flat lapping

7/29/2019 Flat Lapping

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Flat LappingPart I of a Two Part ArticleBy: J. D. WiseA while back I had a small part made from tool steel which needed to be flatter and smootherthan I could machine it. Lapping seemed to be the answer, but although I knew that lappingcould achieve very high levels of accuracy, I had never actually lapped anything. Over the yearsI had heard and read a number of descriptions of lapping, but many of them seemed tocontradict what the others said. So, as befits an academic, I embarked on a program of research

to discover the truth about lapping.This article summarizes what I found.First a disclaimer: most of this article is based on book learning rather than practical experience.My "formal" training in metalworking did not treat abrasive methods as precision techniques:precision work was done in the lathe and the mill, the grinder was used for rough shaping toolbits by hand, and lapping was something we did to the valves in the car's engine to make it runbetter.Part I. Background1. Precision MachiningThe lathe and mill are the traditional precision machine tools,but at some point they run out of steam. Taking a cut of 1/10,000 inch with a good surface finish

requires a tool which is carefullyshaped, carefully aligned, and very sharp. And of course a workpiece that's soft enough to becut by the tool in the first place,and a tool which is hard and tough enough to stay sharp for the duration of the cut.The next level of precision is typically achieved by abrasive techniques, specifically grinding,honing, and lapping.Precision grinding is basically an extension of milling and turningwhere the tool bit or cutter is replaced by a grinding wheel. This affords several improvements:harder material may be worked, smaller cuts taken, and a smoother finish produced. But as inthe lathe and mill, the resulting accuracy still depends on the precision of the machine.So, for example, cylindrical grinding can be done in the lathe with a toolpost grinder. Although

finer cuts can be taken, the work will be no rounder or straighter than turned work. Also,because normal forces are higher in grinding than in turning, accuracy and surface finish candeteriorate due to deflection or chatter.The precision produced in grinding depends on both the machine and on the wheel. However,there is another class of abrasive operations,typified by honing and lapping, where the precision of the machine contributes little or nothing tothe quality of the final result.Lapping in particular seems like a miraculous process: using only simple hand tools, it canproduce surfaces which are perfectly flat, perfectly round, perfectly smooth, perfectly sharp, orperfectly accurate.Although not actually miraculous, nor capable of absolute perfection, lapping can accomplishsome fairly impressive feats. Under the right circumstances it can:1. Impart or improve precise geometry (flatness, roundness, etc.).2. Improve surface finish.2a.Improve surface quality.3. Achieve high dimensional accuracy (length, diameter, etc.).4. Improve angular accuracy (worm gears, curvic couplings, etc.).5. Improve fit.6. Make tools sharper.The technique that machinists call lapping appears, with occasional variations, in a variety ofother fields. The dictionary definition of lap is "a rotating wheel or disk holding an abrasive or

polishing powder on its surface, used for gems, cutlery, etc." In fact the origin of the word comesfrom "lapidary" (from the Latin lapidarius meaning "of stone") where such a wheel is used to cut,shape, and polish gemstones. Other examples of related techniques include the


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watchmaker's polishing operations, the woodworker's shaping of plane soles and irons, and the

grinding and polishing of mirrors and lenses in optical work.2. Abrasive BasicsLet's start by looking at how an abrasive works. Figure 1a shows an abrasive grain lying on thesurface of a workpiece. If we apply a force, a high level of stress will be produced at the point ofcontact. Since the grain is harder than the work, it will penetrate into the surface of the work, asshown in Figure 1b. If the pressure is small (within the elastic limit of the material) thedeformation will not be permanent.As we increase the pressure and the grain is forced further into thesurface, what happens depends on the nature of the material. For a ductile material, when theelastic limit is exceeded, the material will be displaced by plastic flow (Figure 1c). For a brittlematerial, when the elastic limit is exceeded, a chip will be dislodged by brittle fracture (Figure 2).

