and control it with a template(s). Profiling is done graphically and analytically. Graphical profiling allows you to get a graphical scheme for analytical profiling (get calculation formulas). Graphical profiling allows you to identify gross errors of analytical profiling. In some cases, graphic profiling facilitates the creation of a working drawing of a tool (for example, for a cutter λ 0º). It is possible to obtain the exact value of the cutter profile dimensions both with graphical profiling in CAD systems and with analytical profiling. We will show the graphical and analytical profiling of the PFR using the example of processing a shaped part of an arbitrary profile (Fig. 8). Let's depict the detail profile scheme together with the PFR profile (Fig. 9). An overlap of 1 mm from the side of the end of the bar (from which a shaped part is made on semi-automatic bar lathes) to compensate for the possible non-perpendicularity of the end of the axis of the part will ensure guaranteed processing of the entire profile, and the profile of the cutter, indicated by dots, is intended for cutting a groove for the subsequent cutting of the part from the bar. In educational course projects (works), a section of a profile 5 mm long, indicated by points 5-9, is quite acceptable for a segment. At the same time, an undercut should be provided on the side of the end face of the cutter (point 9) to reduce friction on the end cutting edge. The point of the part profile lying on the circle of the smallest diameter should be taken as the base point. Number 1 should be assigned to such a point. The numbering of all other profile points of the part is indifferent. Since the cutter profile overlap is provided in relation to the end face of the part, then in this case it is advisable to designate with number 1 not the actual point of the part profile, but the point of the profile located on the circle ø16 h1 and 1 mm away from the end of the part, i.e. at the distance of the overlap. For profiling a curved section of the PFR profile intended for processing the arc section of the part profile (in Fig. 8 it is set with radius R14), it is necessary that the coordinates of three points are known on the arc section of the part profile. The drawing shows that the coordinates of points 3 and 4 are known. As the third point of the profile, you should select the point number 10, which is located at the intersection of the arc of the circle and the straight line perpendicular to the axis of the part and passing through the center of the circle. Formulas related to
21 1 data with the determination of the missing dimensions of the profile of the part, having a curved section in the form of an arc of a circle, are given in p. 8. Sketch of the workpiece 9. Schematic profile for PFR profiling
22 Fig. 10. Scheme for analytical profiling of the PFR
23 3 The scheme for analytical profiling of the PFR is shown in fig. 10. Axial dimensions (distances between profile points measured along the axis of the part) of the cutter profile are not distorted compared to the axial dimensions of the part profile, i.e., the dimensions l 1, l 3, etc. are the same on the cutter and the part. Therefore, profiling is reduced to determining the differences in the profile points in the two above-mentioned planes. It is necessary to determine the differences in the planes of the front face C 1 10, C 1 3, C 1 4.9 and in the normal plane h 1 10, h 1 3, h 1 4.9. The rake angle in the plane perpendicular to the axis of the part, for the point of the cutter 10 can be determined by the formula d 1 10 arcsin sin 1. (15) d10 Differences C 1 10, h 1 10 can be determined by the formulas: C1 10 0.5 d10 cos10 0 ,5 d1 cos1, (16) h1 10 C110 cos(1 1). (17) Front and rear angle for any i-th point are determined by the formulas: d 1 i arcsin sin 1 i 1 1 i. (18) d10 A differences for the i-th point according to the formulas: C1 i 0.5 di cos10 0.5 d1 cos1, (19) h1 i C1i cos(1 1). (0) Differences can be determined by other formulas: sin(1 i) C1 i 0.5 di. (1) sin 1 If γ 1 =0, then formula (1) cannot be used. It should be accepted: di d1 C1 i. () In order to make sure that the tool is working, it is necessary to determine the value of the front and especially the rear angle at all points of the cutting edge in cutting planes normal to the cutting edge. They can be determined by the formulas ni arctg, (3) ni arctg, (4) where φ i is the cutter profile angle at the i-th point. It is enclosed between the axis of the part and the tangent to the profile of the cutting edge in given i-th point. Most profile points have two profile corners. For example, at a point, the profile angle, if you move from the side of point 1, will be equal to φ = 0º, and if you move from the side of point 3, then it will be equal to h 3 arctan. l3 At point 3, the profile angle, if moving from the side of the point, will be equal to
24 4 h 3 3 arctg, l3 and from the side of point 10 will be equal to l103 3 arcsin, R "where R" is the radius of the arc part of the cutter profile, the definition of which is disclosed in p. Similarly, the cutter profile angles are found for the remaining points of the profile. If for a given point there are two profile angles, then, as follows from formulas 3 and 4, at this point of the cutter there will be two values of the angles α n and γ n. To ensure satisfactory cutting, it is necessary to maintain the condition ni 0 30". Otherwise, one should either increase the angle α 1, or: the value of the angle α ni ; - to perform undercuts on the cutting edges with φ i = 90. The latter is most often carried out when designing a tool. An angle is marked on the working drawing Profiling a prismatic shaped cutter with a lateral inclination of the front face we will show on the example of profiling a cutter for machining a part whose profile contains an exact cone (Fig. 11).In this case, the circle with the smallest diameter of the conical surface of the part is taken as the base circle.Here we put a point with number 1. The number should indicate the point on the part profile, lying on a circle of the largest diameter nic surface. The setting of all other point numbers is indifferent. The straight generatrix of the cone of the part lies on the line 1-1, coinciding with the diametrical plane of the conical surface. Therefore, the cutting edge of the cutter, processing (profiling) this part of the part, should extend from point 1 to the point (Fig. 11, a), and the distance h 1 determines the difference between points 1 and in the plane perpendicular to the back face of the cutter.
