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There are three terms often used in precision practices and they are often used incorrectly or in a vague manner. The terms are accuracy, repeatability, and resolution. Because the present discussion is on machining and fabrication methods, the definitions will be in terms related to machine tools. However, these terms have applicability to metrology, instrumentation, and experimental procedures, as well.
1.1 Accuracy
It is the ability of a machine to move to a commanded position which it has not visited before. This implies the machine must calculate the new position in terms of its feedback system parameters, or lack thereof, and then move to that position. This does not mean the machine is "shown" or "taught" the position and the feedback parameters are stored, as is often done in robotic applications. Accuracy brings the entire machine, hardware and controls, to bear on the task at hand and is therefore a demanding specification placed on the machine.
In the area of measurements, the quantity to be measured is never known therefore instrument accuracy is extremely important. Here, accuracy is the ability of the instrument to provide a quantitative value for the unknown parameter. This has implications beyond that of accuracy in a machine tool where the "unknown" is the true position of a cutting tool, for example, which was computed and where the phenomena (the machine tool performance) should be known and understood with some level of confidence. In instrumentation, the resolution of the output (how many decimal places are shown) is often mistakenly taken as the instrument accuracy. The accuracy of the instrument is best quantified by comparison with fundamental standards and careful calibration.
1.2 Repeatability
It is the ability of the machine to re-visit a location and has other implications including from which direction is the movement made. If the point is repeatedly approached from the same direction, the term used is repeatability. If the point is approached from two directions, such as the work table on an ordinary milling machine, then the term is bi-directional repeatability. Good bi-directional repeatability is more difficult to achieve than repeatability because it involves hysteresis of mechanical motions, among other possible factors such as feedback dead band.
In instrumentation measurements, the repeatability is again perhaps more complex than in machine tools. The quantity to be measured with an instrument is always influenced by the presence of the instrument and this can change the unknown parameter, especially over time which can have a significant effect on repeatability. This is not to say that metrology tools do not affect machine tools in a similar way. In the figure above, the distribution of the data points is due to repeatability errors associated with the phenomena and the instrument.
1.3 Resolution
It is the least increment of movement the machine is capable of making. Because machines use digital controllers and motors with discrete feedback, such as encoder slits or interferometer fringes, the resolution represents the quantity upon which all motions are made. If the system resolution is n, then all motions are integer multiples of n. This is not to imply the resolution is the least of any system component but rather the largest. A machine controller which can calculate a movement of 0.1 micrometers will not be able to reliably move the machine an increment of 0.1 micrometers if the feedback encoder only has a resolution of reliably 1 micrometer. The control system will never "see" such a small movement. Therefore, one must be very careful in interpreting machine performance figures.
As mentioned above, resolution is the least count of output of an instrument. Because instrumentation is mostly digital, it is very easy to display with many insignificant digits and the user must be very careful when interpreting such data. If a temperature recorder, for example, outputs to one-hundredth of a degree, there is no assurance that it is reporting the correct temperature! One may know the reported temperature with high resolution, but it may be the entirely wrong temperature! Equipment manufacturers and users often use the term "precision" to describe resolution which can lead to a false conclusion about the instrument accuracy
1.4 Accuracy and precision
Accuracy, in science, engineering, industry and statistics, is the degree of conformity of a measured/calculated quantity to its actual (true) value. Precision (also called reproducibility or repeatability) is the degree to which further measurements or calculations will show the same or similar results.
The results of a measurement or calculations can be accurate but not precise, precise but not accurate, neither, or both; if a result is both accurate and precise, it is called valid.
¬¬¬ Material removal by either hard cutting tools or energy beams takes place at the interface of the material and the machining tool. With hard cutting tools such as drills, milling cutters, etc., the interface is more easily identifiable. With energy beams, the interface is often more difficult to identify because energy beams will have some non-uniform energy distribution with respect to spatial dimensions.
