Theory and Design for Mechanical Measurements Prof. Bumkyoo Choi Depart. of Mechanical Engineering

Chapter 1. Basic Concepts 1.1 Introduction The objective in any measurement is to establish the value or the tendency of some variable 1.2 General Measurement System A measurement is an act of assigning a specific value to a physical variable

Chapter 1. Basic Concepts 1.2 General Measurement System A measurement system is a tool for the quantification oh the physical variable  Sensor - transducer stage  Signal – conditioning stage  Output stage  Feedback – control stage ※ The relationship between the input information and system output is established by calibration

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  다음의 3 단계로 진행  Parameter Design Plan 변수와 파라미터의 정의, 그리고 그들을 제어하기 위한 수단  System and Tolerance Design Plan 계측기술, 기기, 오차의 공차 한계를 고려한 테스트 절차의 선택  Data Reduction Design Plan A methodology to analyze, present and use the anticipated data

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Variables Independent variable : can be changed independently of other variables Dependent variable : affected by changes in other variables A variable is controlled if it can be held at a constant value during a measurement

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Variables Discrete variables : ( ) Continuous variables : a pointer 1 through 6 Extraneous variables : cannot be controlled during measurement but affect the value of the variable measured (such as noise and drift)

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Parameters A parameter is defined through a functional relationship between variables A control parameter has an effect on the behavior of the measured variable A control parameter is completely controlled if it can be set and held at a constant value during a set of measurements

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Noise and Interference Noise is a random variation of the value of the measured signal as a consequence of the variation of the extraneous variables A completely controlled variable contains no noise Interference produces undesirable deterministic trends on the measured value because of extraneous variables

Chapter 1. Basic Concepts 1.3 Experimental Test Plan

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Random Tests To minimize the influence of Z j on tests, a random test is taken. A random test is defined by a measurement plan that sets a random order in the value of the indep. variable applied. 랜덤테스트란 적용되는 독립 변수값의 순서를 무작위로 함으로써 독립변수 의 값을 크기 순으로 순차적으로 적용할 때 비교적 나타날 수 있는 느린 외 부변수의 변화에 의한 간섭효과는 없어질 것이다. y = f (X a, X b, …; Z j ) Where X a, X b, …: indep. Variables Z j (j=1, 2, …) : extraneous variables

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Replication and Repetition Repetition : repeated measurements during a single test or on a single batch Replication : an independent duplication of a set of measurements using similar operating conditions

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Replication and Repetition ※ Repetition will not permit an assessment of how exact the operating conditions can be set ※ Replication provides a means to randomize the interference effects of the measurement 일련의 조건들을 장치가 얼마나 잘 재현할 수 있는지 평가

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Replication and Repetition 온도조절기 : 반복측정은 셋팅된 온도를 얼마나 잘 유지 ( 제어 ) 하는지 평가 중복측정은 셋팅된 온도를 잘 재현하는가 ? * 반복 : 평균치와 변이 (variation) 를 알게 해주고 * 중복 : 셋팅을 다른 값으로 한 후 얼마 시간이 지난 후 다시 처음의 셋팅으로 한 후 다시 반복 (another repetition) : The two sets of test data are replications of each other

Chapter 1. Basic Concepts 1.3 Experimental Test Plan  Concomitant Methods ( 동반하는, 부수하는 ) 2 개 이상의 측정에서 타당성 검토 예 ) 실린더 원통의 부피를 측정할 때 - 반지름과 높이를 측정 - 무게 측정하여 비중으로 나눔

Chapter 1. Basic Concepts 1.4 Calibration Apply a known value (standard) of input to a measurement system for the purpose of observing the system output 시스템 출력을 조사할 목적으로 알고 있는 값을 입력시켜 보는 행위

Chapter 1. Basic Concepts 1.4 Calibration  Static Calibration The values of the variables remain constant during a measurement  Dynamic Calibration When time-dependent variables are to be measured, … Involves either a sinusoidal signal or a step changes as the known input signal

Chapter 1. Basic Concepts 1.4 Calibration  Static Sensitivity (Gain) A measure relating the change in the indicated output associated with a given change in a static input.