25 Fig. 11. Scheme for analytical profiling of the PFR with a lateral slope of the front surface 5
26 6 The principle of finding any other point of the cutter profile on the projection a (Fig. 11) will be shown by the example of finding the cutter point corresponding to point 4 of the detail profile. On the projection b (Fig. 11), we draw the generatrix of the cone of the part to the ends of the profile (taking into account the overlap on one side of the part and the additional profile for the cutting tool). Then, through the profile points of the part 3, 4, etc., it is necessary to draw straight lines perpendicular to the axis of the part. At the intersection of these lines and the part forming the cone, points will appear, which should be indicated by the previous numbers with strokes. For example, at the intersection of a straight line that passes through point 4 perpendicular to the axis, and a straight generatrix of the cone of the part, we put a point 4 "(indices "d" and "f" with diameters d 4 denote the points belonging to the part and the continuation of the profile of the part, taking into account the overlap). Point 4 "lies on a circle with a diameter of d 4. Point 4" from projection b (Fig. 11) should be transferred to projection a. On projection a, point 4 "will be located on a straight line 1-1, and the distance from point 0 to point d 4" will be equal to: 04 "4" r4". Through the point 4 "we draw a straight line at an angle γ 1 and find the intersection of this straight line and a circle with a diameter of d 4. Let's denote the intersection point by point 4. It will be on the projection a (Fig. 11) the desired point of the cutter profile. The distance h 1 4 determines the difference cutter points 1 and 4 in a plane perpendicular to the back face of the cutter.Similar constructions are carried out for other points of the cutter profile.Graphic profiling when designing a PFR with a lateral inclination of the front face is mandatory, since this makes it possible to correctly complete the working drawing of the tool. Graphical profiling also reveals the possibility of profiling the cutter for processing the entire profile of the part from the condition that the clearance angle is sufficient for all its profile points. angle α 1 to the line 1 - 1. If any point is on this line, then for it the value of the back angle will be equal to zero, and, therefore, the cutting process in this place is impossible. At the points of the cutter profile lying above the straight line 00 1, there will be negative clearance angles, and the cutting process will be all the more impossible. In the first and second cases, you should go in the following ways: - reduce the front angle; - increase the back angle; - abandon the processing of the entire profile of the part with one cutter, replacing the processing with two cutters; - switch from a trapezoidal profile for a segment to a straight profile (see. rice. 8, 9). When the cutter profile point is below the straight line 00 1, the sufficiency of the rear angle is determined by the calculation in the analytical profiling of the PFR with a lateral inclination of the front face.
27 7 Analytical profiling of a PFR with a lateral inclination of the front face is carried out on the basis of graphical construction and is reduced to determining the differences in profile points, since the axial dimensions of the cutter do not change compared to the axial dimensions of the part profile. Dimensions l 1, l 3, l 3 4, etc. are the same on the cutter and on the part. For such a cutter, it is sufficient to determine the differences in only one secant plane: the plane perpendicular to the rear surface of the cutter. Point differences 1 and are determined by the formula: d d1 h1 cos1. (5) Differences of points 1 and 4 are determined by the formula: d4 y4 d1 h1 4 cos 1 arctg cos1 x, (6) 4 where x 4 and y 4 are the coordinates of point 4 relative to the X0Y coordinate system. d4 Given that r4, d4" r 4", we get: x 4 r4" sin 1 (r4" sin 1) r 4" sin 1 r4 cos, (7) 4 r4 x 4 y. (8) For any i-th coordinate points X i and Y i are defined as: x i i" 1 i" 1 r sin (r sin) r sin r cos, (9) i yi r x. (30) Sign "+" at and at. Accordingly, the difference between the i-th point and point number 1 will be: di yi d1 h1 i cos 1 arctg cos1 x. (31) i Sign "+" at, "-" at. For h 1 i< 0 точки профиля резца дальше удалены от базы («ласточкин хвост») по сравнению с точкой 1. Значения диаметров d i" можно рассчитать по формуле: d d1 di" d1 1i, (3) 1 знак «+» при условии расположения точки i со стороны точки, при расположении точки i cо стороны 1. Задний угол в любой точке профиля будет достаточным, если выдержано условие: yi 1 arctg x. (33) i Угол наклона режущей кромки, обрабатывающей конус детали, определяется по формуле: i i " 1 i 1 1
28 8 d d1 arctg sin 1. (34) 1 The angle of inclination of the front surface of the cutter in the transverse plane (the value is used when sharpening and determining the angle in the normal plane) is determined by the formula: d d1 II arctg tg1. (35) 1 The analysis of the change in the rear angle in the normal plane is carried out according to the formulas given in paragraph ... The front angle in the normal plane for the i-th point can be determined by the formula: ni arctg (tgi cosi) arctg (tg II sin i). (36) The values y i and γ II must be substituted into formulas 33 and 36 with their signs, arctg y x. a i 1 i i 3. METHODOLOGICAL INSTRUCTIONS FOR THE DEVELOPMENT OF WORKING DRAWINGS OF A SHAPED CUTTER AND A TEMPLATE WITH A COUNTER-TEMPLATE FOR IT The tolerance for differences in the profile points of the cutter is determined as /3 of the sum of tolerances for the radii of the characteristic points of the profile of the part corresponding to the difference under consideration. For example, the tolerance for the difference between points 1 and 3 will be equal to: Td3 Td1 T(h) T(r) T(r) 0, 3 