A machine tool is a robot, a kinematic manipulator with various degrees of freedom and dexterity, which carries both the cutting tool(s) and the material(s) to be machined. From a kinematic viewpoint, there is only one function of a machine tool and that is to accurately and repeatedly control the point of contact between the cutting tool and the uncut material, known as the machining interface. This interface is normally better defined with hard cutting tools than with energy beams, but can still be unknown due a variety of factors which will be discussed later. All other functions and structure of the machine tool serve the purpose of maintaining this interface.
The structure of the machine tool which aids in maintaining the contact point is termed the structural loop. Unknown or uncontrollable changes in the structural loop are the primary source of kinematic errors in machining.
The structural loop of the machine includes the cutting tool edge(s), the tool holder, the slides and stages used to move the tool and/or the work piece, the spindle holding the work piece or the tool, the chuck, and fixtures, and internal vibration, eccentricities, and other dynamic effects. Influences outside of the structural loop, which still influence the loop and cause errors, include floor vibration, temperature changes, and cutting fluids, for example.
The attitude wherein all errors are identifiable and can be quantified is termed determinism. One may not have the time and/or resources to identify and quantify all errors, but the attitude of determinism will lead the precision engineer to the solution of many of the sources of error, rather quickly in many cases. This is not to say that statistical analysis is not good, but the reliance on or substitution of statistics for determining the cause of errors will not eliminate or reduce the influence of those errors.
There are many sources of errors in machining. An error will be defined as any influence which detracts from machining the perfect part. A perfect part is an abstraction and has the attributes of exacting dimensions (to as many decimal places as can be imagined), an atomically smooth surface, a geometric shape which is mathematically accurate, and a material which behaves as desired under all possible applications. There is, of course, no such thing as the perfect part. Instead, we are satisfied with acceptable parts where tolerances are within some acceptable range, roughness which does not exceed some allowable limit set by the application, a shape which satisfies the application, and a material with properties which are at least predictable within some range of uncertainty. Machining errors help contribute to all of these non-ideal attributes of a part.
The demand for smaller parts also places more demands on the deviations from the perfect part, especially in terms of tolerances. One definition of precision is that the tolerance on a characteristic dimension does not exceed one part in ten-thousand of that characteristic dimension. As parts become smaller, and the need for precision in terms of absolute numbers becomes more demanding, thermal errors become dominant. However, errors due to temperature variations manifest themselves in a variety of ways. As kinematic and material errors are introduced, keep in mind how thermal growth can also influence these error sources.
2.1. Machining Operations
Most machining operations can be divided into those that remove metal from an item, and those that form metal in an item..
Often an unfinished workpiece will need to have some parts removed or scraped away in order to create a finished product. For example, a lathe is a machine tool that generates circular sections by rotating a metal workpiece, so that a cutting tool can peel metal off, creating a smooth, round surface. A drill or punch press can be used to remove metal in the shape of a hole. Other tools that may be used for various types of metal removal are milling machines, saws, and grinding tools. Many of these same techniques are used in woodworking.
Metal can be formed into a desired shape much more easily than materials such as wood or stone, especially when the metal is heated. A machinist may use a forging machine to hammer or mold a hot metal workpiece into a desired shape. Dies or molds may be used if the metal is soft enough, or under high pressures. A press is used to flatten a piece of metal into a desired shape.
As a commercial venture, machining is generally performed in a machine shop, which consists of one or more workrooms containing major machine tools. Although a machine shop can be a stand alone operation, many businesses maintain internal machine shops which support specialized needs of the business.
The inferior finish found on the machined surface of a workpiece may be caused by insufficent clamping, cutting conditions or perhaps an incorrectly adjusted machine. It is evident by an undulating or irregular finish, and the appearance of waves on the surface.
