Electrical discharge machining
An electrical discharge machine Electric discharge machining (EDM), sometimes colloquially also referred to as spark machining, spark eroding, burning, die sinking or wire erosion,[1] is a manufacturing process whereby a wanted shape of an object, called workpiece, is obtained using electrical discharges (sparks). The material removal from the workpiece occurs by a series of rapidly recurring current discharges between two electrodes, separated by a dielectric liquid and subject to an electric voltage. One of the electrodes is called tool-electrode and is sometimes simply referred to as ‘tool’ or ‘electrode’, whereas the other is called workpiece-electrode, commonly abbreviated in ‘workpiece’. When the distance between the two electrodes is reduced, the intensity of the electric field in the volume between the electrodes is expected to become larger than the strength of the dielectric (at least in some point(s)) and therefore the dielectric breaks allowing some current to flow between the two electrodes. This phenomenon is the same as the breakdown of a capacitor (condenser) (see also breakdown voltage). A collateral effect of this passage of current is that material is removed from both the electrodes. Once the current flow stops (or it is stopped - depending on the type of generator), new liquid dielectric should be conveyed into the interelectrode volume enabling the removed electrode material solid particles (debris) to be carried away and the insulating proprieties of the dielectric to be restored. This addition of new liquid dielectric in the inter-electrode volume is commonly referred to as flushing. Also, after a current flow, a difference of potential between the two electrodes is restored as it was before the breakdown, so that a new liquid dielectric breakdown can occur.
Contents
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1 History 2 Generalities 3 Definition of the technological parameters 4 Material removal mechanism 5 Types o 5.1 Sinker EDM o 5.2 Wire EDM 6 Applications o 6.1 Prototype production o 6.2 Coinage die making o 6.3 Small hole drilling 7 Advantages and disadvantages 8 See also 9 References
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10 External links
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History The EDM process was invented by two Russian scientists, Dr. B.R. Lazarenko and Dr. N.I. Lazarenko in 1943. The first numerically controlled (NC, or computer controlled) EDM was invented by Makino in Japan in 1980. Agie launches in 1969 the world's first series-produced, numerically controlled wire-cut EDM machine.
Generalities Electrical discharge machining is a machining method primarily used for hard metals or those that would be very difficult to machine with traditional techniques. EDM typically works with materials that are electrically conductive, although methods for machining insulating ceramics with EDM have also been proposed. EDM can cut intricate contours or cavities in pre-hardened steel without the need for heat treatment to soften and re-harden them. This method can be used with any other metal or metal alloy such as titanium, hastelloy, kovar, and inconel. EDM is often included in the ‘non-traditional’ or ‘non-conventional’ group of machining methods together with processes such as electrochemical machining (ECM), water jet cutting
(WJ, AWJ), laser cutting and opposite to the ‘conventional’ group (turning, milling, grinding, drilling and any other process whose material removal mechanism is essentially based on mechanical forces). Ideally, EDM can be seen as a series of breakdowns and restorations of the liquid dielectric in-between the electrodes. However, caution should be exerted in considering such a statement because it is an idealized model of the process, introduced to describe the fundamental ideas underlying the process. Yet, any practical application involves many aspects that may also need to be considered. For instance, the removal of the debris from the interelectrode volume is likely to be always partial. Thus the electrical proprieties of the dielectric in the inter-electrodes volume can be different from their nominal values and can even vary with time. The inter-electrode distance, often also referred to as spark-gap, is the end result of the control algorithms of the specific machine used. The control of such a distance appears logically to be central to this process. Also, not all of the current flow between the dielectric is of the ideal type described above: the spark-gap can be short-circuited by the debris. The control system of the electrode may fails to react quickly enough to prevent the two electrodes (tool and workpiece) to get in contact with a consequent short circuit. And this is unwanted because a short circuit contributes to the removal differently from the ideal case. The flushing action can be inadequate to restore the insulating properties of the dielectric so that the flow of current happens always in the point of the inter-electrode volume (this is referred to as arcing), with a consequent unwanted change of shape (damage) of the tool-electrode and workpiece. Ultimately, A description of this process in a suitable way for the specific purpose at hand is what makes the EDM area such a rich field for further investigations and research. To obtain a specific geometry, the EDM tool is guided along the desired path very close to the work, ideally it should not touch the workpiece, although in reality this may happens due to the performance of the specific motion control in use. In this way a large number of current discharges (colloquially also called sparks) happen, each contributing to the removal of material from both tool and workpiece, where small craters are formed. The size of the craters is a function of the technological parameters set for the specific job at hand. They can be with typical dimensions ranging from the nanoscale (in micro-EDM operations) to some hundreds of micrometers in roughing conditions. The presence of these small craters on the tool results in the gradual erosion of the electrode. This erosion of the tool-electrode is also referred to as wear. Strategies are needed to counteract the detrimental effect of the wear on the geometry of the workpiece. One possibility is that of continuously replacing the tool-electrode during a machining operation. This is what happens if a continuously replaced wire is used as electrode. In this case, the correspondent EDM process is also called wire-EDM. The tool-electrode can also be used in such a way that only a small portion of it is actually engaged into the machining process and this portion is changed on a regular basis. This is for instance the case, when using as tool-electrode a rotating disk. The corresponding process is often also referred to as EDM-grinding. A further strategy consists in using a set of electrodes with different sizes and shapes during the same EDM operation. This is often referred to as multiple electrode strategy and is most common when the tool electrode replicates in negative the wanted shape and is advanced towards the blank along a single direction, usually the vertical direction (i.e. z- axis). This resembles the sink of the tool into the dielectric liquid in which the workpiece is immersed, so, not surprisingly, it is often referred to as die-sinking EDM (also called Conventional EDM and Ram EDM). The correspondent machines are often called Sinker EDM. Usually, the electrodes of this types have quite complex forms. If the final geometry is obtained using a usually simple shaped electrode which is moved along several directions and is possibly also subject to rotations often the term EDM-milling is used. In
any case, the severity of the wear is strictly dependent on the technological parameters used in the operation (for instance: polarity, maximum current, open circuit voltage). For example, in micro-EDM, also known as μ-EDM, these parameters are usually set at values which generates sever wear. Therefore, wear is a major problem in that area.