where T(r 3), T(r 4) are the tolerances for the radii of the characteristic points of the part; Td 3, Td 4 tolerances for the diameters of the characteristic points of the part. If it turns out that the calculated tolerance is less than 0.0 mm, then the tolerance on the diameter of the circle corresponding to base point 1 should be tightened, i.e. take Td 1 in the ninth or eighth grade. Then the tolerance field for all other differences will expand. In the latter case, as a rule, a tolerance for a difference of more than 0.0 mm is provided. The sign before the deviation to the differences must be the same for all the differences: “+” or. The tolerance for the axial dimensions of the cutter is taken equal to 1/1/3 of the tolerance for the corresponding axial dimension of the part, but not more than ±0.03. An example of the execution of a working drawing of a round shaped cutter without a lateral inclination of the front plane is shown in Appendix 1. The diameter of the shoulder with end teeth d B \u003d (1.5 1.7) d 0. The angle along the bottom of the teeth can approximately be calculated by the formula:
29 9 tg 3, z where z is the number of teeth. It is also possible to prevent the rotation of a round shaped cutter relative to the mandrel with the help of a finger, one end of which enters the hole at the end of the cutter. Thus, the final design of the working drawing of a round shaped cutter should be coordinated with the design of the tool holder to secure it. In various literature sources, various designs are given for use on various models of machine tools. Therefore, before proceeding with the development of the tool holder design, it is necessary to establish a machine model on which a given part can be manufactured. The length of the ground part of the mounting hole l1 0.5 (B lв) ; B (Ld ln 6...8), where B is the width of the cutter, l n is the width of the cut-off cutter. On the drawing of the cutter, the distance H ra sin (1 1) from the plane of the front surface to the axis of the cutter must be indicated, which must be maintained when regrinding the cutter. Regrinding will ensure the formation of an angle γ 1 of a constant value. The drawing indicates the excess of the axis of the cutter over the top of the cutting edge h. This size is maintained when the cutter is installed on the machine and provides a clearance angle α 1. The values H and h are marked on the end of the cutter. An example of the execution of a working drawing of a prismatic shaped cutter with a lateral inclination of the front plane is shown in the Appendix. The design of the working drawing of the PFR should also be coordinated with the design of the tool holder to secure it. In the literature, various designs are given for use on various models of machine tools. Therefore, it is necessary to determine on which machine the profile of a given part can be processed. In the manufacture of PFR and CFR, the profile is controlled using a template in terms of dimensions in a normal section. When designing a template, it is necessary to provide for the base surface to which the template is applied and the profile is controlled through the light. Usually this is the end of the shaped cutter. To determine the degree of wear of the template, a counter template is provided. A working drawing of a template and a counter-template for measuring the profile of a shaped cutter is shown in Appendices 1 and. The tolerance for the dimensions of the template profile is taken equal to /3 from the tolerance for the cutter profile. The chamfer along the profile of the template makes it possible to more accurately control the profile of the cutter, because with a small thickness of the template, the gap between the cutter and the template is better visible. The template and the counter-template are made of steel 0 followed by carburizing and hardening, or from steel U7, U8 with hardening.
30 30 CONCLUSION Machining of external and internal surfaces with shaped cutters is a highly productive and precise machining method. The efficiency of processing with shaped cutters is largely determined by the constructive shape of the tool, the methods of their regulation, fastening and regrinding. The calculation of shaped cutters, as well as other cutting tools, is a multivariate task. This tutorial discusses the design features of round and prismatic shaped cutters. For each type of cutters, methods for calculating and designing the optimal design option are given, taking into account operating conditions and the required quality of the surfaces obtained. Tables with the necessary reference data for the calculation are given. In addition, examples of calculation of cutters, development of drawings and technical requirements for cutters are given to help students. The content of this tutorial will allow students to study modern methods for calculating and designing shaped cutters and correctly calculate such a tool in course and graduation projects. The textbook is intended for students of higher educational institutions studying in the direction of "Design and technological support of machine-building industries." In addition, this manual will be useful to teachers and graduate students of higher educational institutions.
31 31 REFERENCES 1. Metal-cutting tools: a textbook for universities in the specialties "Technology of mechanical engineering", "Metal-cutting machines and tools" / G. N. Sakharov, O. B. Arbuzov, Yu. L. Borovoy and others. M .: Mechanical Engineering , p.. Shatin, V. P. Handbook of the designer-toolmaker / V. P. Shatin, Yu. V. Shatin. M. : Mashinostroenie, p. 3. Granovsky, G. I. Shaped cutters / G. I. Granovsky, K. P. Panchenko. M. : Mashinostroenie, p. 4. Darmanchev, S. K. Shaped cutters / S. K. Darmanchev. L .: Mechanical engineering, p. 5. Shatin, V. P. Cutting and auxiliary tools: a reference book / V. P. Shatin, P. S. Denisov. M. : Mashinostroenie, p.