To know the position, and therefore the velocity and acceleration, of the machine tool it is necessary for the machine to be under closed-loop control. This requires feedback information. The basic tenet of precision machining and precision engineering is if the position of a specific point is required to be known, then measure the location of that point! This may seem overly simple, but is most often overlooked or is not possible. Referring back to the previous statement regarding the location of the machining interface, the point of contact between the tool and the workpiece is where the feedback device should be located. Needless to say, that is normally not possible. At the other end of the spectrum, a feedback device may often be placed on the actuation mechanism causing the desired, or at least commanded, motion. An example of this is an encoder attached to a drive motor which provides information on a change in angular position of the motor. Simply put, this feedback strategy will only provide information about the angular change in the lead-screw drive mechanism and not about the lead-screw or the linear position of the stage. The motor could be slipping on the lead-screw or the lead-screw may have non-linearities. In either case, false information could be returned.
3.1. Lead-screw Non-linearity
When a lead-screw is used with a ball-nut to provide linear motion from a rotational actuator, such as a motor, it is often assumed the pitch (threads per linear distance) is precisely known. Generally, this information is provided by the manufacturer and is used as a conversion from rotary displacement to linear displacement. This assumes the pitch is constant at every location along the lead-screw. Because leads-screws are machined on machine tools with inaccuracies, the pitch of the lead-screw will not be constant. The pitch may be larger in some regions of the lead-screw and less in other regions. This will give an error in the linear location of the ball-nut and the stage and workpiece attached to it. One bright side to lead-screw non-linearity is that it is built into the mechanism and all other things being constant, can be measured and compensated in software
3.2. Static Deflection
Although the deflection of the machine tool structure is not a feedback signal, it can influence the accuracy of feedback devices. This is especially important for loads on vertically moving stages, such as the spindle in a z-active milling machine. If the spindle weight is not somehow counterbalanced, the lead-screw will stretch due to elastic strain. Because the deflection of an axially loaded member is proportional to the length of the member, when the stage is near the top of the travel the deflection is nearly zero and the true position of the spindle will coincide with the indicated position as measured by an uncoupled feedback device (angular encoder). As the spindle moves toward the bottom of its travel, the member length is relatively large and the axial deflection of the lead-screw and the spindle will be relatively large. The true position of the spindle will be lower than the indicated position as given by the rotary encoder. There are other instances where static deflections can cause feedback errors and these are specific to more particular instances.
3.3. Tool Wear
Again, the wear of the cutting tool is normally not a directly measured variable but can result in an inaccurate machining condition akin to a feedback error. Because the tool edge is not where it is thought to be due to wear, and its location can not be readily measured in use, this results in the same type error as not measuring the location of interest. If the tool edge is assumed to have a constant spatial coordinate or a constant length from some other known point on the tool holder, typically the tool slide at the base of the tool holder sensed by a linear encoder, then any change in that information will result in an error. As the tool edge wears, it is shortened and will result in a larger than commanded workpiece dimension. If the operation is turning, the shaft will be larger in diameter.
3.4. Axis Orthogonality
Traditional (orthogonal) machine tools (opposed to spatial free-form machine tools based on Stewart platforms, for example) are composed of kinematic links ideally situated at right angles to each other. It is assumed the right angles are present and are maintained throughout all operational procedures. Because the axis motions are kinematically coupled, as opposed to physically coupled, errors will result if the axes are not "perfectly" orthogonal. A motion of only the x-axis, which carries the y-axis stage, will result in some amount of y motion due to the axes not being at right angles. A y-motion however would not manifest itself as an x-error. A non-orthogonal z-axis motion could result in motion components in x and y if the non-orthogonality is two dimensional. As most fixed errors, if these angular errors are known, they can be compensated.
As mentioned previously, a machine tool is a spatial manipulator. All manipulators have joints (revolute joints such as a spindle or prismatic joints such as a linear slide), structural elements or links connecting the joints, actuators, and positional feedback sensors. Because machine tools experience forces generated by machining and the weight of the structural elements themselves, all machine tools are subject to errors called machine tool variables. The following variables are not all inclusive but do include many of the more prominent sources of these errors.
