Machinery''''s Handbook 2th Episode 4 Part 9 pptx

Feed on Grinding Machines:: The traversing movement in grinding is equivalent to the feeding movement on other types of machine tools and represents either the axial ment of the work per

MATERIALS 3035 They are then rinsed with water and dried with alcohol Very thin layers of iron sulphide are deposited on the different constituents in different thicknesses, and this gives them dif- ferent colors Austenite remains a pale brown; martensite is given a pale blue and deep blue and brown color; troostite is made very dark; sorbite is uncolored; cementite exhibits a brilliant white; and ferrite is made dark brown When the etching has proceeded to the desired extent, the specimen is at once washed thoroughly in order to remove all trace of the etching reagent Usually it is simply rinsed with water, but frequently the washing is done with absolute alcohol, while ether and chloroform are also sometimes used The apparatus used for examining the etched surfaces of metals is composed of a micro- scope and camera combined with an arc lamp or other means of illumination.

Microscopic Study of Steel: Steel, in particular, shows many changes of structure due to

the mechanical and thermal treatment, so that the microscope has become a very valuable instrument with which to inspect steel To one who understands what the different forma- tions of crystalline structure denote, the magnified surface reveals the temperature at which the steel was hardened, or at which it was drawn, and the depth to which the hardness penetrated It also shows whether the steel was annealed or casehardened, as well as the depth to which the carbon penetrated The carbon content can be closely judged, when the steel is annealed, and also how much of it is in the graphitic state in the high carbon steels The quantity of special elements that is added to steel, such as nickel, chromium, tungsten, etc., can also be estimated, when the alloy to be examined has been put through its pre- scribed heat-treatment Likewise, the impurities that may be present are clearly seen, regardless of whether they are of solid or gaseous origin.

Micarta.—Micarta is a non-metallic laminated product of specially treated woven fabric.

By means of the various processes through which it is passed, it becomes a homogenous structure with physical properties which make it especially adapted for use as gears and pinions Micarta can be supplied either in plate form or cut into blanks It may also be molded into rings or on metal hubs for applications such as timing gears, where quantity production is attained Micarta may be machined in the ordinary manner with standard tools and equipment.

Micarta gears do not require shrouds or end plates except where it is desired to provide additional strength for keyway support or to protect the keyway and bore against rough usage in mounting drive fits and the like When end plates for hub support are employed they should extend only to the root of the tooth or slightly less.

Properties: The physical and mechanical properties of Micarta are as follows: weight per

cubic inch, 0.05 pound; specific gravity, 1.4; oil absorption, practically none; shrinkage, swelling or warping, practically none up to 100 degrees C.; coefficient of expansion per inch per degree Centigrade, 0.00002 inch in the direction parallel to the laminations (edge- wise), 0.00009 inch in the direction perpendicular to the laminations (flat wise) ; tensile strength, edgewise, 10,000 pounds per square inch; compressive strength, flat wise, 40,000 pounds per square inch; compressive strength, edgewise, 20,000 pounds per square inch; bending strength, flatwise, 22,000 pounds per square inch; bending strength, edge- wise, 20,000 pounds per square inch

Monel.—This general purpose alloy is corrosion-resistant, strong, tough and has a

sil-very-white color It is used for making abrasion- and heat-resistant valves and pump parts, propeller shafts, laundry machines, chemical processing equipment, etc.

Approximate Composition: Nickel, 67; copper, 30; iron, 1.4; silicon, 0.1; manganese, 1;

carbon, 0.15; and sulphur 0.01.

Average Physical Properties: Wrought Monel in the annealed, hot-rolled, cold-drawn,

and hard temper cold-rolled conditions exhibits yield strengths (0.2 per cent offset) of 35,000, 50,000, 80,000, and 100,000 pounds per square inch, respectively; tensile strengths of 75,000, 90,000, 100,000, and 110,000 pounds per square inch, respectively;

Machinery's Handbook 27th Edition

3036 MATERIALS

elongations in 2 inches of 40, 35, 25, and 5 per cent, respectively; and Brinell hardnesses of

125, 150, 190, and 240, respectively.

“R” Monel.—This free-cutting, corrosion resistant alloy is used for automatic screw

machine products such as bolts, screws and precision parts.

Approximate Composition: Nickel, 67; copper, 30; iron, 1.4; silicon, 0.05; manganese,

1; carbon, 0.15; and sulphur, 0.035.

Average Physical Properties: In the hot-rolled and cold-drawn conditions this alloy

exhibits yield strengths (0.2 per cent offset) of 45,000 and 75,000 pounds per square inch, respectively; tensile strengths of 85,000 and 90,000 pounds per square inch, respectively; elongations in 2 inches of 35, and 25 per cent, respectively; and Brinell hardnesses of 145 and 180, respectively.

“K” Monel.—This strong and hard alloy, comparable to heat-treated alloy steel, is

age-hardenable, non-magnetic and has low-sparking properties It is used for corrosive cations where the material is to be machined or formed, then age hardened Pump and valve parts, scrapers, and instrument parts are made from this alloy.

appli-Approximate Composition: Nickel, 66; copper, 29; iron, 0.9; aluminum, 2.75; silicon,

0.5; manganese, 0.75; carbon, 0.15; and sulphur, 0.005.

Average Physical Properties: In the hot-rolled, hot-rolled and age-hardened,

cold-drawn, and cold-drawn and age-hardened conditions the alloy exhibits yield strengths (0.2 per cent offset) of 45,000, 110,000, 85,000, and 115,000 pounds per square inch, respec- tively; tensile strengths of 100,000, 150,000, 115,000, and 155,000 pounds per square inch, respectively; elongations in 2 inches of 40, 25, 25, and 20 per cent, respectively; and Brinell hardnesses of 160, 280, 210, and 290, respectively.

“KR” Monel.—This strong, hard, age-hardenable and non-magnetic alloy is more readily

machinable than “K” Monel It is used for making valve stems, small parts for pumps, and screw machine products requiring an age-hardening material that is corrosion-resistant.

Approximate Composition: Nickel, 66; copper, 29; iron, 0.9; aluminum, 2.75; silicon,

0.5; manganese, 0.75; carbon, 0.28; and sulphur, 0.005.

Average Physical Properties: Essentially the same as “K” Monel.

“S” Monel.—This extra hard casting alloy is non-galling, corrosion-resisting,

non-mag-netic, age-hardenable and has low-sparking properties It is used for gall-resistant pump and valve parts which have to withstand high temperatures, corrosive chemicals and severe abrasion.

Approximate Composition: Nickel, 63; copper, 30; iron, 2; silicon, 4; manganese, 0.75;

carbon, 0.1; and sulphur, 0.015.

Average Physical Properties: In the annealed sand-cast, as-cast sand-cast, and

age-hard-ened sand-cast conditions it exhibits yield strengths (0.2 per cent offset) of 70,000, 100,000, and 100,000 pounds per square inch, respectively; tensile strengths of 90,000, 130,000, and 130,000 pounds per square inch, respectively; elongations in 2 inches of and

3, 2, and 2 per cent, respectively; and Brinell hardnesses of 275, 320, and 350, respectively.

“H” Monel.—An extra hard casting alloy with good ductility, intermediate strength and

hardness that is used for pumps, impellers and steam nozzles.

Approximate Composition: Nickel, 63; copper, 31; iron, 2; silicon, 3; manganese, 0.75;

carbon, 0.1; and sulphur, 0.015.

Average Physical Properties: In the as-cast sand-cast condition this alloy exhibits a

yield strength (0.2 per cent offset) of 60,000 pounds per square inch, a tensile strength of 100,000 pounds per square inch, an elongation in 2 inches of 15 per cent and a Brinell hard- ness of 210.

Nichrome.—“Nichrome” is the trade name of an alloy composed of nickel and chromium,

which is practically non-corrosive and far superior to nickel in its ability to withstand high

Machinery's Handbook 27th Edition

MATERIALS 3037 temperatures Its melting point is about 1550 degrees C (about 2800 degrees F.) Nichrome shows a remarkable resistance to sulphuric and lactic acids In general, nichrome is adapted for annealing and carburizing boxes, heating retorts of various kinds, conveyor chains subjected to high temperatures, valves and valve seats of internal com- bustion engines, molds, plungers and conveyors for use in the working of glass, wire bas- kets or receptacles of other form that must resist the action of acids, etc Nichrome may be used as a substitute for other materials, especially where there is difficulty from oxidation, pitting of surfaces, corrosion, change of form, or lack of strength at high temperatures It can be used in electrically-heated appliances and resistance elements Large plates of this alloy are used by some manufacturers for containers and furnace parts, and when perfo- rated, as screens for use in chemical sifting and ore roasting apparatus, for services where temperatures between 1700 degrees F and 2200 degrees F are encountered.

Strength of Nichrome: The strength of a nichrome casting, when cold, varies from

45,000 to 50,000 pounds per square inch The ultimate strength at 200 degrees F is 94,000 pounds per square inch; at 400 degrees F., 91,000 pounds per square inch; at 600 degrees F., 59,000 pounds per square inch; and at 800 degrees F., 32,000 pounds per square inch.

At a temperature of 1800 degrees F., nichrome has a tensile strength of about 30,000 pounds per square inch, and it is tough and will bend considerably before breaking, even when heated red or white hot.

Nichrome in Cast Iron: Because of the irregularity of the castings, the numerous cores

required, and the necessity for sound castings, gray iron with a high silicon content has been the best cast iron available to the automotive industry Attempts have been made to alloy this metal in such a way that the strength and hardness would be increased, but con- siderable difficulty has been experienced in obtaining uniform results Nickel has been added to the cupola with success, but in the case of automotive castings, where a large quantity of silicon is present, the nickel has combined with the silicon in forming large flakes of graphite, which, of course, softens the product To offset this, chromium has also been added, but it has been uncertain just what the chromium content of the poured mixture should be, as a considerable amount of the chromium oxidizes.

