"All Dimensions are Applicable at 20° C (68° F)"

 Tight Tolerances Feel the Heat

Close tolerances are usually specified for a good reason! For example, we use accurate specifications to maximize performance and quality of tight fitting, mating parts. Once the drawings are finished we send them off to manufacturing, and get on with the next job. It is assumed that machine tools and inspection equipment will insure that the right dimensions are obtained. And those tools are remarkably capable. Except that they can be susceptible to variation if exposed to changes in temperature. Production shop floor temperatures are rarely precisely controlled.

The result is that machine tools, positioning systems and gages can produce varying readings depending on prevailing temperatures. In many cases the range of dimensional variation can exceed the total tolerance specified for a feature dimension! For example, a steel diameter such as a crankshaft bearing journal might measure 3.0000 inches  at 90° F but at 70° F it will measure 2.9996 inches. That .0004 inch can represent a large part of the total tolerance. If the journal was undersize by that amount, and the mating bearing was oversize by the same amount, or the reverse was true, what effects would this have on overall performance of the assembly?

According to ANSI (Y14.5M-1982), "Unless otherwise specified, all dimensions are applicable at 20° C (68° F)". The very first standard published by ISO dealt with the same issue. ISO 1 (1975) ratified an international agreement reached originally in 1931. Consisting of just a single sentence, it states: "The standard reference temperature for industrial length measurements is fixed at 20° C."

On the shop floor, however, these standards are usually overlooked, ignored or unknown. Consequently, an opportunity to maintain high quality and process capability is often missed. Although parts may appear to operators to be within tolerance at the time of manufacture, they could be out of tolerance if measured under controlled conditions at 68° F. Over the days and months there will be unnecessary variation in dimensions if they are compared at the true reference temperature.

There is a Solution

But things don’t have to be this way. Modern technologies such as automatic electronic temperature compensation can correct for these errors, if designers bring the need for consideration of thermal effects to the attention of the production floor. All you have to do is to state clearly on drawings: "All Dimensions are Applicable at 20° C (68° F)" (or other reference temperature, if appropriate). This will act as a reminder that tolerances are critical and that thermal variation should be minimized.

Automatic Temperature Compensation Systems provide users with an economically priced method of minimizing thermal errors in precision dimensional measurements. They sense temperatures of the key elements of a measurement system (that is, the workpiece, the gage and the setting master), calculate the amount of thermal error in that system and output a correction signal. That correction, or compensation, can be applied automatically to a precision gage so that measurements reflect true dimension as if all the elements were constantly at the International Reference temperature of 68° F/20° C.

Environmental control such as air conditioning, heating and liquid coolant are expensive and inaccurate. These methods cost hundreds of thousands of dollars to install and operate, and can achieve repeatable thermal control only to within ± 2 or 3 degrees F at best. Temperature compensation systems cost less than a tenth of such solutions, and achieve temperature measurement accuracy in the order of ± 0.5 degrees F.

Temperature compensation systems are designed to work with all electronic gages, including automated, column and other bench top gaging systems. Hundreds of such systems are currently in service in plants making automotive powertrain components, bearings, railroad equipment, printing machinery and similar products. However, production teams who were given adequate warning that temperature fluctuations would generate measurement inaccuracies installed these systems.

 The Designer’s Role

It is not enough to expect those on the production floor to remember to minimize thermal variations. Production personnel deal with many dimensional specifications, and the majority does not require such accurate finishes that temperature needs to be considered. As a result, they may well not be aware of the need to consider temperature on a close tolerance feature unless they are alerted. The designer of the part, however, will know that a close tolerance is being specified, and should attract attention to it by providing an alert on the drawing.

It may be useful to remember that as a rule of thumb, when total tolerance represents 1,000th or less of the nominal dimension of a part feature, temperature is probably going to significantly affect measurement accuracy.

It is important to realize that all gages and positioning systems are affected by temperature. Although there may be offsetting affects caused by the gage or master expanding or contracting along with the part, they invariable change at different rates, due to their different effective expansion coefficients. And it is extremely difficult to control temperatures in a production environment.

Gages are now being used to measure to discriminations and accuracies measured in Microns and Tens of Millionths of an Inch. Influenced by the competitive drive for improved quality, efficiency and manufacturing techniques, tolerances have been steadily getting tighter. Tolerances have become so tight, in many instances, that the subtle effects of temperature have quietly become significant and often unnoticed.

