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Industrial Metrology Instructor and references • Sugeng S Instructor : S d ST.,MS-Eng Supriadi, ST S • Office : Manufacturing Laboratory, Dept. of Mechanical Eng. UI • ext Phone : 7270032 ext. 222 • E-mail : priadi_007@yahoo.com • References : Groover, Mikell P., “Fundamentals of Modern Manufacturing”, Wiley 2nd edition, 1999. Kalpakjian, “Manufacturing Engineering and Technology, McGraw Hill 4th edition, 2001. Jain, RK, “Engineering Metrology”, Khanna Publishers, 1979. Dotson, Connie, “Fundamental of Dimensional Metrology”, 4th ed., Thomson, 2003. Th 2003 Course E l ti C Evaluation Course evaluation : Group Work (Assignment, Lab section) 20% Mid Test 20% Quiz (2 times x 5 %) 10% Final Test 50% Grade Scale G d S l : A/A- 80 - 100 B+/B/B- 70 - 79 C+/C/C- 55 - 69 D+/D/D- 30 - 54 THE PURPOSE OF THIS COURSE 1. y p gy To study basic concept of metrology 2. To understand the application of metrology on manufacturing process Topics covered in this course Week Topics gy Introduction to Metrology Dynamic characteristics of measurement Geometric Specifications G t i S ifi ti Length Metrology Angle Metrology Form and Surface Metrology Screw Thread & Gear Metrology CMM & Machine Tools Metrology Uncertainty analysis and Quality control Lab. Section Metrology : science of measurement of the Geometrical specification Dimension, Position Dimension Position, Form & Surface Geometrical Metrology G i l l Reasons for measuring ? : • To KNOW … : weight, length, area etc everyday life • To measure Quality of the measured object for inspection • To meet design specifications to improve quality the manufactured parts as feedback for f f db k f manufacturing process • etc Measuring : process by which numbers or symbols are assigned to attributes of entities to describe them according to clearly defined rules Components of Measurement Systems Measurement systems Gauges (measurement instruments) Successful Procedures Environment (methods, agreed (temperature, measurement ! units & standards) cleanliness, cleanliness vibration, etc) (sufficient correctness ( ffi i and accuracy for Workpiece Calibration/ particular need) (temperature, (temperature Traceability cleanliness, (units, date, time, fixturing, etc) etc) Operator (skill level) Components of Measurement Instruments (gauges In General, they can be devided into three parts : 1. 1 Stage I St D t t r Tr n d r rS n r t Detector-Transducer or Sensor stage (INPUT) 2. Stage II Intermediate stage : signal conditioning 3. Stage III g Terminating or Read-Out stage g g ( ) (OUTPUT) Stage II & III Output Input Estimation of real value ! Stage I Precision and Accuracy Precision : •The repeatability of a measuring processes •Or Relates to the quality of an operation by which a result is obtained A we close t each other ? Are l to h th Accuracy : •The agreement of the result of a measurement with The the true value of measured quantities q y , •Or Relates to the quality of a result, and is distinguished from precision, which relates to the quality of the operation by which the result is obtained Do we get the taget ? NO ERR ! In most measurements it is only Precision that is needed ! Precision and Accuracy (cont’d) Accuracy with precision Precision with blunder Accuracy with blunder No measurement can be absulutely correct there is always some ERROR ERROR : The difference between the mean of set of readings on some component and the true value (target). •Less is the ERROR, More Accurate is the instrument •TRUE VALUE is NEVER known UNCERTAINTY creeps in the g magnitude of ERROR must be ESTIMATED ! •Depends upon : Components of Measurement Systems (explained before) Accuracy Highly accurate instrument possesses both great sensitivity and consistency. Sensitivity the ratio of the change of inst. indication to the measured change of quantity being measured. Consistency readings are the same all the time. VS Sensitive and Consitent instrument need not necessarily be Accurate, because the standard from which its scale is calibrated may be wrong Errors will be constant at any given reading (possible to calibrate) Notes that !!! : g • An instrument can not be more accurate than its degree of sensitiveness ! • Degree of sensitivity not necessarily the same for all over its range g of readings ! • Highly sensitive instr. Is not necessarily consistent in its readings (cont d) Accuracy (cont’d) Greater accuracy == greater source of errors to be controlled ACCURATE measuring instrument should : 1. It should possess the requisite and constant accuracy 2. As far as possible, the errors should be capable of elimination by adjusment contained within the instrument itself 3. Every important source of inaccuracy should be known 4. When an error cant be eliminated, it should be made as small as possible and capable of measurement by the instrument itself Accuracy and Cost The Metrology : should provide the required accuracy capability at the most economical cost !!! Six factors influencing ACCURACY (as explained before) : 1. ( ) quality of the standards, etc Calibration (C) : methods, q y 2. Operator (O) : skill level, training, sense of precision and accuracy appreciation, attitude 3. 