Definition of the technological parameters Some difficulties have been encountered in the definition of the technological parameters that drive the process. The reasons are explained below. On the one hand, two broad categories of generators, also known as power supplies, are in use on EDM machines commercially available: the group based on RC circuits and the group based on transistor controlled pulses. In the first category, the main parameters that a practitioner may be expected to choose from at set-up time are the resistance(s) of the resistor(s) and the capacitance(s) of the capacitor(s). In an ideal condition these quantities would then affect the maximum current delivered in an ideal discharge, which is expected to be associated with the charge accumulated on the capacitors at a certain moment in time. Little control, however is expected to be possible on the time duration of the discharge, which is likely to depend on the actual spark-gap conditions (size and pollution) at the moment of the discharge. Yet, this kind of generators can allow the user to obtain short time durations of the discharges relatively easier than with the a pulse controlled generator. This advantage is however going to be diminished with the progress in the production of electronic components.[2] Also, the open circuit voltage (i.e. the voltage between the electrodes when the dielectric is not yet broken) can be identified as steady state voltage of the RC circuit. In the second group of generators, based on transistor control usually enables the user to deliver a train of pulses of voltage to the electrodes. Each pulse can be controlled in shape, for instance quasi-rectangular. In particular, the time between two consecutive pulses and the duration of each pulse can be set. The amplitude of each pulse constitutes the open circuit voltage. In this framework, the maximum time duration of a current discharge is equal to the duration of a pulse of voltage in the train. Two pulses of current are then expected not to occur for a duration equal or larger than the time interval between two consecutive pulses of voltage. The maximum current during a discharge that the generator deliver can also be controlled. Design of generators different from that described above is likely to be commercially available. Thus, the parameters that a user may actually set on his own machine may be quite different and generatormanufacturer dependent. Moreover, the manufacturers are usually quite reluctant to unveil the details of their generators and control systems to their user base not to give a potential competitive advantage to their competitors. And, conversely, the average users are usually more interested in a ‘machine that can do the job’, rather than in through understanding of the EDM process. This circumstance constitutes another barrier to the attempt of describing unequivocally the technological parameters of the EDM process. Moreover, the parameters affecting the phenomena occurring between tool and electrode are related not only to the generator design but also to the controller of the motion of the electrodes. A framework to define and measure the electrical parameters during an EDM operation directly on inter-electrode volume with an oscilloscope external to the machine has been recently proposed by Ferri et al.[3] These authors conducted their research in the filed of μ-EDM, but the same approach can be used in any EDM
operation. This would enable the user to estimate directly the electrical parameter that affect their operations in an open way, without relying upon machine manufacturer's claims. Finally, it is worth mentioning that, quite unexpectedly, when machining different materials in identical nominal set-up conditions the actual electrical parameters of the process are significantly different.[3]
Material removal mechanism The first serious attempt of providing a physical explanation of the material removal during electric discharge machining is perhaps that of Van Dijk [4]. In his work, Van Dijk present a thermal model together with a computational simulation to explain the phenomena between the electrodes during electric discharge machining. However, as Van Dijk himself admitted in his study, the number of assumptions made to overcome the unavailability of experimental data at that time was quite significant. Further enhanced models trying to explain the phenomena occurring during electric discharge machining in terms of heat transfer theories were developed in the late eighties and early nineties. Possibly the most advanced explanation of the EDM process as a thermal process was developed during an investigation carried out at TeXas A&M University with the support of AGIE, now Agiecharmilles, a company with headquarters in Switzerland. This stream of research resulted in a series of three scholarly papers: the first presenting a thermal model addressing the material removal on the cathode [5] , the second, presenting a thermal model for the erosion occurring on the anode [6] and the third introducing a model describing the plasma channel that is formed during the passage of the discharge current through the dielectric liquid [7]. Validation of these models is carried out also using experimental data provided by AGIE. These models constitute the most authoritative support for the claim that EDM is a thermal process, describing how the material is removed from the two electrodes because of melting and/or vaporization processes in conjunction with pressure dynamics established in the spark-gap by the collapsing of the plasma channel. However, from a careful reading of these papers it emerges that for small discharge energies the presented models are quite inadequate to explain the experimental data. Also, all these models hinge on a number of assumptions, often taken from such disparate research areas as submarine explosions, discharges in gases, and failure of transformers. So it is not surprising that alternative models have been proposed more recently in the literature trying to explain the EDM process. Among these, the model from Sigh and Ghosh [8] re-connects the removal of material from the electrode to the presence of an electrical force on the surface of the electrode that would be able to mechanically remove material and create the craters. This would be made possible by the fact that the material on the surface has reduced mechanical proprieties due to an increased temperature caused by the passage of electrical current. The authors simulated their models and showed how they might explain EDM better than a thermal model (melting and/or evaporation), especially for small discharge energies, which are typically used in μ-EDM and in finishing operations. In the light of the many available models, it appears that the material removal mechanism in EDM is not yet well understood and that further investigation is necessary to clarify it.[3] Especially considering the lack of experimental scientific evidence to build and validate the current EDM models.[3]
Types Sinker EDM Sinker EDM sometimes is also referred to as cavity type EDM or volume EDM. Sinker EDM consists of an electrode and workpiece that are submerged in an insulating liquid such as oil or dielectric fluid. The electrode and workpiece are connected to a suitable power supply. The power supply generates an electrical potential between the two parts. As the electrode approaches the workpiece, dielectric breakdown occurs in the fluid forming an ionization channel, and a small spark jumps. The resulting heat and cavitation vaporize the base material, and to some extent, the electrode. These sparks strike one at a time in huge numbers at seemingly random locations between the electrode and the workpiece. As the base metal is eroded, and the spark gap subsequently increased, the electrode is lowered automatically by the machine so that the process can continue uninterrupted. Several hundred thousand sparks occur per second in this process, with the actual duty cycle being carefully controlled by the setup parameters. These controlling cycles are sometimes known as "on time" and "off time". The on time setting determines the length or duration of the spark. Hence, a longer on time produces a deeper cavity for that spark and all subsequent sparks for that cycle creating a rougher finish on the workpiece. The reverse is true for a shorter on time. Off time is the period of time that one spark is replaced by another. A longer off time for example, allows the flushing of dielectric fluid through a nozzle to clean out the eroded debris, thereby avoiding a short circuit. These settings are maintained in micro seconds. The typical part geometry is to cut small or odd shaped angles. Vertical, orbital, vectorial, directional, helical, conical, rotational, spin and indexing machining cycles are also used.
Wire EDM In wire electrical discharge machining (WEDM), or wire-cut EDM, a thin single-strand metal wire, usually brass, is fed through the workpiece, typically occurring submerged in a tank of dielectric fluid. This process is used to cut plates as thick as 300mm and to make punches, tools,and dies from hard metals that are too difficult to machine with other methods. The wire, which is constantly fed from a spool, is held between upper and lower diamond guides. The guides move in the x–y plane, usually being CNC controlled and on almost all modern machines the upper guide can also move independently in the z–u–v axis, giving rise to the ability to cut tapered and transitioning shapes (circle on the bottom square at the top for example) and can control axis movements in x–y–u–v–i–j–k–l–. This gives the wire-cut EDM the ability to be programmed to cut very intricate and delicate shapes. The wire is controlled by upper and lower diamond guides that are usually accurate to 0.004 mm, and can have a cutting path or kerf as small as 0.12 mm using Ø 0.1 mm wire, though the average cutting kerf that achieves the best economic cost and machining time is 0.335 mm using Ø 0.25 brass wire. The reason that the cutting width is greater than the width of the wire is because sparking also occurs from the sides of the wire to the work piece, causing erosion. This "overcut" is necessary, predictable, and easily compensated for. Spools of wire are typically very long. For example, an 8 kg spool of 0.25 mm wire is just over 19 kilometers long. Today, the smallest wire diameter is 20 micrometres and the geometry precision is not far from +/- 1 micrometre. The wire-cut process uses water as its dielectric with the water's resistivity and other electrical properties carefully
controlled by filters and de-ionizer units. The water also serves the very critical purpose of flushing the cut debris away from the cutting zone. Flushing is an important determining factor in the maximum feed rate available in a given material thickness, and poor flushing situations necessitate the reduction of the feed rate. Along with tighter tolerances multiaxis EDM wire-cutting machining center have many added features such as: Multiheads for cutting two parts at the same time, controls for preventing wire breakage, automatic self-threading features in case of wire breakage, and programmable machining strategies to optimize the operation. Wire-cutting EDM is commonly used when low residual stresses are desired. Wire EDM may leave residual stress on the workpiece that are less significant than those that may be left if the same workpiece were obtained by machining. In fact in wire EDM there are not large cutting forces involved in the removal of material. Yet, the workpiece may undergo to a significant thermal cycle, whose severity depends on the technological parameters used. Possible effects of such thermal cycles are the formation of a recast layer on the part and the presence of tensile residual stresses on the workpiece. If the process is set up so that the energy/power per pulse is relatively little (typically in finishing operations), little change in the mechanical properties of a material is expected in wire-cutting EDM due to these low residual stresses, although material that hasn't been stressed relieved can distort in the machining process.
Applications Prototype production The EDM process is most widely used by the mould-making tool and die industries, but is becoming a common method of making prototype and production parts, especially in the aerospace, automobile and electronics industries in which production quantities are relatively low. In Sinker EDM, a graphite, copper tungsten or pure copper electrode is machined into the desired (negative) shape and fed into the workpiece on the end of a vertical ram.
Coinage die making For the creation of dies for producing jewelry and badges by the coinage (stamping) process, the positive master may be made from sterling silver, since (with appropriate machine settings) the master is not significantly eroded and is used only once. The resultant negative die is then hardened and used in a drop hammer to produce stamped flats from cutout sheet blanks of bronze, silver, or low proof gold alloy. For badges these flats may be further shaped to a curved surface by another die. This type of EDM is usually performed submerged in an oil-based dielectric. The finished object may be further refined by hard (glass) or soft (paint) enameling and/or electroplated with pure gold or nickel. Softer materials such as silver may be hand engraved as a refinement.