4.1. Accuracy, Resolution, Repeatability
Each of these variables was defined previously and are summarized as a group. Machined parts are made by commanding the machine tool to move the tool and/or workpiece to locations within a three-dimensional volume, called the work volume or work envelope. The locations to move to are computed by CAD/CAM software or by the machine controller based on user commands. This implies that each move of the tool or workpiece is to a location the machine has not previously visited (memorized or been taught) and a certain set of feedback (encoder) parameters is unknown. The ability of the machine tool to locate the desired point(s) for the machining operation will affect the accuracy.
Accuracy will be affected by resolution, for example. All moves are integer multiples of the minimum, or worst, machine resolution. A linear motor with high resolution, fed by low resolution encoder feedback, can have high resolution moves but low resolution of known position, and therefore low accuracy. The machine can not interpolate between the least counts of the resolution, and therefore will stop as soon as the commanded position is met. This can cause repeatability errors depending from which direction the commanded point is approached.
The previous statements are not meant to imply that feedback sensors can not be interpolated. For example, a laser interferometer may use interference fringes where the dark-to-dark fringe pattern can be interpolated in a "gray-scale" manner. Most oftern, a heterodyne interferometer is used where the Doppler shift in a two-beam beat frequency is integrated over time to determine changes in position. Incremental encoders utilizing quadrature techniques are capable of interpolating between encoder slits to improve resolution and even detect rotation direction. The point is, the least count of resolution will affect both accuracy and repeatability, but high resolution is subsequently easy to accomplish so the actual affect on accuracy and repeatability is generally small. Overall machine tool accuracy and repeatability is also closely coupled with many of the other error sources described
4.2. Stiffness
Machine tools are generally massive. Historically, this is because high structural stiffness is desired to reduce deformation under the influence of machining forces and the static weight of the machine structure itself. Deflection will cause the structural loop to deform resulting in uncertainty and error in the interface point between the tool edge and the work piece.
Machine tool stiffness tends to have several other influences. Stiff structures tend to transmit vibration at higher frequencies than compliant (un-stiff) structures. Machining causes vibration, period. Stiff machines, with low internal or external damping, will transmit this vibration throughout the structure. This vibration will cause time-varying deflections of the structure which, if the vibrations are near a fundamental frequency of the machine, can be amplified in the machined part. Therefore, a very stiff machine tool is not necessarily an ideal solution to deformations. One could argue the best way to compensate for a deflection, especially a time-varying deflection which may be difficult to predict, is to continually sense the deflection and compensate for it with the machine motions. This may require high frequency measurements and motions which are impossible to attain, however it demonstrates the attitude of determinism where it may be possible to sense at high frequency, filter to low frequency, and perform the required compensation.
Associated with stiffness, is the ability of the machine to dampen vibrations created or transmitted by high stiffness. Different materials have different internal damping characteristics and so the material from which the machine and the structural loop are made also impacts the performance of the machine. The damping characteristic of steel is different from cast iron and from granite, for example. Additional damping can be realized in granite, for example, by casting the shapes from a mix of granite particles and elastomers in a matrix material. Different materials may also have non-linear damping characteristics whereby one material may dampen the vibration very well during the first few milliseconds but then "ring" for a relatively long time. Other materials may lower the vibration more gradually at first but at a more constant rate so the vibration dies out faster than the material that rings. One needs to investigate these phenomena if machine stiffness is to be fully quantified¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬
4.3. Spindle Vibration
Because the work piece or cutting tool is rotated in a spindle, vibration of the spindle has two primary effects. First, the spindle vibration can permeate throughout the structural loop exciting the machine structure. Generally, spindle vibration will have a relatively high frequency. Depending on the dynamic characteristics of the machine, the spindle can excite modes of vibration within the structural loop. Damping in the structural loop is important to help reduce the amplitude level. The natural frequency of the structural loop, relative to the spindle frequency, is also important because the displacement transmissibility will asymptotically approach zero for input frequencies well above the natural frequency. The effect is more pronounced for larger values of damping between the natural frequency and approximately 1.4 times the natural frequency and less at an input frequency ratio greater than 1.4. This reiterates the fact that the machine and the process must be well understood and quantified (fundamental of a deterministic viewpoint) to be made precise.