Material RemovalNow, suppose that after pressing the grain into the surface of the work, we move it laterally. Ifthe pressure is light and we haven't exceed the material's elastic limit, the material will move outof the way ahead of the grain and return to its original place behind, like a boat moving slowlythrough water. At this level of pressure, the grain is simply rubbing along the surface of the work.Because of the friction between the grain and the work, force is required to move it and heat willbe produced.If we increase the force past the yield point, the workpiece material will be permanentlydisplaced into a raised region on either side of the groove formed by the grain, as in a plowedfurrow. This is called, appropriately enough, plowing, and is accompanied by the production ofheat, both from the sliding friction between the grain and the work, and from the internal friction

of the material as it is deformed.As the pressure and resultant depth of penetration continue to increase, the amount of materialbuilt up in front is more easily displaced ahead of, rather than to the side of the grain, and a chipis formed (Figure 3). We have finally reached the regime of cutting.

Figure 3.This is similar to the way in which a chip is produced by a cutting tool, but because of the highlynegative effective rake angle it isformed by extrusion rather than by shear. Note that in the cutting regime, both plowing andrubbing are also taking place. In a brittle material, there will be a succession of fractured chips,rather than a continuous extruded chip.The effort required to remove a given amount of material (called the "specific energy") dependson the size of the chip. Regardless of the chip size, a certain amount of the applied lateral forcegoes into rubbing and plowing, which removes no material. At the onset of cutting, these forcespredominate, and a large force is required to produce a small chip. As the normal forceincreases, the depth of penetration and hence the thickness of chip increase and a greaterproportion of the applied force goes into producing the chip. Hence as the size of the chipincreases, the work required to remove a given volume of material decreases.

This is why a coarse grit removes material faster than afine grit:With coarse grit, a small number of large grains penetrate

deeply into the work, producing a small number of largechips with high efficiency.With a finer grit, the applied normal force is spread over alarger number of smaller grains so the depth of penetrationof each will be less. More of the lateral force goes torubbing and plowing and less to removing material.


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Abrasive Wear and BreakdownSo much for the workpiece, what happens to the abrasive grain itself?Although very hard, it's not infinitely strong and is subject to failure or breakdown via severalmechanisms.Because it is typically quite brittle, it will fracture when local stresses exceed its elastic limit.Since stresses are highest at the sharpest points, these tend to be the first to break. Dependingon its friability, the grain may either fracture in such a way as to leave another sharp point oredge behind, or the sharp corners may be broken off, leaving behind a smoother, less sharp

surface.If the grain is held in a fixed orientation, this will take the form of a "wear flat." If free to rotate, itwill eventually assume a "round" shape.This wear can be accelerated chemically. For example, the mutual affinity of iron and carbonmeans that a diamond will wear rapidly when used to grind steel, in spite of its much higherhardness.

Flat Lapping Part II of a Three Part ArticleBy: J. D. Wise3. Flat LappingLet's suppose that our goal is to produce a flat, smooth surface on a piece of (possibly

hardened) steel. For convenience, assume that it is already "almost flat." Suppose further thatwe have a reference surface (e.g. a surface plate) that is "flat enough."We could transfer the flatness of the reference indirectly by scraping: high spots are marked bya layer of dye on the surface plate and removed by the scraper. But by making the referencesurface abrasive, we can transfer its flatness directly.3.1. Lapping with Bonded AbrasiveIf we lay a piece of sandpaper grit side up on the surface plate, then surface of sandpapershould also be flat. Now lay the work side-to-be-flattened down on top of the sandpaper. AsFigure 4 shows, the high spots on the work will contact the abrasive grains (as at a and b) whilethe low spots will not. This is the same situation as in scraping except instead of marking dye wehave abrasive grains between the surfaces.

Now, if we slide the work over the plate, the highspots will be marked, not with blue spots, but withscratches. Furthermore, instead of a small spot ofblue being added to the work, a small chip will beremoved from it. If we continue to rub the work overthe sand paper, the high spots will gradually be worndown. Eventually, the entire surface of the work willbe in contact with the surface of the sandpaper, andsince it was flat, the work must be flat.In fact, things are more complex than this. For onething, although the surface plate may be a precisioncomponent, the sandpaper isn't. The thickness of the

paper and the abrasive coating are not precisely controlled, and the abrasive grains are not allthe same size. So the local thickness of the sandpapervaries and its surface is not as flat as the surfaceplate.Another problem is that although the grainsthemselves are hard, the paper is soft. As pressureis applied between the work and the plate, the softpaper backing is compressed, and lower parts ofthe work will be abraded as shown in Figure 5.

