He also provided practical information on machining econometrics, including tool Reference works such as Machinery's Handbook cannot carry the same. eBook Machining Handbook. Reference: File format: *.pdf (approx. MB)»Download now for FREE«Printed books (similar). Results 1 - 10 These are "selected'' or. "built in'' from the basic forms. I call the basic drawings “ Blooks,'' after myself. PART Fundamentals of CNC.

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MACHINE TOOLS. •Turning and Related Operations. •Drilling and Related Operations. •Milling. •Machining Centers and Turning Centers. •Other Machining . + Refrain from automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine translation, optical. Best Practices Machining Parameters 3-‐18 Vertical Machining Center (VMC) Motion. Read the Reading Assignment for each lesson (PDF).

Wang and Armarego [5] have suggested a method to optimize the machining parameters for milling operations. But this is restricted to only face milling operations. Similarly, other methods like genetic algorithms [6], Scatter search [7] and the simulated annealing algorithm [8] have been used to solve face milling operations.

Some researchers have considered power as the only constraint and ignored the other constraints, such as cutting force, tool life and surface finish. The method of feasible directions is used to solve the problem. Recently, this problem has been solved by Tabu search, the continuous ant colony algorithm and particle swarm optimization to obtain more accurate results [10].

In the present work, the Genetic Algorithm GA , one of the recently emerged optimisation techniques in the area of metaheuristics, is applied successfully to optimise the parameters of multi- tool milling operations. The search mechanisms used in GA result in optimisation procedures with the ability to escape local optimum points. The advantage with this approach is that it can be used for solving a diverse array of complex optimisation problems [11, 12]. The results exhibit the efficiency of the GA over other methods.

GA is applied to optimize machining parameters for multi-tool milling operations involved in machining a work piece by a CNC machining centre. The maximum profit rate is considered as the objective function. The optimum values are obtained for each tool and each pass. The depth of cut is taken as the maximum permissible depth for a given work piece and cutting tool combination.

Therefore, the problem of determining the machining parameters is reduced to determining the proper cutting speed and feed rate combination. An example is taken from the literature [9] for comparing the results obtained by GA with other methods.

Objective Function The objective function is to maximise the total profit rate, and can be determined by: 1 The unit cost can be represented as: 2 The unit time to produce a part in the case of multi-tool milling can be defined as: 3 2.

Constraints In practice, the possible ranges for the cutting speed and feed rate are limited by the following constraints: 1. Maximum machine power 2. Surface finish requirement 3. Maximum cutting force permitted by the rigidity of the tool 4. The required machining power should not exceed the available motor power.

Therefore, the power constraint can be written as: 4 where, 5 2. Therefore, the surface finish of the face milling operation can be expressed by the following equation: 6 where, 7 and for end milling: 8 where, 9 2. The permitted cutting force for each tool is considered as its maximum limit for cutting forces.

Therefore, the cutting force constraint becomes: 10 Where 11 2. Face milling: 0. Corner milling: 0. Pocket milling: 0. Slot milling 1: 0. Karl Apro has been in the industry longer than Mastercam.

He started running multiaxis equipment in the days when all the axes where driven mechanically by cam plates and elaborate lever systems. The experience taught him that no software is ever perfect for every job.

Automatic, "easy-to-use," packages can leave your stranded if the "automatic" routines do not work.

Mastercam gives you that control. They know that the end product developed is not simply a CD in a fancy box. The end product is the ability to empower the users to generate reliable G-Code which will govern the motions of a CNC machine in order to manufacture any part.

The diameters of the American standard wire and lettersize drills are shown in Fig. For metric drill sizes see Fig.

When producing the tapped hole, be sure that the correct class of fit is satisfied, i. The composite drilling table shown in Fig. Spade Drills and Drilling. Spade drills are used to produce holes ranging from 1 in to over 6 in in diameter. Very deep holes can be produced with spade drills, including core drilling, counterboring, and bottoming to a flat or other shape. The spade drill consists of the spade drill bit and holder. The holder may contain coolant holes through which coolant can be delivered to the cutting edges, under pressure, which cools the spade and flushes the chips from the drilled hole.