EDM control panel (Hansvedt machine). Machine may be adjusted for a refined surface (electropolish) at end of process.
Master at top, badge die workpiece at bottom, oil jets at left (oil has been drained). Initial flat stamping will be "dapped" to give a curved surface.
Small hole drilling Small hole drilling EDM is used to make a through hole in a workpiece in through which to thread the wire in Wire-cut EDM machining. The small hole drilling head is mounted on wire-cut machine and allows large hardened plates to have finished parts eroded from them as needed and without pre-drilling. There are also stand-alone small hole drilling EDM machines with an x–y axis also known as a super drill or hole popper that can machine blind or through holes. EDM Drills bore holes with a long brass or copper tube electrode that rotates in a chuck with a constant flow of distilled or deionized water flowing through the electrode as a flushing agent and dielectric. The electrode tubes operate like the wire in wire-cut EDM machines, having a spark gap and wear rate. Some small-hole drilling EDMs are able to drill through 100 mm of soft or
through hardened steel in less than 10 seconds, averaging 50% to 80% wear rate. Holes of 0.3 mm to 6.1 mm can be achieved in this drilling operation. Brass electrodes are easier to machine but are not recommended for wire-cut operations due to eroded brass particles causing "brass on brass" wire breakage, therefore copper is recommended.
Advantages and disadvantages Some of the advantages of EDM include machining of: • • •
complex shapes that would otherwise be difficult to produce with conventional cutting tools extremely hard material to very close tolerances very small work pieces where conventional cutting tools may damage the part from excess cutting tool pressure.
Some of the disadvantages of EDM include: • • •
The slow rate of material removal. The additional time and cost used for creating electrodes for ram / Sinker EDM. Reproducing sharp corners on the workpiece is difficult due to electrode wear.
Dielectric A dielectric is a nonconducting substance, i.e. an insulator. The term was coined by William Whewell in response to a request from Michael Faraday.[1] Although "dielectric" and "insulator" are generally considered synonymous, the term "dielectric" is more often used to describe materials where the dielectric polarization is important, such as the insulating material between the metallic plates of a capacitor, while "insulator" is more often used when the material is being used to prevent a current flow across it. Dielectrics is the study of dielectric materials and involves physical models to describe how an electric field behaves inside a material. It is characterized by how an electric field interacts with an atom and is therefore possible to approach from either a classical interpretation or a quantum one. Many phenomena in electronics, solid state and optical physics can be described using the underlying assumptions of the dielectric model. This can mean that the same mathematical objects can go by many different names.
Contents
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1 Definitions o 1.1 Classical o 1.2 Behavior 2 Dielectric model applied to vacuum 3 Applications o 3.1 Capacitors o 3.2 Cable insulation 4 Some practical dielectrics 5 See also 6 References
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7 External links
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Definitions
Electric field interaction with an atom under the classical dielectric model. Von Hippel, in his seminal work, Dielectric Materials and Applications, stated: Dielectrics... are not a narrow class of so-called insulators, but the broad expanse of nonmetals considered from the standpoint of their interaction with electric, magnetic, or electromagnetic fields. Thus we are concerned with gases as well as with liquids and solids, and with the storage of electric and magnetic energy as well as its dissipation.[2]
Classical In the classical approach to the dielectric model, a material is made up of atoms. Each atom consists of a cloud of negative charge bound to and surrounding a positive point charge at its centre. Because of the comparatively huge distance between them, none of the atoms in the dielectric material interact with one another[citation needed]. Note: Remember that the model is not attempting to say anything about the structure of matter. It is only trying to describe the interaction between an electric field and matter. In the presence of an electric field the charge cloud is distorted, as shown in the top right of the figure. This can be reduced to a simple dipole using the superposition principle. A dipole is characterized by its dipole moment, a vector quantity shown in the figure as the blue arrow labeled M. It is the relationship between the electric field and the dipole moment that gives rise to the behavior of the dielectric. Note: The dipole moment is shown to be pointing in the same direction as the electric field. This isn't always correct, and it is a major simplification, but it is suitable for many materials.[citation needed] When the electric field is removed the atom returns to its original state. The time required to do so is the so-called relaxation time; an exponential decay.
Behavior This is the essence of the model in physics. The behavior of the dielectric now depends on the situation. The more complicated the situation the richer the model has to be in order to accurately describe the behavior. Important questions are: • •
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Is the electric field constant or does it vary with time? o If the electric field does vary, at what rate? What are the characteristics of the material? o Is the direction of the field important (isotropy)? o Is the material the same all the way through (homogeneous)? o Are there any boundaries/interfaces that have to be taken into account? Is the system linear or do nonlinearities have to be taken into account?
The relationship between the electric field E and the dipole moment M gives rise to the behavior of the dielectric, which, for a given material, can be characterized by the function F defined by the equation: . When both the type of electric field and the type of material have been defined, one then chooses the simplest function F that correctly predicts the phenomena of interest. Examples of possible phenomena:
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Refractive index Group velocity dispersion Birefringence Self-focusing Harmonic generation
May be modeled by choosing a suitable function F.
Dielectric model applied to vacuum From the definition it might seem strange to apply the dielectric model to a vacuum, however, it is both the simplest and the most accurate example of a dielectric. Recall that the property which defines how a dielectric behaves is the relationship between the applied electric field and the induced dipole moment. For a vacuum the relationship is a real constant number. This constant is called the permittivity of free space, ε0.
Applications Capacitors Commercially manufactured capacitors typically use a solid dielectric material with high permittivity as the intervening medium between the stored positive and negative charges. This material is often referred to in technical contexts as the "capacitor dielectric" [3] . The most obvious advantage to using such a dielectric material is that it prevents the conducting plates on which the charges are stored from coming into direct electrical contact. More significantly however, a high permittivity allows a greater charge to be stored at a given voltage. This can be seen by treating the case of a linear dielectric with permittivity ε and thickness d between two conducting plates with uniform charge density σε. In this case, the charge density is given by
and the capacitance per unit area by
From this, it can easily be seen that a larger ε leads to greater charge stored and thus greater capacitance. Dielectric materials used for capacitors are also chosen such that they are resistant to ionization. This allows the capacitor to operate at higher voltages before the insulating dielectric ionizes and begins to allow undesirable current flow.
Cable insulation The term "dielectric" may also refer to the insulation used in power and RF cables[citation needed]. Common materials used as electrical insulations are electrical insulation paper and plastics.
Some practical dielectrics Dielectric materials can be solids, liquids, or gases. In addition, a high vacuum can also be a useful, lossless dielectric even though its relative dielectric constant is only unity. Solid dielectrics are perhaps the most commonly used dielectrics in electrical engineering, and many solids are very good insulators. Some examples include porcelain, glass, and most plastics. Air, nitrogen and sulfur hexafluoride are the three most commonly used gaseous dielectrics. • •
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Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment. Mineral oil is used extensively inside electrical transformers as a fluid dielectric and to assist in cooling. Dielectric fluids with higher dielectric constants, such as electrical grade castor oil, are often used in high voltage capacitors to help prevent corona discharge and increase capacitance. Because dielectrics resist the flow of electricity, the surface of a dielectric may retain stranded excess electrical charges. This may occur accidentally when the dielectric is rubbed (the triboelectric effect). This can be useful, as in a Van de Graaff generator or electrophorus, or it can be potentially destructive as in the case of electrostatic discharge. Specially processed dielectrics, called electrets (also known as ferroelectrics), may retain excess internal charge or "frozen in" polarization. Electrets have a semipermanent external electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry. Some dielectrics can generate a potential difference when subjected to mechanical stress, or change physical shape if an external voltage is applied across the material. This property is called piezoelectricity. Piezoelectric materials are another class of very useful dielectrics. Some ionic crystals and polymer dielectrics exhibit a spontaneous dipole moment which can be reversed by an externally applied electric field. This behavior is called the ferroelectric effect. These materials are analogous to the way ferromagnetic materials behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors.