This isn't a serious problem: since the pressureis higher in the compressed areas, the high spots willstill wear more quickly.What is more of a problem is that the surfacebeneath the work is lower than the surrounding surface, like a shallow basin. Since the work isadapting to the surface of the grit, and this surface is curved at the edges of the work, the edges


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of the work will be rounded off as shown at (a) in Figure 5. A similar basin will result if only aportion of the sheet is used. The active grains will be worn down, leaving the surrounding grainsnot only higher, but sharper.These problems can be reduced by using a thinner, harder backing and a finer abrasive. Forexample, lapping film uses a 0.003" thick Mylar backing coated with very fine abrasive.In spite of its shortcomings, this procedure works fairly well. In particular this is the process thatwoodworkers refer to as lapping and use to flatten the soles of planes and the backs of planeirons and chisels. The idea of transferring an accurately flat abrasive surface to the work is also

used in surface grinding and in sharpening with an oilstone. However, as the wheel or stonewear and loose their flatness, they must be resurfaced by dressing, while replacing the wornsandpaper restores both sharpness and flatness.3.2. Lapping with Free AbrasiveThe problems caused by flexibility and uneven coating could be eliminated by placing theabrasive grains directly on the flat reference surface. You wouldn't want to try this with yoursurface plate but the idea appears frequently using less expensive (and somewhat less flat)reference surfaces.Watchmakers use loose grit or a mixture of grit and oil on a piece of glass as the first step inpolishing flat steel pieces. Another technique employed by woodworkers uses a hardened and

ground piece of steel called a lapping plate which is

sprinkled with loose grit and rubbed with the planeiron or chisel to be flattened. Optical workers produceextremely accurate flat (or spherical) surfaces using aslurry of grit and water between pieces of cast iron orglass.Let's see how this works. Assume we have twopieces of material, the tool which is "flat enough," andthe work, which is "almost flat," with loose abrasivegrains between them. Figure 6 shows the site of oneof these grains. For now let's also assume that bothpieces are of the same material, e.g. hardened steel.

If we apply a force between the work and tool, we produce a sort of mutual hardness tester withthe grit as the indenter and the work and tool as the test pieces. Since the work and tool are ofthe same material, the grain will penetrate to the same depth into each.Now if we slide the work over the tool, this will cause the grain to roll, as shown in Figure 7. If thepenetration is deep enough, the advancing edge of the grain will dislodge a chip from the work,the tool, or both. However, unlike the case with bound abrasive, this chip will be a small particle,rather than a long thin sliver. There will also be a pit with a raised edge left behind due to plasticdeformation, similar to the plowing caused by a sliding grain. If the tool and work are brittle (e.g.glass) the result will be similar, but the chips will result from brittle fracture and the pits will nothave raised edges.In an actual application, there are a large number of grains between the two surfaces so thesituation is similar to that with sandpaper, except that the grains are in direct contact with thereference surface and they are free to roll rather than fixed in position and orientation. If the workand tool are rubbed together, those grains in contact with both surfaces will roll, pitting thesurfaces and dislodging small, dustlike chips.In a ductile material, the pits are typically a small fraction of the grain size (2% to 5% forhardened steel). In a brittle material such as glass the strain can propagate well beyond thepoint of contact. In this case the depth of the pit can be a significant fraction of the diameter ofthe abrasive grain, large enough to hold and immobilize some of the grains.If the rolling of the grit is free and unimpeded, the wear on both the work and the tool will be inthe form of uniform pitting, which has a dull, gray appearance. If the rolling of the grains is

retarded, for example by a heavy grease vehicle, or if some grains become stuck in the tool (orwork) then the surface will be a combination of a dull "background" along with brighter,directional scratches.3.3. Distribution of WearIf the surface of the work is uneven, the pressure, and hence the rate of wear, will be greatest atthe high spots of the work, tending to flatten it. However, unlike the case with sandpaper, this