The back-taper angle should be 0. The cutting speeds for spade drills are normally 10 to 15 percent lower than those for standard twist drills. See the tables of drill speeds and feeds in the preceding section for approximate starting speeds.

Heavy feed rates should be used with spade 5. The table shown in Fig. Horsepower and Thrust Forces for Spade Drilling. The following simplified equations will allow you to calculate the approximate horsepower requirements and thrust needed to spade drill various materials with different diameter spade drills. Calculate the horsepower at the cutter, required horsepower of the motor, the required thrust force, and the feed in inches per minute, to spade drill carbon steel with a hardness of to Bhn, using a 2.

Find the feed rate for the 2. Select the P factor for the material and drill size from Figure 5. Step 3. Calculate cutter horsepower: Calculate motor horsepower: Chp Calculate thrust force: Calculate feed, ipm: If the thrust force cannot be obtained, reduce the feed, ipr, from Fig.

Reamers usually have two or more flutes which may be straight or spiral in either left-hand or right hand spiral. Reamers are made for manual or machine operation. Reamers are also produced in cobalt alloys, and these may be run at speeds 25 percent faster than HSS reamers. Reamer feeds depend on the type of reamer, the material and amount to be removed, and the final finish required.

Material-removal rates depend on the size of the reamer and material, but general figures may be used on a trial basis and are summarized here: Hole diameter Up to 0. Cobalt-alloy and carbide reamers may be run at speeds 25 percent faster than those shown in Fig.

Carbide-tipped and solid-carbide chucking reamers are also available and afford greater effective life than HHS and cobalt reamers without losing their nominal size dimensions.

Speeds and feeds for carbide reamers are generally similar to those for the cobalt-alloy types. Forms of Reamers. Machine speeds and feeds for HSS reamers. These reamers are used to produce and maintain holes for American standard Morse taper shanks. They usually come in a set of two, one for roughing and the other for finishing the tapered hole. Taper-pin reamers. Taper-pin reamers are produced in HSS with straight, spiral, and helical flutes.

Dowel-pin reamers. The nominal reamer size is slightly smaller than the pin diameter to afford a force fit. These reamers are used as milling cutters to join closely drilled holes. Reamer blanks. Reamer blanks are available for use as gauges, guide pins, or punches. Fractional sizes through 1. Shell reamers. These reamers are designed for mounting on arbors and are best suited for sizing and finishing operations. Most shell reamers are produced from HSS.

Expansion reamers.

The hand expansion reamer has an adjusting screw at the cutting end which allows the reamer flutes to expand within certain limits.

The recommended expansion limits are listed here for sizes through 1. Reamer size: Expansion reamer stock sizes up to 3. Keyways in gear and sprocket hubs are broached to an exact dimension so that the key will fit with very little clearance between the hub of the gear or sprocket and the shaft. The cutting teeth on broaches are increased in size along the axis of the broach so that as the broach is pushed or pulled through the workpiece, a progressive series of cuts is made to the finished size in a single pass.

Broaches are driven or pulled by manual arbor presses and horizontal or vertical broaching machines. A single stroke of the broaching tool completes the machining operation. Broaches are commonly made from premium-quality HSS and are supplied either in single tools or as sets in graduated sizes and different shapes.

Broaches may be used to cut internal or external shapes on workpieces. Blind holes also can be broached with specially designed broaching tools. The broaching 5.

The teeth of a broach include roughing teeth, semifinishing teeth, and finishing teeth. All finishing teeth of a broach are the same size, while the semifinishing and roughing teeth are progressive in size up to the finishing teeth.

A broaching tool must have sufficient strength and stock-removal and chipcarrying capacity for its intended operation. An interval-pull broach must have sufficient tensile strength to withstand the maximum pulling forces that occur during the pulling operation. An internal-push broach must have sufficient compressive strength as well as the ability to withstand buckling or breaking under the pushing forces that occur during the pushing operation.

