Effects of Spherical Targets on Capacitive Displacement Measurements

[+] Author and Article Information
R. Ryan Vallance

Precision Systems Laboratory, The George Washington University, 738 Phillips Hall, 801 22nd St., N.W., Washington, DC 20052

Eric R. Marsh

Machine Dynamics Research Laboratory, The Pennsylvania State University, 21 Reber Building, University Park, PA 16802

Philip T. Smith

Mechanical Engineering, University of Kentucky, 015 Ralph G. Anderson Building, Lexington, KY 40506

J. Manuf. Sci. Eng 126(4), 822-829 (Feb 04, 2005) (8 pages) doi:10.1115/1.1813476 History: Received January 13, 2004; Revised April 02, 2004; Online February 04, 2005
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


ANSI/ASME B5.54, 1992, Methods for Performance Evaluation of Computer Numerically Controlled Machining Centers, ASME, New York.
ANSI/ASME B5.57, 2000, Methods for Performance Evaluation of Computer Numerically Controlled Lathes and Turning Centers, ASME, New York.
ANSI/ASME B89.3.4M, 1985, Axes of Rotation–Methods for Specifying and Testing, ASME, New York.
Grejda, R. D., 2002, “Use and Calibration of Ultra Precision Axes of Rotation with Nanometer Level of Metrology,” Ph.D. thesis, Penn State University, State College, PA.
Morgan,  V. T., and Brown,  D. E., 1969, “A Differential-Capacitance Transducer for Measuring Small Displacements,” J. Phys. E, 2, pp. 793–795.
Jones,  R. V., and Richards,  J. C. S., 1973, “The Design and Some Applications of Sensitive Capacitance Micrometers,” J. Phys. E, 6, pp. 589–600.
Stacey,  F. D., Rynn,  J. M. W., Little,  E. C., and Croskell,  C., 1969, “Displacement and Tilt Transducers of 140 dB Range,” J. Phys. E, 2, pp. 945–949.
Schofield,  J. W., 1972, “A Linear Capacitance Micrometer,” J. Phys. E, 5, pp. 822–825.
Sydenham,  P. H., 1972, “Microdisplacement Transducers,” J. Phys. E, 5, pp. 721–733.
Rigden,  J. D., 1977, “A Capacitive Bore Gauge,” J. Phys. E, 10, pp. 1276–1278.
Hicks,  T. R., Reay,,  N. K. and Atherton,  P. D., 1984, “The Application of Capacitance Micrometry to the Control of Fabry-Perot Etalons,” J. Phys. E, 17, pp. 49–55.
Wolfendale,  P. C. F., 1968, “Capacitive Displacement Transducers with High Accuracy and Resolution,” J. Phys. E, 2, pp. 817–818.
de Jong,  G. W., and Meijer,  G. C. M., 1997, “An Efficient Retrieving Algorithm for Accurate Capacitive Position Sensors,” Sens. Actuators, A, 58, pp. 75–84.
Kolb,  P. W., Decca,,  R. S. and Drew,  H. D., 1988, “Capacitive Sensor for Micropositioning in Two Dimensions,” Rev. Sci. Instrum., 69(1), pp. 310–312.
Hague, B., and Foord, T. R., 1971, Alternating Current Bridge Methods, Pittman, London.
Hugill,  A. L., 1982, “Displacement Transducers Based on Reactive Sensors in Transformer Ratio Bridges,” J. Phys. E, 15, pp. 597–606.
Dratler,  J., 1977, “Inexpensive Linear Displacement Transducer Using a Low Power Lock-In Amplifier,” Rev. Sci. Instrum., 48(3), pp. 327–335.
Huang,  S. M., Stott,  A. L., Green,  R. G., and Beck,  M. S., 1988, “Electronic Transducers for Industrial Measurement of Low Value Capacitances,” J. Phys. E, 21, pp. 242–250.
Ashrafi,  A., and Golnabi,  H., 1999, “A High Precision Method for Measuring Very Small Capacitance Changes,” Rev. Sci. Instrum., 70(8), pp. 3483–3487.
Lányi,  S., and Hrukovic,  M., 2001, “Linearization of Inverse-Capacitance-Based Displacement Transducers,” Meas. Sci. Technol., 12, pp. 77–81.
Fritsch,  K., 1987, “Linear Capacitive Displacement Sensor With Frequency Readout,” Rev. Sci. Instrum., 58(5), pp. 861–863.
Richards,  J. C. S., 1976, “Linear Capacitance Proximity Gauges with High Resolution,” J. Phys. E, 9, 639–646.
Maxwell, J. C., 1873, A Treatise on Electricity and Magnetism, Vol. 1, Oxford Univ. Press, New York.
Heerens,  W. C., and Vermeulen,  F. C., 1975, “Capacitance of Kelvin Guard-Ring Capacitors with Modified Edge Geometry,” J. Appl. Phys., 46, pp. 2486–2490.
Heerens,  W. C., 1976, “The Solution of Laplace’s Equation in Cylindrical and Toroidal Configurations with Rectangular Sectional Shapes and Rotation-Symmetrical Boundary Conditions,” J. Appl. Phys., 47(8), pp. 3740–3744.
Heerens,  W. C., 1986, “Application of Capacitance Techniques in Sensor Design,” J. Phys. E, 19, pp. 897–906.
Lazzarini,  A., 1986, “Sources of Error in Dynamic Applications of Electronic Displacement Sensors,” Rev. Sci. Instrum., 57(12), pp. 3099–3106.
Hicks, T., and Atherton, P. D., 2000, Nanopositioning Book, Penton Press, London.
Rosa,  E. B., and Dorsey,  N. E., 1907, Bull. Bur. Stds., 3, pp. 433–604.
Khan,  A. R., Brown,  I. J., and Brown,  M. A., 1980, “The Behavior of Capacitance Displacement Transducers Using Epoxy Resin as an Electrode-Guard Ring Spacer,” J. Phys. E, 13, pp. 1280–1281.
Genossar,  J., and Steinitz,  M., 1990, “A Tilted-Plate Capacitance Displacement Sensor,” Rev. Sci. Instrum., 61(9), pp. 2469–2471.
Harb, S. M., Chetwynd, D. G., and Smith, S. T., 1995, “Tilt Errors in Parallel Plate Capacitive Micrometry,” International Progress in Precision Engineering 8th International Precision Engineering Seminar, Elsevier, Compiegne, France pp. 147–150.
Brown,  M. A., and Bulleid,,  C. E., 1978, “The Effect of Tilt and Surface Damage on Practical Capacitance Displacement Transducers,” J. Phys. E, 11, pp. 429–432.
Puers,  R., and Lapadatu,  D., 1996, “Electrostatic Forces and Their Effects on Capacitive Mechanical Sensors,” Sens. Actuators, A, 56, pp. 203–210.
Bonse,  M. H. W., Mul,  C., and Spronck,  J. W., 1995, “Finite-Element Modelling as a Tool for Designing Capacitive Position Sensor,” Sens. Actuators, A, 46-47, pp. 266–269.
Ansel,  Y., Romanowicz,  B., Renaud,,  P. and Schrofer,  G., 1998, “Global Model Generation for a Capacitive Silicon Accelerometer by Finite Element Analysis,” Sens. Actuators, A, 67, pp. 153–158.
Khan,  S. H., Grattan,  K. T. V., and Finkelstein,  L., 1999, “Investigation of Leakage Flux in a Capacitive Angular Displacement Sensor Used in Torque Motors by 3D Finite Element Field Modeling,” Sens. Actuators, A, 76, pp. 253–259.
Kuijpers,  A. A., Krijnen,  G. J. M., Wiegerink,  R. J., Lammerink,  T. S. J., and Elwenspoek,  M., 2003, “2D-Finite-Element Simulations for Long-Range Capacitive Position Sensor,” J. Micromech. Microeng., 13, pp. S183–S189.
Lányi,  S., 1998, “Analysis of Linearity Errors of Inverse Capacitance Position Sensors,” Meas. Sci. Technol., 9, pp. 1757–1764.
Gladwin,  M. T., and Wolfe,  J., 1975, “Linearity of Capacitance Displacement Transducers,” Rev. Sci. Instrum., 46(8), pp. 1099–1100.
Smith, P., 2003, Analysis and Application of Capacitive Displacement Sensors to Curved Surfaces, Master’s thesis, University of Kentucky, Lexington, KY.