Chapter 1. Basic Concepts 1.4 Calibration  Range Input span r i =x max – x min output span r 0 =y max – y min : full-scale-operating range (FSO) (FSO : full-scale-operating range)

Chapter 1. Basic Concepts 1.4 Calibration  Accuracy (A) Ability to indicate a true value exactly Absolute error E = true value – indicated value

Chapter 1. Basic Concepts 1.4 Calibration  Precision and Bias Errors Precision error is a measure of the random variation to be expected during repeatability trials Bias error is the difference between the average and true values

Chapter 1. Basic Concepts 1.4 Calibration

Chapter 1. Basic Concepts 1.4 Calibration  Precision and Bias Errors

Chapter 1. Basic Concepts 1.4 Calibration  Sequence Calibration Applies a sequential variation in the input value over the desired input range 요구되는 입력범위에 걸쳐서 입력 값을 순차적으로 증가시키 거나 감소시키면서 수행

Chapter 1. Basic Concepts 1.4 Calibration  Hysteresis Sequece calibration 이 hysterisis error 를 인식하고 정량화 하는데 좋은 도구 Hysteresis error refers to differences between an upscale sequence calibration and a downscale sequence calibration

Chapter 1. Basic Concepts 1.4 Calibration  Hysteresis

Chapter 1. Basic Concepts 1.4 Calibration  Random Calibration ( 임의 보정 ) Applies a randomly selected sequence of values of a known input over the intended calibration range 임의 보정은 간섭의 영향을 최소화시킨다. 또, 다음의 오차를 정량화시킨다.

Chapter 1. Basic Concepts 1.4 Calibration  Linearity Error

Chapter 1. Basic Concepts 1.4 Calibration  Sensitivity and Zero Errors The sensitivity error (e k ) : a measure of the precision error in the estimate of the slope of the calibration curve

Chapter 1. Basic Concepts 1.4 Calibration  Sensitivity and Zero Errors ※ The sensitivity error reflects calibration results at a constant reference ambient temperature The thermal sensitivity error was found by calibration at different temps

Chapter 1. Basic Concepts 1.4 Calibration  Zero error (e z ) Zero shift (null) error The shift of the zero intercept of the calibration curve : e z

Chapter 1. Basic Concepts 1.4 Calibration  Instrument Repeatability The ability to indicate the same value upon repeated but independent application of the same input. (within a given lab) Reproducibility : performed in differnent labs Instrument Precision : refer to the results of separate repeatability tests Overall Instrument Error : e I = [ e e … e M 2 ] 1/2

Chapter 1. Basic Concepts 1.5 Standards  Instrument Repeatability When a measurement system is calibrated, it is compared with some standard whose value is presumably known. Mass, Time, Length, Temperature etc.

Chapter 1. Basic Concepts 1.5 Standards  Hierarchy of standards 2 차 표준 (secondary standards) 은 기본표준과 상당히 근접 하나 보정의 목적상 훨씬 더 쉽게 사용되어 짐. Error ( ℃ ) Primary standardFixed thermodynamic pts.± 0 Interlaboratory transfer standard Platinum resistance thermometer ± Local standardPlatinum resistance thermometer ± 0.01 Working instrumentGlass bulb thermometer± 0.1

Chapter 1. Basic Concepts 1.5 Standards  Test standards 잘 정비된 실험절차, 기술적 용어, 시험시편과 장치를 구성하 는 방법 또는 데이터 변환을 위한 방법들 목적은 어떠한 타입의 측정을 수행할 때나 보고할 때 실험시설 사이의 일관성을 제공하기 위함.

Chapter 1. Basic Concepts  Measurement Overview  Objective : Identify the variables to be measured  Plan Develop a strategy for variation of the indep. variables & randomization of the extraneous variables Can the acquired information meet the objective? Use concomitant methods to check results for bias

Chapter 1. Basic Concepts  Measurement Overview  Methodology Assessment 여러가지 방법을 다 동원하여 가장 적당한 것 선택  Uncertainty Analysis Decide the min. level of accuracy that can be tolerated in the final data results and still meet the objective  Cost

Chapter 1. Basic Concepts  Measurement Overview  Calibration 계측에서의 오차감소를 위함. 시간과 비용  Data Acquisition ( 데이터 획득 )  Data Reduction ( 데이터 변환 )

Chapter 1. Basic Concepts  Several important statements  A sufficient no. of variables should be measured  A change in one parameter does not affect the values of the other parameters  The measured variable is the only depend. process variable during each measurement other variables should be controlled

Chapter 1. Basic Concepts  Several important statements  The sensor should be sensitive to the variable to be measured but not sensitive to other variables  The signal path of the measurement system should be designed to minimize the effects of extraneous variables  The test plan should randomize the effects of extraneous variables