3 influences cleanliness, properties Workpiece (W) : ambient influences, cleanliness elastic properties, etc 4. Procedures (P) : ambient influences (thermal expansion), stability with time, standards, methods, etc 5. Instrument (I) : hysteresis, backlash, friction, deformation, etc 6. Environment (E) : temperature heat radiation from light, heating of p y g p p , , , components by sunlight or people, vibration, sounds, etc Accuracy and Cost (cont’d) Selection of measuring instruments involves proper analysis of cost-to- accuracy consideration COST rises Exponentially with ACCURACY Cost t Accuracy Accuracy should be 10% of Tolerance ! Manufacturing Processes, Accuracy and Measuring Instruments anufactured parts and state-of-the art of Tolerance Semilog Plot of Trends in Limiting Values of Tolerances in Normal, Precision and Ultraprecision Regimes with Examples of State-of-the Art p g p Errors Measurement error : The difference between the indicated and the actual values of the measurand Level of Accuracy of instruments Expressed •Expressed either as an absolute error OR on a relative scale •Contributed by one or more Components of Measurement systems •Must be examined in order to : ea g a d te p etat o s o e os get causes, meaning and interpretations of the errors obtain methods for reducing or circumventing the errors Four types of (Source of) ERRORS in measurement : 1. Systematic errors (controllable errors) not susceptible to statistical 1 analysis : calibration errors, error of technique, uncorrected loading errors, limits of resolutions, ambient conditions, misalignment of workpiece and instr. location errors, etc. repeated consistently. Random errors ( 2. R d id t l ) lack f i t i (accidental errors) l k of consistency : enviromental t l variations, certain types of human errors, etc. magnitude and sign can not be predicted. 3 g ( 3. Illegitimate errors should not exist : blunder or mistake (carelessness, , improper training, emotions, etc), computational errors, etc. 4. Static errors result from intrinsic imperfections or limitations in hardware and apparatus compared to ideal instruments. Errors (cont’d) Statistical parameters are used to assess Random Errors to achieve consistency (precision) of values and not their accuracy (approach to th ) truth value) !!! : x1 + x2 + x3 + ... + xn •Arithmatic mean x= n ( ) 2 Σ xi − x •Standard deviation (mean of the mean) σ= n • Error Distribution = Gaussian Distribution : most of the f h examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other. error Probability density Probability distribution of random errors Erros (cont’d) x2 1 P ( x1 < x < x 2 ) = 2 / 2σ 2 σ 2π ∫ x1 e− x dx X1 X2 Probability that X (error value) lies within the interval X1 dan X2 •Error Accumulation can be measured interm of root-mean-square y (LE) g ( ) Total static errors = linearity errors ( ) + reading errors (RE) + characteristic error (CE) + environmental errors (EF) ( LE1 + LE2 + ...) 2 = + RE 2 + CE 2 + EF12 + EF22 + ... Characteristic error deviation of the output of a measuring instr. from the predicted (nominal) performance specification Errors (cont’d) • Variance of Error Distribution 1 n 2 measure of error distribution σ = ∑ xi 2 n i =1 Large variance ! Small variance ! Bias, Repeatability and Reproducibility (R& What is Gauge (instrument) R&R ? It is a statistical approach of determining if a instrument (gauge or a measurement. gauging system) is suitable for the process under measurement Purpose : Measurement is an integral part of any manufacturing unit and is useful in predicting the quality of the manufacturing process . The technique is very useful in predicting the inherent variation in the process, if any, as too much in-process variations can cause serious problems. Type of Measurement Variation : 1. Bias 2. Repeatability 3. Reproducibility Bias, Repeatability and Reproducibility (R&R (cont d) (cont’d) Bias : th diff between the observed average of measurement and the difference b t th b d f t d the reference value. It is the systematic error that is an indication of a measuring instrument. instrument The reference value is determined by averaging several measurements using standard measuring equipment. Bias Reference value Observed average value Bias, Repeatability and Reproducibility (R&R) (cont d) (cont’d) Example : Consider the following ten measurements by an appraiser. The reference value determined by layout inspection equipment is 0.80 mm 0 75 X1 = 0.75 0 80 X6 = 0.80 X2 = 0.75 X7 = 0.75 X3 = 0.80 X8 = 0.75 X4 = 0.80 X9 = 0.75 X5 = 0.65 X10 = 0.70 10 The observed average is the sum of the measurements divided by 10. Bias = Observed Average – Reference Value Bias = 0.75 – 0.80 = - 0.05 Bias, Repeatability and Reproducibility (R&R) (cont d) (cont’d) Repeatability : The variation in measurements obtained with one measurement instrument when used several times by an appraiser while measuring the identical characteristic on the same part. y q p It is also commonly known as equipment variation. Gage A Gage B In the above figure, the repeatability of Gage A is more than that of Gage B as shown by their probability density functions. Bias, Repeatability and Reproducibility (R&R) (cont d) (cont’d) Reproducibility : The variation in the average of measurements made by different appraisers using the same instrument when measuring the identical characteristic on the same part. It is commonly known as appraiser variation. Operator B Operator C Operator A Bias, Repeatability and Reproducibility (R&R) (cont d) (cont’d) Repeatability + Reproducibility = Stability Stability : 1. The total variation in the measurements obtained with a h measurement system on the same master or parts when h measuring a single characteristic over an extended time period. 