Nichrome (Grade B) may be added to the ladle to obtain chromium and nickel in definite controllable amounts The analysis of this nichrome is, approximately: Nickel, 60 per cent; chromium, 12 per cent; and iron, 24 per cent It is claimed that the process produces cast- ings of closer grain, greater hardness, greater resistance to abrasion, increased durability, improved machinability, and decreased brittleness Nichrome-processed iron is suitable for casting internal-combustion engine cylinders; electrical equipment, where a control of the magnetic properties is desired; cast-iron cams; iron castings of thin sections where machinability and durability are factors; electrical resistance grids; pistons; piston-rings; and water, steam, gas, and other valves.

Nickel Alloy for Resisting Acids.—The resistance of nickel to acids is considerably

increased by an addition of tantalum Ordinarily from 5 to 10 per cent may be added, but the resistance increases with an increasing percentage of tantalum An alloy of nickel with

30 per cent tantalum, for example, can be boiled in aqua regia or any other acid without being affected The alloy is claimed to be tough, easily rolled, capable of being hammered

or drawn into wire The nickel loses its magnetic quality when alloyed with tantalum The alloy can be heated in the open air at a high temperature without oxidizing The method of producing the alloy consists in mixing the two metals in a powdered form, compressing them at high pressure, and bringing them to a high heat in a crucible or quartz tube in a vac- uum For general purposes, the alloy is too expensive.

Duronze.—An alloy of high resistance to wear and corrosion, composed of aluminum,

copper, and silicon, with a tensile strength of 90,000 pounds per square inch Developed for the manufacture of valve bushings for valves that must operate satisfactorily at high pressures and high temperatures without lubrication.

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3038 MATERIALS

Aluminum Alloys, Wrought, Sheet.—Physical Properties: In the form of sheets, the

tensile strength varies from 35,000 for soft temper to 62,000 pounds per square inch for heat-treated sheets, and the elongation in 2 inches from 12 to 18 per cent The yield strength

of a heat-treated sheet is about 40,000 pounds per square inch minimum.

Plow-steel Wire Rope.—The name “plow” steel originated in England and was applied

to a strong grade of steel wire used in the construction of very strong ropes employed in the mechanical operation of plows The name “plow” steel, however, has become a commer- cial trade name, and, applied to wire, simply means a high-grade open-hearth steel of a ten- sile strength in wire of from 200,000 to 260,000 pounds per square inch of sectional area.

A strength of 200,000 pounds per square inch is obtained in wire about 0.200 inch in eter Plow steel when used for wire ropes has the advantage of combining lightness and great strength It is a tough material, but not as pliable as crucible steel The very highest grade of steel wire used for wire rope is made from special steels ranging in tensile strength

diam-in wire from 220,000 to 280,000 pounds per square diam-inch of sectional area This steel is especially useful when great strength, lightness, and abrasive resisting qualities are required.

Type Metal.—Antimony gives to metals the property of expansion on solidification, and

hence, is used in type metal for casting type for the printing trades to insure completely ing the molds Type metals are generally made with from 5 to 25 per cent of antimony, and with lead, tin and sometimes a small percentage of copper as the other alloying metals The compositions of a number of type metal alloys are as follows (figures given are per- centages): lead 77.5, tin 6.5, antimony 16; lead 70, tin, 10, antimony 18, copper, 2; l e a d 63.2, tin 12, antimony 24, copper 0.8 ; lead 60.5, tin 14.5, antimony 24-25, copper 0.75; lead 60, tin 35, antimony 5; and lead 55.5, tin 40, antimony 4.5.

fill-A high grade of type metal is composed of the following percentages: lead 50; t i n 2 5 ; and antimony 25.

Vanadium Steel.— The two most marked characteristics of vanadium steel are its high

tensile strength and its high elastic limit Another equally important characteristic is its great resistance to shocks; vanadium steel is essentially a non-fatigue metal, and, there- fore, does not become crystallized and break under repeated shocks like other steels Tests

of the various spring steels show that, when subjected to successive shocks for a able length of time, a crucible carbon-steel spring was broken by 125,000 alternations of the testing machine, while a chrome-vanadium steel spring withstood 5,000,000 alterna- tions, remaining unbroken Another characteristic of vanadium steel is its great ductility Highly-tempered vanadium-steel springs may be bent sharply, in the cold state, to an angle

consider-of 90 degrees or more, and even straightened again, cold, without a sign consider-of fracture; dium-steel shafts and axles may be twisted around several complete turns, in the cold state, without fracture This property, combined with its great tensile strength, makes vanadium steel highly desirable for this class of work, as well as for gears which are subjected to heavy strains or shocks upon the teeth Chromium gives to steel a brittle hardness which makes it very difficult to forge, machine, or work, but vanadium, when added to chrome- steel, reduces this brittle hardness to such an extent that it can be machined as readily as an 0.40-per-cent carbon steel, and it forges much more easily Vanadium steels ordinarily contain from 0.16 to 0.25 per cent of vanadium Steels of this composition are especially adapted for springs, car axles, gears subjected to severe service, and for all parts which must withstand constant vibration and varying stresses Vanadium steels containing chro- mium are used for many automobile parts, particularly springs, axles, driving-shafts, and gears

vana-Wood’s Metal.—The composition of vana-Wood’s metal, which is a so-called “fusible metal,”

is as follows: 50 parts of bismuth, 25 parts of lead, 12.5 parts of tin and 12.5 parts of mium The melting point of this alloy is from 66 to 71 degrees centigrade (151 to 160 degrees F approximately).

cad-Machinery's Handbook 27th Edition

MATERIALS 3039

Lumber.—Lumber is the product of the saw and planing mill not further manufactured

than by sawing, resawing, and passing lengthwise through a standard planing machine, cross-cutting to length and working When not in excess of one-quarter inch thickness and intended for use as veneering it is classified as veneer According to the Simplified Practice Recommendations promulgated by the National Bureau of Standards, lumber is classified

by its principal use as: yard lumber, factory and shop lumber, and structural lumber.

Yard lumber is defined as lumber of all sizes and patterns which is intended for general

building purposes Its grading is based on intended use and is applied to each piece without reference to size and length when graded and without consideration to further manufac- ture As classified by size it includes: strips, which are yard lumber less than 2 inches thick and less than 8 inches wide; boards, which are yard lumber less than 2 inches thick but 8 inches or more wide; dimension, which includes all yard lumber except strips, boards and timbers; and timbers, which are yard lumber of 5 or more inches in the least dimension.

Factory and shop lumber is defined as lumber intended to be cut up for use in further

manufacture It is graded on the basis of the percentage of the area which will produce a limited number of cuttings of a specified, or of a given minimum, size and quality.

Structural lumber is defined as lumber that is 2 or more inches thick and 4 or more inches

wide, intended for use where working stresses are required The grading of structural ber is based on the strength of the piece and the use of the entire piece As classified by size

lum-and use it includes joists lum-and planks—lumber from 2 inches to but not including 5 inches

thick, and 4 or more inches wide, of rectangular cross section and graded with respect to its strength in bending, when loaded either on the narrow face as joist or on the wide face as

plank; beams and stringers—lumber of rectangular cross section 5 or more inches thick

and 8 or more inches wide and graded with respect to its strength in bending when loaded

on the narrow face; and posts and timbers—pieces of square or approximately square cross

section 5 by 5 inches and larger and graded primarily for use as posts or columns carrying longitudinal load, but adapted to miscellaneous uses in which strength in bending is not especially important.

Lumber, Manufactured.—According to the Simplified Practice Recommendations

pro-mulgated by the National Bureau of Standards, lumber may be classified according to the extent which It Is manufactured as:

Rough lumber which is lumber that is undressed as it comes from the saw.

Surfaced lumber which is lumber that is dressed by running it through a planer and may

be surfaced on one or more sizes and edges.

Worked lumber which is lumber that has been run through a matching machine, sticker or molder and includes: matched lumber which has been worked to provide a close tongue- and-groove joint at the edges or, in the case of end-matched lumber, at the ends also; ship- lapped lumber which has been worked to provide a close rabbetted or lapped joint at the edges; and patterned lumber which has been shaped to a patterned or molded form.

Lumber Water Content.—The origin of lumber has a noticeable effect on its water

con-tent Lumber or veneer (thin lumber produced usually by rotary cutting or flat slicing, sometimes by sawing), when produced from the log, contains a large proportion of water, ranging from 25 to 75 per cent of the total weight One square foot (board measure, one inch thick) of gum lumber, weighing approximately five pounds when sawed, will be reduced to about three pounds when its water content of approximately one quart has been evaporated Oak grown on a hillside may contain only a pint (approximately 1 lb.) and swamp gum may have from 2 to 4 pints of water per square foot, board measure This water content of wood exists in two forms—free moisture and cell moisture The former is readily evaporable in ordinary air drying, but the latter requires extensive air drying (sev- eral years) or artificial treatment in kilns It is possible to use artificial means to remove the free moisture, but a simple air exposure is usually more economical.

Machinery's Handbook 27th Edition

Wheatstone Bridge.—The most generally used method for the measurement of the

ohmic resistance of conductors is by the use of the Wheatstone bridge In a simple form

(See Fig 1.) it comprises two resistance coils the ratio of the resistances of which is known, and a third, generally adjustable, resistance of known value These are connected in circuit with the unknown resistance to be measured, a galvanometer, and a source of current, as in the diagram

Fig 1 Wheatstone Bridge The adjustable resistance and the “bridge arms,” if necessary, are adjusted until the gal- vanometer indicates no flow of current The value of the unknown resistance is thus mea- sured in terms of the known resistance and the known ratio of the bridge arms In the

diagram, R1, R2, R3, and R4 are resistances, B a source of electromotive force and I1, I2, I3and 14 currents through the resistances; G is a galvanometer If the relation of the various resistances is such that no current flows through G, then I1 equals I2, and I3 equals I4; also

11R1 equals 13R3, and 12R2 equals 14R4, there being no electromotive forces in the triangles

R1R3G and R2R4G It follows, therefore, that

TOOLING 3041

Wheatstone bridges are made in many forms The three known resistances are made adjustable and are usually made of many spools of special resistance wire The resistances are usually varied by short-circuiting a greater or smaller number of these spools.