Grahic Jump Location
Representative capacitive displacement sensor (Lion Precision C1-C)
Grahic Jump Location
Axisymmetric electrodes in representative sensor and spherical target
Grahic Jump Location
Finite element analysis procedure
Grahic Jump Location
Electric potential (0–9 V) within air gap and epoxy in vicinity of electrodes
Grahic Jump Location
Electric field in vicinity of sensing electrode
Grahic Jump Location
Lumped capacitances between conductive electrodes
Grahic Jump Location
Inverse capacitance for low sensitivity (−0.394 V/μm) as a function of the gap and target diameter
Grahic Jump Location
Inverse capacitance for high sensitivity (−1.694 V/μm) as a function of the gap and target diameter
Grahic Jump Location
Voltage as a function of the change in gap for each spherical target and low sensitivity (predicted by FEA)
Grahic Jump Location
Voltage as a function of the change in gap for each spherical target and high sensitivity (predicted by FEA)
Grahic Jump Location
Fixture used to compare the output of sensors targeting spherical and flat surfaces. The sensors are stationary while the target surfaces move using the cross axis of the measuring machine.
Grahic Jump Location
Comparison of experimental sensor output for different target diamenters (a) for −0.3937 V/μm and (b) for −1.969 V/μm
Grahic Jump Location
Residual nonlinearity in experimental sensor output (a) −0.3937 V/μm and (b) for −1.969 V/μm




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In