2. Sometimes referred to as drift. Stability Time 2 Time 1 Linearity • Maximum deviation of the output of the measuring system from a specified stright line applied to a plot of data points on curve of measured values vs. the measurand input values Reference Reference value value Smaller bias Larger bias value value Observed Average Observed Average value value ( g part g ) (Higher p of Range) (Lower part of Range) (L t fR ) Reference line : 1. Terminal line : drawn from origin to the data point at full scale output 2. End point line : drawn between the end points of the data plot 3. Best fit line : the mid-way line of two parallel lines enclosing all data poin 4. Least square line : sum of the square of deviations of data points from th line is minimized Part Variation The Part Variation is essentially a measure of the variation of the process. If a large number of parts made by a process are measured, 99%(5.15 s) of the limits. parts would be within the variation limits The Part Variation is always less than or equal to the total variation. In most industrial processes the part variation is large compared to the gage variation nd the mpti n th t th b r d t nd rd d i ti n i ppr im t l and so th assumption that the observed standard deviation is approximately equal to the total population standard deviation holds good. Methods to determine Repeatability and Reproducibi (R&R) There are three basic and widely used methods for determining the Instr. R&R Range method g Average and Range method Analysis of Variance method (ANOVA) Average and Range method The Average and Range method is a statistical method that provides an estimat of the following components. Part Variation Repeatability Reproducibility R&R Total Variation Thi method computes the total measurement system variability, which can be This m th d mp t th t t l m r m nt t m ri bilit hi h n b separated into components like repeatability, reproducibility and part variation. Average Range Method he Average and Range method q p parts, appraisers and quires multiple p pp als to quantify the repeatability and producibility. The following is a pical Data sheet used in industries. Average Range Method (cont’d) Assumes the following example : (Taken from Measurement System Analysis Reference Manual) No. of Appraisers = 2 No of Trials No. =3 No. of parts =5 Average Range Method (cont’d) Repeatability – Equipment Variation (EV) : EV = R * K 1 = 2.5 x 3.00 =757.5 Note: All calculations are based upon predicting 5.15σ (99% area under the normal curve) K1 = 5.15/d2 where d2 depends on the no. of trials (m) and the number of parts times the no. of pp i e (g). l e is obt ined from Table 1 appraisers (g) The value of d2 i obtained f om T ble 1. In this case m = 3 and g = 2 x 5 = 10. Looking up Table 1 we get d2 = 1.72. Therefore K1 = 5.15/1.72 = 3.00. Reproducibility – Appraiser Variation (AV) : AV = (X DIFF * K 2 ) 2 − ( EV 2 / nr ) = ( 0 . 6 * 3 . 65 ) 2 − ( 7 . 5 2 / 5 * 3 ) = 1 . 0461 Note: If a negative value is calculated under the square root sign, the value AV defaults to zero. n = No.of parts and r = No.of Trials K2 = 5.15/d2 where d2 depends on the no. of appraisers (m) and g is 1, since there is only one range calculation. In this case m = 2. Looking up Table 1 we get d2 = 1.41 Therefore K2 = 5.15/1.41 = 3.65. Average Range Method (cont’d) h i i hi limits(UCL d d h All the points are within li i (UCLR and LCLR) and so the measurement process is under control and is said to be consistent. Average Range Method (cont’d) Repeatability and Reproducibility (R&R) : R & R = EV 2 + AV 2 = 7.5 2 + 1.04612 = 7.57 Part Variation (PV) : PV = R p * K 3 = 6.15 * 2.08 = 12.79 Note: K3 = 5.15/d2 where d2 is dependent on the no.of parts (m) and g = 1, since there is only one range calculation. 1. 2.48. In this case m = 5 and g = 1 Looking up Table 1 we get d2 = 2 48 Therefore K3 = 5.15/2.48 = 2.08. Average Range Method (cont’d) There are three points that fall outside the limits and so the measurement process is not adequate to detect part-to-part variations. UCL X = X + A2 R LCL X = X − A2 R For constant A2 look up Table 2. Average Range of Method (cont’d) Total Variation (TV) : TV = ( R & R ) 2 + ( PV ) 2 = 7.57 2 + 12.79 2 = 14.86 Summary : Average Range Method (cont d) (cont’d) Average Range Method (cont d) (cont’d) Table 2. Control Chart constants