Tools and Tooling Rotary Files and Burs.—Rotary files and burs are used with power-operated tools, such

as flexible- or stationary-shaft machines, drilling machines, lathes, and portable electric or pneumatic tools, for abrading or smoothing metals and other materials Corners can be bro- ken and chamfered, burs and fins removed, holes and slots enlarged or elongated, and scale removed in die-sinking, metal patternmaking, mold finishing, toolmaking and casting operations.

The difference between rotary files and rotary burs, as defined by most companies, is that the former have teeth cut by hand with hammer and chisel, whereas the latter have teeth or flutes ground from the solid blank after hardening, or milled from the solid blank before hardening (At least one company, however prefers to differentiate the two by use and size: The larger-sized general purpose tools with 1 ⁄ 4 -inch shanks, whether hand cut or ground, are referred to as rotary files; the smaller shanked – 1 ⁄ 8 -inch – and correspondingly smaller- headed tools used by diesinkers and jewelers are referred to as burs.) Rotary files are made from high-speed steel and rotary burs from high-speed steel or cemented carbide in various cuts such as double extra coarse, extra coarse or rough, coarse or standard, medium, fine, and smooth Standard shanks are 1 ⁄ 4 inch in diameter.

There is very little difference in the efficiency of rotary files or burs when used in electric tools and when used in air tools, provided the speeds have been reasonably well selected Flexible-shaft and other machines used as a source of power for these tools have a limited number of speeds which govern the revolutions per minute at which the tools can be oper- ated.

The carbide bur may be used on hard or soft materials with equally good results The principal difference in construction of the carbide bur is that its teeth or flutes are provided with negative rather than a radial rake Carbide burs are relatively brittle and must be treated more carefully than ordinary burs They should be kept cutting freely, in order to prevent too much pressure, which might result in crumbling of the cutting edges.

At the same speeds, both high-speed steel and carbide burs remove approximately the same amount of metal However, when carbide burs are used at their most efficient speeds, the rate of stock removal may be as much as four times that of ordinary burs It has been demonstrated that a carbide bur will last up to 100 times as long as a high-speed steel bur of corresponding size and shape.

Tooth-rest for Cutter Grinding.—A tooth-rest is used to support a cutter while grinding

the teeth For grinding a cylindrical cutter having helical or "spiral" teeth, the tooth-rest must remain in a fixed position relative to the grinding wheel The tooth being ground will then slide over the tooth-rest, thus causing the cutter to turn as it moves longitudinally, so that the edge of the helical tooth is ground to a uniform distance from the center, through- out its length For grinding a straight-fluted cutter, it is also preferable to have the tooth- rest in a fixed position relative to the wheel, unless the cutter is quite narrow, because any warping of the cutter in hardening will result in inaccurate grinding, if the toothrest moves with the work The tooth-rest should be placed as close to the cutting edge of the cutter as

is practicable, and bear against the face of the tooth being ground

3042 MACHINING OPERATIONS

Machining Operations Feed Rate on Machine Tools.— The rate of feed as applied to machine tools in general,

usually indicates (1) the movement of a tool per work revolution, (2) the movement of a tool per tool revolution, (3) or the movement of the work per tool revolution

Rate of Feed in Turning: The term "feed" as applied to a lathe indicates the distance that

the tool moves during each revolution of the work There are two ways of expressing the rate of feed One is to give the actual tool movement per work revolution in thousandths of

an inch For example, the range of feeds may be given as 0.002 to 0.125 inch This is the usual method Another way of indicating a feed range is to give the number of cuts per inch

or the number of ridges that would be left by a pointed tool after turning a length of one inch For example, the feed range might be given as 8 to 400 In connection with turning and other lathe operations, the feed is regulated to suit the kind of material, depth of cut, and in some cases the finish desired

Rate of Feed in Milling: The feed rate of milling indicates the movement of the work per

cutter revolution.

Rate of Feed in Drilling: The rate of feed on drilling machines ordinarily indicates the

feeding movement of the drill per drill revolution.

Rate of Feed in Planing: On planers, the rate of feed represents the tool movement per

cutting stroke On shapers, which are also machines of the planing type, the rate of feed represents the work movement per cutting stroke.

Rate of Feed on Gear Hobb era: The feed rate of a gear hobbing machine represents the

feeding movement of the hob per revolution of the gear being hobbed.

Feed on Grinding Machines:: The traversing movement in grinding is equivalent to the

feeding movement on other types of machine tools and represents either the axial ment of the work per work revolution or the traversing movement of the wheel per work revolution, depending upon the design of the machine

move-Billet.—A “billet,” as the term is applied in rolling mill practice, is square or round in

sec-tion and from 1 1 ⁄ 2 inches in diameter or square to almost 6 inches in diameter or square Rolling mills used to prepare the ingot for the forming mills are termed “blooming mills,”

“billet mills,” etc.

Milling Machines, Lincoln Type.—The well-known Lincoln type of milling machine is

named after George S Lincoln of the firm then known as George S Lincoln & Co., ford, Conn Mr Lincoln, however, did not originate this type but he introduced an improved design Milling machines constructed along the same general lines had previ- ously been built by the Phoenix Iron Works of Hartford, Conn., and also by Robbins & Lawrence Co., of Windsor, Vt Milling machines of this class are intended especially for manufacturing and are not adapted to a great variety of milling operations, but are designed for machining large numbers of duplicate parts Some milling machines which are

Hart-designed along the same lines as the Lincoln type are referred to as the manufacturing type.

The distinguishing features of the Lincoln type are as follows: The work table, instead of being carried by an adjustable knee, is mounted on the solid bed of the machine and the outer arbor support is also attached directly to the bed This construction gives a very rigid support both for the work and the cutter The work is usually held in a fixture or vise attached to the table, and the milling is done as the table feeds longitudinally The table is not adjustable vertically but the spindle head and spindles can be raised or lowered as may

be required.

Saddle.—A machine tool saddle is a slide which is mounted upon the ways of a bed,

cross-rail, arm, or other guiding surfaces, and the saddle metal-cutting tools or a work-holding table On holding either metal-cutting tools or a work-holding table On a knee-type mill- ing machine the saddle is that part which slides upon the knee and which supports the work-holding table The saddle of a planer or boring mill is mounted upon the cross-rail

Machinery's Handbook 27th Edition

MACHINING OPERATIONS 3043 and supports the tool-holding slide The saddle of a lathe is that part of a carriage which slide The saddle of a lathe is that part of a carriage which slides directly upon the lathe bed and supports the cross-slide.

Cold Extrusion.—In simplest terms, cold extrusion can be defined as the forcing of

unheated metal to flow through a shape-forming die It is a method of shaping metal by plastically deforming it under compression at room temperature while the metal is within a die cavity formed by the tools The metal issues from the die in at least one direction with the desired cross-sectional contour, as permitted by the orifice created by the tools Cold extrusion is always performed at a temperature well below the recrystallization temperature of the metal (about 1100 to 1300 degrees F for steel) so that work-hardening always occurs In hot extrusion, recrystallization eliminates the effects of work-hardening, unless rapid cooling of the extrusion prevents recrystallization from being completed Extrusion differs from other processes, such as drawing, in that the metal is always being pushed under compression and never pulled in tension As a result, the material suffers much less from cracking While coining is closely related to extrusion, it differs in that metal is completely confined in the die cavity instead of being forced through openings in the die Some forging operations combine both coining and extrusion

The pressure of the punch against the metal in an open die, and the resultant shaped part obtained by displacing the metal along paths of least resistance through an orifice formed between the punch and die, permits considerably higher deformation rates without tearing and large changes in the shape Extrusion is characterized by a thorough kneading of the material The cross-sectional shape of the part will not change due to expansion or contrac- tion as it leaves the tool orifice The term "cold extrusion" is not too descriptive and is not universally accepted Other names for the same process include impact extrusion, extru- sion-forging, cold forging, extrusion pressing, and heavy cold forming Impact extrusion, however, is more frequently used to describe the production of non-ferrous parts, such as collapsible tubes and other components, while cold extrusion seems to be preferred by manufacturers of steel parts In Germany, the practice is called Kaltspritzen-a literal trans- lation of which is "cold-squirting."

One probable reason for not using impact extrusion in referring to the cold extrusion of steel is that the term implies plastic deformation by striking the metal an impact blow Actually, the metal must be pushed through the die orifice, with pressure required over a definite period of time One disadvantage of the terminology "cold extrusion" is the possi- ble confusion with the older, more conventional direct extrusion process in which billets of hot metal are placed in a cylinder and pushed by a ram through a die (usually in a large, horizontal hydraulic press) to form rods, bars, tubes, or irregular shapes of considerable length

Another possible disadvantage is the connotation of the word "cold." While the process

is started with blanks, slugs, tubular sections, or pre-formed cups at room temperature, the internal, frictional resistance of the metal to plastic flow raises the surface temperature of the part to 400 degrees F or more, and the internal temperature even higher (depending on the severity of the operation) These are still below the recrystallization temperature and the extrusions retain the advantages of improved physical properties resulting from the cold working

Transfer Machines.—These specialized machine tools are used to perform various

machining operations on parts or parts in fixtures as the parts are moved along on an matic conveyor which is part of the machine tool set-up In a set-up, the parts can move in

auto-a strauto-aight line from their entry point to their exit point, or the setup mauto-ay be constructed in auto-a U-shape so that the parts are expelled near where they start.

Machinery's Handbook 27th Edition

3044 FASTENERS

Fasteners Stove Bolt.— This bolt has been so named because of its use in stove building It is made

in a number of different forms, either with a round button, or flat countersunk head, the head having a slot for a screwdriver and the threaded end being provided with a square or hexagon nut.

