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).

These systems are cheap, fun, and easy to build. However, they have rather short life spans. You cannot compare their metal counterparts and typically they are not consistently accurate. There are sev- eral companies that manufacture aluminum framing materials, which are available in a wide variety of shapes and sizes.

Using this type of material, one can literally build a CNC system much like an erector set. Be advised that these materials and connectors are rather expensive in comparison to an all-steel built and welded counterpart. The makers of this type of extruded aluminum can cut to your dimensions and have a large array of fasteners and brackets that can be used for assembly. It is especially advantageous to use the extruded aluminum framing for movable spans, CNC Machines 19 such as on a plasma table or router because of its lighter mass.

Although this effect is minor, it can affect overall system accuracy as well. In most cases it is customary to bolt together sections of differing materials that cannot be welded. For example, a system that is bolted together will, in fact, have a tendency to eventually work its way out of square over time and obviously be less rigid as compared to it being welded together.

There will be a notable difference in the overall rigidity. If you are downloading a unit as applicable you should ask the manufacturer if the unit is a one-piece table or a bolt together. With points c and d as centers, draw circular arcs with radii longer than half the distance between points c and d.

These arcs intersect at point e, and line fe is the required perpendicular. With point f as a center, draw the circular arc which will intersect both points A and B.

With each of these points as a center and the same radius, describe arcs which intersect each other. Through the points of intersection, draw lines fb and fd.

The intersection point of these two lines is the center of the circle or circular arc.

At point f, draw a line CD at right angles to OA. Line CD is the required tangent to point f on the circle. Bisect OB and with this point d as center and a radius dC, draw arc Ce.

With center C and radius Ce, draw arc ef. Cf is then a side of the pentagon. Step off distance Cf around the circle using a divider. With the same radius, Of, and with points 6 and 3 as centers, draw arcs intersecting the circle at points 1, 2, 4, and 5, and connect the points. To draw a geometrically correct octagon in a square Fig. With the corners of the square b and d as centers and a radius of half the diagonal distance Od, draw arcs intersecting the sides of the square at points 1 through 8, and connect these points.

The concentric-circle method: On the two principle diameters ef and cd which intersect at point O, draw circles. Each quadrant of the concentric circles may be divided into as many equal angles as required or as dictated by the size and accuracy required. Divide aO into any number of equal parts, and divide ae into the same number of equal parts. Draw lines through points 1 through 4 from points c and d.

The intersection of these lines will be points on the ellipse. From the divisions on ab, draw lines converging at O.

Lines drawn parallel to line OA and intersecting the divisions on Oa will intersect the lines drawn from point O. These intersections are points on the parabola.

These offsets vary as the square of their distance from point O. Number the divisions from Oa and Ob, 1 through 6, etc. The intersection of points 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, and 6 and 1 will be points on the parabola. Through any point k on the axis Op, draw lines parallel to AB.

With distance kO as a radius and f as a center, draw an arc intersecting the line through k, thus locating a point on the parabola. Repeat for Oj, Oi, etc. Divide the lead into a number of equal parts, say Divide the circle of the front view into the same number of equal parts, say Project points 1 through 12 from the top view to the stretch-out of the helix in the right view. Draw tangents at these points. Line a2 is perpendicular to radial line O2, line b3 is perpendicular to radial line O3, etc.

Lay off on these tangent lines the true lengths of the arcs from the point of tangency to the starting point, 1. For accuracy, the true lengths of the arcs may be calculated see Fig. The involute of the circle is the basis for the involute system of gearing. Another method for finding points mathematically on the involute is shown in Sec. Divide the radius O8 into the same number of equal parts, numbering from the center of the circle.

CNC Machining Handbook ( ).pdf

To draw the spiral of Archimedes. The spiral curve is defined by the points of intersection of the radii and the concentric circles at points a, b, c, d, e, f, g, and h. Connect the points with a smooth curve. The Archimedean spiral is the curve of the heart cam, which is used to convert uniform rotary motion into uniform reciprocating motion.

See Chap. Referring to Figs. From this example it is apparent that the setting height can be found for any sine bar length simply by multiplying the length of the sine bar times the natural sine value of the required angle.

Handbook of MacHining and Metalworking Calculations

The simplicity, speed, and accuracy possible for setting sine bars with the aid of the pocket calculator renders sine bar tables obsolete. Method 1. Convert the required angle to decimal degrees. Find the natural sine of the required angle.

