MECH 373 Instrumentation and Measurement Lecture ??? (Course Website: Access from your “My Concordia” portal) Contents of today’s lecture: • Dynamic measurements – Zero order, first order, second order systems – Time constant, response time, rise time, settling time – Frequency response

Experimental Design Experimental design is the first step in any measurement experiment. It involves developing a measurement test plan following three steps: Parameter Design Plan – test objective and identification of process variables and parameters and a means for their control. You should ask: What question am I trying to answer ? What variables to be measured ? What variables will affect my results ? System and Tolerance Design Plan – selection of measurement technique, equipment and test procedure based on some preconceived tolerance limits for error. You should ask: How will I do the measurement and how good do the results have to be ?

Experimental Design (cont’d) 3. Data Reduction Design Plan – Plan ahead on how to analyze, present, and use the anticipated data. You should ask: How will I interpret the resulting data ? How will I use the data to answer my question ? Step 1 needs the following important concepts: Variables Parameters Noise and Interference Random Tests Replication and Repetition Concomitant Methods

Variables One variable in the measurement system is obviously the targeted measured variable, but there might be other variables that affect the outcome All known process variables should be listed and evaluated for any possible cause and effect relationships A variable that can be changed independently of other variables is known as an independent variable A variable that is affected by changes in one or more other variables is known as a dependent variable Variables that cannot be controlled during measurements but that affect the value of the measured variables are called extraneous variables. If the values of a variable can be enumerated it is called discrete. Otherwise it is called continuous

Variables Example: For the following calibration system. Identify the independent, dependent, and possible extraneous variables. Answer: Independent variables: piston displacement x, temperature T Dependent variables: gas pressure p Extraneous variables: noise effects due to room temperature; line voltage variations, connecting wires

Parameters A parameter is a function relationship between variables A parameter that has an effect on the behavior of the measured variable is called a control parameter A control parameter is completely controlled if it can be set and held at a constant value during a set of measurements Example (Pendulum): period Ratio of l and g is a completely controlled parameter because l is fixed and g is known

Noise and Interference The way of extraneous variables affects measured data can be classified into 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 Interference produces undesirable deterministic trends on the measured value because of extraneous variables Example:

Random Tests It is important to minimize the effects of extraneous variables in a measurement using random tests A random test is defined by a measurement matrix that sets a random order in the value of the independent variable applied to measure the dependent variable Example: Extraneous Variable Pressure Transducer + Voltmeter Independent Varables Dependent Variable Apply Random Sequence (holding temperature constant)

Random Tests (cont’d) Assuming that we can hold the temperature fixed, applying a random sequence of volume values rather than a sequential sequence will allow us to average out the effects of extraneous variables We will see later that when the measurement system is subject to hysteresis, applying an increasing sequence of values for the independent variable produces a different result as compared to the case of applying the same set of values in a decreasing order A random sequence enables us to deal with this effect by providing a unique value of the independent variable for each value of the dependent variable in the random sequence After applying several random sequencies the results are averaged out to find a best-fit curve

Random Tests (cont’d) We have seen that random tests are effective for the local control of extraneous variables that change in a continuous manner Discrete extraneous variables can also be dealt with by performing a random test The use of different instruments and different test operators are examples of discrete extraneous variables that can affect the outcome of a measurement These effects are usually reduced by randomizing a test matrix by using random blocks A block consists of a data set of the measured variable in which the control variable is varied but the extraneous variable is fixed The extraneous variable is then varied between blocks

Example: Randomized Matrix The manufacture of a particular composite material requires mixing a percentage by weight of binder with resin to produce a gel. The gel is used in a lay-up procedure to impregnate the fiber. The strength will depend on both the percent binder in the gel and the test operator performing the lay-up. Formulate a test matrix to find the percent binder influence on strength Solution: Pick three different bider-gel ratios A, B, C and three typical operators to produce N separate composite test samples for each of the 3 ratios Create the following test pattern:

Replication and Repetition In general the estimated value of a variable improves with the number of measurements. The mean over measurements is taken as the estimated value Repeated measurements made during any single test run or on a single batch are called repetitions. It allows for quantifying the variation in a measured variable as it occurs during any one test or batch while the operating conditions are held under nominal control An independent duplication of a set of measurements using similar operating conditions is referred to as a replication. It allows for quantifying the variation in a measured variable as it occurs between different tests, each having the same nominal values of operating conditions

Concomitant Methods A good strategy is to incorporate the use of concomitant methods in a measurement plan. The goal is to obtain two or more estimates for the result, each based on a different method, which can be compared as a check for agreement Example: Establish the volume of a cylindrical rod of known material. Method 1: Measure the diameter and length Method 2: Measure the weight and compute volume based on specific weight of material