Flattening Test.—This term as applied to tubing refers to a method of testing a section of

tubing by flattening it until the inside walls are parallel and separated by a given usually equal to three times the wall thickness for seamless tubes and five times the wall thickness for lap-welded tubes Boiler tubes subjected to this test should show no cracks or flaws The flattening test applied to rivets, consists in flattening a rivet head while hot to a diameter equal to 2 1 ⁄ 2 times the diameter of the shank or body of the rivet Good rivet steel must not crack at the edges of the flattened head

distance-Rivets, Cold Formed.—In permanently assembling various Light parts, it is often

possi-ble to greatly reduce the cost and yet secure sufficient strength by cold forming in an assembling die, the rivet or rivets as an integral part of one of the assembled sections Fig- ures 1a , 1b , and 1c illustrate how a steel spring is cold riveted to the heavier section Plain round punches descend and form the rivets by forcing metal down through the holes in the spring (see Fig 1b ) ; the metal at the edge is then turned back by the die as shown in Fig 1c , thus completing the riveting at one stroke of the press In this particular case, about sixty assemblies per minute are obtained.

Embossed Dowels and Hubs: When dowel-pins are required to insure the accurate

loca-tion of parts relative to each other, small projecloca-tions or bosses may be formed directly on many die-made products, the projection being an integral part of the work and serving as a dowel-pin Figure 1d illustrates how the dowel is formed The method may be described as

a partial punching operation, as a punch penetrate about one-half the stock thickness and forces the boss into a pocket in the die which controls the diameter and compresses the

metal, thus forming a stronger projection than would be obtained otherwise The height h

of the dowel or boss should not exceed one-half of the dowel diameter d and h should not exceed one-half of the stock thickness t This is a practical rule which may be applied either

to steel or non-ferrous metals, such as brass.

3046 THREADS AND THREADING

In 1886 the large majority of American manufacturers threaded pipe to practically the Briggs Standard, and acting jointly with The American Society of Mechanical Engineers they adopted it as a standard practice that year, and master plug and ring gages were made Later at various conferences representatives of the manufacturers and the ASME estab- lished additional sizes, certain details of gaging, tolerances, special applications of the standard, and in addition tabulated the formulas and dimensions more completely than was done by Mr Briggs.

Until the manufacturers adopted the Briggs thread in 1886, it seems that each turer of necessity threaded his pipe and fittings according to his best judgment After 1886 there was some attempt to work toward better interchangeability However, the need for a better gaging practice resulted in the adoption of the thin ring gage and the truncation of the plug and ring gages to gage the flanks of the thread This practice of threading fittings and couplings which provides threads to make up joints with a wrench was standardized about 1913.

manufac-In 1913 a Committee on the Standardization of Pipe Threads was organized for the pose of re-editing and expanding the Briggs Standard The American Gas Association and The American Society of Mechanical Engineers served as joint sponsors After six years of work, this committee completed the revised standard for taper pipe thread which was pub-

pur-lished in the ASME “Transactions” of 1919, and was approved as an American Standard

by the American Engineering Standards Committee, later named the American Standards Association in December 1919 It was the first standard to receive this designation under the ASA procedure, and was later published in pamphlet form.

In the years which followed, the need for a further revision of this American Standard became evident as well as the necessity of adding to it the recent developments in pipe threading practice Accordingly, the Sectional Committee on the Standardization of Pipe Threads, B2, was organized in 1927 under the joint sponsorship of the A.G.A and the ASME.

During the following 15 years, several meetings were held leading to approval by the members of the Sectional Committee, of the April 1941 draft The revision was approved

by the sponsors and ASA and published as an American Standard in October, 1942 Shortly after publication of the 1942 standard, the Committee undertook preparation of a complete revision The text and tables were rearranged and expanded to include Dryseal pipe threads, and an extensive appendix was added to provide additional data on the appli- cation of pipe threads and to record in abbreviated form the several special methods which were established for gaging some of the various applications of pipe threads.

The resulting proposal was approved by letter ballot of the Sectional Committee ing its acceptance by the sponsor bodies, the draft was submitted to the American Stan- dards Association and designated an American Standard on December 11, 1945.

Follow-At a subsequent meeting of the Sectional Committee it was agreed that for the nience of users, the standards covering Dryseal pipe threads should be published under separate cover Consequently, the section included in ASA B2.1-1945 on Dryseal pipe threads was deleted from the 1960 revision to that standard and used as a basis for the development of a separate proposal for Dryseal pipe threads The text and tables were expanded to completely document the various series threads and gages, and appendices

conve-covering formulas, drilled hole sizes and special series threads were added The E 1 internal

diameter and the L 1 hand type engagements for the 1 ⁄ 8 and 1 ⁄ 4 inch sizes were revised to rect for a disproportionate number of threads for hand tight engagement This proposal was approved by letter ballot vote of the Sectional Committee and submitted to the A.G.A and the ASME Following approval by the sponsor organizations, it was approved by the American Standards Association on April 29, 1960, and designated as ASA B2.1-1960, Pipe Threads (Except Dryseal).

cor-Machinery's Handbook 27th Edition

THREADS AND THREADING 3047 The present revision of this standard constitutes a general updating In line with their cur- rent policy, the A.G.A has withdrawn sponsorship of this standard, while remaining active

in the work of the standards committee In compliance with the rules of the United States of America Standards Institute (formerly ASA) the previously designated Sectional Commit- tees are now called Standards Committees.

Following approval by the Standards Committee B2 and the sponsor, ASME, the sion was approved by the United States of America Standards Institute on November 29, 1968.

revi-Lock-Nut Pipe Thread.—The lock-nut pipe thread is a straight thread of the largest

diameter which can be cut on a pipe Its form is identical with that of the American or Briggs standard taper pipe thread In general, “Go” gages only are required These consist

of a straight-threaded plug representing the minimum female lock-nut thread, and a straight-threaded ring representing the maximum male lock-nut thread This thread is used only to hold parts together, or to retain a collar on the pipe It is never used where a tight threaded joint is required.

Thread Grinding.—Thread grinding is applied both in the manufacture of duplicate parts

and also in connection with precision thread work in the tool-room.

Single-edged Grinding Wheel: In grinding a thread, the general practice in the United

States is to use a large grinding wheel (for external threads) having a diameter of possibly

18 to 20 inches The width may be 5/16 or 3 ⁄ 8 inch The face or edge of this comparatively narrow wheel is accurately formed to the cross-sectional shape of the thread to be ground The thread is ground to the correct shape and lead by traversing it relative to the grinding wheel This traversing movement, which is equivalent to the lead of the screw thread for each of its revolutions, is obtained from a lead-screw On one type of thread grinder, this lead-screw is attached directly to the work-spindle and has the same lead as the screw thread to be ground; hence, there is a separate lead-screw for each different lead of thread

to be ground On another design of machine, the lead-screw arrangement is similar to that

on a lathe in that the required lead on the ground thread is obtained by selection of the proper change gears The grinding wheel may have a surface speed of 7000 feet a minute, whereas the work speed may range from 3 to 10 feet per minute The grinding wheel is inclined to suit the helix angle of the thread and either right- or left-hand threads may be ground Provision is also made for grinding multiple threads and for relieving taps and hobs The wheel shape is accurately maintained by means of diamond truing tools On one type of machine, this truing is done automatically and the grinding wheel is also adjusted automatically to compensate for whatever slight reduction in wheel size may result from the truing operation.

An internal thread may also be ground with a single-edged wheel The operation is the same in principle as external thread grinding The single-edged wheel is used whenever the highest precision is required, grinding the work either from the solid or as a finishing oper- ation.

Grinding “from the Solid”: On some classes of work, the entire thread is formed by

grinding “from the solid,” especially if the time required is less than would be needed for a rough thread-cutting operation followed by finish-grinding after hardening Grinding threads from the solid is applied to the finer pitches In some plants, threads with pitches up

to about 1/16 inch are always ground by this method.

Multi-edged Grinding Wheel: An entire screw thread, if not too long, may be ground

completely in one revolution by using a multi-edged type of grinding wheel The face of this wheel is formed of a series of annular thread-shaped ridges so that it is practically a number of wheels combined in one The principle is the same as that of milling screw threads by the multiple-cutter method If the length of the thread to be ground is less than the width of the wheel, it is possible to complete the grinding in practically one work revo- lution as in thread milling A grinding wheel having a width of, say, 2 1 ⁄ 2 inches, is provided

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3048 THREADS AND THREADING

with annual ridges or threads across its entire width The wheel is fed in to the thread depth, and, while the work makes one single revolution, the wheel moves axially a distance equal

to the thread lead along the face of the work Most threads which require grinding are not longer than the width of the wheel; hence, the thread is completed by one turn of the work.

If the thread is longer than the wheel width, one method is to grind part of the thread and then shift the wheel axially one or more times for grinding the remaining part For exam- ple, with a wheel 2 1 ⁄ 2 inches in width, a thread approximately 12 inches long might be ground in five successive steps A second method is that of using a multi-edged tapering wheel which is fed axially along the work The taper is to distribute the work of grinding over the different edges or ridges as the wheel feeds along.

Hand Chaser.—A hand chaser is a type of threading tool used either for cutting or chasing

external or internal threads The tool is supported upon a rest and is guided by the hand; it

is used mainly on brass work, for slightly reducing the size of a thread that has been cut either by a die or threading tool A hand chaser may also be used for truing up battered threads in repair work and for similar purposes.

Thread-Cutting Methods.—The two general methods of forming screw threads may be

defined as the cutting method and the rolling or displacement method The cutting methods

as applied to external threads are briefly as follows:

1) By taking a number of successive cuts with a single-point tool that is traversed along the part to be threaded at a rate per revolution of the work depending upon the lead of the thread (Common method of cutting screw threads in the engine lathe.)

2) By taking successive cuts with a multiple-point tool or chaser of the type used to some extent in conjunction with the engine lathe and on lathes of the Fox or monitor types 3) By using a tool of the die class, which usually has four or more multiple-point cutting edges or chasers and generally finishes the thread in one cut or passage of the tool 4) By a single rotating milling cutter, which forms the thread groove as either the cutter or the work is traversed axially at a rate depending upon the thread lead.

5) By a multiple rotating milling cutter which completes a thread in approximately one revolution of the work.

6) By a multiple rotating cutter which also has a planetary rotating movement about the work which is held stationary See Planamilling and Planathreading.

7) By a grinding wheel having its edge shaped to conform to the groove of the screw thread.

8) By a multi-edged grinding wheel which, within certain limits as to thread length, will grind the complete thread in practically one revolution of the work.