Multiply the natural sine of the angle by the length of the sine bar to find the bar setting height see Fig. Formulas for Finding Angles. See also Fig. This will help in the setting of compound sine plates when it is required to set a compound angle. Setting Compound Sine Plates. To find the amount the intermediate plate must be raised from the base plate X dimension in Fig. Find the natural cosine of the second angle Find the arctangent of this product, and then find the natural sine of this angle.

This natural sine is now multiplied by the length of the sine plate to find the X dimension in Fig. Set up the Jo-blocks to equal the X dimension, and set in position between base plate and intermediate plate. To find the amount the top plate must be raised Y dimension in Fig. Find the natural sine of the second angle, and multiply this times the length of the sine plate. Set up the Jo-blocks to equal the Y dimension, and set in position between the top plate and the intermediate plate.

Taper Fig. Solve for x if y is given; solve for y if x is given; solve for d. Use the tangent function: To find the tool travel from the edge of the hole Fig. Now, solve for y, the tool advance: To find tool travel from edge of hole Fig.

Given dimensions shown in Fig. The following figures show in detail how basic trigonometry and algebra are used to formulate the solutions to these geometric figures. The Pentagon. Where See Fig. When one of these parts is known, the other parts may be found in relation to the given part.

When drilling a hole, it is often useful to know the distance from the cylindrical end of the drilled hole to the point of the drill for any angle point and any diameter drill.

What is the advance t for a 0. Finding taper angles under a variety of given conditions is an essential part of machining mathematics. Following are a variety of taper problems with their associated equations and solutions. For taper in inches per foot, see Fig. Figure 4. This is found simply by solving the triangle formed by the axis line, which is 1 in long, and half the taper angle, which is Solve one of the rightangled triangles formed by the tangent function: The taper in inches per foot is equal to 12 times the taper in inches per inch.

Thus, in Fig. Typical Taper Problems 1. Set two disks of known diameter and a required taper angle at the correct center distance L see Fig. Solve for L. Find the angle of the taper when given the taper per foot see Fig. Taper per foot T. Find the taper per foot when the diameters of the disks and the length between them are known see Fig.

Solve for T. Find the angle of the taper when the disk dimensions and their center distance is known see Fig. Find the taper in inches per foot measured at right angles to one side when the disk diameters and their center distance are known see Fig. Solve for T, in inches per foot. Set a given angle with two disks in contact when the diameter of the smaller disk is known see Fig.

Solve for D, diameter of the larger disk. Angles of extreme precision are possible to set using this type of tool. The diameters of the disks may be machined precisely, and the center distances between the disks may be set with a gauge or Jo-blocks. Also, any angle may be repeated when a record is kept of the disk diameters and the precise center distance. Checking Angles and Notches with Plugs. A machined plug may be used to check the correct width of an angular opening or machined notch or to check templates or parts which have corners cut off or in which the body is notched with a right angle.

This is done using the following techniques and simple equations. In Figs. To check the width of a notched opening, see Fig. Right-angle notch. Also, the equation for finding the correct plug diameter that will contact all sides of an oblique or non-right-angle triangular notch is as follows see Fig.

The simple equation for calculating the diameter D for any angle A is as follows: In this case, the calculation becomes simple. Finding the radius. Another accurate method of finding or checking the radius on a part is illustrated in Figs. In this method, we may calculate either an inside or an outside radius by the following equations: The diameter D of the rolls or plugs also must be measured precisely and the height h measured with a telescoping gauge or inside micrometers.

Measuring Dovetail Slides. The accuracy of machining of dovetail slides and their given widths may be checked using cylindrical rolls such as a drill rod or wires and the following equations see Figs. Also, the diameter of the rolls or wire should be sized so that the point of contact e is below the corner or edge of the dovetail.

Taper Problem and Calculation Procedures. The given or known dimensions are shown here, and it is required to solve for the unknown dimensions and the weight of the part in ounces, after machining.

R1, R3, bc, d2, L2, L3, and L4; then calculate the volume and weight of the part, when the material is specified. Per the dimensions given in Fig. The part consists of two sections, both of which are frustums of a cone.

The equation for calculating the volume of a frustum of a cone is: Calculate what the measurement L over pins should be, when the diameter of the pins is 0. With an X dimension of 2. These equations were calculated symbolically for these other variables in the basic equation; Sec. Refer to Figs.

For Fig. The coefficient of friction of steel on steel is generally taken as 0. In Fig. The distance d to the centerline of the cutter is calculated as follows: From Eq. How deep is the plunge h from the surface of the work piece? Find distance ab from: Find y from: Find h from: Step 1. A V groove is to be machined to a width of 0. Calculate the tool plunge depth y, and then check the width of the groove by calculating the height h that should be measured when a ball bearing of 0.

