Chapter 1. Fundamentals of Error Analysis and their Uncertainties in Dimensional Metrology Applied to Science and Technology

Transcription

1 Chapter 1. Fundamentals of Error Analysis and their Uncertainties in Dimensional Metrology Applied to Science and Technology Introduction to uncertainties in dimensional metrology Definition of standards Definition of errors and uncertainties in dimensional metrology What is the difference between error and uncertainty? Why make a calculation of errors uncertainty? Reminder of basic errors and uncertainties Properties of uncertainty propagation Reminder of random basic variables and their functions Properties of random variables of common functions Errors and their impact on the calculation of uncertainties Accidental or fortuitous errors Systematic errors Errors due to apparatus Errors due to the operator Errors due to temperature differences Random errors Applications based on errors in dimensional metrology Absolute error δ = E a Relative error δ = E r Systematic error Accidental error (fortuitous error) Expansion effect on a bore/shaft assembly Correction of possible measurement errors Overall error and uncertainty Uncertainty due to calibration methods Capability of measuring instruments... 47

2 vi Applied Metrology for Manufacturing Engineering 1.7. Estimation of uncertainties of measurement errors in metrology Definitions of simplified equations of uncertainty measurements Issue of mathematical statistics evaluation of uncertainties in dimensional metrology Uncertainty range, coverage factor k and range of relative uncertainty Approaches for determining type A and B uncertainties according to the GUM Introduction Properties Brief description of type-a uncertainty evaluation method Type-B uncertainty methods Principle of uncertainty calculation: types A and B Error on the repeated measure: calculation of compound standard uncertainty Applications on the laboratory calculations of uncertainties Simplified models for the calculations of measurement uncertainties Laboratory model of dimensional metrology Measurement uncertainty evaluation discussion Contribution of the GUM in dimensional metrology Summary Bibliography Chapter 2. Fundamentals of Dimensional and Geometrical Tolerances According to ISO, CSA (Canada), and ANSI (USA) Introduction to geometrical products specification Dimensional tolerances and adjustments Adjustments with clearance: Ø80 H8/f Adjustments with uncertain clearance: Ø80 H7/k Adjustments with clamping or interference Approach for the calculation of an adjustment with clearance Dimensioning according to ANSI and CSA Definition of geometrical form constraints International vocabulary of metrology Local nominal dimensions according to ISO/DIS Definition of the axis extracted from a cylinder or a cone Definition of the local size extracted from a cylinder

3 vii Definition of local size extracted from two parallel surfaces Notion of simulated element and associated element GPS standard covering ISO/TR Principle of independency according to ISO (classic case) Envelope requirement according to ISO Maximum material principle according to ISO (classic case) Form tolerances Flatness tolerances Straightness tolerance Roundness Cylindricity Orientation tolerances Parallelism (straight line/straight line) Parallelism plane/plane (plane/straight line) on CMM A workshop exercise on dimensional metrology Angularity Positioning tolerances Tolerance of single radial flap (radial runout) Tolerance of single axial flap (axial runout) Zone of tolerance applied to a restricted portion of the piece (as in // and in ) Projected tolerance zone according to ISO (classic case) Conicity according to ISO Conicity calculation: slope, tan(α), large and small diameter Linear dimensional tolerances Consequence: size tolerancing Consequence: independency with regard to the form Positioning a group of elements GPS standards according to the report CR ISO/TR14638 of Rational dimensioning for a controlled metrology: indices of capability and performance indices statistical process specification Summary and discussion Bibliography Chapter 3. Measurement and Controls Using Linear and Angular Standards Key dimensional metrology standards Time and frequency standards Force and pressure standards

4 viii Applied Metrology for Manufacturing Engineering Electrical standards Temperature standards Photometric standards Measurement, comparison, and control Meter, time, and mass The meter Time Mass Deformations and mechanical causes of errors Quantitative assessment of gauge blocks Assessment of cylindrical rod and ball gauges (spheres). Local crashing of cylindrical rods K Recommendations for correct block staking Punctual contact (spherical buttons, beads, and thread flanks of a thread buffer) K Total flattening of cylindrical gauges (k p ) Total flattening of balls (spheres)k sph Measurement and precision with micrometer Marble, V-blocks, gauge blocks, and dial gauges Control of flat surfaces on marble Measurement by comparison of small marble surfaces V-shaped block Parallel blocks Dial gauge Mechanical dial gauges with inside and outside contacts Sizes of fixed dimensions, or Max Min Bore gauges Bore gauges Plain rings Spindle bores Inside gauges (micrometer) Depth gauges Telescopic bore gauges Example of a laboratory model Table of experimental measurements Precision height Directions for use of height masters (or height gauges) Adjustable parallel gauge blocks and holding accessories Example of a laboratory model Table of experimental measurements Precision height gauge check master Caliper gauge control The universal protractor vernier