Milling machine
Example of a CNC vertical milling center
A CAD designed part (top) and physical part (bottom) produced by CNC milling. This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please improve this article by introducing more precise citations where appropriate. (October 2008) A milling machine is a machine tool used for the shaping of metal and other solid materials. Milling machines exist in two basic forms: horizontal and vertical, which terms refer to the orientation of the cutting tool spindle. Unlike a drill press, in which the workpiece is held stationary and the drill is moved vertically to penetrate the material, milling also involves movement of the workpiece against the rotating cutter, the latter which is able to cut on its flanks as well as its tip. Workpiece and cutter movement are precisely controlled to less than 0.001 inches (.025 millimeters), usually by means of precision ground slides and leadscrews or analogous technology. Milling machines may be manually operated, mechanically automated, or digitally automated via computer numerical control (CNC). Milling machines can perform a vast number of operations, some very complex, such as slot and keyway cutting, planing, drilling, diesinking, rebating, routing, etc. Cutting fluid is often pumped to the cutting site to cool and lubricate the cut, and to sluice away the resulting swarf.
Contents
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1 Types o 1.1 Comparing vertical with horizontal o 1.2 Other milling machine variants and terminology 2 Computer numerical control o 2.1 Milling machine tooling 3 History o 3.1 1810s-1830s o 3.2 1840s-1860 o 3.3 1860s o 3.4 1870s-1930s o 3.5 1940s-1970s o 3.6 1980s-present 4 See also 5 References 6 Further reading
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Types There are many ways to classify milling machines, depending on which criteria are the focus: Criterion Control
Example classification scheme
Comments
Manual; Mechanically automated via cams; Digitally automated via NC/CNC
In the CNC era, a very basic distinction is manual versus CNC. Among manual machines, a worthwhile distinction is nonDRO-equipped versus DRO-equipped
Number of axes (e.g., 3-axis, 4-axis, or more); Within this scheme, also: Control (specifically among CNC machines)
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Pallet-changing versus nonpallet-changing
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Full-auto tool-changing versus semi-auto or manual tool-changing
Spindle axis orientation
Vertical versus horizontal; Turret versus non-turret
Among vertical mills, "Bridgeport-style" is a whole class of mills inspired by the Bridgeport original
Purpose
General-purpose versus specialpurpose or single-purpose
Purpose
Toolroom machine versus production Overlaps with above machine
Purpose
"Plain" versus "universal"
A distinction whose meaning evolved over decades as technology progressed, and overlaps with other purpose
classifications above; more historical interest than current Size
Power source
Micro, mini, benchtop, standing on floor, large, very large, gigantic Line-shaft-drive versus individual electric motor drive
Most line-shaft-drive machines, ubiquitous circa 1880-1930, have been scrapped by now
Hand-crank-power versus electric
Hand-cranked not used in industry but suitable for hobbyist micromills
Comparing vertical with horizontal In the vertical mill the spindle axis is vertically oriented. Milling cutters are held in the spindle and rotate on its axis. The spindle can generally be extended (or the table can be raised/lowered, giving the same effect), allowing plunge cuts and drilling. There are two subcategories of vertical mills: the bedmill and the turret mill. Turret mills, like the ubiquitous Bridgeport, are generally smaller than bedmills, and are considered by some to be more versatile. In a turret mill the spindle remains stationary during cutting operations and the table is moved both perpendicular to and parallel to the spindle axis to accomplish cutting. In the bedmill, however, the table moves only perpendicular to the spindle's axis, while the spindle itself moves parallel to its own axis. Also of note is a lighter machine, called a mill-drill. It is quite popular with hobbyists, due to its small size and lower price. These are frequently of lower quality than other types of machines, however. A horizontal mill has the same sort of x–y table, but the cutters are mounted on a horizontal arbor (see Arbor milling) across the table. A majority of horizontal mills also feature a +15/-15 degree rotary table that allows milling at shallow angles. While endmills and the other types of tools available to a vertical mill may be used in a horizontal mill, their real advantage lies in arbormounted cutters, called side and face mills, which have a cross section rather like a circular saw, but are generally wider and smaller in diameter. Because the cutters have good support from the arbor, quite heavy cuts can be taken, enabling rapid material removal rates. These are used to mill grooves and slots. Plain mills are used to shape flat surfaces. Several cutters may be ganged together on the arbor to mill a complex shape of slots and planes. Special cutters can also cut grooves, bevels, radii, or indeed any section desired. These specialty cutters tend to be expensive. Simplex mills have one spindle, and duplex mills have two. It is also easier to cut gears on a horizontal mill.
A miniature hobbyist mill plainly showing the basic parts of a mill.
Other milling machine variants and terminology • •
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Box or column mills are very basic hobbyist bench-mounted milling machines that feature a head riding up and down on a column or box way. Turret or vertical ram mills are more commonly referred to as Bridgeport-type milling machines. The spindle can be aligned in many different positions for a very versatile, if somewhat less rigid machine. Knee mill or knee-and-column mill refers to any milling machine whose x-y table rides up and down the column on a vertically adjustable knee. This includes Bridgeports. C-Frame mills are larger, industrial production mills. They feature a knee and fixed spindle head that is only mobile vertically. They are typically much more powerful than a turret mill, featuring a separate hydraulic motor for integral hydraulic power feeds in all directions, and a twenty to fifty horsepower motor. Backlash eliminators are almost always standard equipment. They use large NMTB 40 or 50 tooling. The tables on Cframe mills are usually 18" by 68" or larger, to allow multiple parts to be machined at the same time. Planer-style mills are large mills built in the same configuration as planers except with a milling spindle instead of a planing head. This term is growing dated as planers themselves are largely a thing of the past. Bed mill refers to any milling machine where the spindle is on a pendant that moves up and down to move the cutter into the work. These are generally more rigid than a knee mill. Ram type mill refers to a mill that has a swiveling cutting head mounted on a sliding ram. The spindle can be oriented either vertically or horizontally, or anywhere in between. Van Norman specialized in ram type mills through most of the 20th century, but since the advent of CNC machines ram type mills are no longer made. Jig borers are vertical mills that are built to bore holes, and very light slot or face milling. They are typically bed mills with a long spindle throw. The beds are more accurate, and the handwheels are graduated down to .0001" for precise hole placement.
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Horizontal boring mills are large, accurate bed horizontal mills that incorporate many features from various machine tools. They are predominantly used to create large manufacturing jigs, or to modify large, high precision parts. They have a spindle stroke of several (usually between four and six) feet, and many are equipped with a tailstock to perform very long boring operations without losing accuracy as the bore increases in depth. A typical bed would have X and Y travel, and be between three and four feet square with a rotary table or a larger rectangle without said table. The pendant usually has between four and eight feet in vertical movement. Some mills have a large (30" or more) integral facing head. Right angle rotary tables and vertical milling attachments are available to further increase productivity. Floor mills have a row of rotary tables, and a horizontal pendant spindle mounted on a set of tracks that runs parallel to the table row. These mills have predominantly been converted to CNC, but some can still be found (if one can even find a used machine available) under manual control. The spindle carriage moves to each individual table, performs the machining operations, and moves to the next table while the previous table is being set up for the next operation. Unlike any other kind of mill, floor mills have floor units that are entirely movable. A crane will drop massive rotary tables, X-Y tables, and the like into position for machining, allowing the largest and most complex custom milling operations to take place.
Computer numerical control
Thin wall milling of aluminum using a water based coolant on the milling cutter Most CNC milling machines (also called machining centers) are computer controlled vertical mills with the ability to move the spindle vertically along the Z-axis. This extra degree of freedom permits their use in diesinking, engraving applications, and 2.5D surfaces such as relief sculptures. When combined with the use of conical tools or a ball nose cutter, it also significantly improves milling precision without impacting speed, providing a cost-efficient alternative to most flat-surface hand-engraving work.