32 3 APPENDIX 1 An example of calculation of a round shaped cutter 1.1. Determination of the outer diameter of the cutter and the diameter of the hole for the mandrel We choose a two-sided fixing of the cutter, because the length of the part is more than 30 mm. We determine the specific cutting force for the recommended feed S = 0.06 mm / rev; P beats = 60 N/mm. The main component of the cutting force: P z \u003d P beat l and \u003d 60 10 \u003d N. Preliminary diameter of the mounting hole: d 0prev \u003d 0.78 L d 0.33 P z 0.5 \u003d 0.7810 0.5 \u003d 50.3 mm. We accept S = 0.03 mm / rev; P beats = 150 N/mm. P z \u003d P beats l and \u003d \u003d N. d 0limit \u003d 0.78 L d 0.33 P z 0.5 \u003d 0.7810 0.5 \u003d 39.7 mm. Finally, we choose the standard values: da = 15 mm; d 0 = 40 mm; e = 6 mm; R = 3 mm. 1.. Selection of the front and rear corners 1 = 0 0, 1 = Graphic profiling of a round shaped cutter with a lateral inclination of the front surface and (0) Set the width of the KFR, taking into account the need to overlap the length of the part with processing: l=16 mm. We put down the characteristic points on the profile of the part (p. 1, 3, 4, 5, 6), select as the base point 1, located on the smaller diameter of the cone. We depict the workpiece in the selected scale in two projections. We calculate the excess of the KFR axis over the axis of the part: h \u003d R 1 sin 1 \u003d 6.5 sin1 0 \u003d 1.994 mm. Based on the known values of h and R 1, we draw the KFR contour. We check the sufficiency of the rear angle α for all profiled points: all points, except point 6, are below the line of centers O u and O 1. Therefore, at point 6 the rear angle is negative. We refuse to process the part with one cutter. Step l 56 is not processed. Further, since all the constructions are made in the AutoCAD program, we take readings from the resulting image: R 1 = 6.500 mm;
33 R = 5.760 mm; R 3 = 64.38 mm; R 4 = 65.095 mm; 1 = 9.740 mm; 13 = 1.88 mm; 14 =.595 mm; λ=3, Analytical profiling of KFR We introduce the YO 1 X coordinate system centered on the part axis. The coordinates of the center of the KFR t. O And will be: y 0i \u003d h \u003d R 1 sin 1 \u003d 6.5 sin1 0 \u003d 1.994 mm. x 0i \u003d R 1 cos 1 + r 1 \u003d 6.5 cos \u003d 81.134 mm. Find the coordinates of t. 1.3: For point 1: y 1 = 0; x 1 \u003d r 1 \u003d 0 mm. For a point: y = 0; x = r = 30 mm. For point 3: r 3 = 18 mm; r 3 \u003d r 1 \u003d 0 mm x r sin (r sin) r sin 1 r 3 cos 1; x 3 0sin 0 17.9850 mm; y 3 r3 x 3 "; 0 (0sin 0 0) 0 sin cos y,9850 0.7334 mm. For point 4: r 4 = 18 mm; k = arctg[(r r 1)/l 1] = arctg[( 300)/50] = 11.30993 deg r 4 = r 1 l 14 tg k = 0 4 tg11, = 11.6000 mm x r sin (r sin) r sin 1 r 4 cos 1; x 4 11.600sin 17.855 mm ; y 4 r4 x 4" 0 ; 0 (11.600sin. y 4 = ± 18-17.855 = -, 767 mm
34 R (you y) (xou x) Similarly for other points: ; 34 R = (1.944-0) + (81.134-30) = 5.760 mm. R 3 (1.944 0.7334) (81.134 17.9850) 64.38 R 4 = (1.944 + 768) + (81.134-17.8554) = 65.095 mm. Based on the found CFR radii, we calculate the corresponding differences in the cutter profile: 1 = R R 1 =5.760 6.500 = 9.740 mm. Similarly for other points: 13 \u003d R 3 R 1 \u003d 64.38 6.500 \u003d 1.88 mm; 14 \u003d R 4 R 1 \u003d 65.095 6.500 \u003d. 595 mm. We calculate the rear and front angles in the plane of rotation of the part: For point 1: 1 "= 1 =1 0; 1" = 1 = 0 0. For t. (y/x); = arctg[(1.994 0)/(81.134 30)] arctg(0/30) =14.58 deg; = 1 + arctg(y/x); = arctg(0/30) =0 deg. Similarly for other points: For point 3: 3 = arctan[(1.994 0.733)/(81.134 17.985)] arctan(0.733/17.985) = = 8.65 deg; 3 = arctg(0.733/17.985) =.335 deg. For point 4: 4 = arctan[(1.994 +.77)/(81.134 17.855)] arctan(.77/17.855) = = 1.733 deg; 3 = arctg(.77 / 17.855) = 0.834 deg. Determine the angles in the plan. For points 1, : = 1 = arctg (l 1 / R 1 R) = arctg (50 / 6.5005.760) = 78.9763 deg. For points 3, 4: 3 \u003d 4 \u003d arctg (l 34 / R 4 R 3) \u003d arctg (4 / 65.09564.38) \u003d 88.9538 deg. We calculate the values of the rear and front angles in the normal section (perpendicular to the projection of the cutting edge on the main plane): For point 1: n1 = arctg(tg 1 sin 1); n1 \u003d arctg (tg1 0 sin78.976 0) \u003d 11.784 deg. n1 = arctg(tg 1 sin 1); n1 \u003d arctg (tg0 0 sin78.976 0) \u003d 19.659 deg. For a point: n = arctg(tg sin); n = arctg(tg14.58 0 sin78.976 0) =14.005 deg. mm;