5 ix Direct angle measurement Indirect angular measurement Vernier height gauge Gear tooth vernier caliper Vernier calipers Various measurements of a dimension using a caliper Possible errors when using a caliper Micrometer or Palmer Principle of micrometric screw Manipulations to perform a measurement with a Palmer Adjusting micrometers Control of parallelism and flatness of the micrometer s measuring surfaces using optical glass Measurement of screw threads by three-wire method Ruler and gauges for the control of screw threads Micrometer with fine point Disc micrometers to measure shoulder distances Outside micrometer caliper type Summary Bibliography Chapter 4. Surface Control Control and measurement of angles Angles defects Surfaces of revolution Fundamentals of the analysis of conical surfaces control Control by comparison to a standard Using the buffer and the cone-shaped ring Measuring angles with gauges and balls Principle of measurement called sine Metric thread (M) measurement on gauge Laboratory control of the conicity with balls and gauges Controls of cones on machine-tools Method of swivel slide Method of lateral displacement of the tailstock of a lathe Control of flat surfaces Properties of a dihedron Control of large flat surfaces Control of cylindrical surfaces (of revolution) Cylindrical surface Associated definitions Cylindricity defects

6 x Applied Metrology for Manufacturing Engineering Control of a cylinder on three contact tips on a V-block Practical control of the straightness of the generatrix of a cylinder Control of the perpendicularity of the generatrix and the drive circle Control of surfaces of revolution with spherical forms Description and functioning of a spherometer Laboratory (workshop) simulated on the appropriate use of spherometer Control and measurement with spherometer (second approach) Generating a spherical surface Control of the relative positions of surfaces Control of parallelism for surfaces or edges Control of parallelism for two dihedral edges Control of the angular position of surfaces, distance between the axis of a bore and the plane Control of distance between the sphere center and the plane Control of the position of the edge of a dihedron Methods of dimensional measurement Direct method (calibration curve) Indirect method (by comparison or differential) Indirect method known under the term at zero Measurement of flatness defect Method for measuring flatness deviation Operating procedure for flatness deviation measurement Relative position of measuring instruments and the workpiece Control of the perpendicularity of a line to a plane Relative position of measuring instruments and the workpiece Other controls of dimensions in relative positions Direct measurement of an intrinsic dimension using micrometer Summary on relative positions Bibliography Chapter 5. Opto-Mechanical Metrology Introduction to measurement by optical methods Description of profile projector (type Mitutoyo PH-350H) Presentation of the main operating functions of GEOCHECK Selecting the point of origin (preset operation, zero reset) The main functions of optical comparator Metrology laboratories on profile projector

7 xi Plates measurement standards for profile projector Principle of interferential metrology (example: prism spectroscope) Function of two sine-waves interference Statistical description Flatness measurement by optical planes Principle of interferoscope Control of parallelism (case of parallel gauge-blocks) Numerical example of laboratory Conclusion Bibliography Chapter 6. Control of Surface States Introduction to surface states control for solid materials Terminology and definition of surface states criteria Surface states (texture) and sampling lengths Waviness parameters Instruments for measuring surface state Selecting cutoff for roughness measurements Symbols used in engineering drawings to describe the appropriate surface state according to ANSI/ASME Y14. 36M Surface characteristics in a drawing using CAD CAO software Expressions of the terms of surface roughness Description of the main surface states Presentation of Mitutoyo Surftest Components of rugosimeter Calibration of Mitutoyo rugosimeter Measurement Practical example on the application of Surftest Portable rugosimeter SJ-400 of Mitutoyo The main normalized parameters of surface states used in the industry, their formulas and definitions Waviness parameters Example on the control of the roughness of a plate grade Questionnaire and laboratory approach Table of calibrated measurement results in [micrometer] and [microinch] Plotting using MathCAD Software Plotting with the aid of MathCAD Graphical results of arithmetic means R a Discussions