Five-axis machining center with rotating table and computer interface CNC machines can exist in virtually any of the forms of manual machinery, like horizontal mills. The most advanced CNC milling-machines, the 5-axis machines, add two more axes in addition to the three normal axes (XYZ). Horizontal milling machines also have a C or Q axis, allowing the horizontally mounted workpiece to be rotated, essentially allowing asymmetric and eccentric turning. The fifth axis (B axis) controls the tilt of the tool itself. When all of these axes are used in conjunction with each other, extremely complicated geometries, even organic geometries such as a human head can be made with relative ease with these machines. But the skill to program such geometries is beyond that of most operators. Therefore, 5-axis milling machines are practically always programmed with CAM. With the declining price of computers, free operating systems such as Linux, and open source CNC software, the entry price of CNC machines has plummeted. For example, Sherline, Prazi, and others make desktop CNC milling machines that are affordable by hobbyists.
High speed steel with cobalt endmills used for cutting operations in a milling machine.
Milling machine tooling There is some degree of standardization of the tooling used with CNC Milling Machines and to a much lesser degree with manual milling machines. CNC Milling machines will nearly always use SK (or ISO), CAT, BT or HSK tooling. SK tooling is the most common in Europe, while CAT tooling, sometimes called V-Flange Tooling, is the oldest variation and is probably still the most common in the USA. CAT tooling was invented by Caterpillar Inc. of Peoria, Illinois in order to standardize the tooling used on their machinery. CAT tooling comes in a range of sizes designated as CAT-30, CAT-40, CAT-50, etc. The number refers to the Association for Manufacturing Technology (formerly the National Machine Tool Builders Association (NMTB)) Taper size of the tool.
CAT-40 Toolholder An improvement on CAT Tooling is BT Tooling, which looks very similar and can easily be confused with CAT tooling. Like CAT Tooling, BT Tooling comes in a range of sizes and uses the same NMTB body taper. However, BT tooling is symmetrical about the spindle axis, which CAT tooling is not. This gives BT tooling greater stability and balance at high speeds. One other subtle difference between these two toolholders is the thread used to hold the pull stud. CAT Tooling is all Imperial thread and BT Tooling is all Metric thread. Note that this affects the pull stud only, it does not affect the tool that they can hold, both types of tooling are sold to accept both Imperial and metric sized tools. SK and HSK tooling, sometimes called "Hollow Shank Tooling", is much more common in Europe where it was invented than it is in the United States. It is claimed that HSK tooling is even better than BT Tooling at high speeds. The holding mechanism for HSK tooling is placed within the (hollow) body of the tool and, as spindle speed increases, it expands, gripping the tool more tightly with increasing spindle speed. There is no pull stud with this type of tooling. The situation is quite different for manual milling machines — there is little standardization. Newer and larger manual machines usually use NMTB tooling. This tooling is somewhat similar to CAT tooling but requires a drawbar within the milling machine. Furthermore, there are a number of variations with NMTB tooling that make interchangeability troublesome.
Boring head on Morse Taper Shank Two other tool holding systems for manual machines are worthy of note: They are the R8 collet and the Morse Taper #2 collet. Bridgeport Machines of Bridgeport, Connecticut so dominated the milling machine market for such a long time that their machine "The Bridgeport" is virtually synonymous with "Manual milling machine." The bulk of the machines that Bridgeport made from about 1965 onward used an R8 collet system. Prior to that, the bulk of the machines used a Morse Taper #2 collet system.
As an historical footnote: Bridgeport is now owned by Hardinge Brothers of Elmira, New York.
History 1810s-1830s Milling machines evolved from the practice of rotary filing—that is, running a circular cutter with file-like teeth in the headstock of a lathe. Both rotary filing and later true milling were developed in order to reduce the time and effort spent on hand-filing. The full, true story of the milling machine's development will probably never be known, because much of the early development took place in individual shops where generally no one was taking down records for posterity. However, the broad outlines are known. Rotary filing long predated milling. A rotary file by Jacques de Vaucanson, circa 1760, is well known. It is clear that milling machines as a distinct class of machine tool (separate from lathes running rotary files) first appeared between 1814 and 1818. Joseph W. Roe, a respected founding father of machine tool historians, credited Eli Whitney with producing the first true milling machine. However, subsequent scholars, including Robert S. Woodbury and others, suggest that just as much credit belongs to various other inventors, including Robert Johnson, Simeon North, Captain John H. Hall, and Thomas Blanchard. (Several of the men mentioned above are sometimes described on the internet as "the inventor of the first milling machine" or "the inventor of interchangeable parts". Such claims are oversimplified, as these technologies evolved over time among many people.) The two federal armories of the U.S. (Springfield and Harpers Ferry) and the various private armories and inside contractors that shared turnover of skilled workmen with them were the centers of earliest development of true milling machines (as distinct from lathe headstocks tooled up for rotary filing). James Nasmyth built a milling machine very advanced for its time between 1829 and 1831. It was tooled to mill the six sides of a hex nut that was mounted in a six-way indexing fixture. A milling machine built and used in the shop of Gay & Silver (aka Gay, Silver, & Co) in the 1830s was influential because it employed a better method of vertical positioning than earlier machines. For example, Whitney's machine (the one that Roe considered the very first) and others did not make provision for vertical travel of the knee. Evidently the workflow assumption behind this was that the machine would be set up with shims, vise, etc. for a certain part design and successive parts would not require vertical adjustment (or at most would need only shimming). This indicates that the earliest way of thinking about milling machines was as production machines, not toolroom machines.
1840s-1860 Some of the key men in milling machine development during this era included Frederick W. Howe, Francis A. Pratt, Elisha K. Root, and others. (These same men during the same era were also busy developing the state of the art in turret lathes. Howe's experience at Gay & Silver in the 1840s acquainted him with early versions of both machine tools. His machine tool designs were later built at Robbins & Lawrence, the Providence Tool Company, and Brown & Sharpe.) The most successful milling machine design to emerge during this era was the Lincoln miller, which
rather than being a specific make and model of machine tool is truly a family of related tools built by various companies over several decades. It took its name from the first company to put one on the market, George S. Lincoln & Company. During this era there was a continued blind spot in milling machine design, as various designers failed to develop a truly simple and effective means of providing slide travel in all three of the archetypal milling axes (X, Y, and Z—or as they were known in the past, longitudinal, traverse, and vertical). Vertical positioning ideas were either absent or underdeveloped.
1860s
Brown & Sharpe's groundbreaking universal milling machine, 1861. In 1861, Frederick W. Howe, while working for the Providence Tool Company, asked Joseph R. Brown of Brown & Sharpe for a solution to the problem of milling spirals, such as the flutes of twist drills. These were filed by hand at the time. Brown designed a "universal milling machine" that, starting from its first sale in March 1862, was wildly successful. It solved the problem of 3axis (XYZ) travel much more elegantly than had been done in the past, and it allowed for the milling of spirals using an indexing head fed in coordination with the table feed. The term "universal" was applied to it because it was ready for any kind of work and was not as limited in application as previous designs. (Howe had designed a "universal miller" in 1852, but Brown's of 1861 is the one considered groundbreakingly successful.) Brown also developed and patented (1864) the design of formed milling cutters in which successive sharpenings of the teeth do not disturb the geometry of the form. The advances of the 1860s opened the floodgates and ushered in modern milling practice.
1870s-1930s
Two firms which most dominated the milling machine field during these decades were Brown & Sharpe and the Cincinnati Milling Machine Company. However, hundreds of other firms built milling machines during this time, and many were significant in one way or another. The archetypal workhorse milling machine of the late 19th and early 20th centuries was a heavy knee-and-column horizontal-spindle design with power table feeds, indexing head, and a stout overarm to support the arbor. A. L. De Leeuw of the Cincinnati Milling Machine Company is credited with applying scientific study to the design of milling cutters, leading to modern practice with larger, more widely spaced teeth. Around the end of World War I, machine tool control advanced in various ways that laid the groundwork for later CNC technology. The jig borer popularized the ideas of coordinate dimensioning (dimensioning of all locations on the part from a single reference point); working routinely in "tenths" (ten-thousandths of an inch, 0.0001") as an everyday machine capability; and using the control to go straight from drawing to part, circumventing jig-making. In 1920 the new tracer design of J.C. Shaw was applied to Keller tracer milling machines for die-sinking via the three-dimensional copying of a template. This made diesinking faster and easier just as dies were in higher demand than ever before, and was very helpful for large steel dies such as those used to stamp sheets in automobile manufacturing. Such machines translated the tracer movements to input for servos that worked the machine leadscrews or hydraulics. They also spurred the development of antibacklash leadscrew nuts. All of the above concepts were new in the 1920s but would become routine in the NC/CNC era. By the 1930s, incredibly large and advanced milling machines existed, such as the Cincinnati Hydro-Tel, that presaged today's CNC mills in every respect except the CNC control itself.