35 35 n = arctg(tg sin); n \u003d arctg (tg0 0 sin78.976 0) \u003d 19.659 deg. For point 3: n3 = arctg(tg 3 sin 3); n3 \u003d arctg (tg8.65 0 sin88.954 0) \u003d 8.651 deg. n3 = arctg(tg 3 sin 3); n3 = arctg(tg.335 0 sin88.954 0) =.33 deg. For point 4: n4 = arctg(tg 4 sin 4); n4 = arctg(tg1.733 0 sin88.954 0) = 1.731 deg. n4 = arctg(tg 4 sin 4); n4 \u003d arctg (tg0.834 0 sin88.954 0) \u003d 0.831 deg. To ensure cutting it is necessary that: ni > 0 0 ; ni > 0 0. These conditions are satisfied for all points. The angle of the lateral inclination of the front surface λ and the front angle in the transverse plane γ pop. arctg(tan k sin 1); arctg(tg11.3099 sin 0) 3.913 ; pop arctg(tgktg1); pop arctg(tg11.3099 tg0) 4.1634. H = R 1 sin()= 6.5sin()= 33.10 mm Tolerances for differences and axial dimensions of the CFR The tolerance for the difference in the CFR is determined as the difference in tolerances for the radii of the characteristic points of the part corresponding to the considered difference. When obtaining too tight tolerances for CFR drops, it is necessary to reassign the tolerance to the diameter of one of the characteristic points (better than the base one) of the drop in the direction of tightening. Workpiece diameter tolerances: T d1 = 0.1 mm; T d = 0.1 mm; T d3 = T d4 = 0.6 mm. Drop tolerances: T 1 \u003d 0.7 (T d / + T d1 /) \u003d 0.7 (0.1 / + 0.10 /) \u003d 0.077 mm. T 13 \u003d T 13 \u003d 0.7 (T d3 / + T d1 /) \u003d 0.7 (0.6 / + 0.10 /) \u003d 0.5 mm. The deviation sign is accepted for all differences. Tolerances for the axial dimensions of the KFR are assigned as ½ ... ⅓ part of the tolerance for the corresponding axial dimensions of the part.
36 36 APPENDIX Options for designing a shaped cutter
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71 71 ANNEX 3
72 APPENDIX 4 7
73 ANNEX 5 73
74 ANNEX 6 74
75 75 APPENDIX 7
76 APPENDIX 8 76
77 77 APPENDIX 9
78 Educational publication SMIRNOV Maxim Yurievich KIREEV Gennady Ivanovich Demidov Valeriy Vasilyevich CALCULATION AND DESIGN OF SHAPED CUTTERS Study guide Editor M. V. Shtaeva LR from Signed for printing Format 60 84/16. Conv. oven l. 4.53. Circulation 100 copies. Order 3. Ulyanovsk State Technical University 4307, Ulyanovsk, st. Sev. Venets, d. 3. Printing house of UlGTU, 4307, Ulyanovsk, st. Sev. Venets, 3.
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RULES FOR APPLYING DIMENSIONS ON DRAWINGS CONTENTS 1. The concept of dimensions on a drawing ... 2 2. Types of dimensions of a part ... 2 3. Dimensional elements ... 3 4. Symbols ... 6 5. Methods of applying dimensions ... 8 6.
UDC 621.813 INFLUENCE OF REST ON THE PRECISION AND QUALITY OF WORKPIECES IN TURNING Vlasov MV, student Russia, 105005, Moscow, MSTU im. N.E. Bauman, Department of Materials Processing Technologies
Ministry Agriculture RF Federal State Educational Institution of Higher Professional Education "Michurinsk State Agrarian University" Department of Applied Mechanics
UDC 514.181.24:621.9.65.015.13 Masyagin V.B. APPLICATION OF A GEOMETRIC IMAGE IN THE FORM OF AN EDGE FOR MODELING THE SHAPE OF PARTS OF THE TYPE OF BODIES OF ROTATION TAKING INTO ACCOUNT MANUFACTURING ERRORS IN DIMENSIONAL ANALYSIS Omsk
B. M. Mavrin, E. I. Balaev IMAGE OF BODIES OF ROTATION Practicum Samara 2005
STATE EDUCATIONAL INSTITUTION OF HIGHER PROFESSIONAL EDUCATION "SAMARA STATE AEROSPACE UNIVERSITY named after Academician S.P. QUEEN (NATIONAL RESEARCH UNIVERSITY)"
CONTENT OF THE WORKING PROGRAM OF THE EDUCATIONAL DISCIPLINE. OP.05 "General fundamentals of metalworking technology and work on metal-cutting machines" Names of sections and topics Topic 1. Physical foundations of the cutting process
METHOD OF CALCULATION OF DISC SHAPED CUTTER
1.1.1. Initial data:
Detail: type of workpiece; brand of material; hardness and tensile strength; dimensions, accuracy and roughness of the machined surfaces of the part.
Equipment: machine model.
Selecting a base point on the part profile.
The base point lies on the smallest part radius.
1.1.3. Selection of the number of nodal points N on the part profile
Nodal points are determined by the intersections of the linear sections of the part profile.