Broaches are produced in sizes ranging from 0. The term button broach is used for broaching tools which produce the spiral lands that form the rifling in gun barrels from small to large caliber. Broaches may be rotated to produce a predetermined spiral angle during the pull or push operations. Calculation of Pull Forces During Broaching.

The allowable pulling force P is determined by first calculating the cross-sectional area at the minimum root of the broach.

Knowing the length L and the compressive yield point of the tool steel used in the broach, the following relations may be used in designing or determining the maximum push forces allowed in push broaching. Most push broaches are short enough that the maximum compressive strength of the broach material will allow much greater forces than the forces applied during the broaching operation. The maximum allowable compressive force pounds force for a long push broach is determined from the following equation: You need to push-broach a 0.

Your square broach has a rise per tooth R of 0. Use the following equation shown previously for flat-surface broaches.

Handbook of MacHining and Metalworking Calculations

Then check to see if your broach can withstand the lb push force P required to broach the hole: Also, any size work which requires extreme accuracy is usually jig bored. Extensive tables of jig boring coordinates are not necessary with the modern CNC jig boring or vertical boring machines. Figures 5. Vertical boring machines with tables up to in in diameter are produced for machining very large and heavy workpieces.

For manually controlled machines with vernier or digital readouts, a table of jig boring dimensional coordinates is shown in Fig. Since the dimensions or coordinates given in the table are for xy table movements, the machine operator may use these directly to make the appropriate machine settings after converting the coordinates for the required circle diameter to be divided.

The coordinates are taken from the table in Fig. If a different-diameter circle is to be divided, simply multiply the coordinate values in the table by the diameter of the required circle; i. The radius R is therefore 2.

H cos A modern removable insert boring head. The y or vertical ordinate is then found from: V sin We can check these answers by using the pythagorean theorem: Sheet metal parts are used in countless commercial and military products.

Sheet metal parts are found on almost every product produced by the metalworking industries throughout the world.

Sheet metal gauges run from under 0. Cold-rolled steel sheets are generally available from stock in sizes from 10 gauge 0. Large manufacturers who use vast tonnages of steel products, such as the automobile makers, switch-gear producers, and other sheet metal fabricators, may order their steel to their own specifications composition, gauges, and physical properties.

The steel sheets are supplied in flat form or rolled into coils. Flat-form sheets are made to specific standard sizes unless ordered to special nonstandard dimensions. The following sections show the methods used to calculate flat patterns for brake-bent or die-formed sheet metal parts.

The later sections describe the geometry and instructions for laying out sheet metal developments and transitions. Also included are calculations for punching requirements of sheet metal parts and tooling requirements for punching and bending sheet metals. Tables of sheet metal gauges and recommended bend radii and shear strengths for different metals and alloys are shown also. The designer and tool engineer should be familiar with all machinery used to manufacture parts in a factory.

These specialists must know the limitations of the machinery that will produce the parts as designed and tooled. Coordination of design with the tooling and manufacturing departments within a company is essential to the quality and economics of the products that are manufactured. Modern machinery has been designed and is constantly being improved to allow the manufacture of a quality product at an affordable price to the consumer. Medium- to large-sized companies can no longer afford to manufacture products whose quality standards do not meet the demands and requirements of the end user.

The processing of sheet metal begins with the hydraulic shear, where the material is squared and cut to size for the next operation. These types of machines are the workhorses of the typical sheet metal department, since all operations on sheet metal parts start at the shear. Figure 6. Blanks which are used in blanking, punching, and forming dies are produced on this machine, as are other flat and accurate pieces which proceed to the next stage of manufacture.

The flat, sheared sheet metal parts may then be routed to the punch presses, where holes of various sizes and patterns are produced.

Many branches of industry use large quantities of sheet steels in their products. The electrical power distribution industries use very large quantities of sheet steels in 7-, , , and gauge thicknesses. A lineup of electrical power distribution switchgear is shown in Fig. Gauging Systems. To specify the thickness of different metal products, such as steel sheet, wire, strip, tubing, music wire, and others, a host of gauging systems were developed over the course of many years.