Use the following two equations to calculate distances y and h: The reason for this substitution is that the cosecant function cannot be NOTE. Since the cosecant, secant, and cotangent are equal to the reciprocals of the sine, cosine, and tangent, respectively, this substitution must be made, i. Arc Height Calculations. The simple equation for calculating h is given as follows: To calculate an inside radius or arc, see Fig.

Calculate the blending radius R2 that is tangent to a given arc of radius R1. Distances X and Y and radius R1 are known. Keyway depth, calculating. Find the depth x the milling cutter must be sunk from the radial surface of the shaft to cut a shaft keyway with a width W of 0. Keyway Cutting Dimensions. Compound Trigonometric Problem. For side a, use the law of sines: Transpose as shown to find cos A and cos B from: From Fig. If you need more accuracy, use more decimal places in the variables.

Calculations Involving Properties of the Circle. These include finding arc length, chord length, maximum height b, and the x, y ordinates. If we want to find a missing dimension, such as x in Fig. The dimension 2. Therefore, a and c are the measured dimensions; b and x are the actual sizes.

This procedure is useful, but is only as accurate as the drawing and the measurements taken on the drawing. This procedure can also be used on objects in photographs that do not have perspective distortion, where one aspect or dimensional feature is known and can be measured. Useful Geometric Proportions. In reference to Fig. From the law of cosines units in degrees and inches: The dimensions of three sides of a triangle are known.

Altitude x, and the location of x by dimensions y and z. Finding angle C: What is the diameter of the countersink D when we want the head of the flathead bolt or screw to be 0.

Solve the right triangle shown in Fig. Measure the diameter of the head of the screw or bolt Hd with a micrometer prior to doing the calculations. Different manufacturers produce different head diameters on flathead screws or bolts, according to the tolerances allowed by ANSI standards for fasteners.

The diameter of 0. From the compound angle relations shown in Fig. First, calculate the length of side OA: First, calculate the length of side AB: Check angle ABC for a right triangle.

Using more decimal places for the calculated sides and angles will produce more accurate results, if required. A rectangular block, shown in Fig.

Referring to Table 4. We must know or measure the distances ov, om, and mn. Prove the following relationship from Table 4. First, find the length of the diagonal vm: So, the relationship is valid.

The accuracy of the preceding relationship, as calculated, is accurate to within The preceding calculations are useful in machining work and tool setup, and also show the validity of the angular and trigonometric relationships of compound angles on three-dimensional objects, as shown in Figs.

Figure 5. The machining center is capable of highly accurate and rapid production of machined parts. These modern machining centers are the counterparts of engine lathes, turret lathes, and automatic screw machines when the turned parts are within the capacity or rating of the machining center. Cutting Speed. Cutting speed is given in surface feet per minute sfpm and is the speed of the workpiece in relation to the stationary tool bit at the cutting point surface.

At what revolutions per minute rpm should the machine be set to rotate the work? Lathe Cutting Time. The time required to make any particular cut on a lathe or turning center may be found using two methods. When the cutting speed is given, the following simple relation may be used: The volume of metal removed during a lathe cutting operation can be calculated as follows: Machine Power Requirements Horsepower or Kilowatts.

It is often necessary to know the machine power requirements for an anticipated feed, speed, and depth of cut for a particular material or class of materials to see if the machine is capable of sustaining the desired production rate. The following simple formulas for calculating required horsepower are approximate only because of the complex nature and many variables involved in cutting any material. The following formula is for approximating machine power requirements for making a particular cut: The national manufacturers of cutting tools at one time provided the users of their materials with various devices for quickly approximating the various machining calculations shown in the preceding formulas.

With the pocket calculator, these devices are no longer required, and the calculations are more accurate. Available machine power 2. Condition of the machine 3.

Size, strength, and rigidity of the workpiece 4. Size, strength, and rigidity of the cutting tool Prior to beginning a large production run of turned parts, sample pieces are run in order to determine the exact feeds and speeds required for a particular material and cutting tool combination. Power Constants. The surface speed sfpm , depth of cut in , and feed ipr for various materials using highspeed steel HSS , cast-alloy, and carbide cutting tools are shown in Fig.