8 xii Applied Metrology for Manufacturing Engineering 6.7. Calculations of the overall uncertainty in the GUM method compared to the Monte Carlo method using the software GUMic Summary Bibliography Chapter 7. Computer-Aided Metrology-CAM Coordinate-measuring machine (CMM) Morphology of the CMM The CMM and its environment Advantages of CMM in metrology Commonly-used geometric models in dimensional metrology Constructive solid geometry models Boundary representation models (B-REP) Hybrid models CSG/B-REP (solid + surfaces) NURBS (Non-Uniform Rational Beta-Splines) TTRS (Technologically and Topologically Related Surfaces) models Real forms, real geometric elements, real geometrical surfaces Nominal geometric elements Modeling the ideal geometric form of a workpiece Model of real geometric elements, reference surface (SR) Substitution surfaces models Description of styli and types of probing Styli with ruby ball Hemispherical-ended styli Sharp styli or styli with small radius Disc styli (or simply discs) Cylindrical stylus Accessories and styli extensions Software and computers supporting the CMM Geometric control Surface control Coordinates systems and probes calibration Starting a B504B-Mitutoyo CMM Number of probing points Key measuring functions of the Mitutoyo B504B CMM Measurements on CMM using the Cosmos software Case of circle-to-circle distance STATPAK-Win of Cosmos, Mitutoyo Examples of applications using CMM Compiling the technical file

9 xiii Constitution of the CMM laboratory report under Cosmos (or other) Chapter summary and future extensions of CMMs Bibliography Chapter 8. Control of Assembly and Transmission Elements Introduction to the control of components for temporary assembly and elements for power transmission: threads, gears, and splines Method of obtaining threads and tapping in mechanical manufacturing General description of thread dimensioning Designation of threads and tapped holes for blind holes Helical surface for screw threads Technological processes for tapping and its control (Go Not Go) Tapping (by hand) with tap wrench and set of taps The main threads in the industry ISO Threads American Standard pipe threads The Whitworth thread BRIGGS tapered threads; cone 6.25% American Standard thread, NC and NF series Pipe threads called GAS Main threads implemented in Canada Principles of threads control Defects of the helical surface Control, without measurement, of threads Control of a thread pitch using ruler and gauge Checking the straightness of tapping tools by squaring Screws resistance and quality classes Minimum torques for screws with diameters of 1 to 10 mm Example of calculations of efforts on threads (North American concept) Control of screw thread by mechanical and optical comparison Laboratory example on threads control Introduction to gear control Parallel spur gears Metrological control of the main types of gears Spur gears with helical teeth Helical gears with parallel axes Parallel spur gears with helical teeth Bevel or concurrent gears Worm gears

10 xiv Applied Metrology for Manufacturing Engineering Racks Control of gears with a vernier calipers Chordal thickness measurement Over wire measurement Measuring thickness of rack teeth Introduction to spline control Dimensional control of splines Control of the geometric correction of splines Woodruff key standardized ANSI B (R1998) Control of key-seats Calculating the depth of the housing (groove) and the distance from the top of the key Summary Bibliography Chapter 9. Control of Materials Hardness Testing Introduction to non-destructive testing Measurements of hardness by indentation Presentation of the main hardness tests Principle and description of the Rockwell hardness Comparison of indentation methods (Table 9.4) Typical applications of Rockwell scales Rockwell superficial hardness test Rockwell hardness tests of plastics Comparison between Shore and Rockwell hardness ball testing Overall description of the Rockwell hardness testing machine Brinell hardness test Applied load and diameter of the ball Thickness of the tested metal Meyer hardness test (named after Rajakovico and Meyer) Operating procedure for Brinell hardness test Principle of the Vickers hardness test Knoop hardness (HK) Barcol hardness Rebound hardness test by Shore test (scleroscope) Comparison of the indenters for the Rockwell and Shore tests Mohs hardness for minerals Mohs scale of hardness minerals How should the hardness of a mineral be measured? IRHD rubber hardness tester Control of rubber and other elastomers by IRHD and Shore test.. 561

11 xv Comparison of the three main hardness tests and a practical approach for hardness testing: Brinell HB, Rockwell HR, and Vickers HV Main mechanical properties of solid materials Flow testing Tensile testing of solid materials Impact test for steels Mechanical tests on plastic materials Tensile strength, strain, and modulus ASTM D638 (ISO 527) Flexural strength and modulus ASTM D 790 (ISO 178) Impact test Interpretation of resistance to impacts ASTM compared to ISO Izod impact strength ASTM D 256 (ISO 180) Fatigue failure and dimensional metrology for the control of the dimensioning of materials assembled by welding Fatigue testing Tenacity General tolerances for welded structures according to ISO Summary There is seriously no universal solution to conduct hardness tests Some criteria for choosing hardness testing apparatus Indentation reading mode The expected result Bibliography Chapter 10. Overall Summary Glossary Lexicon of terms frequently used in metrology Warning Bibliography Appendix Appendix Appendix Appendix Appendix Appendix Index