? Mechanical measurements are a quantitative comparison between a measurand and a predefined standard. ? A measurand is a particular physical phenomenon. e.g. temperature, length, time, etc. ? Standards:Usually prescribed by an organization. e.g. NIST, ISO, ANSI. Mechanical Measurements Defined Mechanical Measurements Significance ? Provide understanding of physical world. ? Test of any new theory or design. ? Basic element of control processes. Direct comparison, e.g. a ruler. Use of a calibrated system, e.g. multimeter. Next lab will use Data Acquisition Systems (DAQ) Mechanical Measurements Acquisition Mechanical Quantities Two types: Analog: Signal varies continuously with time. Digital: Stepwise change in signal. Analog vs. Digital Signals Gray line is analog Red line is digital 1. Transducer Stage 2. Signal Conditioning 3. Reporting Stage Idealized Measurement System Transducer Stage ?A device actuated by power from one system and supplying power in the same or any other form to a second system.? * Senses the measurand while remaining almost insensitive to other inputs. Unwanted sensitivity leads to errors: a rapidly varying error is noise, a slowly varying error is drift. *Merriam Webster Unabridged Dictionary Idealized Measurement System Signal Conditioning Stage Modifies the sensor stage so it is acceptable to the third stage. Also may perform filtering, integration, differentiation, or amplification. Idealized Measurement System Reporting Stage Presents information to human or controller. e.g. dial gauge Records to medium, e.g. text file. Idealized Measurement System This idealized measurement system is called a sensor*. * Thanks to Dr. David Thompson Idealized Measurement System Mechanical Quantities Time-dependent Characteristics Static e.g. Diameter of a piston. Dynamic Steady-state and periodic. e.g. Radio carrier wave. Mechanical Measurement Uncertainties Two Types Bias: Constant error. e.g. wad of gum on a scale. Cannot be uncovered by statistical approaches. Precision: Randomly occurring. e.g. Fluctuations in 60 HZ power line frequency. Can be dealt with using statistics. Exponential Decay Some systems decay at a rate proportional to the amount left. e.g. Convection cooling, radioactive emissions. Exponential Decay Decay proportional to amount left can be written as: Where N = amount of substance, t = time, lambda = constant. dN dt =??N Rearranging: dN N =??dt Integrating both sides: Take exponential of both sides: ln N 0 =??t N= 0 e ??t Exponential Decay Example 0 30.0 60.0 90.0 120.0 150.0 180.0 210.0 240.0 0 5 10 15 20 25 30 35 40 45 Temperature vs Time T emperatur e (deg C) Time (sec) T=T 0 e -t/? Experimental Data Colin Selleck Lecture_Measurement.key