1940s-1970s By 1940, automation via cams, such as in screw machines and automatic chuckers, had already been very well developed for decades. By the close of World War II, many additional ideas involving servomechanisms were in the air. These ideas, which soon were combined with the emerging technology of digital computers, transformed machine tool control very deeply. The details (which are beyond the scope of this article) have evolved immensely with every passing decade since World War II. During the 1950s, numerical control (NC) made its appearance. During the 1960s and 1970s, NC evolved into CNC, data storage and input media evolved, computer processing power and memory capacity steadily increased, and NC and CNC machine tools gradually disseminated from the level of huge corporations to the level of medium-sized corporations.
1980s-present Computers and CNC machine tools continue to develop rapidly. The PC revolution has a great impact on this development. By the late 1980s small machine shops had desktop computers and CNC machine tools. After that hobbyists began obtaining CNC mills and lathes
G-code This article is about the machine tool programming language. For the video recorder programming system, see Video recorder scheduling code. G-Code, or preparatory code or function, are functions in the Numerical control programming language. The G-codes are the codes that position the tool and do the actual work, as opposed to M-codes, that manages the machine; T for tool-related codes. S and F are tool-Speed and toolFeed, and finally D-codes for tool compensation. The programming language of Numerical Control (NC) is sometimes informally called G-code. But in actuality, G-codes are only a part of the NC-programming language that controls NC and CNC machine tools. The term Numerical Control was coined at the MIT Servomechanisms Laboratory, and several versions of NC were and are still developed independently by CNCmachine manufacturers. The main standardized version used in the United States was settled by the Electronic Industries Alliance in the early 1960s. A final revision was approved in February 1980 as RS274D. In Europe, the standard DIN 66025 / ISO 6983 is often used instead. Due to the lack of further development, the immense variety of machine tool configurations, and little demand for interoperability, few machine tool controllers (CNCs) adhere to this standard. Extensions and variations have been added independently by manufacturers, and operators of a specific controller must be aware of differences of each manufacturers' product. When initially introduced, CAM systems were limited in the configurations of tools supported. Today, the main manufacturers of CNC control systems are GE Fanuc Automation (joint venture of General Electric and Fanuc), Siemens, Mitsubishi, and Heidenhain, but there still exist many smaller and/or older controller systems. Some CNC machine manufacturers attempted to overcome compatibility difficulties by standardizing on a machine tool controller built by Fanuc. Unfortunately, Fanuc does not remain consistent with RS-274 or its own previous versions, and has been slow at adding new features, as well as exploiting increases in computing power. For example, they changed G70/G71 to G20/G21; they used parentheses for comments which caused difficulty when they introduced mathematical calculations so they use square parentheses for macro calculations; they now have nano technology recently in 32-bit mode but in the Fanuc 15MB control they introduced HPCC (high-precision contour control) which uses a 64-bit RISC processor and this now has a 500 block buffer for look-ahead for correct shape contouring and surfacing of small block programs and 5-axis continuous machining.
This is also used for NURBS to be able to work closely with industrial designers and the systems that are used to design flowing surfaces. The NURBS has its origins from the ship building industry and is described by using a knot and a weight as for bending steamed wooden planks and beams.
Contents • • •
1 Common Codes 2 Example Program 3 See also
•
4 External links
Common Codes G-codes are also called preparatory codes, and are any word in a CNC program that begins with the letter 'G'. Generally it is a code telling the machine tool what type of action to perform, such as: • • •
• •
rapid move controlled feed move in a straight line or arc series of controlled feed moves that would result in a hole being bored, a workpiece cut (routed) to a specific dimension, or a decorative profile shape added to the edge of a workpiece. change a pallet set tool information such as offset.
There are other codes; the type codes can be thought of like registers in a computer X absolute position Y absolute position Z absolute position A position (rotary around X) B position (rotary around Y) C position (rotary around Z) U Relative axis parallel to X V Relative axis parallel to Y W Relative axis parallel to Z M code (another "action" register or Machine code(*)) (otherwise referred to as a "Miscellaneous" function") F feed rate S spindle speed N line number R Arc radius or optional word passed to a subprogram/canned cycle P Dwell time or optional word passed to a subprogram/canned cycle
T Tool selection I Arc data X axis J Arc data Y axis. K Arc data Z axis, or optional word passed to a subprogram/canned cycle D Cutter diameter/radius offset H Tool length offset (*) M codes control the overall machine, causing it to stop, start, turn on coolant, etc., whereas other codes pertain to the path traversed by cutting tools. Different machine tools may use the same code to perform different functions; even machines that use the same CNC control. •
Partial list of M-Codes M00=Program Stop (non-optional) M01=Optional Stop, machine will only stop if operator selects this option M02=End of Program M03=Spindle on (CW rotation) M04=Spindle on (CCW rotation) M05=Spindle Stop M06=Tool Change M07=Coolant on (flood) M08=Coolant on (mist) M09=Coolant off M10=Pallet clamp on M11=Pallet clamp off M30=End of program/rewind tape (may still be required for older CNC machines)
Code G00 G01 G02 G03 G04 G05.1 Q1. G05 P10000 G07 G09 G10/G11 G12 G13 G17 G18
Common FANUC G Codes for Mill Description Rapid positioning Linear interpolation CW circular interpolation CCW circular interpolation Dwell Ai Nano contour control HPCC Imaginary axis designation Exact stop check Programmable Data input/Data write cancel CW Circle Cutting CCW Circle Cutting X-Y plane selection X-Z plane selection
G19 G20 G21 G28 G30 G31 G33 G34 G40 G41 G42 G43 G44 G45 G46 G47 G48 G49 G50 G53 G54 to G59 G54.1 P1 to P48 G73 G74 G76 G80 G81 G82 G83 G84 G84.2 G90 G91 G92 G94/G95 G96 G97 G98/G99
Y-Z plane selection Programming in inches Programming in mm Return to home position 2nd reference point return Skip function (used for probes and tool length measurement systems) Constant pitch threading Variable pitch threading Tool radius compensation off Tool radius compensation left Tool radius compensation right Tool offset compensation negative Tool offset compensation positive Axis offset single increase Axis offset single decrease Axis offset double increase Axis offset double decrease Tool offset compensation cancel Define the maximum spindle speed Machine coordinate system Work coordinate systems Extended work coordinate systems High speed drilling canned cycle Left hand tapping canned cycle Fine boring canned cycle Cancel canned cycle Simple drilling cycle Drilling cycle with dwell Peck drilling cycle Tapping cycle Direct right hand tapping canned cycle Absolute programming (type B and C systems) Incremental programming (type B and C systems) Programming of absolute zero point Inch per minute/Inch per revolution feed (type A system) Note: Some CNCs use the SI unit system Constant surface speed Constant Spindle speed Return to Initial Z plane/R plane in canned cycle
A standardized version of G-code known as BCL is used, but only on very few machines. G-code files may be generated by CAM software. Those applications typically use translators called post-processors to output code optimized for a particular machine type or family. Postprocessors are often user-editable to enable further customization, if necessary. G-code is also output by specialized CAD systems used to design printed circuit boards. Such software must be customized for each type of machine tool that it will be used to program. Some G-code is written by hand for volume production jobs. In this environment, the inherent inefficiency of CAMgenerated G-code is unacceptable. Some CNC machines use "conversational" programming, which is a wizard-like programming mode that either hides G-code or completely bypasses the use of G-code. Some popular examples are Southwestern Industries' ProtoTRAK, Mazak's Mazatrol, Hurco's Ultimax and Mori Seiki's CAPS conversational software.