Over the last one hundred and fifty years tolerances have steadily and regularly decreased. During the Industrial Revolution a tolerance of 0.1mm was considered tight. By 1950s and 60s 0.01mm tolerances were appearing on drawings. Now it is not uncommon to find tolerances measured in .001mm units (microns).

Thermal expansion of part features during the production and post-production processes can now exceed total tolerance. However, since the effects of temperature are so subtle, and the eye cannot discern changes in dimension that are measured in microns or tenths of thousandth of an inch, it is easy to overlook this phenomenon. The time to think about this issue is during the design phase and the preparation of technical drawings.

The same technological trend that has driven tolerances down into the microscopic realm has provided the know-how for dealing with thermal problems. Electronic temperature compensation systems can correct for temperature-induced errors in real time, but most gages do not have such systems built into them unless the end-user requests them. Designers of components can assist everyone by giving early notification that temperature needs to be considered for the tight tolerances they specify. Just clearly mark drawings:

"All Dimensions are Applicable at 20° C (68° F)".

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 So, you don’t think you have a temperature problem?

The Myth

It’s easy to believe that your precision inspection systems and gages are giving you accurate dimensional control. Your gage readouts or SPC charts tell you that you are in control, right? And those gages have been shown to have a Gage R&R below 10%, so they must be correct. No problem!

Would it shake your confidence if you learned that despite a 10% Gage R&R, gage accuracy can drift over time by as much as 50% to 100% of tolerance without you being aware of it? If a gage appeared to give you accurate readings but was in fact off by a large factor, what would it be doing to your process? Your process could be out of control and you wouldn’t know it. Wouldn’t it be like being on a diet and thinking you were shedding several pounds a month, only to find that the scales were wrong and you were, in fact, gaining weight? Well, that is the kind of invisible effect that temperature changes can have on shop floor gages. And those gages are performing a vital function! Don’t be fooled by the myth of short term Gage R&R. Gages that operate on the shop floor, even in supposedly controlled environments, more often than not are subject to temperature induced drift. It is just too subtle an effect to be obvious, so it is often overlooked or ignored.

However, you can easily test this for yourself. Measure the same feature on a workpiece repeatedly, in the same gage, over a period of a few weeks. Write each measurement down. If you have a thermometer you might also want to write down the ambient temperature at the time of each measurement. After you have taken several measurements, compare them. You will probably see variation, and this variation will probably correlate with recorded temperature variations. (Of course, there may also be other thermal influences than ambient variations that would account for these differences. Machining operations, coolants, washers, etc., may be causing temperature changes as well.) Fig 1 shows an example of such a study. The same crank pin on the same crank shaft was measured about 60 times over a period of two weeks at a major automobile engine plant, on the same shop floor gage. As can be seen from the graph, measurements varied by 13 microns on a part with control limits 14 microns apart! That is almost 100% variation. However, the gage used for this test had been certified to have a Gage R&R of better than 10%. Temperature accounted for 90% of the variation seen in this chart.

Well, what about those Gage R&R and Process Capability studies?

Gage studies are generally performed in controlled situations. They are performed over a short period of time or in temperature controlled environments, so that temperature does not have time to have an influence. The effects of temperature are deliberately eliminated. However, gages are then used in shop floor environments where ambient temperatures fluctuate from hour to hour and month to month, and where workpieces vary in temperature as the result of operations or seasonal ambient variations. Of course, if no further tests are performed, this fact will never become apparent. You put your trust in the gage. However, you will be producing parts that vary significantly in relative size over time, none the less. Fig. 2 illustrates the variations that can affect a one inch (25.4mm) steel diameter. Other diameters of the same material would be affected proportionately, and aluminum parts show twice the thermal growth.

Over the long term, temperature will cause uncorrected gages to produce varying dimensions. The argument that changes in ambient temperature will cause offsetting errors in workpiece and gage is generally untrue. Usually the gage and workpiece expand and contract at differing rates as temperatures change. They have different effective coefficients of expansion. Gages are particularly prone to exhibiting unexpectedly high effective thermal coefficients, due to their complex geometries, mixtures of components, electronic drift, etc. They have been seen to exhibit coefficients 10 to 20 times greater than that of a workpiece. Moreover, it is worth repeating that workpieces are frequently exposed to operations that can cause them to be at varying temperatures – washers, coolants, machining all effect temperature, so they are frequently not at the same temperature as the gage.

