ISO/TR 16015:2003 幾何学的製品仕様（GPS）—熱の影響による長さ測定の系統的誤差と測定の不確かさへの寄与 | ページ 6

3.1.1

熱膨張係数

a

温度変化に対する長さの分数変化の比率

注記 2:ここで、温度範囲は ISO 1 に従って 20°C を基準にしています。

注記 3記号αには，被加工物の熱膨張係数 (すなわちα_w ) 及び作業標準 (すなわちα_s ) を示す下付き文字が追加される。

注記 4:熱膨張係数は、複合作業標準や異なる材料のアセンブリであるワークピースなどの非均質な物体の挙動を表すことができます。このドキュメントでは、均一な作業標準と複合作業標準またはワークピースの膨張係数を区別していません。

3.1.2

測定された熱膨張係数

αm_m

特定の個々の物体の実験的に決定された熱膨張係数

注記 1:この係数は、認定された測定研究所の校正サービスまたは適切に実施された実験から取得できます。

注記 2記号α_mには，ワークピースの測定された熱膨張係数 (すなわちα_mw ) と作業標準 (すなわちα_ms ) を示す下付き文字が追加される。

3.1.3

公称熱膨張係数

α_n

20 °C からTまでの温度範囲での熱膨張係数の近似値

注記1記号α_nには，被加工物の公称熱膨張係数（すなわちα_nw ）及び作業標準（すなわちα_ns ）を示す下付き文字が追加される。 α_nwおよびα_nsの推定値は、同様のオブジェクトでの実験または公開されたデータから取得できます。

3.1.4

熱膨張の不確実係数

u ( α )

熱膨張係数に合理的に起因する可能性のある値の分散を特徴付けるパラメータ

注記 1記号u ( α)には，ワークピースの熱膨張係数の不確かさ [つまりu ( α_w) ] と作業標準 [つまりu ( α_s) ] を示す下付き文字が追加される。このような値は、 α自体の値と同様に、想定される確率分布に基づく推定値であるか、 αを測定するために実行された実験の結果である必要があります。

注記 2α_nの不確実性は通常α_mの不確実性よりもはるかに大きい。

3.2.1

thermal expansion

Δ_E

change in length of a body, such as a workpiece or working standard, in response to a temperature change

3.2.2

thermal expansion based on nominal or measured coefficients of thermal expansion

Δ_neorΔ_mE

estimate of the thermal expansion of an object from 20 °C to its average temperature at the time of measurement

Note 2 to entry: To the symbol Δ_nEorΔ_mE are added subscripts to denote the thermal expansion based on nominal/measured coefficients of thermal expansion for the workpiece (i.e. Δ_nEworΔ_mEw) and the working standard (i.e. Δ_nEsorΔ_mEs).

3.2.3

corrected length

L_c

measured length adjusted for the computed thermal expansion based on either the measured or nominal thermal expansion

3.2.4

differential thermal expansion

difference between the changes in the lengths of the workpiece and the working standard in response to temperature changes from 20 °C to their temperatures at the times of the measurements

Note 1 to entry: If not corrected, differential thermal expansion can cause a systematic error in a measurement result.

3.2.5

differential thermal expansion based on nominal or measured coefficients of thermal expansion

Δ_nDEorΔ_mDE

difference between the thermal expansion of the workpiece and the working standard(s)

3.2.6

uncertainty of thermal expansion due to uncertainty of α

u_E( L )

uncertainty in the thermal expansion arising from uncertainty in the coefficient of thermal expansion

Note 2 to entry: An additional subscript is added to each symbol to specify values for a workpiece (“… _w”) or working standard (“… _s”).

3.2.7

uncertainty of differential thermal expansion due to uncertainties of α_w and α_s

u_de( L )

combined standard uncertainty of the uncertainties of thermal expansion of the workpiece and working standard due to uncertainties in their coefficients of expansion

Note 2 to entry: The estimates of the coefficients of thermal expansion of the workpiece and working standard can be assumed to be uncorrelated when they are obtained from different sources.

Note 3 to entry: When nominal values are used to estimate the coefficients of thermal expansion, this quantity has historically been called the uncertainty of nominal differential expansion (UNDE).

3.3.1

dimensional thermal response

amplitude of length variation of an object as a thermal response to the magnitude and time-dependency of a temperature fluctuation

3.3.2

thermal response time

soak-out time

time interval between the instant when the environmental temperature is subjected to a specified abrupt change and the instant when the temperature of an object reaches and remains within specified limits around its final steady value

Note 1 to entry: When a change in environmental temperature is experienced, such as occurs when an object is transported from one room to another, there will be some period of time during which the object equilibrates, within specified limits, to its new environmental temperature.

3.3.3

differential thermal response

length difference between any two objects measured simultaneously in an environment with varying temperature and caused solely by the variation in temperature of the objects with time

3.3.4

dimensional variation due to environmental temperature variation

E_ETV

estimate of the possible length measurement variation induced solely by deviation of the environment from average conditions over a time interval equivalent to the adjustment cycle time

Note 1 to entry: The dimensional variation due to environmental temperature variation, E_ETV, is usually determined from the results of two drift test(s) (3.4.5) , one of the working standard and comparator and the other of the workpiece and comparator. However, drift tests performed at a single position cannot reveal all thermally-induced errors, particularly where spatial temperature gradients exist. It is the responsibility of the instrument user to ensure that such effects are detected and the appropriate uncertainties added.