While calculating the natural frequency of the machine elements can be difficult, it is one way to estimate which spindle speeds should be avoided. Easier methods require some level of instrumentation, but not beyond what is normally available. Mapping the vibration signature of the basic machine requires some time, but is well worth the investment. A few accelerometers placed around the structural loop, particularly one at the tool tip and one at the workpiece will yield a great deal of information. By electronically taking the difference of the vibration signatures at these two points, as a function of spindle speed for example, can give a good predictor for vibration induced errors. If the two signals are in phase and of the same amplitude, there is essentially rigid body motion and no relative motion between the tool tip and the workpiece. As a first order approximation, this is a desired condition. If however, there are vast differences in the amplitude and/or phase of the motions, there will undoubtedly be larger levels of imprecision in the cutting operation. This approach can also be used under actual machining conditions as another approximation of vibration errors.
Other relatively simple methods to identify vibration errors reside in the frequency domain of the machine and the machined part. Surface metrology will be presented in a subsequent section, but looking at the frequency content of a machined part by analyzing the power spectral density, for example, will quickly reveal the dominant frequency components in the machined surface. The two components will be those which are artifacts of the desired machining condition, and those which are errors. By knowing the machining conditions, such as feed per revolution, the desired effects (or at least those which would still be present under "perfect" conditions) can be identified. All other effects are undesirable and by knowing their frequency content, one can quickly identify the physical parameter contributing to that error.
It would seem a foregone conclusion that the material to be machined must be selected based on the operational requirements of the finished part. However, several factors associated with the work piece material and how it is machined can also lead to uncertainty in the finished results.
5.1. Part Fixture
As the requirement for high precision machining becomes more demanding, more care must be taken when constraining the work piece against the cutting forces. By its nature, a part fixture induces stresses into the work piece, and the stresses are particularly high where the fixture structure contacts the work material. If the contact force is too small, the part may move during machining so the normal tendency is to apply a large clamping force. A large force (ie large stress) also induces strain (surface and internal displacement and stored strain energy) in the work piece. If the material is then machined to a high precision when clamped, upon unclamping the work piece the stored strain energy will be released and the part will change shape. It will relax to a configuration with minimal internal energy. This change of shape will cause the machined shape to change resulting in a machining error
5.2. Material and Heat Treatment
Different materials will behave differently when machined and this can influence surface finish, precision, etc. About the only way to quantify these factors is through experimentation. Materials which machine at either the large or small scales with one tool material may well machine differently with another tool material. One such material is 6061-T6 aluminum. Using a steel or carbide tool, this material generally adheres to the tool leaving a built-up edge and relatively poor surface finish. This is also generally true with polycrystalline diamond which is a composite material made of a metallic binder with diamond particles imbedded into it. Single crystal diamond however, will give relatively good surface finish although over time aluminum can be seen adhering to the rake face of the tool. This may take a low power microscope to observe this. Generally, the built-up aluminum can be removed by a weak hydroxide solution.
Generally, harder materials will give more precise machining results than softer materials. Reasons include fewer burrs and shorter chips, which will interfere less with the cutting action. When properly machined, most ductile materials (aluminum and copper included) will form long continuous chips. The chips will break only due to high strain induced by handling, by their own weight, by chip breakers associated with the tool, or by wrapping around the tool and/or the rotating workpiece. Except for the use of chip breakers, the methods for reducing continuous chips are not desirable. It may be necessary to alter the machining conditions, such as depth of cut or surface speed, to reduce or eliminate long continuous chips.
Other methods for increasing the machining precision is to use a material with some level of heat treatment or solution treating to reduce the ductility of the material without significantly changing its in-use properties. Brass may be needed instead of pure copper, for example. This is of course specific to the application.