So-called "tempering" – the use of air conditioning to reduce the extremes of temperature fluctuations, while not completely controlling the temperature at the ISO standard 20°C / 68°F – can also lead to misplaced confidence in gages. Tempering tends to keep shop floor temperatures within +/- 10°F (5.5°C) of some arbitrary value other than the ISO standard 20°C / 68°F. Precision measuring instruments can still be rendered inaccurate by this much variation (see Fig 3. and the accompanying paragraphs describing the effects of 5°C variation), and tempering ignores process induced temperature variations such as have already been mentioned, i.e. from machining, coolants, washers, etc.

A long term test can reveal the problem, and suggest a solution.

By testing a measurement system over a long term, while operating temperatures vary naturally in the regular shop floor environment, you can obtain realistic data about true shop floor gage performance. In the example shown in Fig 3 data was taken from a gage in three runs, each of which was conducted over a period of several hours.

In the first run of 100 parts, conducted over a short period of time, temperatures were held reasonably stable. Ambient temperature rose by just 0.9°C (1.6°F) during the test. In the second run, the same 100 parts were measured while ambient temperature gradually increased by 5°C (9°F). Look at the negative effect that this had on true process capability.

The dramatic improvement obtained by using automatic temperature compensation can be seen by looking at the results of the third run. In the final long term run temperatures were again allowed to rise by 5°C (9°F) while the same 100 parts were being measured, but in this case "temp comp" was applied. These results were obtained from a regular shop floor post process precision gage, operating in a typical shop floor environment. Many such gages have successfully applied temperature compensation systems so as to obtain such improved results.

Temperature Compensation

Temperature compensation systems consist of a microprocessor based controller equipped with temperature sensors and a selection of I/O ports. They communicate with electronic gaging systems over analog or digital interfaces. Their temperature sensors are designed to be attached to the gage fixture so as to monitor temperatures of the part being measured, the gage fixture and the calibrating master or masters during gaging operations.

These temperature compensation systems can be programmed with the effective coefficients of expansion of the gage, part and master. During measuring operations they continuously sense temperature variations and compute and send a correcting signal to the gage in real time. The gage then displays the correct measurement after eliminating thermal errors.

Temperature compensation systems have been installed on automatic, bench top and hand held gages. Users are extremely pleased with the robust performance of these systems, often volunteering to be the subjects of technical articles and papers for publication. More recently, Albion Devices, Inc., Solana Beach, CA (www.AlbionDevices.com) has begun to install systems on in-process gages for applications such as grinding and honing. These systems actually sense the temperature of parts and in-process gages during the machining operation and provide a correcting offset to the gage. The result is that dimensions are measured as if temperatures were being controlled at reference temperature (20° C / 68° F) while operating temperatures are considerably different than this. However, since the system is displaying the size that parts would be at if they were at reference temperature, they can be machined directly to final size without having to allow time for cooling before making final measurements and performing a finishing grind.

Don’t miss an opportunity to improve quality and process capability.

By turning a blind eye to the issue of temperature you can miss a valuable opportunity to improve quality and process capability. As tolerances become increasingly tight even a small temperature variation from the ISO standard 20°C / 68°F will cause significant gaging error. It is easy to be fooled into thinking that you don’t have a problem. But just because your data is grouped nicely, it does not necessarily mean that it is accurate (Fig 4). As a repeatable gage drifts with temperature it will appear to continue to give good results. We tend to believe what the indicator or the gage display shows. However, that data may be grouped tightly, while still being considerably off target. Don’t be misled.

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Gage R & R and Temperature on the Shop Floor

The specified accuracies of gages as determined by Gage R & R studies can only be achieved if they operate at 20° C (68° F)

"Gage R & R" is a standard for determining the ability of a gage and its operator to obtain the same result while taking successive measurements. It is important to understand, however, that a gage with a good R & R is not necessarily accurate. It may just keep giving the same wrong answer. For example, a gage that read 3.0008 inches 30 times in succession while measuring a 3.0000 inch diameter would produce an excellent Gage R & R result. It would have remarkable repeatability, or "precision". However, it would not be giving accurate readings. This is what happens to gages as temperatures change. A heated 3.0000 inch diameter measures 3.0008 – until it cools down later. Since the true dimension should be that which is obtained at 20° C (68° F), if temperatures are not at 20° C (68° F) then measurement inaccuracies will occur, while the gage will appear to be giving good readings. The specified accuracies of gages can only be achieved if they operate at 20° C (68° F) (reference temperature) and their masters and workpieces are at the same temperature, or if compensation is made for differences in temperature from the reference temperature.