Internal screw threads, or those in holes, may or may not be produced by the same general method that is applied to external work There are three commercial methods of impor- tance, namely:

1) By the use of a single-point traversing tool in the engine lathe or a multiple-point chaser in some cases.

2) By means of a tap which, in machine tapping, usually finishes the thread in one cut or passage of the tool.

3) By a rotating milling cutter of either the single or the multiple type.

Dies operated by hand are frequently used for small and medium-sized parts, especially when accuracy as to the lead of the thread and its relation to the screw axis is not essential and comparatively few parts need to be threaded at a time When a large number of pieces must be threaded, power-driven machines equipped with dies are commonly employed If the operation is simply that of threading the ends of bolts, studs, rods, etc., a “bolt cutter” would generally be used, but if cutting the thread were only one of several other operations necessary to complete the work, the thread would probably be cut in the same machine per- forming the additional operations For instance, parts are threaded in turret lathes and auto- matic screw machines by means of dies and in conjunction with other operations When

Machinery's Handbook 27th Edition

THREADS AND THREADING 3049 screws are required which must be accurate as to the pitch or lead of the thread, and be true relative to the axis of the work, a lathe is generally used; lathes are also employed, ordi- narily, when the threaded part is comparatively long and large in diameter Many threads which formerly were cut in the lathe are now produced by the milling process in special thread-milling machines The method often depends upon the equipment at hand and the number of parts to be threaded Very precise threads may be produced by grinding.

Taps.—A tap is an internal thread-cutting tool having teeth which conform to the shape of

the thread Taps may be classified according to the kind of thread with which they are vided, as U S Standard thread taps, square thread taps, and Acme thread taps, etc The most important classification of taps, however, is according to their use.

pro-Hand taps: as the name implies, are intended primarily for tapping holes by hand but are

often used in machines All taps used by hand are not termed “hand” taps as there are many special taps used by hand which are known by specific names.

Tapper taps: are used for tapping nuts in tapping machines They are provided with a

long chamfered part on the end of the threaded portion, and a long shank.

Machine nut taps: are also used for tapping nuts in tapping machines This type is

designed for more severe duty than the tapper tap and is especially adapted for tapping holes in materials of tough structure Machine nut taps are chamfered and relieved in a dif- ferent, manner from tapper taps.

Machine screw taps: may be either hand taps or machine nut taps, but are known by the

name “machine screw tap,” because they constitute a class of special taps used for tapping holes for standard machine screw sizes.

Screw machine taps: for tapping in the screw machine are provided with shanks fitting

either the turret holes of the machine or bushings inserted in these holes As these taps narily cut threads down to the bottom of the hole, they are provided with a very short cham- fer.

ordi-Pulley taps: are simply a special type of taps used for tapping holes which cannot be

reached by ordinary hand taps, as, for instance, the set-screw or oil-cup holes in the hubs of pulleys They are simply hand taps with a very long shank.

Die taps: also known as long taper die taps, are used for cutting the thread in a die in a

single operation from the blank, and are intended to be followed by a sizing hob tap Die taps are similar to machine nut taps.

Hob taps: are used for sizing dies They are intended only for the final finishing of the

thread and can only take a slight chip They are made to the same dimensions as regular hand taps, but fluted differently.

Pipe taps: are used for tapping holes for standard pipe sizes These tans are taper taps There is also a special form of pipe tap termed straight pipe tap, which is simply a hand

corresponding in diameter and number of threads per inch to standard pipe sizes.

Pipe hobs: are similar to pipe taps, but are intended only for sizing pipe dies after the

thread has been cut either by a pipe tap or in a lathe.

Boiler taps: are used in steam boiler work where a steam-tight fit is required They are

made either straight or tapered The straight boiler tap is practically only a hand tap.

Mud or washout taps: are used in boiler or locomotive work They are sometimes also

called arch pipe taps Patch bolt taps are used in boiler and locomotive work These are taper taps similar to mud or washout taps.

Staybolt taps: are used on locomotive boiler work They are usually provided with a

reamer portion preceding the threaded part, and have generally a long threaded portion and

a long shank A special form of staybolt tap is known as a spindle staybolt tap which revolves on a central spindle with a taper guide on the front end.

Stove-bolt taps and carriage-bolt taps are taps which have derived their names from the

uses to which they were originally put These taps have special forms of threads.

Bit-brace taps differ in no essential from the hand tap on the threaded portion, but are

provided with a special shank for use in a bit brace.

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3050 MACHINE ELEMENTS

Blacksmiths’ taper taps are made for general rough threading and are used especially in

repair work, where an accurately fitting thread is not required.

Inserted cutter taps may belong to any of the classes mentioned and constitute a separate

type only because they are not solid, but have the cutting teeth on blades inserted and held rigidly in a tap body.

Machine Elements Nordberg Key.—This is a taper key of circular cross-section This type of key may be

used for attaching hand wheels to their shafts or for other similar light work requiring an inexpensive type of key The Nordberg key has a taper of 1/16 inch per foot The center of the key hole is located at the joint line between the shaft and hub A small hole may be drilled first to prevent the larger drill from crowding over into the cast-iron hub A general rule for determining the size of the key is to make the large key diameter equal to one- fourth the shaft diameter.

Woodruff Keys.—In the Woodruff key system, half-circular disks of steel are used as

keys, the half-circular side of the key being inserted into the keyseat Part of the key projects and enters into a keyway in the part to be keyed to the shaft in the ordinary way The advantage of this method of keys is that the keyway is easily milled by simply sinking

a milling cutter, of the same diameter as the diameter of the stock from which the keys are made, into the shaft The keys are also very cheaply made, as they are simply cut off from round bar stock and milled apart in the center Dimensions of Woodruff keys are given in engineering handbooks.

Saddle Key.—This form of key has parallel sides and is curved on its under side to fit the

shaft it is slightly tapered on top so that, when it is driven tightly in place, the shaft is held

by frictional resistance This key should be fitted so that it bears lightly on the sides and heavily between the shaft and hub throughout its entire length As the drive with this type of key is not positive, it is only used where there is little power to transmit It is an inex- pensive method of keying, as the shaft does not need to be machined.

Locomotive Development.—The first steam locomotive which ever ran on rails was built

in 1804 by Richard Trevithick, an Englishman, and the first one to be used on a commercial basis was built by Matthew Murray, another Englishman In 1811, Blenkinsop of Leeds, had several locomotives built by Murray in order to operate a railway extending from Mid- dletown Colliers to Leeds, a distance of three and one-half miles Trevithick’s impractica- ble design had a single cylinder only, but Murray used two cylinders which were utilized in driving the same shaft on which cranks were set at right angles an important arrangement common to all modern locomotives A cog-wheel, or gear, meshing with a continuous rack laid along the road-bed was employed These locomotives were used daily for years and were examined by George Stephenson when he began his work on locomotive develop- ment Several years after the construction of Murray’s locomotives Hedley and Stephen- son demonstrated that the gear and rack method of propulsion was unnecessary, and that the frictional resistance of smooth drivers would supply adequate tractive power Stephen- son’s name will always be associated with locomotive development owing to his accom- plishments in perfecting the locomotive and in establishing it on a commercial basis His first locomotive was tried on the Killing worth Railway in 1814 The first locomotive to be used in the United States was imported from England in 1829.

Percentages of Radial and Thrust Loads.—There are three types of bearing that are

combined load carriers: First, the annular ball bearing, which is primarily designed for radial loads and has no angle of contact incorporated in its design, therefore having mini- mum thrust capacity (approximately 20 per cent of its radial capacity) Second, the one- direction angular contact bearing, which has a thrust capacity depending upon race design and the angle incorporated, which is generally made so that the thrust capacity is 100 per cent of the radial capacity (This bearing, however, when used for combined loads, can

Machinery's Handbook 27th Edition

MACHINE ELEMENTS 3051 only be used in pairs, and must have a threaded or shim adjustment incorporated in the mounting design to allow for initial adjustment.) Third, the double angular type bearing which is really two of the previously mentioned bearings built as a self-contained unit The functioning of this bearing is not dependent on any exterior adjustment, and the angle of contact is generally such that it will sustain approximately 150 per cent of its radial capac- ity as thrust.

Roller Bearing.—The load on roller bearings is supported by cylindrical or conical rollers

interposed between two races, one race being mounted on the shaft and one other in the bearing proper There are three principal designs of roller bearings One is for straight radial loads, the lines of contact of the rollers with the races being parallel with the shaft axis, as shown by the left-hand diagram; another design is for combined radial and thrust loads (See Fig 3b.) With this design, the rollers are tapering so that the lines of contact of the rollers with the races, and the axis of the rollers, will intersect, if extended, at the same point on the shaft axis A third design is intended for thrust or axial loads exclusively Bear- ings for radial loads may have solid rollers, or the hollow helically-wound type such as is used in the Hyatt bearing Although anti-friction bearings have replaced a great many plain

or sliding bearings, the trend is toward a much wider application, and evidently will include eventually the heaviest classes of service since modern anti-friction bearings not only greatly reduce friction losses, but lower maintenance and repair costs.

Ball Bearing Lubrication.—To obtain the full measure of efficiency and service from

ball and roller bearing equipment, the kind and quality of the lubricant, as well as the tem of applying it, must be adapted to the design of the bearing, the design of the machine, and the operating conditions.

sys-Operating Temperatures: Under ordinary conditions the temperature of a bearing while

running will be from 10 to 60 degrees F above that of the room If it exceeds 125 degrees F., ordinary greases will frequently prove unsatisfactory They will tend to soften and flow continuously into the path of the rolling elements, causing a rise in the normal operating temperature due to the increased frictional resistance introduced This may eventually result in the separation of the oil and soap base, with a complete loss of lubricating quali- ties In some cases, greases developed for use at high temperatures may be employed Care should be taken, however, to see that they meet all the requirements for adequate lubrica- tion.

Mineral oil of proper physical and chemical properties is an ideal lubricant for ball and roller bearings when the housing is designed to control the quantity entering the bearing and to prevent leakage and protect the bearing from the entrance of foreign matter A ball

or roller bearing should not be subjected to temperature in excess of 300 degrees F., because of the danger of drawing the temper of the hardened steel races and balls.