Shown in Fig. The steel sheets column in Fig. This gauging system can be recognized immediately by its gauge equivalent of 0. The Brown and Sharpe system is also shown in Fig. Aluminum Sheet Metal Standard Thicknesses. Aluminum is used widely in the aerospace industry, and over the years, the gauge thicknesses of aluminum sheets have developed on their own. Aluminum sheet is now generally available in the thicknesses shown in Fig. The fact that the final weight of an aerospace vehicle is very critical to its performance has played an important role in the development of the standard aluminum sheet gauge sizes.

There are three methods for performing the calculations to determine flat patterns which are considered normal practice. The method chosen also can determine the accuracy of the results. The three common methods employed for doing the work include 1. By bend deduction BD or setback 2. By bend allowance BA 3. By inside dimensions IML , for sharply bent parts only Other methods are also used for calculating the flat-pattern length of sheet metal parts.

Some take into consideration the ductility of the material, and others are based on extensive experimental data for determining the bend allowances. The methods included in this section are accurate when the bend radius has been selected properly for each particular gauge and condition of the material.

When the proper bend radius is selected, there is no stretching of the neutral axis within the part the neutral axis is generally accepted as being located 0. Methods of Determining Flat Patterns. By bend deduction or setback: Calculating the neutral axis radius and length. By bend allowance: Method 3. By inside dimensions or inside mold line IML: Bend allowance by neutral axis c. You may use this chart to determine bend deduction or setback when the angle of bend, material thickness, and inside bend radius are known.

In this case, it can be seen that the line 6. If we check this setback or bend deduction value using the appropriate equations shown previously, we can check the value given by the J chart.

The accuracy of this chart has been shown to be of a high order. Figures 6. For other bend radii in different materials and gauges, see Table 6.

The methods included here will prove useful in many design and working applications. These methods have application in ductwork, aerospace vehicles, automotive equipment, and other areas of product design and development requiring the use of transitions and developments.

The tabulated values of the minimum bend radii are given in multiples of the material thickness. The values of the bend radii should be tested on a test specimen prior to die design or production bending finished parts. When sheet metal is to be formed into a curved section, it may be laid out, or developed, with reasonable accuracy by triangulation if it forms a simple curved surface without compound curves or curves in multiple directions.

Sheet metal curved sections are found on many products, and if a straight edge can be placed flat against elements of the curved section, accurate layout or development is possible using the methods shown in this section.

The full-scale models used in aerospace vehicle manufacturing facilities are commonly called mock-ups, and the models used to transfer the compound curved surfaces are made by tool makers in the tooling department. Skin Development Outside Coverings. Skin development on aerospace vehicles or other applications may be accomplished by triangulation when the surface is not double curved. If we wish to develop the outer skin or sheet metal between stations The master lines of the curves at stations In actual practice, the curves are developed by the master lines engineering group of the company, or you may know or develop your own curves.

The procedure for layout of the flat pattern is as follows see Fig. Divide curve A into a number of equally spaced points. Use the spline lengths arc distances , not chordal distances. Lay an accurate triangle tangent to one point on curve A, and by parallel action, transfer the edge of the triangle back to curve B and mark a point where the edge FIGURE 6.

Then parallel transfer all points on curve A back to curve B and label all points for identification. Draw the element lines and diagonals on the frontal view, that is, 1A, 2B, 3C, etc. Construct a true-length diagram as shown in Fig. The true distance between the two curves is Transfer the element and diagonal true-length lines to the triangulation flatpattern layout as shown in Fig. The triangulated flat pattern is completed by transferring all elements and diagonals to the flat-pattern layout.

When the planes of the curves A and B Fig. The remainder of the procedure is as explained in Fig.