Gages that operate on the shop floor are subject to temperature induced drift. Gage studies are generally performed in controlled situations. They are performed over a short period of time or in temperature controlled environments, so that temperature does not have time to have an influence. The effects of temperature are deliberately eliminated from these studies. However, gages are then used in shop floor environments where ambient temperatures fluctuate from hour to hour and month to month, and where workpieces vary in temperature as the result of operations or seasonal ambient variations.

A long term test can reveal the problem, and suggest a solution.

By testing a measurement system over a long term, while operating temperatures vary naturally in the regular shop floor environment, you can obtain realistic data about true shop floor gage performance. Gages that produce a Gage R & R of 10% or less in a controlled test may obtain results that are closer to 100% or more if temperatures are allowed to drift during the test as they would in normal operating conditions on the shop floor. Similarly, process capability studies can be heavily influenced by temperature.

In the example shown in Fig 1 data was taken from a gage in three runs, each of which was conducted over a period of several hours. In the first run of 100 parts, conducted over a short period of time, temperatures were held reasonably stable. Ambient temperature rose by just 0.9°C (1.6°F) during the test. In the second run, the same 100 parts were measured while ambient temperature gradually increased by 5°C (9°F). Look at the negative effect that this had on true process capability.

The dramatic improvement obtained by using automatic temperature compensation can be seen by looking at the results of the third run. In the final long term run temperatures were again allowed to rise by 5°C (9°F) while the same 100 parts were being measured, but in this case "temp comp" was applied. These results were obtained from a regular shop floor post process precision gage, operating in a typical shop floor environment. Many such gages have successfully applied temperature compensation systems so as to obtain such improved results.

Similar studies conducted by Ford Motor Company personnel at their Livonia Transmission Plant revealed process improvements of over 100%.

Gage R & R and Temperature Compensation

The addition of temperature compensation to a gage that obtains a 10% R & R in an environment that is completely controlled at 20° C (68° F) cannot improve the system performance. Indeed, since the addition of any components to any measuring system will inevitably add some error. So, under perfect environmental conditions, Albion Devices, Inc., cannot claim to improve Gage R & R. Indeed, under such circumstances our systems may contribute to a measurement system degradation of a percentage point or so.

However, shop floor measurement systems do not perform under perfect conditions from day to day. Rather, they are exposed to thermal variations which, as shown above, can cause their actual R & R to vary by over 100%. Albion’s temperature compensation systems are intended to eliminate most of this thermally induced drift. Thus, Gage R & R might drift by 100% on the shop floor without temperature compensation while temperatures were uncontrolled. If temperature compensation were applied to the same gage, R & R would be held closer to the value established under controlled conditions (say, 10%), give or take some minor system error. In other words, under shop floor conditions, true Gage R & R would be in the region of 100%. Adding temperature compensation to the same gage would bring R & R back down to 10% +/- some minor system error.

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Eliminate Temperature Electronically and Improve Capability

Precision dimensional control is an important part of manufacturing, yet it is still common practice to ignore the single largest cause of precision measurement error: temperature. Typical tests of precision measuring systems fail to address this problem. A short-term capability study on a process or gaging system may lead to the belief that a very acceptable G R & R, Cp or Cpk can be obtained. However, it may hide the fact that over the long term, thermal effects can cause significant deterioration in performance.

A recent study demonstrated not only the detrimental effect of temperature over the long term on an apparently good process control gage, but also the benefit of using electronic temperature compensation to overcome this problem. A short term study of a gage used to measure mass produced 18 mm (0.71 inch) diameter spool valves indicated that the process could be controlled with a Cp value of 2.77. That should be pretty good. However, a long-term study, during which ambient temperature increased by just 5° C (9° F), showed a deterioration of the Cp value to 1.56. Moreover, Cpk fell from 2.12 to just 0.35! Fortunately, the Quality Manager responsible for system implementation provided for the gage to be equipped with an electronic temperature compensation system from Albion Devices, Inc., that uses Albion’s proven and patented thermal correction method. When this was connected, the same long-term test (with temperatures rising by 5° C) produced a Cp of 3.11 and a Cpk of 2.81. Table A and Fig. 1 summarize these results.