Quantity of Lubricant Required: In no case does a ball or roller bearing require a large

quantity of lubricant On the contrary, a few drops of oil, or a corresponding amount of grease, properly distributed over the running surfaces of the bearing, will provide satisfac- tory lubrication for a considerable period of time A large volume of lubricant within a Fig 3a Bearing for Radial Load Fig 3b Bearing for Radial and Thrust Loads

Machinery's Handbook 27th Edition

3052 ENGINE GOVERNORS

bearing will usually result in high operating temperatures, due to the working or churning

of the lubricant by the rolling elements and retainer This may seriously impair the useful life of the lubricant through oxidation or sludging of the oil or actual disintegration of greases.

Use of Grease: If grease is used, the housing should not be kept more than one-fourth to

one-half full of the lubricant Unlike oil, there is no way of controlling with any degree of exactness the quantity of grease in a housing, and greater care must therefore be taken to avoid overloading A bearing that runs at too high a temperature will often return to normal temperature if some of the lubricating grease is removed.

Grease is being used successfully for the lubrication of ball bearings at high speeds, but great care is necessary, both from the standpoint of housing design and selection of the lubricant, in order to obtain satisfactory results Any system employed must be designed to feed only a limited amount of grease to the bearing For the average application at operat- ing speeds up to 3600 revolutions per minute, a grease of soft consistency, such as a No 2 grease, will usually be found satisfactory, provided it is suitable in other respects Hard greases, such as No 3, may be used if the grease is to serve as a packing medium around the shaft to prevent the entrance of dirt, water, or other corrosive substances.

Sealed Bearings: : Bearings for certain classes of service must operate over long periods

without relubrication, as, for example, a motor installation on an airplane beacon; hence the efforts of ball-bearing manufacturers to produce bearings so completely sealed as to enable them to retain their original charge of grease for many months In appreciation of this requirement, the petroleum industry has developed lubricants that will maintain lubri- cation for a long period without change in structure, homogeneity, lubricating properties,

or leakage.

Engine Governors.—Governors may be of a purely centrifugal type such as the fly-ball

or pendulum design previously referred to, or the principle of inertia may be introduced to secure better speed regulation Thus, there are two general classes of governors known as centrifugal and inertia governors The method of utilizing the motion of the governing ele- ment for regulating the speed varies; as applied to steam engines, there is the general type

of governor which controls the speed by operating a throttling valve which increases or diminishes the amount of steam admitted to the steam-chest, and another general type which regulates the speed by changing the point of cut-off and consequently the amount of expansion in the cylinders.

In the design of governors, the sensitiveness, effort, and stability of the governor are important factors The sensitiveness of a fly-ball governor is indicated by the amount that the governing sleeve is displaced for a given change in speed, the displacement being rela- tively large for a given speed change if the governor is sensitive.

The term “effort” as applied to a governor relates to the energy it is capable of exerting upon the governing mechanism Thus, in the case of a fly-ball governor, the effort indicates the energy exerted on the sleeve while the governor speed is increasing or diminishing If the energy stored in a revolving governor is small, its sensitiveness will be reduced, because a larger speed change is necessary to obtain the power for operating the governing mechanism than would be required with a governor which exerts greater energy for a given speed change.

When a governor occupies a definite position of equilibrium for any speed within the range of speeds controlled by the governor, it is said to be “stable.” If the load on an engine having a fly-ball governor is diminished, the balls of a stable governor will move outward

to a new position as the speed increases, although there will usually be a temporary lating movement on each side of this new position, the oscillations gradually diminishing.

oscil-If the governor were instable (and therefore useless) the oscillations would increase until the limiting points were reached.

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ENGINE GOVERNORS 3053

Loaded or Weighted Fly-ball Governors.—As the arms of a governor of the conical

pendulum type swing outward toward the horizontal position as the result of increasing

speed, the change in height h (see Fig 1 ) is small for given changes in speed For instance,

if the speed is changed from 50 to 70 revolutions per minute, the difference between the

values of h is nearly 7 inches, whereas if the speed changes from 200 to 300 revolutions per minute, the difference in height h for the two speeds is only about 1 ⁄ 2 inch Hence, the simple pendulum governor is not suitable for the higher speeds, because then the movement which accompanies the speed changes is too small to secure proper regulation through the governing mechanism Fly-ball governors are adapted for much higher speeds by loading them The load may be in the form of a weight which surrounds the spindle, as illustrated

by Fig 1 This is known as a Porter governor.

In the following formula, w = the weight of one governor ball in pounds; c = the weight of the additional load; h = the height in feet indicated by the diagram, Fig 1; n = speed of gov-

ernor in revolutions per minute:

If the governor is constructed as indicated by the diagram Fig 2, the height h is not

mea-sured from the points at which the arms or rods are suspended, but from the point where the axes of the rods intersect with the vertical center line The outward movement of the balls may be resisted by a spring instead of a weight, as in the case of the Hartnell governor, which is known as a spring-loaded type.

Sensitiveness and Stability of Governors.—The sensitiveness of one governor may be

compared with that of another by determining the coefficient of speed variations If C = the coefficient of speed variations, M = maximum speed within limits of the governor action;

M1 = minimum speed within limits of governor action; m = mean speed within these limits;

then,

The minimum value of coefficient C necessary to obtain stability in a pendulum type of governor is given by the following formula in which y = distance the fly-balls move hori- zontally in feet; F = mean centrifugal force of fly-balls in pounds; H = indicated horse- power of engine; W = the weight of engine flywheel in pounds; S = revolutions per minute

of main shaft; R = the flywheel radius in feet.

n2 - e+w

-=

Machinery's Handbook 27th Edition

3054 ROPE SPLICING

The factor x in this formula represents that weight which would be equivalent to the

weights of the various moving parts, if it were centered at a point corresponding to the

cen-ter of gravity of the fly-balls To decen-termine the value of x, first decen-termine the weights of the

different moving parts of the governor, such as the balls, the central weight or load (in the case of a Porter governor), the sleeve, etc.; multiply the weight of each part by the square of the distance it moves from one position to the other; add the various products thus obtained, and divide the total sum by the square of the corresponding movement of the fly- balls at right angles to the governor spindle.

Shaft Governors.—Shaft governors are so named because the governing mechanism is

carried by the main shaft and is commonly attached in some way to the flywheel One type

is so arranged that, in the case of a steam engine, the action of centrifugal force on a pivoted and weighted lever, to which a spring is attached, changes the position of the eccentric which operates the slide valve, thus increasing or decreasing the valve travel and changing the point of cut-off Another type is so designed that the inertia of a pivoted “weight arm” accelerates the governing action by acting in conjunction with the effect of centrifugal force, thus increasing the sensitiveness of the governor With the inertia governor, the effort or force needed to actuate the governing mechanism increases as the rate of velocity change increases; hence this type is adapted to engines liable to sudden load changes When the load remains practically constant, the centrifugal type of shaft governor is often employed in preference to the inertia type The design of these governors depends upon the arrangement of the governing mechanism and upon varying factors.

Rope Splicing.—Splicing is the operation when two pieces of rope are joined by unlaying

the strands and weaving or intertwining the strands of one end with those of the other.

Short Splice: The first step in making a short splice is to unlay or untwist the strands at the end of each rope After the ropes are placed together, as shown at A, Fig 1a , the strands on

one side, as shown at d, e, and f, are either held together by the left hand or are fastened

together with twine, in case the rope is too large to be held by the hand The splicing

oper-ation is started by taking one of the strands as at a, and passing it across or over the adjacent strand d and then under the next strand e, after having made an opening beneath strand e The strands b and c are next treated in the same manner, first one and then the other being

passed over its adjoining strand and then under the next successive one These same

oper-ations are then repeated for the strands d, e and f of the other rope The splice will now appear as shown at B, Fig 1b In order to make it stronger and more secure, the projecting strands of each rope are again passed diagonally over the adjoining strands and under the next successive ones The splice should then be subjected to a strong pull, in order to tighten the strands and make them more compact The projecting ends of the strands should

then be cut off, thus completing the splice as shown at C For making the openings beneath

the strands on the rope, what is known as a marlin spike is generally used This is merely a tapering, pointed pin made of wood or iron.

Fig 1a Method of Making a Short Splice

×

=

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3056 ROPE SPLICING

Fig 2c How a Long Splice is Made

Eye-Splice: When a loop is formed at the end of a rope by splicing the free end to the main

or standing part of the rope, this is known as an eye-splice The end of the rope is first unlaid

about as far as it would be for making a short splice After bending the end around to form

a loop of the required size, the middle strand a, Fig 3a , is tucked under a strand on the main

part of the rope The strand b is next inserted from the rear side under the strand on the main part which is just above the strand under which a was inserted Since strand b is pushed

under the strand on the main part from the rear side, it will come out at the point where

strand a went in, as Fig 3b The third strand c is now passed over the strand under which

strand a was inserted, and then under the next successive one, as Fig 3c These three strands are next pulled taut and then about one-third of the fiber should be cut from them; they are next tucked away by passing a strand over its adjoining one and under the next suc- cessive strand Cutting away part of the fiber or yarns is to reduce the size of the splice and give it a neater appearance By gradually thinning out the fiber, the over-lapping strands may be given a gradual taper, as Fig 3d which shows the completed eye-splice.

Fig 3a Eye -Splice Fig 3b Eye -Splice Fig 3c Eye -Splice Fig 3d Eye -Splice

Machinery's Handbook 27th Edition

Guide to the Use of Tables and

Formulas in Machinery’s Handbook

27th Edition

BY JOHN M AMISS, FRANKLIN D JONES, AND

HENRY H RYFFEL

CHRISTOPHER J MCCAULEY, EDITOR

RICCARDO HEALD, ASSOCIATE EDITORMUHAMMED IQBAL HUSSAIN, ASSOCIATE EDITOR

2004INDUSTRIAL PRESS INC

NEW YORK

Guide to Machinery's Handbook 27th Edition

COPYRIGHT 1931, 1939, 1951, 1954, © 1959, © 1964, © 1968, © 1971,©

1975, © 1980, © 1984, © 1988, © 1992, © 1996, © 2000, © 2004 by Industrial Press Inc., New York, NY.