In aerospace terminology, the locations of points on the craft are determined by station, waterline, and buttline. These terms are defined as follows: The numbered locations from the front to the rear of the craft. The vertical locations from the lowest point to the highest point of the craft. The lateral locations from the centerline of the axis of the craft to the right and to the left of the axis of the craft.

There are right buttlines and left buttlines. With these three axes, any exact point on the craft may be described or dimensioned. Developing Flat Patterns for Multiple Bends. Developing flat patterns can be done by bend deduction or setback. The flat-pattern part is bent on the brake, with the center of bend line CBL held on the bending die centerline. If you study the figure closely, you can see how the dimensions progress: The bend deduction is drawn in, and the next dimension is taken from the end of the first bend deduction.

The next dimension is then measured, the bend deduction is drawn in for that bend, and then the next dimension is taken from the end of the second bend deduction, etc. Note that the second bend deduction is larger because of the larger radius of the second bend 0. On many sheet metal parts that have large areas, stiffening can be achieved by creasing the metal in an X configuration by means of brake bending. On certain parts where great stiffness and rigidity are required, a method called beading is employed.

The beading is carried out at the same time as the part is being hydropressed, Marformed, or hard-die formed. Another method for stiffening the edge of a long sheet metal part is to hem or Dutch bend the edge. In aerospace and automotive sheet metal parts, flanged lightening holes are used.

The lightening hole not only makes the part lighter in weight but also more rigid. This method is used commonly in wing ribs, airframes, and gussets or brackets. The lightening hole need not be circular but can take any convenient shape as required by the application. Typical Transitions and Developments. The following transitions and developments are the most common types, and learning or using them for reference will prove helpful in many industrial applications.

Using the principles shown will enable you to apply these to many different variations or geometric forms. Development of a Truncated Right Pyramid. Draw the projections of the pyramid that show 1 a normal view of the base or right section and 2 a normal view of the axis. Lay out the pattern for the pyramid and then superimpose the pattern on the truncation.

Since this is a portion of a right regular pyramid, the lateral edges are all of equal length. The lateral edges OA and OD are parallel to the frontal plane and consequently show in their true length on the front view. On it, step off the six equal sides of the hexagonal base obtained from the top view, and connect these points successively with each other and with the vertex O1, thus forming the pattern for the pyramid.

The intersection of the cutting plane and lateral surfaces is developed by laying off the true length of the intercept of each lateral edge on the corresponding line of the development. The true length of each of these intercepts, such as OH, OJ, etc.

The path of any point, such as H, will be projected on the front view as a horizontal line. To obtain the development of the entire surface of the truncated pyramid, attach the base; also find the true size of the cut face, and attach it on a common line. Development of an Oblique Pyramid. Since the lateral edges are unequal in length, the true length of each must be found separately by rotating it parallel to the frontal plane.

Similarly, lay out the pattern for the remaining three lateral surfaces, joining them on their common edges. The stretchout is equal to the summation of the base edges. If the complete development is required, attach the base on a common line.

Development of a Truncated Right Cylinder. The development of a cylinder is similar to the development of a prism. Draw two projections of the cylinder: A normal view of a right section 2. A normal view of the elements In rolling the cylinder out on a tangent plane, the base or right section, being perpendicular to the axis, will develop into a straight line.

For convenience in drawing, divide the normal view of the base, shown here in the bottom view, into a number of equal parts by points that represent elements. These divisions should be spaced so that the chordal distances approximate the arc closely enough to make the stretchout practically equal to the periphery of the base or right section. Project these elements to the front view. Draw the stretchout and measuring lines, the cylinder now being treated as a many-sided prism. Transfer the lengths of the elements in order, either by projection or by using dividers, and join the points thus found by a smooth curve.

This development might be the pattern for one-half of a two-piece elbow. Three-piece, four-piece, and five-piece elbows may be drawn similarly, as illustrated in Fig. Since the base is symmetrical, only one-half of it need be drawn. In these cases, the intermediate pieces such as B, C, and D are developed on a stretchout line formed by laying off the perimeter of a right section. If the right section is taken through the middle of the piece, the stretchout line becomes the center of the development.