Choice of tool material
Disk shaped cutters are made in one piece from high-speed steels or prefabricated with a cutting part made of hard alloy. When processing workpieces made of structural and alloy steels, cutters made of high-speed steels of the R6M5 type and hard alloys of the TI5K6 type are used; for processing workpieces made of cast iron and non-ferrous alloys, cutters made of hard alloys of the VK8 type are used.
Selection of the main parameters of the disk shaped cutter
The main design parameters of the disk shaped cutter is the outer diameter D, mandrel hole diameter d, cutter width L, cutter attachment elements α2 and l 2(fig.1.1.1).
The design dimensions of the cutters (Fig. 1.1.1) are selected according to Table 1.1.1, depending on the maximum profile depth of the workpiece
tmax = Rmax – Rmax, mm, (1.1.1)
where Rmax and Rmax- respectively, the maximum and minimum radii of the part, mm.
Table 1.1.1
Design parameters of disk shaped cutters, mm
| Part Profile Depth tmax | Form cutter parameters | |||||||
| Diameters | Width bmax | Gap To | Radius R | Diameter d2 | Length l 2 | |||
| Dh13 | αH8 | d1 | ||||||
| Up to 4 | - | - | ||||||
| 4 – 6 | ||||||||
| 6 – 8 | ||||||||
| 8 – 10 | ||||||||
| 10 – 12 | ||||||||
| 12 – 16 | ||||||||
| 16 – 18 | ||||||||
| 18 – 21 |
Fig 1.1.1.
Table 1.1.2
Geometrical parameters of disk shaped cutters
| Processed material | Tensile strength, σ b , MPa | Hardness, HB | Rake angle γ | Rear corner α | |
| cutting material | |||||
| high speed steel | Hard alloy | ||||
| Copper, aluminum | - | - | 25 – 30 | - | 8 – 15 |
| Steel | up to 500 | up to 150 | 20 – 35 | 10 – 15 | 10 – 12 |
| Steel | 500 – 800 | 150 – 235 | 10 – 20 | 10 – 15 | 10 – 12 |
| Steel | 800 – 1000 | 235 – 290 | 10 – 15 | 0 – 5 | 10 – 12 |
| Steel | 1000–1200 | 290 – 350 | 5 – 10 | 0 – 5 | 10 – 12 |
| Bronze, brass | - | - | 0 – 5 | - | 8 – 10 |
| Cast iron | - | up to 150 | 8 – 10 | ||
| Cast iron | - | 150 – 200 | 8 – 15 | ||
| Cast iron | - | 200 – 250 | 8 – 10 |
Notes: 1. It is allowed to use tabular values of non-wired diameters D for smaller values tmax
2. The length of the polished belts l 1 \u003d (0.5-1.0) d(see Fig. 4); recesses for the bolt head l 3 \u003d 0.8 d 1(see fig. 4)
3. Cutter width L determined by the calculation below.
4. Unspecified limit deviations of the dimensions of holes according to the quality H14, shafts - according to the quality h14,
the rest by qualification ±IT14/2.
The choice of geometric parameters of the cutting part of the cutter
Front γ and rear α the angles of the cutter at the peripheral point are selected depending on the grade and physical and mechanical properties of the material being processed and the grade of the tool material according to Table. 1.1.2.
Determining the cutting height
Relative to machine center line
h p = R sind 0, mm, (1.1.2)
where R– outer radius of the cutter, mm; d0- back angle of the cutter at the peripheral point of the profile, degrees (see Fig. 1.1.1)
Determination of distance
From the axis of the cutter to the plane of the front surface
H p \u003d R sin (γ 0 + α 0), mm, (1.1.3)
where γ 0 - front angle of the cutter at the peripheral point of the profile, degrees (see Fig. 1.1.1)
1.1.9. Determining the length of the cutter (see Fig.1.1.4)
When processing blanks from forgings and castings
L = log+ (4..6), mm. (1.1.4)
When processing blanks from a bar
L \u003d lg + S 1 + 2S 2 + S 3, mm. (1.1.5)
where S1– additional cutting edge for cutting off the part from the bar ( S1 0.5 - 1.0 mm more than the width of the cut-off tool); S2– cutting edge overlap equal to 2..3 mm; S3- hardening part of the cutter, equal to 2..5 mm.
Flute sizing
For unhindered chip flow, it is necessary to provide a sufficient sharpening depth along the front surface of the cutter (see Fig. 1.1.1). The size To depends on the maximum profile depth of the part tmax is selected according to Table 1.1.1.
Corrective calculation of the cutter profile
The work of a round shaped cutter is possible with a positive clearance angle. The day the formation of such an angle, the front surface of the cutter must be displaced below the center by an amount hp(see fig. 1.1.1). From formula (1.1.2) it follows that the clearance angle α is not the same along the entire length of the cutting edge, but varies depending on the distance of the cutting edge to the center of the cutter: the closer any point of the cutting edge is to the center of the cutter, the greater the clearance angle. In practice, the values of the rear angles for different points of the cutting edge of a disk shaped cutter can vary within 6..15 0 .
Due to the displacement of the center of the disk shaped cutter relative to the center of the part and the presence of a positive rake angle, only the point (see Fig. 1.1.1) of the cutter profile will lie on the axis of the part, and all the rest below it. This indicates that the cutter profile is not identical to the part profile. To obtain an accurate profile of the part, the profile of the disk shaped cutter is subjected to graphical or analytical correction.
