Aleksandr Gorbashev
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National Institute of Standards and Technology: Solution to Decrease Uncertainty in Measurement Tape Calibration. 
December 14, 2007 Acknowledgements:
TABLE OF CONTENTS 1.0 Introduction 4 1.1 Introduction to LSCMG and Measuring Tapes 4 1.2 Introduction to Research Problem 5 1.3 Sources of Error 5 1.4 Proposed Solution 5
2.1 NIST Organizational Structure 6 2.2 LSCMG Purpose 6 2.2.1 Tape Calibration Lab 6 2.3 Measurement System 8 2.3.1 Introduction to Measurement System Components 8 2.3.2 Measurement System – Component Functions 10 2.3.3 How the Measurement System Works 15 2.5 Calibration Procedure 16
3.1 Abbé Error 17 3.2 Operator Error 18
5.1 Experimental Comparison 22 5.1.1 Introduction 22 5.1.2 Experiment Setup Description 23 5.1.3 Simulation 1: Manual Leveling Procedure 24 5.1.4 Simulation 2: Pitch Correction with Wyler Fowler Level Procedure 25
6.1 Experimental Results 26 6.2 Concluding Discussion 27 6.3 Future Steps 28 Appendices 1.0 Introduction National Institute of Standards and Technology (NIST) functions to advance U.S. innovation and industrial competitiveness. As a federal agency of the U.S.A. it achieves such goals by advancing measurement science, standards, and technology in ways that enhance economic security and improve the quality of life. The Large Scale and Coordinate Metrology Group (LSCMG) under the Manufacturing Engineering Lab at NIST provides a service to improve such measurement science. 1.1 Introduction to LSCMG and Measuring Tapes LSCMG provides calibration services for metal measuring tapes that are used in industry such as oil gauging, surveying and telecommunications for distance measurement. Because such industries require accurate measurement, companies from these industries send in their master tapes to be calibrated. The companies then use the calibrated master tape as the basis for which the duplicates are made. The accuracy of calibration for companies is important to reduce cost. A measurement too short would cheat the customer while a measurement too long would promote money loss for the company. To meet client needs, the LSCMG would like to improve their equipment to perform a calibration within a 10 micrometer uncertainty as opposed to the current 250 micrometer uncertainty. Typically the types of tapes calibrated by LSCMG are chrome clad tapes and chain tapes (Figure 1.0).  
Figure 1.0 – Tape Types, Chrome Clad (Top right), Chain (Bottom right) 1.2 Introduction to Research Problem C  urrently, the LSCMG uses outdated equipment called the microscope carriage (Figure 1.1) to create tape calibrations. I was hired to redesign the microscope carriage to reduce the measurement uncertainty during calibration. My goal was to reduce the measurement uncertainty from 250 micrometers to 10 micrometers.
To reduce the uncertainty by a factor of 25 it was necessary to reconfigure the microscope c Figure 1.1 – Microscope Carriage arriage to decrease operator error and Abbé Error1. 1.3 Sources of Error When a tape is received, an operator lays out the tape on a 60 meter bench in the laboratory. The operator then rolls the microscope carriage along the bench and over the tape from graduation to graduation to calibrate the tape. Because the bench surface is not completely flat, an uncertainty in displacement measurement between graduations occurs as the microscope carriage “pitches” or tilts. Due to such tilt behavior, a linear positioning error or Abbé Error is created. In the current procedure, to decrease uncertainty due to Abbé Error the operator manually re-adjusts the tilt of the carriage to eliminate calibration error. Yet, such manual tilt adjustment technique creates another source for error, or operator error. The goal is to limit the Abbé and operator error as much as possible to decrease the measurement uncertainty. 1.4 Proposed Solution Originally it was desired by the LSCMG to reduce uncertainty due to Abbé error and operator error by incorporating an electromechanical self leveling system on the microscope carriage. Such system would automatically align the carriage during calibration to eliminate its tilt while eliminating operator error. During the research term a revolutionary idea was discovered. To eliminate the error due to tilt, I proposed an approach that would determine the tilt of the microscope carriage. By using the magnitude of tilt through mathematical calculations, the origin of the true measurement value can be found. This approach would reduce the Abbé Error while eliminating the need for manual operator adjustment. 2.0 Background Because I conducted research within the Large Scale Coordinate Metrology Group, it is important to provide background on the LSCMG and its mission. This section provides detail on the group facility, the tape calibration laboratory, laboratory components and the process of tape calibration. 2.1 NIST Organization Structure National Institute of Standards and Technology is divided into multiple engineering laboratories such as Materials Science Engineering Lab (MSEL), Electronics and Electrical Engineering Lab (EEEL) and Manufacturing Engineering Lab (MEL). Each lab is divided into divisions, as each division is also divided into groups of particular disciplines. The Large Scale Coordinate Metrology Group belongs to the precision engineering division, where Large Scale is considered to be a field of metrology in within the micrometer (1x10-6 meter) scale. 2.2 LSCMG Tape Calibration Lab This section introduces the LSCMG Facility. Specifically it covers the calibration laboratory and the measurement system used to create tape calibrations. 2.2.1 Tape Calibration Lab 
The tape calibration laboratory is a 82m x 4m x 3m concrete tunnel located approximately two meters underground (Figure 1.2). This underground arrangement creates good thermal and vibration isolation f
expand with temperature changes. Climate Control System The tunnel has a climate controlled environment created by an air distribution system, which originates in the ceiling in the form of vertical laminar3 flow and flows down along the sides of the room. The air is recalculated via an air return located 0.3 meters from the floor. This allows the tunnel to be kept at 20°4 Celsius ±0.1° at a single point and a ±0.25 °C maximum temperature difference over full length.  