Most shop floor gages are subject to significant thermal variation. They may easily see 5 to 10° C (9 to 18° F) temperature changes between early morning and noon, particularly in summer. Very few mass production plants find it practical or affordable to control temperatures accurately. If a gage run-off is performed in such a factory over a short term, say, half-an-hour to an hour only small thermal variations will be experienced during the test. However, the tool or gage will be used over much longer periods of time, and then it will be exposed to greater thermal changes. It is rare to test a gage over several hours, or while temperatures change a few degrees, but if the gage is going to be used under such conditions, it should be tested under such conditions.

The gage referred to above was evaluated in this way and its performance was improved as a result of understanding its thermal behavior. In the test one hundred parts were run through the gage three times. The conditions were changed for each run, while data were recorded.

First, the short-term capability of the gage was assessed. The one hundred parts were sent through a conveyor that fed the automatically controlled gage. The gage controller is equipped with computerized data collection and SPC software. It calculates statistics and displays them in real time. It is intended for use on a production line immediately following a grinding operation to produce outside diameters to micron tolerances.

While attempts were made to control ambient temperatures during this run, there was nevertheless a typically unavoidable morning ambient increase of 0.6° C during the approximately 50 minutes that it took to measure the parts. Fig. 2 plots each measurement taken during the run independently and shows a trend line that indicates a shallow deterioration of approximately 2 microns in mean value since the temperature rose slightly during the course of the data gathering. Since the thermal change was not large, Fig. 3 shows a histogram with an apparently very acceptable distribution.

Now take a close look at the results of the second run, during Now take a close look at the results of the second run, during which ambient temperature rose by just 5° C, such as might easily be experienced in a morning of production. Fig. 4 shows a trend line in which mean diameter varies by 8 microns. Note that the mean value decreases. Of course, the reverse might occur during an evening or night shift as temperatures dropped. Since in this case the dimensions are apparently decreasing, this indicates that the gage or gage tooling is expanding at a higher rate than the workpiece. As further studies determined, the gage was in fact expanding at a very high rate, which is not uncommon. Gages and gage fixtures are typically complex mechanical and electrical assemblies that for several reasons are heavily affected by thermal changes. For example, steel expands at an approximate rate of 6.8 parts per million per degree F, and aluminum at a rate of 13 parts per million per degree F. By comparison, this gage expands and contracts at the rate of 33.3 parts per million per degree F. Since the gage fixture expands as temperature increases, the meauring probes must extend further so as to contact the workpiece, thus giving the impression that the part is smaller.

In a practical application this could lead to acceptance of oversized parts. In a system in which machine compensation (automatic feedback to a machining operation) was being used, the gage would actually instruct the machine tool to make oversized parts. On most shop floors, temperatures vary continuously. As temperatures change, so will measured values of critical dimensions. Fig. 5 shows the effect that the 5° C drift had on the distribution of measured diameters during the second run. Clearly, the wider distribution of measured data points led to a considerable reduction in calculated capability (Cp) and the trend in the direction of decreasing mean size caused a major deterioration of Cpk value (capability centered around nominal size).

For the third and final run, a GageComp temperature compensation system from Albion Devices, Inc., of Solana Beach, CA (www.albiondevices.com) was added to the gaging system. GageComp’s custom designed industrial sensors monitored temperatures of workpieces, the setting master and the gage as parts were measured. GageComp then calculated a correction based on predetermined correction coefficients, and electronically sent this correction in real time to the gage. (See Fig. 8). The computerized gage mixed the correction from GageComp with the measured dimension to produce a temperature corrected measurement of each part. Effectively, the gage now displayed the dimension that would have been obtained if each measurement had been taken while parts, master and gage were held at the International Reference Temperature of 20° C (68° F).

Compare Figs. 3, 5 and 7 (runs 1, 2 and 3 respectively), and you will see that original gage capability (run number 1, Fig 3) is severely compromised when temperature variations influence measurements (Fig 5). By applying temperature compensation while temperatures changed in run number 3 (Fig .7), original gage capability (run number 1) is restored. In fact, it is even improved.