The graphical method of correction of shaped cutters is less accurate, and it is used in cases where there are no high requirements for the calculation of cutters. The analytical correction method described below gives more accurate results.
Appointment of tolerances and specifications
Roughness parameters of the front and rear surfaces of the cutter Ra= 0.4..0.2 µm; mounting hole Ra= 0.3..0.4 µm ; hardness of the cutting part of high-speed cutters HRC 62..65.
On the overall dimensions of the cutters D and L tolerances are assigned according to 12..13 qualifications, and for the landing diameter of the cutter d- for 7..8 qualifications.
Tolerances for the linear and diametrical dimensions of the profile of a shaped cutter are taken equal to 1/3 of the tolerances for the corresponding dimensions of the machined part. Tolerances for diametrical dimensions are usually 0.02..0.06 mm.
NUMERICAL EXAMPLE OF CALCULATION
DISC SHAPED CUTTER
Initial data
Rice. 1.1.2
Detail - fitting; blank - hexagonal bar B = 14 mm; material grade - steel 45; hardness - I80 HB; tensile strength - σ in= 650 MPa; dimensions, accuracy and roughness of the machined surfaces - Fig.2.
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MINISTRY OF SCIENCE AND EDUCATION OF UKRAINE
UKRAINIAN ENGINEERING AND PEDAGOGICAL ACADEMY
SETTLEMENT AND EXPLANATORY NOTE
to the course project in the discipline: "Tool Design"
Work done by C
Group ZMB-A8-1
checked
Kharkov, 2012
Assignment to the course project
Exercise 1
Design a round shaped cutter for machining the part shown in the sketch. Material: B95 aluminum 
.
Figure 1 - Sketch
Task 2
Design a round broach to machine a hole. Detail material: bronze BrA9Zh3L (HB100), hole diameter after pulling mm, hole length mm. Roughness of the machined surface µm.
Task 3
Design a gear cutter for processing a gear with the following parameters: mm, , . The degree of accuracy of the wheels is 7-B.
 |
1. Designing a round radial shaped cutter
1.1 Theoretical information
A shaped cutter is a tool intended mainly for use in serial and mass production, where automatic machines, universal and special automatic machines and semi-automatic machines, are becoming increasingly important. In this regard, the most significant task of designing shaped cutters is to provide conditions for the rational use of automatic equipment. These conditions include: high resistance of shaped cutters, wide technological capabilities and minimal loss of time for a change, and regrinding of blunt cutters.
Shaped cutters are used for processing external, internal and end surfaces of various profiles and differ in their constructive form, method of sharpening, method of installation in the working position and the nature of the main cutting movement.
According to the constructive form, shaped cutters are divided into flat or rod, prismatic and round.
The principle of operation of radial shaped cutters is based on the gradual cutting in the form of chips of the entire volume of metal to be removed with a cutting blade. As the cutter moves, more and more new points of the cutting blade enter into work, and by the end of the work, the chips are cut off by the entire cutting blade. Therefore, each point of the cutting blade works for a certain time.
Round shaped cutters are used for processing both external and internal shaped surfaces. They are more technologically advanced than prismatic ones, as they are bodies of revolution and allow more regrinding and grind down to the residual value according to the strength condition.
The rear corners of round cutters are obtained by setting their axis above the axial plane on the workpiece in special tool holders.
1.2 Calculation of a round radial shaped cutter
Let us determine the total length of kfr by the formula:
where is the length of the workpiece, mm;
- area for overlapping the profile of the part, mm; – length of the shoulder with radial corrugation, mm.
Parameters of gear corrugations.
The number of teeth is 32.
Feed selection according to the table 5 mm/rev.
The components of the cutting force are determined by the formula:
The diameter of the mounting hole is determined by the formula:
Round up to the nearest larger size from the standard range:
. Since , fastening kfr in two support holders. Determine the outer diameter of the cutter by the formula:
(1.4)
where is the maximum radius kfr, mm;
– profile depth, mm;
- area for placing chips, mm;
– cutter wall thickness to ensure strength, mm.
Round up to the nearest integer multiple of five:
We select the corners at the base point according to table 4:
1.3 Correction calculation of KFR
When calculating the kfr, we use the dimensions in their middle of the tolerance field, for sizes without tolerances we assign 14 quality. For linear dimensions, we use 14 degrees of accuracy, and a tolerance field of , which allows the use of nominal dimensions. We draw a workpiece on the sketch, put down all the necessary dimensions, indicate the nodal points of the workpiece, put down all the necessary dimensions. For points with the same diameter, all parameters are the same, so you do not need to calculate them.
It is necessary to design a shaped cutter for processing the part shown in the sketch.
Fig.1
Job option - 5234
Workpiece reference data
Part dimensions
D1=69mm D2= 55.5mm D3= 13mm L1=5mm L2= 10mm
L3=13mm R1=28mm D4=62.5mm D5=58.5mm D6=55.5mm
D7=53.5mm D8=52.5mm L4=13mm L5=3mm L6=6mm
L7=9.5mm D9=49mm D10=44mm L8=12mm L9=10mm
Part material - Steel 50
The hardness of the material of the part HB, MPa - 2364
The workpiece is a body of revolution and has cylindrical, conical, spherical sections and a section specified by coordinates.