Different materials will also wear the tool at different rates. Focusing on single crystal diamond, ferrous (and a few other) materials will rapidly wear the diamond because these materials have a high affinity for carbon. As machining takes place, the temperature at the cutting interface will increase and the rate of diffusion of the diamond into the work material will greatly increase. Examples of the wear of diamond on chromium and copper have been quantified.
5.3. Coolants
Associated with material removal is the use of coolants and/or lubricants. These materials have the functions of reducing the coefficient of friction between the tool and the work material (before and after the chip is made), and to help reduce the temperature of the cutting action to increase tool life and reduce material property changes which can come about by increased temperature. In micromachining, the ability to reduce the coefficient of friction might be questionable because of the very light cut. However, because of a light cut, there is more plastic deformation and extrusion and the influence of the lubricant is not well understood. However, the use of a lubricant will, in most cases, give a better surface finish with most metals such as copper and aluminum. In some micromachining, such as drilling, the use of a fluid is mandatory to help remove chips from the drilled hole since microdrills do not have spiral flutes to assist with chip removal.
While fluids help the basic machining process, it is important to keep in mind that the fluid (liquid particularly) has a relatively high thermal mass (specific heat) and therefore if at a different temperature than the work and tool, can cause thermal expansion/contraction errors. The ideal fluid would be one which can remove all heat generated by cutting, yet remain at a constant temperature. This would tend to suggest that phase change cooling might be an area for further research since phase change is a constant temperature process.
With great care, many of the previous errors can be reduced. However, the effects of the environment on the machining process can introduce new errors which may be more difficult to control.
6.1. Vibration
Aside from vibrations arising from the motions of the machine, vibration can be carried into the machine system through contact with a vibrating floor. Floor vibrations can come from a number of sources including other machine tools, elevators, walking people, outside seismic vibrations by passing trucks and trains. Normally, efforts are made to reduce the transmitted vibration to the machine tool by using pneumatic isolation, similar to that used in high quality optical tables
Much can be done to reduce vibration effects if the vibration source frequency is known. This can be learned by using accelerometers placed directly on the floor, or by being able to identify and quantify the vibration source. Most machine tools, because of their mass, will have a low rigid body natural frequency of perhaps only a few Hertz. This frequency is often excited by nearby walking or manual movements. For higher frequencies, there will probably be some degree of effective damping by an isolation system. This effect can be seen from the typical transmissibility chart. At higher frequency, less isolation damping is wanted to limit the transmission of the excitation. The force transmitted by the damper is proportional to the velocity of the input and a higher frequency displacement results in a higher velocity and a larger transmitted force to the machine. The isolation system must be carefully tuned to the dominant source(s) of vibration.
Vibration induced by people talking near the machine can also cause surface finish variations. Air spindles and bearings have lower stiffness than mechanical or hydrostatic oil bearings so acoustic vibration can be a problem. Recall that the original Edison phonograph was literally a lathe with a foil workpiece and a stylus which machined acoustic noise (speech, music) into the surface of the foil. To play back the recording, the stylus traveled in the machined grooves. This same effect can occur if loud acoustic energy is being produced nearby.
6.2 Spindle Warpage and Windage
Many precision and micromachining tools use air spindles for part or tool rotation. Air spindles have internal orifices through which compressed air is passed to develop the load carrying capability of the spindle. The air has been compressed and then dried, normally by refrigeration-type dryers which cool the air to condense out water. The cooled and compreesed air is then expanded in the bearing and further Joule-Thomson cooling takes place. If the spindle is allowed to sit motionless for prolonged periods with cold air impinging on the same location(s), differential contraction among locations in the spindle will take place causing the spindle to warp. This warpage can cause out-of-round motion due to a bending of the spindle and a localized reduction in the size of the spindle which will alter the interior clearances and the stiffness. This effect can be reduced by shutting off the air supply if the spindle will be idle for extended periods of time or by slowly rotating the spindle with the air on, if the idle time is not excessive. This will help reduce temperature gradients in the spindle reducing warping.