The climate control system uses calibrated thermistors5 (Figure 1.4) throughout the tunnel length to measure both the ambient temperature and the tape bench surfaces. These temperatures are then read by the calibration system control c Figure 1.4 – Thermistors omputer to ensure that the readings are consistent within the acceptable temperature range. If the temperature is not consistent, the climate is adjusted accordingly by the computer. 2.3 Measurement System In the tape calibration lab the calibration measurements are performed using a laser-based displacement interferometer system. This system combines four main subsystems: Software, Laser and Interferometer, Microscope Carriage and A - Frame tensioning unit. Section 2.3.1 will introduce each subsystem and what it is, while Section 2.3.2 will introduce how each subsystem works. At the end it will shown how a combination of such subsystems is used to create a displacement measurement. 2.3.1 Introduction to Measurement System Components A- Frame Tensioning Subsystem D  uring calibration, each tape must be placed under tension. The A - Frame tensioning subsystem (Figure 1.5) is used for this task. This system incorporates two pulleys with near-frictionless bearings of Grade “A” quality to allow tensioning of the tape by a suspended weight. For tensioning tapes of various lengths, this subsystem is mounted i
Figure 1.5 – A - Frame ndependently of the bench to allow mobility from the zero end of the tape calibration b Figure 2.2 - A – Frame Pulley Subsystem ench to the 61m end. Laser and Interferometer Subsystem The primary tool used for tape calibrations is a displacement measurement laser interferometer subsystem (Figure 1.6). This subsystem combines an interferometer with a two - frequency helium neon laser. With a range of 80 meters, the laser beam is used to create a displacement measurement along the bench. The interferometer is an optical device located between the laser and the microscope carriage to combine the o Laser Interferometer utgoing reference beam from the laser with the reflected measurement beam [from the retroreflector on microscope carriage].
Computer Software B  efore the calibration measurement can be recorded, it has to be processed and calculated through computer software (Figure 1.7). The laboratory software was derived for this purpose by a senior level engineer Daniel Sawyer using Visual Basic programming. Also called Renishaw software, it is responsible for processing multiple signals and input values to output a measurement calculation based on the laboratory environment. The environment is analyzed based on the t
Figure 1.7 – Renishaw Software emperature, humidity and pressure readings which are gathered through laboratory sensors. Humidity and pressure readings are attained through barometers and hydrometers located within laboratory (Figure 1.8). 
Figure 1.8 – Hygrometer (Humidity Sensor - Left) Barometer (Pressure Sensor - Right) 
The microscope carriage was the focus of this research project. This subsystem consists of a rolling carriage constructed by the NIST personnel (Figure 1.9). The carriage transports a bubble level, a retroreflector and 20X microscope. As one of the most important parts of the measurement system, the carriage is used to locate the t Figure 1.9 – Microscope Carriage ape graduations for calibration by the operator. 2.3.2 Measurement System – Component Functions Laser and Interferometer Subsystem  The Renishaw helium neon laser is used to create a displacement measurement along the bench length through the use of a light beam. As the beam travels to the location of the microscope carriage and back to the laser from the retroreflector (Figure 2.1), a d
Figure 2.0 – Laser Beam isplacement measurement can be calculated by the comparison of the reference and measurement beam. 
Figure 2.1 – Beam Path T Figure 2.2 – Interferometer Beam Combination ombination to create a displacement measurement signal. The Renishaw displacement signal is then sent to the Renishaw software for further possessing to calculate a displacement value in micrometers8. Computer Software Due to multiple factors, the Renishaw laser signal must be corrected by software processing. To output a final displacement reading acceptable for recording, the software must create a calculation to correct for the temperature, pressure and humidity variances9. Humidity and pressure readings are used to correct the change in laser beam wavelength due to the refractive index of air in laboratory. Similarly, temperature monitoring is necessary for correction of tape length variance due to the thermal expansion of metal material defined by the coefficient of thermal expansion10. In addition to the signal processing, the Renishaw software is designed to serve as an operator interface (Figure 2.3) with the procedure. Through the use of the software the operator is able to start and stop a calibration, zero the laser, record displacement values, monitor the laboratory environment and view the output measurement file. The software incorporates the following interface features (Figure 2.3): Software features: Bench Temperature Profile Display – displays the temperature value for each of the thermistors along the bench length. Warning in a form of a red flash will appear next to the temperature if it exceeds the tolerance. Pressure and Humidity Display – displays the pressure and humidity values gathered from the hygrometer and barometer. Signal Strength Display – displays the strength of the laser beam which is dependent on the alignment of the laser and optical devices for displacement measurement. Previous and Current Measurement Display – displays the previously recorded displacement measurement (Figure 2.3 – Bottom Readout) and the real time displacement measurement (Figure 2.3 – Top Readout) in micrometers. Coefficient of Thermal Expansion Display – displays the coefficient of thermal expansion with respect to the temperature difference. 