Graphical and mathematical expression of the shaped profile of the workpiece
shaped cutter worm cutter
The graphical and mathematical expression of the shaped profile of the workpiece is determined relative to the X and Y coordinate axes. The center of the 0 coordinate axes is at the 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 choice of overall dimensions of the shaped cutter
The overall dimensions of the shaped cutter are selected depending on the maximum depth Tmax of the shaped profile of the workpiece and the coefficient K, which are determined by the formulas:
Tmax = ,
where Dmax and Dmin - the maximum and minimum diameter of the shaped profile of the workpiece
L is the total length of the shaped profile of the workpiece (along the X axis).
Tmax = = 12.5 mm
The choice of overall dimensions of the prismatic shaped cutter
The overall dimensions of the prismatic shaped cutter (Fig. 3) are selected from table 2. [ 6, p. 10]
For Tmax \u003d 12.5 and K \u003d 3.84, the overall dimensions of the shaped cutter are as follows
The width Lp is determined after the design of the shaped profile of the cutting part of the cutter; the angle φ of the elements of the fastening part of the shaped cutter is assumed to be 60°; the angle in is determined by the formula
c \u003d 90o - (b + d)
where b and d are the front and rear corners of the shaped cutter, depending on the material of the workpiece and tool material.
Rice. 3.
Choice of front and back corners of the shaped cutter
The front and back angles are selected from table 4 depending on the material of the workpiece.
When processing steel 50 HB = 2364 MPa
r=12°; b=8°.
at=90°-12°-8°=70°.
Calculation of the depth of the shaped profile of a prismatic shaped cutter
To process a section of a part whose profile is a segment of a straight line parallel to the axis of the part, the depth of the shaped profile of the cutter is constant for all values of X and is calculated by the formula
Cp = M),
where M is the coefficient characterizing the segment of a straight line, is taken equal to b0
In the interval 0?X?5 M = 27.75 mm
Ср = 27.75*) = 27.75*) = 27.75* *4.519 = 27.75*0.0436*4.5199 = 5.46 mm.
To process a section of a part whose profile is a segment of a straight line inclined to the axis of the part, the depth of the shaped profile of the cutter for each value from X1 to X2 is calculated by the formula
Ср = (NX +Q) ],
where the coefficients N and Q characterize a segment of a straight line and are taken equal to
Wed \u003d (-0.188 * 26 + 22.188)] \u003d
17,3*) = 17,3* = 17,3*(-
0.0523)*4.519 = 4.09 mm
Wed \u003d (-0.188 * 38 + 14.875)] \u003d
7,731*) = 7,731* =
7.731*(-0.1074)*4.519 = 3.75mm
To process a section of a part whose profile is a segment of a line defined along a circle, the depth of the shaped profile of the cutter for each value from X1 to X2 is calculated by the formula
where the coefficients S, G, B and W characterize the line segment and are taken equal to:
Cp=(1*6.5)*sin
= (1* +6.5)*sin (12- =
34.0499*sin(12-7°40?)*4.5199 = 34.099*0.0756*4.5199=11.64mm
Cp=(1*6.5)*sin
34.3388*sin(12-7°40?)*4.5199 = 34.338*0.0756*4.5199=11.74mm
To process a section of a part whose profile is a segment of a line specified by a coordinate method, the depth of the shaped profile of the cutter for each X value is calculated by the formula
Wed \u003d 31.25 *) * \u003d 31.25 * sin (12-
*=31.25* sin(12-*4.5199=31.25*0.0640*4.5199= 9.04 mm
Wed \u003d 29.25 *) * \u003d 29.25 * sin (12-
*=29.25* sin (12-*4.5199 = 29.25*0.0523*4.5199 = 6.92 mm
Wed \u003d 27.25 *) * \u003d 27.25 * sin (12-
*=27.25* sin (12-*4.5199 =27.25*0.0436*4.5199 = 5.37 mm
For X = 22.5
Wed = 26.75*)* = 26.75*
26.75*0.0378*4.5199 = 4.57mm
For X = 26.0
Wed \u003d 26.25 *) * \u003d 26.25 * sin (12-
*= 23.25*sin (12- *4.5199 = 26.25*0.0349*4.5199 = 4.36 mm
Structural design of the shaped cutter
The construction of the shaped profile of the cutter is carried out in a coordinate way. For a prismatic shaped cutter, the coordinates are the depth Cp of the cutter shaped profile and the X dimension along the axis of the workpiece.
Width Lr of the shaped profile of the workpiece (along the axis of the workpiece); T1 and T2 - dimensions that determine additional reinforcing edges of the shaped profile of the cutter. Since our part is made from a piece blank, then T1 = T2.
where T3 - the size is taken equal to 1 ... 2 mm, T4 is taken equal to 2 ... 3 mm.
We take T3 and T4 equal to 2 mm.
Lp = 48+2*4 = 54 mm
Size T5 is selected from the ratio
where Tmax is the maximum depth of the shaped profile of the workpiece
We accept T5 = 12 mm
The size T6 is taken equal to T5 with an overlap of 2 ... 3 mm.
T6 \u003d 12.5 + 3 \u003d 15 mm
The angle is assumed to be 15°.
Rice. 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.
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 task 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 when different values 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 a computer SM-2M" / 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, we used various modules: APM Saft, APM Bear, APM Joint, APM Trans and APM WinMachine database toolkit.
Efficiency The use of the proposed toolkit allows you to drastically reduce the time of designing the cutter 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 fastening shaped cutters, it is necessary to carefully carry out general rules fixing incisors.
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 a relatively large sizes 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.