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wear is taking place both on the high spots of the work, and on the reference surface directlybeneath the high spots. If the work and reference have the same hardness, they will wear at thesame rate, and the flatness of the reference will be destroyed at the same rate that that of thework is improved.This would indeed be the case if we simply moved the work back and forth in a fixed pattern.However, if we move the work over the tool in such a way that each point on the work is movedover each point on the tool, each point on the tool will be worn by the same amount. Althoughthe tool's surface will be lower, it will keep the same shape, i.e. it will still be flat. On the other

hand, since the high spots on the work are staying in the same place on the work, they will beworn faster than the surrounding areas, until they are no longer high. Eventually, all spots on thework will be even with the tool and the work will be flat.3.4 Mutual RefinementImplicit in the principle of uniform wear is the assumption that the reference surface is smooth sothat it is possible for every point on it to be rubbed and worn by the work. Suppose that insteadof a flat tool and an unflat piece of work, we have two pieces, neither of which is flat. Forconvenience, let's assume they are of the same material, shape (round), and size.If the two surfaces are placed together, they will come in contact at their relative "high spots." If alayer of abrasive is introduced between the two and they are rubbed together, material will beremoved most rapidly at the points of closest contact. As these points are worn down, other

points will come into contact and begin to wear. Eventually, all points of the two surfaces will bein contact, and they will be perfectly matched. What's more, they will be in contact at any pointalong the path of rubbing.If the two are rubbed together with frequent changes in relative orientation and direction ofmotion, then the resulting surfaces will be in contact at any relative position or orientation. Theonly curve satisfying these conditions is the sphere, so the surfaces must be spherical, oneconcave, the other convex. This principle is used in optical work to produce and refine thespherical surfaces of lenses and mirrors.If the surfaces are horizontal, and the work and tool are roughly the same size and shape, thenthe surface on top will tend to become concave (or more concave) and the one on the bottomconvex (or less concave). Variations in the pattern of rubbing can also control the direction and

rate of change of the radius of curvature.If three surfaces are rubbed together in all possible pairings until each is in uniform contact with

the other two, then each surface must be (a)spherical, (b) convex, and (c) concave. Since theonly sphere which is both convex and concave isone of infinite radius, then each of the three surfaceswill be perfectly flat.Mutual refinement can also take place in the lappingprocess itself, where the level of precision isimproved or maintained as the work and the toolwear against each other. This is the case incylindrical lapping where, due to the geometry, theroundness and straightness of both the work and thelap are simultaneously improved. In lappingmachines, steel cylinders called "truing rings"provide a controlled wear mechanism which tends to

return the plate to flatness.3.5 Lapping with Embedded AbrasiveIn the previous three sections, we assumed that the work and the tool were both of the samehardness, with the grit rolling between the two. What happens if one is significantly softer thanthe other? Figure 8 shows the situation where the tool is softer than the work (and of course

both are softer than the grit). Since the pressure between the grain and the tool is approximatelythe same as that between the grain and the work, the grain will penetrate more deeply into thesofter tool. If a lateral force is now applied, the grain will tend to stay embedded in the tool and a"long" chip will be removed from the work.If this is done by sprinkling grit on the tool and rubbing with the work, some grains will roll aroundbefore becoming embedded and there will be some wear on the lap as is the case with hard lap


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and work. It is also possible to "charge" the lap before use by covering it with grit and driving itinto the plate without rubbing, either with a hardened roller or a hardened plate. Even so, grainswill become dislodged during the course of working and cause some wear to the lap. However,this will be significantly less than the rate of wear of the work, so the lap should hold its formwell, especially if its entire surface is used uniformly.An embedded lap us usually recharged regularly by adding fresh grit and rubbing, rolling, orpounding it in. However, some rotary embedded laps, particularly those using diamond grit, areused extensively with only an initial charge. These may be thought of as being diamond grinding

wheels rather than laps.The general rule for lapping with embedded abrasive is that the tool should be softer than thework. The softer the lap, the more secure the embedding. Hence copper and lead laps are usedfor softer work or for finishing. The sign that embedding is occurring is the nature of the surfaceof the work: a dull, pitted surface implies rolling while a bright, scratched one implies embedding.4. Summary: The Principles of Lapping4.1 Abrasive BasicsPrinciple 1: For a given grain size, the rate of removal of material is proportional to the localpressure between the grain and the work.Principle 2: For the same applied forces, both the depth of penetration (and hence scratches)and the net rate of removal decrease as the grain size decreases.