A - Frame Pulley Subsystem
The A - Frame tensioning subsystem (Figure 2.4) is used to place the tape under t Weight ension by applying a specified tensioning force. Through the use of two near frictionless pulleys, the t Figure 2.4 – A -Frame ape is placed under tension through a method of dead weight load. Such method places the tape under tension by suspending calibrated weights from the tape as seen in Figure 2.4. This approach is highly efficient as it creates a precise and consistent tension force for calibration. Tapes are placed under tension during calibration to resemble the field environment. Because of the material properties of metal, the tape can elastically deform under various tensioning forces based on its modulus of elasticity E11. As the graduation spacing depends on the applied tension, the same tensioning force is applied during calibration as in the field. M  icroscope Carriage
The microscope carriage is a subsystem build to allow motion along the bench surface for tape calibration. Through the use of the incorporated 20X microscope, the operator manually locates the scale graduations for calibration. The retroreflector at the front of the carriage reflects the laser beam back to the interferometer for the r Figure 2.5 – Microscope Carriage eference and measurement beam combination.  Unfortunately, the carriage motion along the bench also involves angular motion or tilt (Figure 2.6) due to imperfections of the tape bench. As explained previously, such tilt is responsible for Abbé error and operator error. To eliminate Abbé error during calibration, the carriage is designed so that the tilt of the carriage can be detected by the operator through a b
Figure 2.6 – Carriage Tilt ubble level. Using the bubble level reading, the operator then manually adjusts the pitch of the carriage by microscrew to eliminate the tilt and minimize calibration uncertainty. The following are the incorporated features of the microscope carriage: Incorporated Features: Retroreflector - optical component that receives the reference laser beam and reflects a measurement beam back to the interferometer for beam combination. Microscope - used to sequentially center the microscope carriage on the tape graduation to be calibrated via cross hairs. A battery operated L.E. D. illumination system is used to illuminate the graduation. Magnification value: 20X Bubble Level - leveling device with a precision of 5 arc seconds used to detect the tilt (pitch) of the carriage. Microscrew - a manually adjustable screw mechanism [located in the front of the carriage] used to perform correction of the microscope carriage tilt with respect to the bubble level. Linear Bearing - bearings arranged in a linear fashion to allow vertical travel of the carriage front12. Magnet - secures the carriage against the test bench edge to prevent falling during movement. Teflon Pads - create frictional force to stop the carriage after moment and prevent movement after aligning. 2.3.3 How the Measurement System Works Phase 1: The metal tape is laid out along the bench surface and placed under tension by dead weight load using the A – Frame. Phase 2: Computer software and laser interferometer subsystems are loaded and warmed up. Using the software, the origin of measurement (Zero Mark13) is defined for the Renishaw laser. As an uninterrupted process, the laser sends a reference beam to the retroreflector located on the carriage as it passes through an interferometer. The reference beam is then reflected back [now measurement beam] to the interferometer for beam combination. Phase 3: Within the interferometer, the reference beam and the measurement beam are combined for analysis by the Renishaw laser. Through detection of the interference fringes, a displacement signal from Renishaw laser is made. This signal is than processed by the Renishaw software to create a precise distance measurement value ready for recording. Figure 2.7 – Measurement System Setup 
2.5 Calibration Procedure The procedure for calibrating a tape is as follows:
2. Turn on and load the system software and allow it to evaluate the environment signals (i.e. temperature, pressure and humidity conditions).
At the end of calibration, system software creates a .txt file with recorded time stamped measurement, temperature, humidity and pressure values. The measurement data consists of the measured displacements d1,d2, …, dn between the tape graduations defining nominal calibrated lengths L1, L2… Ln. Using these values a calibration report is assembled for the customer. Based on the calibration data the companies are able to adjust tape manufacturing for better measurement accuracy. 3.0 Calibration Problems Multiple problems are present with the current design of the microscope carriage and the technology on board. Both of these factors contribute to the magnitude of uncertainty involved with tape calibration. Two main sources of such uncertainty are the Abbé error and operator error. 3.1 Abbé Error A  bbé error is a significant source of error in positioning applications. It refers to a linear error caused by the combination of an underlying angular motion and a dimensional offset (
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he tape calibration bench2 is a 60 meter stainless steel bench that runs three quarters of the tunnel length along the left concrete wall. The bench is a specially designed adjustable calibration bench constructed of stainless steel bars. The bench is supported on p
he outgoing beam from the laser (reference beam) and the returning beam from the retroreflector6 (measurement beam) are combined through the interferometer (Figure 2.2). The beam combination is then sent to the light sensor within the Renishaw laser system for comparison of light wavelengths between the measurement and reference beam. The sensor detects interference fringes7 found in the beam c 