Error in MeasurementThe purpose of taking measurement is to produce information so that appropriate actions can be taken. The information is incomplete if the measurement is not done with an acceptable degree of accuracy. It must be stressed that not only the dimension needs to be measured but also its accuracy of determination.

Example:For a gauge block;Nominal Size = 30mmMeasurement Error = -0.0002mmAccuracy of determination = +/- 0.0004mm

Action;If the gauge block is required to determine the datum of a vernierheight gauge which can be read to 0.02mm, the error on the gauge block is small and can be ignored.

If used to prepare a comparator which has reading division of 0.001mm, the measurement error becomes significant and the accuracy of the gauge block must be taken into account in determining the accuracy of determination of the comparator.

Error in Measurement (Cont’)Accuracy is the quality of conformity. Erros in measurement is the difference between indicated value and true value of a measured quantity.

Important to know all sources of error in a measuring system. Classification and analysis of causes of errors are helpful in attaining necessary knowledge of achieved accuracy.

Error can be categorised into two groups;

A. Systematic Error

Error in several measurements of the same part which remains constant or changes in a predictable way.

Error which can be eliminated, mostly, through calibration, consideration of temperature, expansion, etc.

Error in Measurement (Cont’)B. Random Error

Error in several measurements of the same part which changes in an unpredictable way. Erros which cannot be avoided (uses statistic to treat, take a lot of readings and take average).

Errors that can be avoided Errors that cannot be avoidedAlignment ErrorSurrounding ErrorElastic Deformation Error

Scale ErrorReading ErrorMeasuring Error

Error in Measurement (Cont’)Alignment Error

(1) Cosine/trigonometric Error

Happens if measuring instrument is not aligned with the workpiece.

(2) Parralax Error

Happens when direction of sight is not in line with the scale onmeasuring instrument.

Surrounding Error

(1) Temperature (workpiece & surrounding)International measuring temperature standard = 20oC (68oF), surrounding temperature must be aintained at the stated level.Workpiece temperature must be ensured to be at the same level (minimum touching of workpiece, if touched, allow time to stabilise)

For high accuracy measurement, recommended step; stabilization time = 20mins for every 25mm gauge length. Position workpiece on a good heat conductor, eg. Cast iron.

Error in Measurement (Cont’)Surrounding Error (Cont’)

Temperature effect should be considered in two different situations.1.1 Direct MeasurementExample: Block gauge measured directly with interferometer.Error cause by non-standard temperature is directly proportional with temperature difference.

Since coefficient of expansion values are lo, error is small as long as both materials are at the same temperature (in comparator measurement, it is more important to measure at the same temperature than to measure at as near as possible to the standard temperature).

Error = l α (t – ts) Where, l = nominal lengthα = coefficient of expansion

(t-ts) = deviation from standard temperature

1.2 Indirect MeasurementExample: two gauges with different coefficientsError cause by non-standard temperature.

Error = l (α1 – α2)(t – ts)

Error in Measurement (Cont’)Surrounding Error (Cont’)2. Other Ambient Conditions.

Other ambient conditions can also affect measurement result.

All elastic bodies experience elastic deformation under loading.Deformation magnitude depends on; (a) mahniture of load, (b) area of contact, (c) mechanical properties.

Relative humidity, atmospheric pressure, CO2 content in atmosphere.

Example: if gauge block is measured using interferometry, parameters that influence the reflective index of the atmosphereshould be noted and corrections made:

Elastic Deformation Error1. Measuring Load

For most instruments in fine measuring, the measurement pressurecan be said constant, so the main problem is in differing type of contact while calibrating and while measuring.

Error in Measurement (Cont’)Elsatic Deformation Error (Cont’)2. Body deflecting under its own weight

Sir G.B. Airy showed that position of support can produce minimum error for two different situations;

2.1 Gradient at both ends = ZEROSurfaces at both ends are parallel(eg – for line standards and end bars) Known as Airy Points.

2.2 Deflection at ends = deflection in middleDeflection is minimum, so change in overall length is minimum (eg: for straight edge). Known as Bessel points.

Error in Measurement (Cont’)Elsatic Deformation Error (Cont’)3. Abbe’s PrincipleThe axis or line measurement of the measured part should coincide with the measuring scale of the axis of measurement of the measuring instrument.

Scale ErrorIf scales on measuring instrument have errors, the reading will contain error. Method of overcoming; calibrating the whole length of scale using a known standard.In comparator measurement, the effect of scale error can be minimized by; (a) using as short a scale as is possible, (b) selecting master setting with size as close as possible to the gauge size measured.

Error in Measurement (Cont’)Reading ErrorHow accurate can a scale be read depends on; (a) thickness of scale making, (b) interval of scale marking/division, (c) thickness of the pointer/datum.As a guide; (a) the reading of a pointer directly on a scale can be taken as having an accuracy of +/- 10% of the scale division, (b) estimation of accuracy of reading when the pointer is situated between two markings is +/- 20% of the scale division

Note:

If measurement is done using a comparator, this error happens twice, first when setting the measuring instrument on the master gauge,second when taking measurement on workpiece.

Error in Measurement (Cont’)Measuring ErrorScale error and reading error are commulativeExample: consider measuring error on a plug gauge, nominal diameter = 25mm. Assume measurement to be taken using a comparator, whichis set on a gauge block (nominal length = 25mm and known to have an error = -0.0001mm, and accuracy of determination = +/- 0.0002mm)

Error in Measurement (Cont’)Measuring Error (Cont’)

Compound Error

Error in Measurement (Cont’)Compound Error (Cont’)

Error in Measurement (Cont’)5 elements of a measuring system that affect accuracy of evaluation1. Factors affecting the standard

Examples: Traceability, geometric compatibility, coefficient of thermal expansion, calibration interval, stability, elastic properties, position of support in use (Airy points).

2. Factors affecting the workpieceExamples: geometric truth (hidden geometry), related characteristics (eg surface finish, waviness, scratch depth), elastic properties, cleanliness, surface defects, thermal equalisation, mass affecting elastic deformation, truth of supporting features, adequate datums on workpiece.

3. Factors affecting the personExamples: training, skill, sense of precision appreciation, competent attitudes towards personal accuracy achievements, planning measurements techniques form minimum cost, consistent with precision requirements, appreciation of scope of accuracy evaluation, ability to select appropriate standards and instruments with required geometrical and precision capabilities, sensible appreciation of measurement costs.

Error in Measurement (Cont’)5 elements of a measuring system that affect accuracy of evaluation4. Factors affecting the instrument

Examples: adequate amplification for accuracy objective amplification checked under condition of use, effects of friction, backlash, hysteresis or zero drift, electric, optical or pneumatic input to amplifying system, contact geometry correct for both workpiece and standard, contact pressure control, contacts in correct geometrical relationship and inspected for wear or chipping, slides, ways or moving elements not adversely affected by wear or damage, deformation effect in instrument when heavy workpiece is measured, auxiliary elements (eg wires, rolls, angles, plates) calibrated and checked, magnification of errors by contact geometry, repeatability and readability adequate for accuracy objective.

5. Factors affecting the environmentExamples: standard temperature, temperature equalization betweenstandard, workpiece and instrument, thermal expansion due to lights, heating components, sunlight and people, impinging drafts of air, effects of cycles in temperature control, thermal effect from manual handling, clean surrounding and minimum vibration, atmospheric refraction effects in optical measuring, thermal gradient (either vertical or lateral) in the measuring area.