Принципы нанометрологии, страница 3

2188.2.6.3 Maximum height of the profile, Rz .............. 2188.2.6.4 Mean height of the profileelements, Rc ............................................ 2198.2.6.5 Total height of the surface, Rt ....................2198.2.7 Amplitude parameters (average of ordinates)............ 2198.2.7.1 Arithmetical mean deviation of theassessed profile, Ra................................... 2198.2.7.2 The root mean square deviation of theassessed profile, Rq ..................................

2218.2.7.3 Skewness of the assessed profile, Rsk ......... 2228.2.7.4 Kurtosis of the assessed profile, Rku...........2238.2.8 Spacing parameters ............................................... 2248.2.8.1 Mean width of the profile elements,RSm ........................................................ 2248.2.9 Curves and related parameters................................

2248.2.9.1 Material ratio of the profile......................... 2248.2.9.2 Material ratio curve ................................... 2258.2.9.3 Profile section height difference, Rdc.......... 2268.2.9.4 Relative material ratio, Rmr ....................... 2268.2.9.5 Profile height amplitude curve....................2268.2.10 Profile specification standards ................................ 2278.3 Areal surface texture characterisation ................................. 2298.3.1 Scale-limited surface ...............................................

2298.3.2 Areal filtering ..........................................................2308.3.3 Areal specification standards .................................... 2328.3.4 Unified coordinate system for surface textureand form................................................................. 2348.3.5 Areal parameters ..................................................... 235Contents8.3.6 Field parameters .....................................................2358.3.6.1 Areal height parameters...............................2368.3.6.1.1 The root mean square valueof the ordinates, Sq .....................2368.3.6.1.2 The arithmetic mean of theabsolute height, Sa ......................2368.3.6.1.3 Skewness of topography heightdistribution, Ssk ..........................2368.3.6.1.4 Kurtosis of topography heightdistribution, Sku..........................2368.3.6.1.5 The maximum surface peakheight, Sp ...................................2378.3.6.1.6 The maximum pit height of thesurface, Sv..................................2378.3.6.1.7 Maximum height of thesurface, Sz..................................2378.3.6.2 Areal spacing parameters.............................2378.3.6.2.1 The auto-correlation length, Sal ....2378.3.6.2.2 Texture aspect ratio of thesurface, Str .................................2388.3.6.3 Areal hybrid parameters...............................2388.3.6.3.1 Root mean square gradient of thescale-limited surface, Sdq ............2388.3.6.3.2 Developed interfacial area ratioof the scale-limited surface, Sdr ...2398.3.6.4 Functions and related parameters.................2398.3.6.4.1 Areal material ratio of the scalelimited surface ............................2398.3.6.4.2 Areal material ratio of thescale-limited surface, Smc(c) .......2398.3.6.4.3 Inverse areal material ratio of thescale-limited surface, Sdc(mr) ......2398.3.6.4.4 Areal parameters for stratifiedfunctional surfaces of scalelimited surfaces...........................2408.3.6.4.5 Void volume, Vv(mr).....................2418.3.6.4.6 Material volume, Vm(mr) ..............2418.3.6.4.7 Peak extreme height, Sxp .............2418.3.6.4.8 Gradient density function .............2428.3.6.5 Miscellaneous parameters............................2428.3.6.5.1 Texture direction of thescale-limited surface, Std.............2428.3.7 Feature characterisation ...........................................2438.3.7.1 Step 1 – Texture feature selection ................243xixiiContents8.3.7.2 Step 2 – Segmentation ................................

2438.3.7.2.1 Change tree................................. 2458.3.7.3 Step 3 – Significant features........................2488.3.7.4 Step 4 – Selection of feature attributes......... 2488.3.7.5 Step 5 – Quantification of featureattribute statistics ....................................... 2498.3.7.6 Feature parameters .....................................2498.3.7.6.1 Density of peaks, Spd ..................

2508.3.7.6.2 Arithmetic mean peak curvature,Spc ............................................ 2508.3.7.6.3 Ten point height of surface, S10z... 2508.3.7.6.4 Five point peak height, S5p.......... 2508.3.7.6.5 Five point pit height, S5v ............. 2508.3.7.6.6 Closed dale area, Sda(c)............... 2508.3.7.6.7 Closed hill area, Sha(c) ................ 2518.3.7.6.8 Closed dale volume, Sdc(c) .......... 2518.3.7.6.9 Closed hill volume, Shv(c) ............ 2518.4 Fractal methods ................................................................

2518.4.1 Linear fractal methods .............................................2528.4.2 Areal fractal analysis................................................ 2558.4.2.1 Volume-scale analysis.................................. 2558.4.2.2 Area-scale analysis...................................... 2558.5 Comparison of profile and areal characterisation .................. 2578.6 References .......................................................................258CHAPTER 9 Coordinate metrology ....................................................