3.3.5

uncertainties of workpiece and working standard temperatures

u ( θ_w) and u (θ_s)

uncertainty of time-averaged temperature of the workpiece and working standard

Note 1 to entry: These uncertainties arise from the calibration of the thermometer, thermometer mounting procedures, and instrumental variations.

Note 2 to entry: The time over which the temperature is averaged is usually the period of a measurement cycle.

3.3.6

uncertainty of length due to temperature measurement

u_TM( L )

uncertainty in a measured length due to uncertainty in the measurement of the temperature at which the length measurement was made

Note 2 to entry: where u (θ_w) and u (θ_s ) are the uncertainties of the workpiece and the working standard temperatures (3.3.5) in measurement. The temperature measurements of the workpiece and the working standard are assumed to be uncorrelated, an assumption which is valid if the two temperatures are measured using two different thermometers, each traceable to the international temperature scale (ITS-90) through different calibration processes.

Note 3 to entry: In cases where the standard is a laser interferometer, the coefficient relating wavelength to the temperature of the propagation medium is used for the coefficient of expansion of the working standard. In the case where the medium is “standard” air, the value for α_ns is 0,93 × 10 ^{− 6}/°C.

3.3.7

uncertainty of length due to environmental temperature variation

u_ETV( L )

uncertainty in the estimate of the possible length measurement variation induced solely by deviation of the environmental temperature from average conditions over a time interval equivalent to the adjustment cycle time

Note 1 to entry: The dimensional uncertainty of length due to environmental temperature variation, u_ETV( L ), arises from the range of the drift of the instrument/working standard/workpiece system over times equivalent to the adjustment cycle time. It is established from measurements or estimates of dimensional variation due to environmental temperature variation, E_ETV.

Note 2 to entry: In computing u_ETV( L ), note that the maximum error is the range observed in the drift test, depending on whether the setting was done at the lowest temperature and the measuring at the highest temperature, or vice versa. The probability density function may be “U-shaped” as, for example, for a sinusoidally varying temperature. However, the probability that the setting and measuring are exactly displaced in time by the period of the sinusoidally varying temperature is low. The setting-measuring process involves taking pairs of points from the U-shaped probability distribution function and then differencing them. The consequence of this procedure is that the measurement process has a different probability distribution function from “U-shaped”. The default is to use a uniform distribution [see 5.4 and Equation (13)].

3.4.1

comparator

measuring device used to perform a comparison of a workpiece and a working standard

Note 1 to entry: A comparator can be a simple short-range indicating device such as a gauge block comparator or a complex comparator such as a coordinate measuring machine.

3.4.2

working standard

standard that is used routinely to calibrate or check material measures, measuring instruments or reference materials

[SOURCE: VIM:1993, definition 6.7]

Note 1 to entry: A working standard is usually calibrated against a reference standard (see VIM:1993, definition 6.6).

Note 2 to entry: A working standard used routinely to ensure that measurements are being carried out correctly is called a check standard. While it is recognized that the use of working standard versus check standard has not yet been perfectly resolved, at the time of publication this terminology remained the only practical solution possible. The subject is to be re-examined at the next revision of this Technical Report.

Note 3 to entry: For procedures in accordance with this Technical Report, such working standards are dimensional and can be in the form of the wavelength of light, a gauge block, a line standard, a lead screw, etc.

3.4.3

adjustment

operation of bringing a measuring instrument into a state of performance suitable for its use

[SOURCE: VIM:1993, definition 4.30]

Note 1 to entry: Adjustment may be automatic, semi-automatic or manual.

3.4.4

adjustment cycle time

period between successive adjustments of a comparator

3.4.5

drift test

experiment conducted to determine the slow change in the metrological characteristic of a measuring instrument

3.4.6

tolerance

TOL

difference between the upper and lower tolerance limits

[SOURCE: ISO 3534-2:1993, definition 1.4.4]

Note 1 to entry: For the purpose of this Technical Report, the abbreviation TOL is used instead of the standard “T” (for target value), in order to avoid confusion with other symbols or abbreviations using thesameletter .

3.4.7

target uncertainty

U_T

uncertainty determined as the optimum for the measuring task

[SOURCE: ISO/TS 14253-2:1999, definition 3.10]

3.4.8

systematic error

mean that would result from an infinite number of measurements of the same measurand carried out under repeatability conditions minus a true value of the measurand

Note 1 to entry: Systematic error is equal to error minus random error.

Note 2 to entry: Like true value, systematic error and its causes cannot be completely known.

Note 3 to entry: For a measuring instrument, see bias (VIM:1993, definition 5.25).

[SOURCE: VIM:1993, definition 3.14]

3.5.1

standard uncertainty component due to thermal effects

u_cT( L )

standard uncertainty component for a length measurement made at a temperature other than 20 °C

3.5.2

thermal error

te

estimate of the maximum error that might reasonably be expected to occur if a length measurement is not corrected for a nominal differential expansion

Note 2 to entry: If length measurements are made at other than 20 °C, and in the special case where corrections are not made for the nominal differential thermal expansion between working standard and workpiece, then, in order to be in accordance with this Technical Report, the thermal error has to be evaluated and reported.

3.5.3

thermal error index

TEI

fraction of the tolerance that is consumed by the thermal error

Note 2 to entry: In the case where a target uncertainty, U_T, exists, the thermal error index is computed using Equation (10), with TOL replaced by 2 U_T.

Note 3 to entry: The TEI is a component of uncertainty management; large values of the TEI may require that a measurement result has to be corrected for the differential thermal expansion in order to prove workpiece conformance.