In all cases, especially where combinations of values are selected that have not been used previously on a given machine, the selected values should have their required horsepower or kilowatts calculated. Use the approximate calculations shown previously, or use one of the machining calculators available from the cutting tool manufacturers. The method indicated earlier for calculating the required horsepower gives a conservative value that is higher than the actual power required.

In any event, on a manually controlled machine, the machinist or machine operator will know if the selected speed, depth of cut, and feed are more than the given machine can tolerate and can make corrections accordingly. Use the preceding speed, feed, and depth of cut figures as a basis for these choices.

Useful tool life is influenced most by cutting speed. The feed rate is the next most influential factor in tool life, followed by the depth of cut doc. When the depth of cut exceeds approximately 10 times the feed rate, a further increase in depth of cut has little effect on tool life. In selecting the cutting conditions for a turning or boring operation, the first step is to select the depth of cut, followed by selection of the feed rate and then the cutting speed. Relation of Speed to Feed.

The following general rules apply to most turning and boring operations: The productivity settings from the machining calculators and any handbook speed and feed tables are suggestions and guides only. A safety hazard may exist if the user calculates or uses a table-selected machine setting without also considering the machine power and the condition, size, strength, and rigidity of the workpiece, machine, and cutting tools.

The defining dimensions and forms for various thread systems are shown in Fig. The dimensions in the figure are in U. M metric and UN unified national. Typical uses: All branches of the mechanical industries. Aerospace industries. Fittings and pipe couplings for water, sewer, and gas lines.

Presently replaced by ISO system. Machine design. Pipe threads, fittings, and couplings. Pipe thread for water, gas, and steam lines. Mechanical industries for motion-transmission screws. Same as Acme, but used where normal Acme thread is too deep. Petroleum industries. Pipe couplings and fittings in the fireprotection and food industries. Threading Operations. Prior to cutting turning any particular thread, the following should be determined: To calculate the helix angle of a given thread system, use the following simple equation see Fig.

Bibliographic Information

Continued Thread systems and dimensional geometry. The helix angle of any helical thread system can be found by using the preceding procedure. For more data and calculations for threads, see Chap. Cutting Procedures for External and Internal Threads: Machine Setups. Increase surface feet per minute rpm. Use positive rake. Use full-profile insert NTC type. Increase chip load. Use more wear-resistant tool. Use positive rake, sharp tool. Use coolant or increase concentration.

Use neutral rake. Alter infeed angle. Decrease chip load. Increase coolant concentration. The milling process employs relative motion between the workpiece and the rotating cutting tool to generate the required surfaces. In some applications the workpiece is stationary and the cutting tool moves, while in others the cutting tool and the workpiece are moved in relation to each other and to the machine.

A characteristic feature of the milling process is that each tooth of the cutting tool takes a portion of the stock in the form of small, individual chips. Typical cutting tool types for milling-machine operations are shown in Figs. The well-known and highly popular Bridgeport-type milling machine is shown in Fig. The Bridgeport machine is often used in tool and die making operations and in model shops, where prototype work is done.

The Bridgeport shown in Fig. The modern machining center is being used to replace the conventional milling machine in many industrial applications. These machines are the modern workhorses of industry and cannot remain idle for long periods owing to their cost. The modern machining center may be equipped for three-, four-, or five-axis operation. The normal or common operations usually call for three-axis machining, while more involved machining procedures require four- or even five-axis operation.

Three-axis operation consists of x and y table movements and z-axis vertical spindle movements. The four-axis operation includes the addition of spindle rotation with three-axis operation. Five-axis operation includes a horizontal fixture for rotating the workpiece on a horizontal axis at a predetermined speed rpm , together with the functions of the four-axis machine.

This allows all types of screw threads to be machined on the part and other operations such as producing a worm for wormgear applications, segment cuts, arcs, etc. Very complex parts may be mass produced economically on a three-, four-, or five-axis machining center, all automatically, using computer numerical control CNC.

Various machining programs are available for writing the operational instructions sent to the controller on the machining center. This particular control panel is from an Enshu V machining center, a photograph of which appears in Fig.

Milling Calculations. The following calculation methods and procedures for milling operations are intended to be guidelines and not absolute because of the many variables encountered in actual practice. Metal-Removal Rates. In face milling, W is measured perpendicular to the axis and H parallel to the axis. Feed Rate. The speed or rate at which the workpiece moves past the cutter is the feed rate f, which is measured in inches per minute ipm.

Production rates of milled parts are directly related to the feed rate that can be used. The feed rate should be as high as possible, considering machine rigidity and power available at the cutter. The cutting speed of a milling cutter is the peripheral linear speed resulting from the rotation of the cutter.