2639.1 Introduction to CMMs........................................................ 2639.1.1 CMM probing systems .............................................. 2669.1.2 CMM software ......................................................... 2669.1.3 CMM alignment....................................................... 2679.1.4 CMMs and CAD ....................................................... 2679.1.5 Prismatic against freeform........................................

2689.1.6 Other types of CMM ................................................. 2689.2 Sources of error on CMMs .................................................. 2689.3 Traceability, calibration and performance verificationof CMMs .......................................................................... 2699.3.1 Traceability of CMMs ...............................................

2709.4 Miniature CMMs ............................................................... 2729.4.1 Stand-alone miniature CMMs.................................... 2739.4.1.1 A linescale-based miniature CMM ................ 2739.4.1.2 A laser interferometer-based miniatureCMM..........................................................2749.5 Miniature CMM probes ......................................................275Contents9.6 Calibration of miniature CMMs ...........................................2819.6.1 Calibration of laser interferometer-basedminiature CMMs ......................................................2839.6.2 Calibration of linescale-based miniature CMMs ..........2839.7 References .......................................................................285CHAPTER 10 Mass and force measurement ......................................

28910.1 Traceability of traditional mass measurement ..................28910.1.1 Manufacture of the Kilogram weight and theoriginal copies...................................................29010.1.2 Surface texture of mass standards.......................29110.1.3 Dissemination of the kilogram ............................29110.1.4 Post nettoyage-lavage stability ............................29210.1.5 Limitations of the current definition ofthe kilogram......................................................29210.1.6 Investigations into an alternative definitionof the kilogram ..................................................29310.1.6.1 The Watt balance approach..................29410.1.6.2 The Avogadro approach........................29410.1.6.3 The ion accumulation approach............29510.1.6.4 Levitated superconductor approach ......29510.1.7 Mass comparator technology...............................29510.1.7.1 The modern two-pan mechanicalbalance..............................................29610.1.7.2 Electronic balances.............................29610.2 Low-mass measurement ................................................29710.2.1 Weighing by sub-division....................................29710.3 Low-force measurement.................................................29810.3.1 Relative magnitude of low forces.........................29810.3.2 Traceability of low-force measurements ...............29810.3.3 Primary low-force balances.................................29910.3.4 Low-force transfer artefacts ................................30110.3.4.1 Deadweight force production................30110.3.4.2 Elastic element methods .....................30110.3.4.3 Miniature electrostatic balancemethods.............................................30410.3.4.4 Resonant methods ..............................30410.3.4.5 Further methods and summary .............30610.4 References ...................................................................308APPENDIX A ................................................................................................311APPENDIX B ................................................................................................315INDEX ..........................................................................................................317xiiiThis page intentionally left blankAcknowledgementsMany people have helped me to put this, my first book, together.

The workhas involved some re-arrangements in my personal life and I thank my lovingpartner, Nikki, for putting up with this (especially with me insisting onhaving the laptop in the living room on a permanent basis).Above all I would like to express thanks to Dr Han Haitjema (MitutoyoResearch Centre Europe, The Netherlands) for his critical comments onmost of the chapter drafts and for his never-ending good humour and a soundbasis in reality!Also, many external folk have contributed and for this they have myeternal gratitude and friendship.

In no particular order, these include: JohnHannaford (himself), Prof Derek Chetwynd (University of Warwick, UK),Dr Andreas Freise (University of Birmingham, UK), Prof Liam Blunt,Dr; Leigh Brown and Prof Xiangqian (Jane) Jiang (University of Huddersfield,UK), Dr Mike Conroy, Mr Daniel Mansfield, Mr Darian Mauger andProf Paul Scott (Taylor Hobson, UK), Dr Roy Blunt (IQE, UK), Dr Jon Petzing(Loughborough University, UK), Dr Georg Wiora (Nanofocus, Germany),Dr Franz Helmli (Alicona, Austria), Dr Lars Lindstrand (Scantron, UK),Prof Chris Brown (Worcester Polytechnic Institute, USA), Prof Paul Shore(Cranfield University, UK), Dr James Johnstone (NanoKTN, UK), Dr RolandRoth (Zeiss, Germany), Prof Gert Jäger (Ilmenau University of Technology,Germany), Dr Ted Vorburger (NIST, USA), Dr Ernst Treffers (XpressPrecision Engineering, Netherlands), Dr Marijn van Veghel (NMi-VSL,Netherlands), Dr Chris King (University College London, UK), Dr TristanColomb (Lyncée Tec, Switzerland), and Dr Katsuhiro Miura and Mr AtsukoNose (Mitaka Kohki Co, Japan).Many folk at NPL have supported me and contributed to the contents ofthe book.