Principle 3: As grit wears, it will become smaller and possibly smoother (round or flat, dependingon whether it is free or bound).4.2 Distribution of WearPrinciple 4: Those regions of the surfaces in closest contact will wear most rapidly.Principle 5: If the rate of wear on a surface is uniform, the surface will retain its shape.4.3 Refinement of FormPrinciple 6: If two surfaces are rubbed together with abrasive between them, they will eventuallybe in contact over their entire areas. The nature of the resulting surface depends on the path ofthe rubbing motion.Principle 7: Two surfaces in contact at all relative positions and orientations must be spherical.Principle 8: Three surfaces, each in contact with the other two in all relative positions and

orientations, must be flat.4.4 The Lapping ProcessPrinciple 9: A flat (or other suitable) reference surface can be transferred to a workpiece via anintermediate layer of abrasive. This layer may be bonded to, imbedded in, or rolling on thereference surface.

5. Lapping in MetalworkingThere are many applications of lapping in precision metalworking. We can divide these into twocategories: equalizing lapping and form lapping. Equalizing lapping is used to establish orimprove the fit between two components of an assembly. In this case, the two shapes mutuallyimprove each other, and a non-embedding form of lapping is usually desired. Examples of thisare lapping together of gears to improve smoothness of running or the lapping of valves intotheir seats to improve the seal.In form lapping, the concern is to establish some absolute geometric shape or dimension, suchas flatness, roundness, parallelism, length, or diameter. For flat surfaces, this is usually done byproducing an accurate reference surface and transferring it to the work by means of embeddedlapping. Cylindrical objects can be lapped by rolling them between two flat laps. Cylindricallapping (both internal and external) may also be performed using a cylindrical lap. Completespheres, such as ball bearings, may be produced to a high degree of accuracy by specializedlapping processes.

In addition to high geometric accuracy, useful characteristics of lapping include low removal rate,cool operation, low surface roughness, and high reflectivity.5.1 Lapping MachinesThe lapidary's lap is a soft metal disk (typically tin or copper) rotating about a vertical axis,charged with an abrasive, and usually run wet. Machines for lapping metal have the same basic


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form,but contain a number of refinements.Figure 9 is a simplified representation of a lapping machine. The lapping plate (usually cast iron)is grooved to insure even distribution of the abrasive, which is applied in the form of a slurry. Theparts to be lapped are placed inside the truing rings which, due to the difference in drag aroundtheir circumference, rotate in the direction shown.This rotation has two purposes: it keeps the workpieces in motion, insuring that they are lappedevenly, and it equalizes the wear on the lapping plate, helping to maintain its flatness. For small

workpieces, a pressure plate fitting inside the ring is used to increase the applied force.

Figure 9.By adding a second lapping plate facing downward and replacing the truing rings withappropriate fixtures, workpieces may be lapped parallel or cylindrical. A high degree ofparallelism may be achieved by redistributing the workpieces several times during the course ofthe lapping. In this way any tendency to form a wedge will be eliminated by redistributing thehigh spots uniformly around the surface. This is how gage blocks are made.

5.2 Hand LappingAlthough conceptually simple, lapping machines are expensive and often quite large. In thehome shop, lapping is usually done by hand. In this case, the lapping plate remains stationaryand the work is rubbed across it by hand. The pattern of rubbing must cover the entire plate to

evenly distribute the wear and maintain flatness.A lapping plate may be produced by grinding, scraping, or the mutual refinement processdescribed above. Plates for finishing are usually smooth, but roughing plates are often groovedin a circular, radial, or square pattern. The grooving provides a reservoir for fresh abrasive and arepository for swarf.The lapping plate may be charged continuously, with loose abrasive, slurry, or paste appliedbefore each use, or it may be given an initial charge with loose abrasive which is rolled orpounded in and used repeatedly before recharging.5.3 Lap MaterialsThe traditional material for the flat lapping of hardened steel are cast iron and brass. Incylindrical lapping, the mutual refinement process is essential to producing accurate geometry,so laps of copper and lead are often used. The softer laps also produce a smoother finish andallow softer materials to be lapped.Some low-precision lapping operations use free abrasives with a hard lap, such as hardenedsteel or glass.5.4 AbrasivesThe abrasives used in lapping include those used in grinding and other metalworking operations:aluminum oxide, silicon carbide, and diamond. These are available as loose grit, as premixedpastes, or in bonded abrasive sheets with cloth, paper, or plastic (lapping film) backings.Because of the low temperatures involved in lapping, diamond may be used successfully onsteel and CBN is not necessary. However, boron carbide lapping compounds are available as

an economical diamond substitute. Other (softer) abrasives are used in polishing, for examplerouge (iron oxide), cerium oxide, tin oxide, and chrome oxide.5.5 FluidsAlthough lapping can be performed dry, in most cases a liquid is used along with the grit. Themost commonly used fluids are water, kerosene, oil, and grease. This fluid may have one ormore of several purposes:


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1. A vehicle for carrying the abrasive. In hand lapping the grit can be sprinkled onto the lappingplate. A more uniform distribution and easier application can be achieved by mixing the grit intoa slurry or paste. In machine lapping where continuous replenishment of the grit is necessary,supplying the abrasive in a slurry is an essential part of the process.2. A lubricant. The lateral force in abrasion due to rubbing between the grain and the work isonly a small fraction of the total, so lubrication can provide only a slight improvement inefficiency. More important is rubbing between the lap itself and the work, where lubrication canprevent sticking and galling.

3. A coolant. Heat is not a problem in hand lapping, but machine lapping, even though muchcooler than grinding, can generate significant amounts of heat.4. Control of grit motion. A viscous medium such as heavy grease can retard the rolling motionof the grit, resulting in an abrasive action which is a hybrid of rolling and cutting.5. Removal of debris. As the work is worn away, particles of swarf collect on the surface of thelap. If these are not flushed away, they will build up to the point where they will clog the lap.6. Chemical action. In some cases the lapping fluid acts chemically on the work material toaccelerate the lapping process.5.6 PolishingAs the lapping process progresses through increasingly finer abrasives, the size of the resultingscratches becomes smaller. As these approach the wavelength of light (about 1/2 micron or

2/100,000 inch) the surface goes from a dull, diffusely reflecting to a bright, specularly reflectingone. However, if the hardness of the lap is maintained as the particle size is reduced, it becomesdifficult to achieve this bright finish uniformly across the surface of the work.In polishing for cosmetic purposes, a soft backing is used to allow the polishing abrasive toconform to the shape of the work. This same principle is used in precision polishing, but caremust be taken to see that the backing is not so soft that it destroys the accuracy of the surface.One approach is to use a lap of softer material, such as tin, copper, lead, or even wood. Anotheris to use an intermediate flexible layer between a hard reference surface and the work.6. Summary: Characteristics of Lapping1. Accurate Geometry. Highly accurate plane, spherical, or cylindrical surfaces may begenerated or imparted by lapping.

2. High Dimensional Accuracy. Material is removed from the workpiece at a slow, consistentrate. This makes it easy to control dimensions to a high degree of accuracy by controlling theamount of time the piece is lapped.3. Slow. The down side of the low removal rate is that unless the work is very close to therequired dimension and shape when lapping is begin, it will take a long time to get it there.4. High Surface Finish. Highly reflective surfaces with roughness down to a few microinches areeasily achieved.5. High Surface Quality. Because of the low temperatures and forces involved, surface damageis much lower than grinding or cutting operations.6. Simple Tools. Unlike conventional machining where high precision requires sophisticatedmachinery, lapping needs only a flat plate and some grit. However, the accuracy achieveddepends strongly on the skill with which these are employed.7. BibliographyAs I said, much of this was learned from books. Here are a few of them.ASTME (1949). Tool engineers handbook. McGraw-Hill, New York.Deve, C. (1945). Optical workshop principles. Adam Hilger, London.Farago, F. T. (1980). Abrasive Methods Engineering, Vol. 2. Industrial Press, New York.Ingalls, A. G., ed. (1946). Amateur telescope making, advanced. Scientific American, New York.Ingalls, A. G., ed. (1951). Amateur telescope making: book one [4th ed.]. Scientific American,New York.Moore, W. R. (1970). Foundations of mechanical accuracy. Moore Special Tool Co., Bridgeport.

Nakazawa, H (1994). Principles of precision engineering. Oxford.Rabinowicz, E. (1970). Polishing. Scientific American, v218, p91.Shaw, M. C. (1996). Principles of Abrasive Processing. Claredon Press, Oxford.Twyman, F. (1952). Prism and lens making; a textbook for optical glassworkers. Hilger & Watts,London

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