Library of Congress Cataloging-in-Publication Data

Amiss, John Milton, 1887-1968

Guide to the use of tables and formulas in Machinery’s Handbook, 27th edition

by John M Amiss, Franklin D Jones, and Henry H Ryffel; Christopher J ley, editor; Riccardo Heald, associate editor; Muhammed Iqbal Hussain, associate editor

McCau-264 p 12.1 × 17.8 cm.

Cover title: Machinery’s handbook 27th guide.

Cover title: Machinery’s handbook twenty seventh guide.

This book should be used in conjunction with the twenty-seventh edition of Machinery’s Handbook.

ISBN 0-8311-2799-6

ISBN 0-8311-2788-0 (electronic edition with math)

1 Mechanical engineering—Handbook, manuals, etc I Title: Machinery’s handbook 27 guide II Machinery’s handbook twenty seventh guide III Jones, Franklin Day, 1879-1967 IV Ryffel, Henry H I920- V McCauley, Christopher J.

VI Heald, Riccardo VII Hussain, Muhammed Iqbal VIII Machinery’s book 27th edition IX Title.

Hand-TJ151.A445 2000

INDUSTRIAL PRESS, INC.

200 Madison Avenue New York, New York 10016-4078

MACHINERY'S HANDBOOK GUIDE

27th Edition First Printing

Printed and bound in the United States of America by

National Publishing Company, Philadelphia, Pa.

All rights reserved This book or parts thereof may not be reproduced, stored in a retrieval system, or transmitted in any form without permission of the publishers.

Guide to Machinery's Handbook 27th Edition

THE PURPOSE OF THIS BOOK

An engineering handbook is an essential part of the equipment

of practically all engineers, machine designers, draftsmen, toolengineers and skilled mechanics in machine shops and toolrooms.The daily use of such a book, with its various tables and generaldata, saves a lot of time and labor To obtain the full value of anyhandbook, however, the user must know enough about the contents

to apply the tables, formulas, and other data, whenever they can beused to advantage

One purpose of this Guide, which is based on MACHINERY’S

HANDBOOK, is to show by examples, solutions, and test questionstypical applications of handbook information in both draftingrooms and machine shops Another function is to familiarize engi-neering students or other users with the HANDBOOK’S contents Athird objective is to provide test questions and drill work that willenable the HANDBOOK user, through practice, to obtain therequired information quickly and easily

MACHINERY’S HANDBOOK, as with all other handbooks, sents information in condensed form so that a large variety of sub-jects can be covered in a single volume Because of this condensedtreatment, any engineering handbook must be primarily a work ofreference rather than a textbook, and the practical application ofsome parts will not always be apparent, especially to those whohave had little experience in engineering work The questions andexamples in this book are intended not only to supplement some ofthe HANDBOOK material, but also to stimulate interest both in thoseparts that are used frequently and in the more special sections thatmay be very valuable even though seldom required

pre-Guide to Machinery's Handbook 27th Edition

THE METRIC SYSTEM

MACHINERY’S HANDBOOK contains a considerable amount ofmetric material in terms of texts, tables, and formulas This mate-rial is included because much of the world now uses the metricsystem, also known as the Système International (SI), and themovement in that direction continues in all countries that intend tocompete in the international marketplace, including the UnitedStates

An explanation of the SI metric system is found on Handbook

pages 142 to 144 and 2544 to 2548 A brief history is given of thedevelopment of this system, and a description is provided for each

of its seven basic units Factors and prefixes for forming decimalmultiples and submultiples of the SI units also are shown Anothertable lists SI units with complex names and provides symbols forthem

Tables of SI units and conversion factors appear on pages 2549

through 2587 Factors are provided for converting English units tometric units, or vice versa, and cover units of length, area, volume(including capacity), velocity, acceleration, flow, mass, density,force, force per unit length, bending moment or torque, moment ofinertia, section modulus, momentum, pressure, stress, energy,work, power, and viscosity By using the factors in these tables, it

is a simple matter of multiplication to convert from one system ofunits to the other Where the conversion factors are exact, they aregiven to only 3 or 4 significant figures, but where they are notexact they are given to 7 significant figures to permit the maximumdegree of accuracy to be obtained that is ordinarily required in themetalworking field

To avoid the need to use some of the conversion factors, variousconversion tables are given on pages 2550 through 2579 Thetables for length conversion on pages 2550 to 2562 will probably

be the most frequently used Two different types of tables areshown The two tables on page 2553 facilitate converting lengths

Guide to Machinery's Handbook 27th Edition

up to 100 inches into millimeters, in steps of one ten-thousandth of

an inch; and up to 1000 millimeters to inches, in steps of a sandth of a millimeter

thou-The table starting on page 2554 enables converting fractionsand mixed number lengths up to 41 inches into millimeters, insteps of one sixty-fourth of an inch

To make possible such a wide range in a compact table, thereader often must take two or more numbers from the table and addthem together, as is explained in the accompanying text The tablesstarting on page 2556 and 2558 have a much more limited range ofconversion for inches to millimeters and millimeters to inches.However, these table have the advantage of being direct-reading;that is, only a single value is taken from the table, and no addition

is required

For those who are engaged in design work where it is necessary

to do computations in the fields of mechanics and strength of rials, a considerable amount of guidance will be found for the use

mate-of metric units Thus, beginning on Handbook page 141, the use ofthe metric SI system in mechanics calculations is explained indetail In succeeding pages, boldface type is used to highlight ref-erences to metric units in the combined Mechanics and Strength ofMaterials section Metric formulas are provided also, to parallelthe formulas for English units

As another example, on page 213, it is explained in boldfacetype that SI metric units can be applied in the calculations in place

of the English units of measurement without changes to the las for simple stresses

formu-The reader also should be aware that certain tables in the book, such as that on page 71, which gives values for segments ofcircles for a radius = 1, can be used for either English or metricunits, as is indicated directly under the table heading There areother instances, however, where separate tables are needed, such

Hand-as are shown on pages 1018 to 1021 for the conversion of tions per minute, into cutting speed in feet per minute on pages

revolu-1018 and 1019, and into cutting speed in meters per minute on

pages 1020 and 1021

Guide to Machinery's Handbook 27th Edition

The metric material in the Handbook will provide considerableuseful data and assistance to engineers and technicians who arerequired to use metric units of measurements It is strongly sug-gested that all readers, whether or not they are using metric units atthe present time, become familiar with the SI System by readingthe explanatory material in the Handbook and by studying the SIunits and the ways of converting English units to them

Guide to Machinery's Handbook 27th Edition

CONTENTS

Guide to Machinery's Handbook 27th Edition

Machinery's Handbook Guide 27th Edition

SECTION 1 DIMENSIONS AND AREAS OF CIRCLES

HANDBOOK Pages 66 and 76

Circumferences of circles are used in calculating speeds ofrotating machine parts, including drills, reamers, milling cutters,grinding wheels, gears, and pulleys These speeds are variouslyreferred to as surface speed, circumferential speed, and peripheralspeed; meaning for each, the distance that a point on the surface orcircumference would travel in one minute This distance usually isexpressed as feet per minute Circumferences are also required incalculating the circular pitch of gears, laying out involute curves,finding the lengths of arcs, and in solving many geometrical prob-lems Letters from the Greek alphabet frequently are used to desig-nate angles, and the Greek letter π (pi) always is used to indicatethe ratio between the circumference and the diameter of a circle:

For most practical purposes the value of π = 3.1416 may be used

Example 1:Find the circumference and area of a circle whose

diameter is 8 inches

On Handbook page 66, the circumference C of a circle is given

as 3.1416d Therefore, 3.1416 × 8 = 25.1328 inches

On the same page, the area is given as 0.7854d2 Therefore, A

(area) = 0.7854 × 82 = 0.7854 × 64 = 50.2656 square inches

Example 2: From page 76 of the Handbook, the area of a

cylin-drical surface equals S = 3.1416 × d × h For a diameter of 8 inches

and a height of 10 inches, the area is 3.1416 × 8 × 10 = 251.328square inches

Example 3: For the cylinder in Example 2 but with the area ofboth ends included, the total area is the sum of the area found in

Example 2 plus two times the area found in Example 1 Thus,

π 3.14159265… circumference of circle

diameter of circle -

Guide to Machinery's Handbook 27th Edition

DIMENSIONS AND AREAS OF CIRCLES

2

251.328 + 2 × 50.2656 = 351.8592 square inches The same resultcould have been obtained by using the formula for total area given

on Handbook page 76: A = 3.1416 × d × (1⁄2d + h) = 3.1416 × 8 ×(1⁄2× 8 + 10) = 351.8592 square inches

Example 4:If the circumference of a tree is 96 inches, what is its

diameter? Since the circumference of a circle C = 3.1416 × d, 96 =

3.1416 × d so that d = 96 ÷ 3.1416 = 30.558 inches.

Example 5:The tables starting on page 1018 of the Handbookprovides values of revolutions per minute required producing vari-ous cutting speeds for workpieces of selected diameters How arethese speeds calculated? Cutting speed in feet per minute is calcu-lated by multiplying the circumference in feet of a workpiece bythe rpm of the spindle: cutting speed in fpm = circumference infeet × rpm By transposing this formula as explained in Formulas

And Their Rearrangement starting on page 8,

For a 3-inch diameter workpiece (1⁄4-foot diameter) and for a ting speed of 40 fpm, rpm = 40 ÷ (3.1416 × 1⁄4) = 50.92 = 51 rpm, approximately, which is the same as the value given on page 1018

cut-of the Handbook

PRACTICE EXERCISES FOR SECTION 1

(See Answers to Practice Exercises For Section 1 on page 221)1) Find the area and circumference of a circle 10 mm in diameter.2) On Handbook page 1020, for a 5-mm diameter tool or work-piece rotating at 318 rpm, the corresponding cutting speed is given

as 5 meters per minute Check this value

3) For a cylinder 100 mm in diameter and 10 mm high, what isthe surface area not including the top or bottom?