Example Program This is a generic program that demonstrates the use of G-Code to turn a 1" diameter X 1" long part. Assume that a bar of material is in the machine and that the bar is slightly oversized in length and diameter and that the bar protrudes by more than 1" from the face of the chuck. (Caution: This is generic, it might not work on any real machine! Pay particular attention to point 5 below.)
Tool Path for program Sample Line Code N01 M216 N02 G00 X20 Z20 N03 G50 S2000 N04 M01
Description
Turn on load monitor Rapid move away from the part, to ensure the starting position of the tool Set Maximum spindle speed Optional stop Select tool #3 from the carousel, use tool offset values located in line 3 of N05 T0303 M6 the program table, index the turret to select new tool G96 S854 M42 Variable speed cutting, 854 ft/min, High spindle gear, Start spindle CW N06 M03 M08 rotation, Turn the mist coolant on N07 G00 X1.1 Z1.1 Rapid feed to a point 0.1" from the end of the bar and 0.05" from the side
N08 N09 N10 N11
G01 Z1.0 F.05 X0.0 G00 Z1.1 X1.0
N12 G01 Z0.0 F.05 N13 M05 M09 N14 G28 G91 X0 N15 M215 N16 M30
Feed in horizontally until the tool is standing 1" from the datum Feed down until the tool is on center - Face the end of the bar Rapid feed 0.1" away from the end of the bar Rapid feed up until the tool is standing at the finished OD Feed in horizontally cutting the bar to 1" diameter all the way to the datum Stop the spindle, Turn off the coolant Home X axis in the machine coordinate system, then home all other axes Turn the load monitor off Program stop, pallet change if applicable, rewind to beginning of the program
Several points to note: 1. There is room for some programming style, even in this short program. The grouping of codes in line N06 could have been put on multiple lines. Doing so may have made it easier to follow program execution. 2. Many codes are "Modal" meaning that they stay in effect until they are cancelled or replaced by a contradictory code. For example, once variable speed cutting had been selected (G96), it stayed in effect until the end of the program. In operation, the spindle speed would increase as the tool neared the center of the work in order to maintain a constant cutting speed. Similarly, once rapid feed was selected (G00) all tool movements would be rapid until a feed rate code (G01, G02, G03) was selected. 3. It is common practice to use a load monitor with CNC machinery. The load monitor will stop the machine if the spindle or feed loads exceed a preset value that is set during the set-up operation. The job of the load monitor is to prevent machine damage in the event of tool breakage or a programming mistake. On small or hobby machines, it can warn of a tool that is becoming dull and needs to be replaced or sharpened. 4. It is common practice to bring the tool in rapidly to a "safe" point that is close to the part - in this case 0.1" away - and then start feeding the tool. How close that "safe" distance is, depends on the skill of the programmer and maximum material condition for the raw stock. 5. If the program is wrong, there is a high probability that the machine will crash, or ram the tool into the part under high power. This can be costly, especially in newer machining centers. It is possible to intersperse the program with optional stops (M01 code) which allow the program to be run piecemeal for testing purposes. The optional stops remain in the program but they are skipped during the normal running of the machine. Thankfully, most CAD/CAM software ships with CNC simulators that will display the movement of the tool as the program executes. Many modern CNC machines also allow programmers to execute the program in a simulation mode and observe the operating parameters of the machine at a particular execution point. This enables programmers to discover semantic errors (as opposed to syntax errors) before losing material or tools to an incorrect program. Depending on the size of the part, wax blocks may be used for testing purposes as well.
6. For pedagogical purposes, line numbers have been included in the program above. They are usually not necessary for operation of a machine, so they are seldom used in industry. However, if branching or looping statements are used in the code, then line numbers may well be included as the target of those statements (e.g. GOTO N99).
MATLAB For the subdistrict in Chandpur District, Bangladesh, see Matlab Upazila. For the computer algebra system, see MATHLAB.
MATLAB
MATLAB R2008a screenshot Developer(s)
The MathWorks
Stable release
R2009a / 2009-03-06; 4 months ago
Written in
C
Operating system Cross-platform[1] Type
Technical computing
License
Proprietary
Website
MATLAB product page
MATLAB Paradigm
imperative
Appeared in
late 1970s
Designed by
Cleve Moler
Developer Typing discipline OS
The MathWorks dynamic Cross-platform
MATLAB is a numerical computing environment and fourth generation programming language. Developed by The MathWorks, MATLAB allows matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages. Although it is numeric only, an optional toolbox uses the MuPAD symbolic engine, allowing access to computer algebra capabilities. An additional package, Simulink, adds graphical multidomain simulation and Model-Based Design for dynamic and embedded systems. In 2004, MathWorks claimed that MATLAB was used by more than one million people across industry and the academic world.[2]
Contents
• • • • • • • •
1 History 2 Syntax o 2.1 Variables o 2.2 Vectors/Matrices o 2.3 Semicolon o 2.4 Graphics 3 Object-Oriented Programming 4 Limitations 5 Interactions with other languages 6 Alternatives 7 Release history 8 See also 9 References 10 Further reading
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11 External links
• •
History MATLAB (meaning "matrix laboratory") was invented in the late 1970s by Cleve Moler, then chairman of the computer science department at the University of New Mexico.[3] He designed it to give his students access to LINPACK and EISPACK without having to learn Fortran. It soon spread to other universities and found a strong audience within the applied mathematics community. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. They rewrote MATLAB in C and founded The MathWorks in 1984 to continue its development. These rewritten libraries were known as JACKPAC.[citation needed] In 2000, MATLAB was rewritten to use a newer set of libraries for matrix manipulation, LAPACK[4].
MATLAB was first adopted by control design engineers, Little's specialty, but quickly spread to many other domains. It is now also used in education, in particular the teaching of linear algebra and numerical analysis, and is popular amongst scientists involved with image processing.[3]
Syntax This article is written like a manual or guidebook. Please help rewrite this article from a neutral point of view. (October 2008) MATLAB, the application, is built around the MATLAB language. The simplest way to execute MATLAB code is to type it in at the prompt, >> , in the Command Window, one of the elements of the MATLAB Desktop. In this way, MATLAB can be used as an interactive mathematical shell. Sequences of commands can be saved in a text file, typically using the MATLAB Editor, as a script or encapsulated into a function, extending the commands available.[5]
Variables Variables are defined with the assignment operator, =. MATLAB is dynamically typed, meaning that variables can be assigned without declaring their type, except if they are to be treated as symbolic objects[6], and that their type can change. Values can come from constants, from computation involving values of other variables, or from the output of a function. For example: >> x = 17 x = 17 >> x = 'hat' x = hat >> x = [3*4, pi/2] x = 12.0000 1.5708 >> y = 3*sin(x) y = -1.6097 3.0000
Vectors/Matrices MATLAB is a "Matrix Laboratory", and as such it provides many convenient ways for creating vectors, matrices, and multi-dimensional arrays. In the MATLAB vernacular, a vector refers to a one dimensional (1×N or N×1) matrix, commonly referred to as an array in other programming languages. A matrix generally refers to a 2-dimensional array, i.e. an m×n array where m and n are greater than or equal to 1. Arrays with more than two dimensions are referred to as multidimensional arrays. MATLAB provides a simple way to define simple arrays using the syntax: init:increment:terminator. For instance: >> array = 1:2:9
array = 1 3 5 7 9
defines a variable named array (or assigns a new value to an existing variable with the name array) which is an array consisting of the values 1, 3, 5, 7, and 9. That is, the array starts at 1 (the init value), increments with each step from the previous value by 2 (the increment value), and stops once it reaches (or to avoid exceeding) 9 (the terminator value). >> array = 1:3:9 array = 1 4 7
the increment value can actually be left out of this syntax (along with one of the colons), to use a default value of 1. >> ari = 1:5 ari = 1 2 3 4 5
assigns to the variable named ari an array with the values 1, 2, 3, 4, and 5, since the default value of 1 is used as the incrementer. Indexing is one-based[7], which is the usual convention for matrices in mathematics. This is atypical for programming languages, whose arrays more often start with zero. Matrices can be defined by separating the elements of a row with blank space or comma and using a semicolon to terminate each row. The list of elements should be surrounded by square brackets: []. Parentheses: () are used to access elements and subarrays (they are also used to denote a function argument list). >> A = [16 3 2 13; 5 10 11 8; 9 6 7 12; 4 15 14 1] A = 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 >> A(2,3) ans = 11
Sets of indices can be specified by expressions such as "2:4", which evaluates to [2, 3, 4]. For example, a submatrix taken from rows 2 through 4 and columns 3 through 4 can be written as: >> A(2:4,3:4) ans = 11 8 7 12 14 1
A square identity matrix of size n can be generated using the function eye, and matrices of any size with zeros or ones can be generated with the functions zeros and ones, respectively. >> eye(3) ans = 1 0 0 0 1 0 0 0 1 >> zeros(2,3) ans = 0 0 0 0 0 0 >> ones(2,3) ans = 1 1 1 1 1 1
Most MATLAB functions can accept matrices and will apply themselves to each element. For example, mod(2*J,n) will multiply every element in "J" by 2, and then reduce each element modulo "n". MATLAB does include standard "for" and "while" loops, but using MATLAB's vectorized notation often produces code that is easier to read and faster to execute. This code, excerpted from the function magic.m, creates a magic square M for odd values of n (MATLAB function meshgrid is used here to generate square matrices I and J containing 1:n). [J,I] = meshgrid(1:n); A = mod(I+J-(n+3)/2,n); B = mod(I+2*J-2,n); M = n*A + B + 1;
Semicolon Unlike many other languages, where the semicolon is used to terminate commands, in MATLAB the semicolon serves to suppress the output of the line that it concludes.