As Fig. 6 shows, the mean dimensional measurement remains flat when temperature compensation is applied. After smoothing out inherent gage R & R variation, average measurements were virtually unaffected by the change in ambient temperature. Further, as was seen in Table A and Fig. 1, Fig. 7 shows an improvement in both Cp and Cpk over run number 2 (in which ambient temperature increased by 5° C) and even run number 1, in which temperatures increased by just 0.6° C. This last observation demonstrates that process improvement can be obtained from using temperature compensation even in environments in which temperatures are held stable to within a degree or two, which is the best that can be held in large plant areas.

Electronic temperature compensation systems are in wide use in a variety of applications. They can interface to just about any electronic gage, but it is best to think of them as a separate, distinct system from that of the mechanical gaging assembly. When discussing this subject with gage suppliers it is helpful to keep this in mind and to differentiate responsibilities between vendors of the different system components. It can be useful to establish criteria for performance of the gage first at stable temperature, then secondly under typical shop floor thermal variations. By separating these requirements, specific responsibilities can be established for performance under varying conditions.

Temperature compensation requires unique experience and expertise and is probably best left to those who specialize in the subject. They can then be held accountable for achievement of reasonable thermal correction specifications.

A relatively small investment of time and money in temperature compensation can pay huge dividends. Increased process capability (see Fig. 1) is well known to yield cost savings, and more importantly, to provide a competitive edge. Mass producers of discrete parts are invariably under pressure to produce. Suppliers of production and inspection equipment feel the same urgencies. It is understandable that they may want to avoid the seemingly time consuming task of a long-term study. However, as the above results clearly reveal, a short-term study of capability is not necessarily a true test. Customers who rely on such studies to certify the quality of a supplier’s process should beware. Similarly, Quality Managers and Manufacturing/Process Engineers everywhere should take note of this opportunity to improve process capability and thereby gain significant advantage in the marketplace and on the bottom line.

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Albion's Temperature Compensation Methodology

A part was repeatedly gaged some sixty times, at the same station, over a period of approximately two weeks (Fig. 1). The gage was known to be highly reliable, and repeatable to tenths of a micron. The only significant variable was environmental temperature, which turned out to be responsible for a range of 13 microns of dimensional variation in the group of measurements.

Albion conducted tests to prove that it could correct for errors such as these. For the purposes of the tests conducted in order to generate the data displayed below, Albion’s GageComp-S Single Channel Temperature Compensation System was attached to an automotive piston gage.

Albion’s temperature compensation instruments and approach have been used successfully in a variety of applications. They include in-process dimensional control, post process measurements and hand held, bench top and automatic gaging in a wide variety of industries.

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The Thermal Error Index (TEI)

A conference, held in Seattle, WA a few years ago now and sponsored by ASPE, focused on, among other things, issues relating to the effects of temperature on manufacturing processes. There is clearly an increasing awareness of this phenomenon, which is becoming more important as machined part accuracies become more critical. Mr. Kenneth Blaedel, of the Lawrence Livermore National Laboratory, delivered a particularly relevant half day tutorial on thermal effects in precision engineering. He referred to a useful formula for calculating the Thermal Error Index contained in ANSI B89.6.2 and referenced again in ANSI B89.1.12M-1990.

The Thermal Error Index (TEI) is intended as an estimation of the maximum possible measurement error due to all thermal effects. It was originally conceived as a tool to assure that temperature control is adequate for the calibration of measuring equipment, as well as the manufacture and acceptance of workpieces. It recognizes that if measurements are not made with all elements of the gaging system being at 68°F (20°C), temperature-induced measurement errors will occur. It also acknowledges that there are uncertainties in estimating coefficients of expansion, and in accurately measuring temperatures.