Often, multiple parts may be planarized or large diameter parts, such as electroformed wafers or thick photoresist, may be planarized. These require a large diameter (4 inches perhaps) spindle face plate. Such a large faceplate, rotating at several thousand revolutions per minute, can cause aerodynamic turbulence and random forces to be experienced by the faceplate. This is especially true if the work has considerable height irregularities causing turbulence.
As the need for precision increases, thermal influences tend to become dominant. Machine bearings, actuators, and controls are sophisticated enough to reduce many of the errors described. However, the influence of temperature, especially non-uniform temperature, overshadows many of the other errors.
7.1 Error Sources
There are two areas of concern regarding thermal errors.
1) Non-time varying thermal disturbance
(a) There was no time varying change in the temperature of the machine system, and no thermal gradients within the machine system, there could still be a fixed temperature difference between the machine and the desired temperature, 20 C for instance. This fixed error could be compensated by analyzing its effect on the dimensions of the work piece. A problem would arise, however, because the machine, the cutting tool, and the work piece are probably of different materials with different thermal expansion coefficients. This can cause warping of machine elements and the work piece if it is rigidly attached to the machine.
(b) No time varying temperature changes, the machine system could have thermal gradients due to temperature differences within the machine structure due to a nearby steady state thermal influence, for example. The gradients could cause further distortion (warping) of machine elements and the work piece which are very difficult to correct, in real time. If the thermal/physical scharacteristics of the machine system can be modeled a priori as a system of distributed lump masses, then monitoring the temperature at a few key points could provide sufficient input to the model to calculate distortions in real time for error correction.

Time varying thermal disturbance
The more complex situation arises when there is a time varying thermal disturbance subjecting the machine system to a periodic or random thermal forcing function. To reduce vibration, deformation due to static and dynamic forces, etc, machines are typically massive. This results in a long thermal time constant and a slow response to the thermal input. This can be good in that the machine will not respond to rapid thermal influences. It can also be bad in that any thermal corrective measures, or even knowledge of the effect of the thermal disturbance on the machine system, is slow to be realized..
Q = h A (Tblock - Troom) = -c p V (dT / dt) ------------------------------(1)
Clearly, machining systems are much more massive than the block and have a much longer time constant, which could approach many hours to perhaps a few days. This is even more important if the system is made of a low expansion material such as granite which has a lower heat transfer coefficient than steel. This would add to the time required to bring the entire structure into thermal equilibrium assuming a constant surrounding temperature. The larger the film coefficient and the greater the machine material thermal conductivity, the faster the machine will respond to thermal disturbances. Some typical film coefficients are given below.
A rapid thermal response is not necessarily a good thing. For metrology tools such as the gage block, or for machine systems which would normally be moved among different thermal environments, a small time constant might be good. However, for a machine system which must function within the same, time varying environment, a long time constant may be better. This is based on the fact that unless the thermal disturbance takes a very long time, which can often be the case due to a slowly varying temperature caused by solar heating or normal daily temperature changes. If the machine is in an environment which has temperature control of some kind, either heating or cooling, the temperature fluctuations will normally be about some mean value which is relatively constant. Such a time varying forcing function, into a first order thermal system will result in a logarithmic response with time lag. This can be easily approximated as a periodic step input (not entirely accurate but easier to visualize for this example). If the input frequency is high, the steady state amplitude of the temperature variation will be small and at high frequency, resulting in small dimensional changes. If the temperature variation frequency is low, the thermal mass of the machine system can follow the input better and larger, lower frequency dimensional changes will result. Because the dimensional changes are required to remain small, the higher the temperature fluctuation frequency the smaller will be the thermally-induced error
Precision engineering deals with many source of error and its solution. Precision is the most important think in the manufacturing field. Machining is the important part of manufacturing process. Many factor like feed back variables, machine tool variables, spindle variabls,wokpice vaiabls,envronmantal effect thermal errors etc.. affect the accuracy of machine. Main goal of precision engineering is to reduce the uncertainty of dimensions. Achieve the exact dimension is vary difficult . So tolerance is allowed on work piece.


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