Graphics Function plot can be used to produce a graph from two vectors x and y. The code: x = 0:pi/100:2*pi; y = sin(x); plot(x,y)
produces the following figure of the sine function:
Three-dimensional graphics can be produced using the functions surf, plot3 or mesh. [X,Y] = meshgrid(-10:0.25:10,10:0.25:10); f = sinc(sqrt((X/pi).^2+(Y/pi).^2)); mesh(X,Y,f); axis([-10 10 -10 10 -0.3 1]) xlabel('{\bfx}') ylabel('{\bfy}') zlabel('{\bfsinc} ({\bfR})') hidden off
[X,Y] = meshgrid(-10:0.25:10,10:0.25:10); f = sinc(sqrt((X/pi).^2+(Y/pi).^2)); surf(X,Y,f); axis([-10 10 -10 10 -0.3 1]) xlabel('{\bfx}') ylabel('{\bfy}') zlabel('{\bfsinc} ({\bfR})')
This code produces a wireframe 3D plot of the two-dimensional unnormalized sinc function:
This code produces a surface 3D plot of the two-dimensional unnormalized sinc function:
Object-Oriented Programming MATLAB's support for object-oriented programming includes classes, inheritance, virtual dispatch, packages, pass-by-value semantics, and pass-by-reference semantics.[8] classdef hello methods function doit(this)
end end
disp('hello')
end
When put into a file named hello.m, this can be executed with the following commands: >> x = hello; >> x.doit; hello
Limitations For a long time there was criticism that because MATLAB is a proprietary product of The MathWorks, users are subject to vendor lock-in.[9][10] Recently an additional tool called the MATLAB Builder under the Application Deployment tools section has been provided to deploy MATLAB functions as library files which can be used with .NET or Java application building environment. But the drawback is that the computer where the application has to be deployed needs MCR (MATLAB Component Runtime) for the MATLAB files to function normally. MCR can be distributed freely with library files generated by the MATLAB compiler. MATLAB, like Fortran, Visual Basic and Ada, uses parentheses, e.g. y = f(x), for both indexing into an array and calling a function. Although this syntax can facilitate a switch between a procedure and a lookup table, both of which correspond to mathematical functions, a careful reading of the code may be required to establish the intent. Many functions have a different behavior with matrix and vector arguments. Since vectors are matrices of one row or one column, this can give unexpected results. For instance, function sum(A) where A is a matrix gives a row vector containing the sum of each column of A, and sum(v) where v is a column or row vector gives the sum of its elements; hence the programmer must be careful if the matrix argument of sum can degenerate into a single-row array.[11] While sum and many similar functions accept an optional argument to specify a direction, others, like plot,[12] do not, and require additional checks. There are other cases where MATLAB's interpretation of code may not be consistently what the user intended[citation needed] (e.g. how spaces are handled inside brackets as separators where it makes sense but not where it doesn't, or backslash escape sequences which are interpreted by some functions like fprintf but not directly by the language parser because it wouldn't be convenient for Windows directories). What might be considered as a convenience for commands typed interactively where the user can check that MATLAB does what the user wants may be less supportive of the need to construct reusable code.[citation needed] Array indexing is one-based which is the common convention for matrices in mathematics, but does not accommodate any indexing convention of sequences that have zero or negative indices. For instance, in MATLAB the DFT (or FFT) is defined with the DC component at index 1 instead of index 0, which is not consistent with the standard definition of the DFT in any literature. This one-based indexing convention is hard coded into MATLAB, making it difficult
for a user to define their own zero-based or negative indexed arrays to concisely model an idea having non-positive indices. Code written for a specific release of MATLAB often does not run with earlier releases as it may use some of the newer features. To give just one example: save('filename','x') saves the variable x in a file. The variable can be loaded with load('filename') in the same MATLAB release. However, if saved with MATLAB version 7 or later, it cannot be loaded with MATLAB version 6 or earlier. As workaround, in MATLAB version 7 save('filename','x','-v6') generates a file that can be read with version 6. However, executing save('filename','x','-v6') in version 6 causes an error message.
Interactions with other languages MATLAB can call functions and subroutines written in the C programming language or Fortran. A wrapper function is created allowing MATLAB data types to be passed and returned. The dynamically loadable object files created by compiling such functions are termed "MEX-files" (for MATLAB executable). [13][14] Libraries written in Java, ActiveX or .NET can be directly called from MATLAB and many MATLAB libraries (for example XML or SQL support) are implemented as wrappers around Java or ActiveX libraries. Calling MATLAB from Java is more complicated, but can be done with MATLAB extension[15], which is sold separately by MathWorks. Through the MATLAB Toolbox for Maple, MATLAB commands can be called from within the Maple Computer Algebra System, and vice versa.
Alternatives MATLAB has a number of competitors. There are free open source alternatives to MATLAB, in particular GNU Octave, FreeMat, and Scilab which are intended to be mostly compatible with the MATLAB language (but not the MATLAB desktop environment). Among other languages that treat arrays as basic entities (array programming languages) are APL and its successor J, Fortran 95 and 2003, as well as the statistical language S (the main implementations of S are S-PLUS and the popular open source language R). There are also several libraries to add similar functionality to existing languages, such as Perl Data Language for Perl and SciPy together with NumPy and Matplotlib for Python. See also: list of numerical analysis software and comparison of numerical analysis software
Release history
version[16]
release name Year
MATLAB 1.0
R?
1984
MATLAB 2
R?
1986
MATLAB 3
R?
1987
MATLAB 3.5
R?
1990
MATLAB 4
R?
1992
MATLAB 4.2c R7
1994
MATLAB 5.0
R8
1996
MATLAB 5.1
R9
MATLAB 5.1.1 R9.1 MATLAB 5.2
R10
MATLAB 5.2.1 R10.1 MATLAB 5.3
R11
MATLAB 5.3.1 R11.1
1997 1998 1999
MATLAB 6.0
R12
2000
MATLAB 6.1
R12.1
2001
MATLAB 6.5
R13
2002
MATLAB 6.5.1 R13SP1 MATLAB 6.5.2 R13SP2 MATLAB 7
R14
MATLAB 7.0.1 R14SP1 MATLAB 7.0.4 R14SP2 MATLAB 7.1
R14SP3
MATLAB 7.2
R2006a
MATLAB 7.3
R2006b
MATLAB 7.4
R2007a
MATLAB 7.5
R2007b
MATLAB 7.6
R2008a
MATLAB 7.7
R2008b
MATLAB 7.8
R2009a
2003 2004 2005 2006 2007 2008 2009