The formula addresses Nominal Differential Expansion (NDE) and the Uncertainty of Nominal Differential Expansion (UNDE). NDE represents the net variation in dimension which can be anticipated as a result of differences in the assumed values of the coefficients of expansion in part, master and gage. UNDE represents the difference between the handbook values and the true values of the coefficients of expansion. The difference is often approximated at 10% of the handbook value. Temperature Variation Error (TVE) is also considered. TVE is defined by ANSI as an estimate of the maximum possible measurement error induced solely by deviation of the environment from average conditions. TVE is determined from the results of two drift tests, one of the master and the comparator and the other of the part and the comparator. The TEI formula, which results in an answer expressed as a percentage of the total tolerance, or Working Tolerance (WT), is as follows:

TEI = [(NDE+UNDE+TVE)/WT] x 100

A calibration, part manufacture, or acceptance procedure complies with this standard if it is carried out with all components of the measurement system at 68°F/20°C, or if it can be shown that the TEI is a reasonable and acceptable percentage of the working tolerance. In applying TEI, for example, to the acceptance testing of a coordinate measuring machine, ANSI declares that the measuring environment is unacceptable if the TEI is greater than 50%. ISO is currently considering the concept of TEI for adoption into their own standards.

Example:

Consider measuring 3 inch diameters of aluminum parts to a tolerance of ± .0002 inches using a steel master and a gage comprising both steel and aluminum. The nominal coefficient of expansion (COE) is about 6.5 ppm (parts per million) per degree F for steel, about 13.1 ppm/°F for aluminum and the effective COE of the comparator (gage) is 10 ppm/°F. Temperatures in the environment can vary by as much as 20°F, but are measured to 1°F, (so they can actually vary by as much as 21°F). Assume that the comparator is mastered immediately before each measurement and therefore the temperature of mastering and measuring will be close.

Case #1: If no compensation is applied to correct for NDE, then

TEI = [(.000416 + .000116 + .000015)/.0004] x 100 = 137% where,

NDE = (13.1 - 6.5) ppm/°F x 21°F x 3 inch = .000416 inch representing the contribution from the difference between the nominal COEs

of the steel master and the aluminum part

UNDE = 1.85 ppm/°F x 21°F x 3 inch = .000116 resulting from the sum of the uncertainty of the COE of the aluminum part, estimated here at about 1.3 ppm/°F (i.e. 10% of the nominal COE) and the uncertainty of the COE for gage block steel, estimated from a number of studies to be about .55 ppm/°F,

TVE = .000015 inch as obtained from a drift check over the course of perhaps 1 minute,

WT = .0004 inch

Without compensation for NDE, this environment is clearly unacceptable.

Case #2: If compensation is applied to correct for NDE, then

TEI = [(.00002 + .000116 + .000015)/.0004] x 100

= 38% where,

NDE = (13.1 - 6.5) ppm/°F x 1°F x 3 inch = .00002 inch because correction for NDE can only be made in this case to the nearest 1°F,

UNDE = 1.85 ppm/°F x 21°F x 3 inch = .000116 inch, the same as above

TVE = .000015 inch as obtained above, and

WT = .0004 inch

With compensation for NDE, and using the guideline that a TEI of less than 50% defines an acceptable environment, this environment is acceptable to make the measurement.

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Temperature compensation of in-process gages during grinding operations.

Measurements: Automatic gages are used to control dimensions in grinding processes. The gage is positioned so that its contacts can measure dimensions of ground work pieces while they are being machined. Feedback is provided to the grinding machine controller so as to regulate the depth of cut. Errors may be caused by temperature changes induced by machining energy, ambient fluctuations and changes in coolant temperature that can cause dimensions and settings of work pieces, gages and setting masters to vary.

Temperature Compensation Approach: Albion’s GageComp Temperature Compensation System uses a proprietary "Diamond Series" sensor to monitor temperatures of workpiece and master and another sensor to track the temperature of the gage fixture.

GageComp applies separate thermal coefficients for each of these three "elements" and computes and transmits a correction via analog signal to the process control gage, where correction amounts are mixed with gaged dimensions to give resulting net compensated measurements for the measured diameter.

Gage Modification: Gage heads are engineered to incorporate Albion’s DS-1 workpiece/master temperature sensor. The sensors are positioned so that they come in contact with the machined surface of the work piece, or as close thereto as possible. These sensors are coolant resistant, durable and designed with the tough environmental considerations of this application specifically in mind. A LG-1 gage temperature sensor is also mounted on the gage head.

Characterization: To determine effective coefficients of expansion (COEs), empirical testing is performed on masters, sample workpieces and the gage head (the "elements" of the measurement system). The uncompensated gage is used to make measurements for these tests with compensation turned off, so that true changes in dimension can be noted. Coefficients are then calculated and compensation is then turned on, to verify the results of the thermal correction applied.

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