Evidently, any elbow could be cut from a single sheet without waste if the seams were made alternately on the long and short sides.

Development of a Truncated Right Circular Cone. Draw the projection of the cone that will show 1 a normal view of the base or right section and 2 a normal view of the axis.

First, develop the surface of the complete cone and then superimpose the pattern for the truncation. Divide the top view of the base into a sufficient number of equal parts that the sum of the resulting chordal distances will closely approximate the periphery of the base. Project these points to the front view, and draw front views of the elements through them. With center A1 and a radius equal to the slant height AFIF, which is the true length of all the elements, draw an arc, which is the stretchout.

Lay off on it the chordal divisions of the base, obtained from the top view. Connect these points 2, 3, 4, 5, etc. Draw a smooth curve through these points.

The pattern for the cut surface is obtained from the auxiliary view. Nondevelopable surfaces are developed approximately by assuming them to be made of narrow sections of developable surfaces. The most common and best method for approximate development is triangulation; that is, the surface is assumed to be made up of a large number of triangular strips or plane triangles with very short bases. This method is used for all warped surfaces as well as for oblique cones. Oblique cones are single-curved surfaces that are capable of true theoretical development, but they can be developed much more easily and accurately by triangulation.

Development of an Oblique Cone. An oblique cone differs from a cone of revolution in that the elements are all of different lengths. The development of a right circular cone is made up of a number of equal triangles meeting at the vertex whose sides are elements and whose bases are the chords of short arcs of the base of the cone.

In the oblique cone, each triangle must be found separately. Draw two views of the cone showing 1 a normal view of the base and 2 a normal view of the altitude. Divide the true size of the base, shown here in the top view, into a number of equal parts such that the sum of the chordal distances will closely approximate the length of the base curve.

Project these points to the front view of the base. Through these points and the vertex, draw the elements in each view. Since the cone is symmetrical about a frontal plane through the vertex, the elements are shown only on the front half of it.

Also, only one-half of the development 6. With the seam on the shortest element, the element OC will be the centerline of the development and may be drawn directly at O1C1, since its true length is given by OFCF.

Find the true length of the elements by rotating them until they are parallel to the frontal plane or by constructing a true-length diagram. The true length of any element will be the hypotenuse of a triangle with one leg the length of the projected element, as seen in the top view, and the other leg equal to the altitude of the cone.

Distances from point O to points on the base of the diagram are the true lengths of the elements. Construct the pattern for the front half of the cone as follows. With O1 as the center and radius O1, draw an arc. With C1 as center and the radius CT1T, draw a second arc intersecting the first at Then O will be the developed position of the element O1. With 11 as the center and radius 1T2T, draw an arc intersecting a second arc with O1 as center and radius O2, thus locating Continue this procedure until all the elements have been transferred to the development.

Connect the points C1, 11, 21, etc. The method used in drawing the pattern is the application of the development of an oblique cone. One-half the elliptical base is shown in true size in an auxiliary view here attached to the front view.

Find the true size of the base from its major and minor axes; divide it into a number of equal parts so that the sum of these chordal distances closely approximates the periphery of the curve. Project these points to the front and top views. Draw the elements in each view through these points, and find the vertex O by extending the contour elements until they intersect.

The true length of each element is found by using the vertical distance between its ends as the vertical leg of the diagram and its horizontal projection as the other leg. As each true length from vertex to base is found, project the upper end of the intercept horizontally across from the front view to the true length of the corresponding element to find the true length of the intercept.

The development is drawn by laying out each triangle in turn, from vertex to base, as in Fig. Draw smooth curves through these points to complete the pattern. Development of Transition Pieces. Transitions are used to connect pipes or openings of different shapes or cross sections. These pieces are always developed by triangulation. The piece shown in Fig. To develop the piece, make a truelength diagram as shown in Fig. The true length of O1 being found, all the sides of triangle A will be known.