4) A steel column carrying a load of 10,000 pounds has a ter of 10 inches What is the pressure on the floor in pounds persquare inch?

diame-5) What is the ratio of the area of a square of any size to the area

of a circle having the same diameter as one side of the square?

rpm cutting speed, fpmcircumference in feet

=

Guide to Machinery's Handbook 27th Edition

DIMENSIONS AND AREAS OF CIRCLES 36) What is the ratio of the area of a square of any size to the area

of a circle having the same diameter as one side of the square? 7) The drilling speed for cast iron is assumed to be 70 feet perminute Find the time required to drill two holes in each of 500castings if each hole has a diameter of 3⁄4 inch and is 1 inch deep.Use 0.010 inch feed and allow one-fourth minute per hole forsetup

8) Find the weight of a cast-iron column 10 inches in diameterand 10 feet high Cast iron weighs 0.26 pound per cubic inch.9) If machine steel has a tensile strength of 55,000 pounds persquare inch, what should be the diameter of a rod to support 36,000pounds if the safe working stress is assumed to be one-fifth of thetensile strength?

10) Moving the circumference of a 16-inch automobile flywheel

2 inches moves the camshaft through how many degrees? (Thecamshaft rotates at one-half the flywheel speed.)

11) The tables beginning on Handbook page 990 give lengths ofchords for spacing off circumferences of circles into equal parts Isanother method available?

Guide to Machinery's Handbook 27th Edition

SECTION 2 CHORDAL DIMENSIONS, SEGMENTS, AND

SPHERES

HANDBOOK Pages 78, 71, and 989— 991

A chord of a circle is the distance along a straight line from onepoint to any other point on the circumference A segment of a cir-cle is that part or area between a chord and the arc it intercepts.The lengths of chords and the dimensions and areas of segmentsare often required in mechanical work

Lengths of Chords.—The table of chords, Handbook page 990,can be applied to a circle of any diameter as explained and illus-trated by examples on that page This table is given to six decimalplaces so that it can be used in connection with precision toolwork

Example 1:A circle has 56 equal divisions and the chordal

dis-tance from one division to the next is 2.156 inches What is thediameter of the circle?

The chordal length in the table for 56 divisions and a diameter

of 1 equals 0.05607; therefore, in this example,

Example 2:A drill jig is to have eight holes equally spaced

around a circle 6 inches in diameter How can the chordal distancebetween adjacent holes be determined when the table, Handbook

page 990, is not available?

One-half the angle between the radial center lines of adjacentholes = 180 ÷ number of holes If the sine of this angle is multi-plied by the diameter of the circle, the product equals the chordaldistance In this example, we have 180 ÷ 8 = 22.5 degrees Thesine of 22.5 degrees from a calculator is 0.38268; hence, the

2.156 = 0.05607×diameterDiameter 2.156

0.05607 - 38.452 inches

Guide to Machinery's Handbook 27th Edition

CHORDS AND SEGMENTS 5chordal distance = 0.38268 × 6 = 2.296 inches The result is thesame as would be obtained with the table on Handbook page 990

because the figures in the column “Length of the Chord” representthe sines of angles equivalent to 180 divided by the different num-bers of spaces

Use of the Table of Segments of Circles—Handbook

page 71 —This table is of the unit type in that the values all apply

to a radius of 1 As explained above the table, the value for anyother radius can be obtained by multiplying the figures in the table

by the given radius For areas, the square of the given radius is

used Thus, the unit type of table is universal in its application

Example 3:Find the area of a segment of a circle, the center angle

of which is 57 degrees, and the radius 21⁄2 inches

First locate 57 degrees in the center angle column; opposite thisfigure in the area column will be found 0.0781 Since the area isrequired, this number is multiplied by the square of 21⁄2 Thus,0.0781 × (21⁄2)2 = 0.488 square inch

Example 4:A cylindrical oil tank is 41⁄2 feet in diameter, 10 feetlong, and is in a horizontal position When the depth of the oil is 3feet, 8 inches, what is the number of gallons of oil?

The total capacity of the tank equals 0.7854 × (41⁄2)2× 10 = 159cubic feet One U.S gallon equals 0.1337 cubic foot (see Hand-book page 2566); hence, the total capacity of the tank equals 159 ÷0.1337 = 1190 gallons

The unfilled area at the top of the tank is a segment having aheight of 10 inches or 10⁄27 (0.37037) of the tank radius The nearestdecimal equivalent to 10⁄27 in Column h of the table starting on

page 71 is 0.3707; hence, the number of cubic feet in the shaped space = (272× 0.401 × 120) ÷ 1728 = 20.3 cubic feet and20.3 ÷ 0.1337 = 152 gallons Therefore, when the depth of oil is 3feet, 8 inches, there are 1190 − 152 = 1038 gallons (See alsoHandbook page 61 for additional information on the capacity ofcylindrical tanks.)

segment-Spheres.—Handbook page 78 gives formulas for calculatingspherical volumes

Guide to Machinery's Handbook 27th Edition

CHORDS AND SEGMENTS

6

Example 5:If the diameter of a sphere is 245⁄8 inches, what is thevolume, given the formula:

Volume = 0.5236d3The cube of 245⁄8 = 14,932.369; hence, the volume of this sphere

= 0.5236 × 14,932.369 = 7818.5 cubic inches

PRACTICE EXERCISES FOR SECTION 2

(See Answers to Practice Exercises For Section 2 on page 221)1) Find the lengths of chords when the number of divisions of acircumference and the radii are as follows: 30 and 4; 14 and 21⁄2; 18and 31⁄2

2) Find the chordal distance between the graduations for sandths on the following dial indicators: (a) Starrett has 100 divi-sions and 13⁄8-inch dial (b) Brown & Sharpe has 100 divisions and

thou-13⁄4 inch dial (c) Ames has 50 divisions and 15⁄8 - inch dial.3) The teeth of gears are evenly spaced on the pitch circumfer-ence In making a drawing of a gear, how wide should the dividers

be set to space 28 teeth on a 3-inch diameter pitch circle?

4) In a drill jig, 8 holes, each 1⁄2 inch diameter, were spaced evenly

on a 6-inch diameter circle To test the accuracy of the jig, plugswere placed in adjacent holes, and the distance over the plugs wasmeasured with a micrometer What should be the micrometer read-ing?

5) In the preceding problem, what should be the distance overplugs placed in alternate holes?

6) What is the length of the arc of contact of a belt over a pulley 2feet, 3 inches in diameter if the arc of contact is 215 degrees?7) Find the areas, lengths, and heights of chords of the followingsegments: (a) radius 2 inches, angle 45 degrees; (b) radius 6inches, angle 27 degrees

Guide to Machinery's Handbook 27th Edition

CHORDS AND SEGMENTS 78) Find the number of gallons of oil in a tank 6 feet in diameterand 12 feet long if the tank is in a horizontal position, and the oilmeasures 2 feet deep.

9) Find the surface area of the following spheres, the diameters ofwhich are: 11⁄2; 33⁄8; 65; 203⁄4

10) Find the volume of each sphere in the above exercise.11) The volume of a sphere is 1,802,725 cubic inches What areits surface area and diameter?

Guide to Machinery's Handbook 27th Edition

FORMULAS 9

If the number of teeth in a gear is 16 and the diametral pitch 6,

then simply put these figures in the place of N and P in the

for-mula, and the outside diameter as in ordinary arithmetic

Example 2:The formula for the horsepower generated by a steam

engine is as follows:

in which H = indicated horsepower of engine;

P = mean effective pressure on piston in pounds per

square inch;

L =length of piston stroke in feet;

A =area of piston in square inches;

N =number of strokes of piston per minute.

Assume that P = 90, L = 2, A = 320, and N = 110; what would

be the horsepower?

If we insert the given values in the formula, we have:

From the examples given, we may formulate the following general

rule: In formulas, each letter stands for a certain dimension or

quantity; when using a formula for solving a problem, replace the letters in the formula by the figures given for a certain problem, and find the required answer as in ordinary arithmetic.

Omitting Multiplication Signs in Formulas.—In formulas, the

sign for multiplication (×) is often left out between letters the

val-ues of which are to be multiplied Thus AB means A × B, and the

formula can also be written

D 16+2

6 - 18

6 - 3 inches

H P×L×A×N

33 000, -

=

H 90×2×320×110

33 000, - 192

=

Guide to Machinery's Handbook 27th Edition

may be written 3A As a general rule, the figure in an expression

such as “3A” is written first and is known as the coefficient of A If

the letter is written first, the multiplication sign is not left out, butthe expression is written "A × 3."

Rearrangement of Formulas.—A formula can be rearranged

or“transposed” to determine the values represented by differentletters of the formula To illustrate by a simple example, the for-

mula for determining the speed (s) of a driven pulley when its diameter (d), and the diameter (D) and speed (S) of the driving pul- ley are known is as follows: s = (S × D)/d If the speed of the

driven pulley is known, and the problem is to find its diameter or

the value of d instead of s, this formula can be rearranged or

changed Thus:

Rearranging a formula in this way is governed by four generalrules

Rule 1 An independent term preceded by a plus sign (+) may be

transposed to the other side of the equals sign (=) if the plus sign ischanged to a minus sign (−)

Rule 2 An independent term preceded by a minus sign may be

transposed to the other side of the equals sign if the minus sign ischanged to a plus sign

As an illustration of these rules, if A = B − C, then C = B − A, and if A = C + D − B, then B = C + D − A That the foregoing are

correct may be proved by substituting numerical values for the ferent letters and then transposing them as shown

dif-Rule 3 A term that multiplies all the other terms on one side of

the equals sign may be moved to the other side if it is made todivide all the terms on that side

As an illustration of this rule, if A = BCD, then A/(BC) = D or according to the common arrangement D = A/(BC) Suppose, in the preceding formula, that B = 10, C = 5, and D = 3; then A = 10 × 5 ×

3 = 150 and 150/(10 × 5) = 3

Rule 4 A term that divides all the other terms on one side of the

equals sign may be moved to the other side if it is made to multiplyall the terms on that side

d = (S×D ) s⁄

Guide to Machinery's Handbook 27th Edition