Increasing the cutting speed alone may shorten the life of the cutter, since the cutter is usually being operated at its maximum speed for optimal productivity. Milling Horsepower. Ratios for metal removal per horsepower cubic inches per minute per horsepower at the milling cutter have been given for various materials see Fig. The K factor represents a particular rate of metal removal and not a general or average rate.

For a quick approximation of total power requirements at the machine motor, see Fig. Typical Milling Problem and Calculations Problem. The milling cutter has 16 teeth, and has a tooth width of 0. Use the following calculations as a guide for milling different materials. Since production rates of milled parts are directly related to the feed rate allowed, the feed rate f should be as high as possible for a particular machine.

Feed rate, ipm, is expressed as: Solve the preceding equation for H: We previously listed the horsepower at the cutter as 5 hp. Then, 3. Now, let us select a cutter of 6-in diameter, and recalculate S: The preceding calculations are for high-speed steel HSS cutters. For carbide, ceramic, cermet, and advanced cutting tool materials, the cutter speed rpm can generally be increased by 25 percent or more, keeping the same feed per tooth Ft, where the higher rpm will increase the feed rate f and give higher productivity.

These catalogs also list the various types and shapes of inserts for different materials to be cut and types of machining applications such as turning, boring, and milling.

1st Edition

Modern Theory of Milling. This was due to the type of tool materials then available HSS and the absence of antibacklash devices on the machines. This method became known as conventional or up milling and is illustrated in Fig.

Climb milling or down milling is now the preferred method of milling with advanced cutting tool materials such as carbides, cermets, CBN, etc.

Climb milling is illustrated in Fig. This allows the heat generated in the cutting process to dissipate into the chip. Climb-milling forces push the workpiece toward the clamping fixture, in the direction of the feed. Conventional-milling upmilling forces are against the direction of feed and produce a lifting force on the workpiece and clamping fixture. The angle of entry is determined by the position of the cutter centerline in relation to the edge of the workpiece.

A negative angle is preferred because it ensures contact with the workpiece at the strongest point of the insert cutter. A positive angle of entry will increase insert chipping. If a positive angle of entry must be employed, use an insert with a honed or negative land. The following milling formulas will allow you to calculate the various milling parameters. Special consideration is given for slot milling, and the following equations may be used effectively to calculate chip load per tooth cpt and inches per minute ipm: It is advantageous to calculate the milling operational horsepower requirements before starting a job.

Lower-horsepower machining centers take advantage of the ability of the modern cutting tools to cut at extremely high surface speeds sfpm. The condition of your milling machine is also critical to obtaining these productivity goals.

Older machines with low-spindlespeed capability should use the uncoated grades of carbide cutters and inserts. Horsepower Calculation. A table of Pf factors is shown in Fig.

Axial cutting forces vary as you change the lead angle of the cutting insert. This is advantageous for weak fixtures and thin web sections. Tangential Cutting Forces.

The use of a tangential force equation is appropriate for finding the approximate forces that fixtures, part walls or webs, and the spindle bearings are subjected to during the milling operation.

The tangential force is easily NOTE. It is important to remember that the tangential forces decrease as the spindle speed rpm increases, i. The ability of the newer advanced cutting tools to operate at higher speeds thus produces fewer fixture- and web-deflecting forces with a decrease in horsepower requirements for any particular machine.

Some of the new high-speed cutter inserts can operate efficiently at speeds of 10, sfpm or higher when machining such materials as free-machining aluminum and magnesium alloys. A time-saving table of surface speed versus cutter speed is shown in Fig. Applying Range of Conditions: Milling Operations. A convenient chart for modifying the speed and feed during a milling operation is shown in Fig. As an example, if there seems to be a problem during a finishing cut on a milling operation, follow the arrows in the chart, and increase the speed while lowering the feed.

For longer tool life, lower the speed while maintaining the same feed. A drill is a rotary-end cutting tool with one or more cutting edges or lips and one or more straight or helical grooves or flutes for the passage of chips and cutting fluids and coolants.

Internet access is required for product activation. For such applications, we recommend the ebook version link above. 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.The equation for calculating the volume of a frustum of a cone is: Case 4. A coolant-hole drill can produce drilled depths to eight or more times the diameter of the drill. All perimeter angles of a chord are equal see Fig. The following calculation methods and procedures for milling operations are intended to be guidelines and not absolute because of the many variables encountered in actual practice. The procedure for layout of the flat pattern is as follows see Fig.