Attach the developments of cones B and B1, then those of triangle C and C1, and so on. By using a partial right-side view of the round opening, the divisions of the bases of the oblique cones can be found. Since the object is symmetrical, only one-half the opening need be divided.

The true lengths of the elements are obtained as shown in Fig. Triangulation of Warped Surfaces. The approximate development of a warped surface is made by dividing it into a number of narrow quadrilaterals and then split- FIGURE 6. Find the true size of one-half the elliptical base by rotating it until horizontal about an axis through 1, when its true shape will be seen.

Flat-Pattern Development. Sheet metal parts sometimes have angled flanges that must be bent up for an exact angular fit.

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In order to lay out the corner notch angle for this type of part, you may use PC programs such as AutoCad to find the correct dimensions and angular cut at the corners, or you may calculate the corner angular cut by using trigonometry. To trigonometrically calculate the corner angular notch, proceed as follows: The triangle ABC begins with known dimensions: That is a triangle where you know two sides and the included angle B. You will need to first find side b, using the law of cosines as follows: Angled flanges.

Then, find angle C using the law of sines: On thicker sheet metal, such as 16 through 7 gauge, you should do measurements and the calculations from the inside mold line IML of the flat-pattern sheet metal. Also, the flange height, shown as 2 in Fig.

Thus, the corner notch angle is a constant angle for every given bent-up angle; i. Note that the shaded area is the half-notch cutout. Stripping forces vary from 2.

This equation is approximate and may not be suitable for all conditions of punching and blanking due to the many variables encountered in this type of metalworking. If you require the shear strength of a material that is not listed in Fig.

Go to a handbook on materials and their uses, and find the ultimate tensile strength of the given material. Take 45 to 55 percent of this value as the approximate shear strength. Sheet steels in the United States are downloadd to these gauge equivalents, and tools and dies are designed for this standard gauging system.

Following these guidelines will prevent buckling or tearing of the sheet metal. Corner relief notches for areas where a bent flange is required is shown in Fig. The minimum edge distance for angled flange chamfer height is shown in Fig. The X dimension in Fig. If the inside bend radius is 0.

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Minimum flanges on bent sheet metal parts are shown in Fig. Bending dies are usually employed to achieve these dimensions, although on a press brake, bottoming dies may be used if the gauges are not too heavy. Stiffening ribs placed in the heel of sheet metal angles should maintain the dimensions shown in Fig.

Stiffening beads placed in the webs of sheet metal parts for stiffness should be controlled by the dimensions shown in Figs. The dimensions shown in these figures determine the allowable depth of the bead, which depends on the thickness gauge of the material.

These functional values of the involute curve are easily calculated with the aid of the pocket calculator. Refer to the following text for the procedure required to calculate the involute function.

The Involute Function: The involute function is widely used in gear calculations. The involute of a circle is defined as the curve traced by a point on a straight line which rolls without slipping on the circle. It is also described as the curve generated by a point on a nonstretching string as it is unwound from a circle. The circle is called the base circle of the involute.

A single involute curve has two branches of opposite hand, meeting at a point on the base circle, where the radius of curvature is zero. All involutes of the same base circle are congruent and parallel, while involutes of different base circles are geometrically similar. Figure 7. The generating line was originally in position G0, tangent to the base circle at P0.

The point P0 on the generating line has moved to P, generating the involute curve I. Another point on the generating line, such as Q, generates another involute curve which is congruent and parallel to curve I. Find the involute function for Using the procedure shown here, it becomes obvious that a table of involute functions is not required for gearing calculation procedures.

It is also safer to calculate your own involute functions because handbook tables may contain typographical errors. The MathCad 8 calculation sheet seen in Fig.There are four possible cases in the solution of oblique triangles: Measurement and Calculation Procedures for Machinists 4.

The method indicated earlier for calculating the required horsepower gives a conservative value that is higher than the actual power required. Eastern Time are typically shipped the same day. Also, any size work which requires extreme accuracy is usually jig bored. The radius of a circle inscribed in any triangle whose sides are a, b, c is: Connect the points C1, 11, 21, etc.