In this paper, a new approach to fitting aspheric surfaces in three-dimensional space is proposed, based on the nonlinear least-squares algorithm. For the conditions tested, there are good indications that this method provides better results than conventional solutions as all the surface parameters can be estimated simultaneously based on the design equation, thus allowing the result to be directly compared to design parameters. Conventionally, aspheric surfaces can be fitted with simplified surface models, such as a second order surface or polynomial model. Using this approach the estimated parameters cannot be compared with the design values, breaking the link between the designed and measured surface. The new method is developed here and tested on computer simulated aspheric surfaces. Both ideal surfaces and surfaces with random irregularities are considered. Issues regarding the application of the fitting method to real measured surfaces are discussed.

/pdf/a-new-approach-to-characterising-aspheric-surfaces-1h60cgz2ly.pdf

A new approach to characterising aspheric surfaces

In this paper a method for measuring the volume of eroded electrical contacts is presented. The main emphasis is on the measurement of volume relative to a contact support surface, allowing severely eroded contacts to be measured. A noncontact system is described, which allows contacts to be evaluated for volume change without the contact being removed from contact supports. The accuracy of the measurement method is discussed and results show how the volume measurement can be used to evaluate contact performance. Results are presented on the erosion characteristics of Ag/SnO/sub 2/ contacts used in automotive relays. A new measurement methodology is presented which will allow for the evaluation of the performance of relay contacts in devices.

/pdf/the-volumetric-erosion-of-electrical-contacts-24hobzpl0v.pdf

The volumetric erosion of electrical contacts

This paper presents a method for the selection of algorithms for the form characterization of nominally spherical surfaces. The form characterization is applied to discrete data obtained from a three-dimensional (3-D) high-precision measurement system. In this paper, five sphere-fitting algorithms are outlined and compared. The fitting algorithms under investigation are: linear and nonlinear least-squares sphere fit, minimum zone sphere fit, four-point sphere fit, and sphere fit by error curve analysis. A method for selection of the best-fit algorithm, based on a spectral analysis of the surface irregularity is suggested and applied to the surface measurement of worn electrical switching contacts.

A method for the selection of algorithms for form characterization of nominally spherical surfaces

Coordinates measuring machines (CMMs) are commonly utilized to take measurement data from manufactured surfaces for inspection purposes. The measurement data are then used to evaluate the geometric form errors associated with the surface. Traditionally, the evaluation of spherical form errors involves an optimization process of fitting a substitute sphere to the sampled points. This paper proposes the computational strategies for sphericity with respect to ASME Y14.5M-1994 standard. The proposed methods consider the trade-off between the accuracy of sphericity and the efficiency of inspection. Two approaches of computational metrology based on genetic algorithms (GAs) are proposed to explore the optimality of sphericity measurements and the sphericity feasibility analysis, respectively. The proposed algorithms are verified by using several CMM data sets. Observing from the computational results, the proposed algorithms are practical for on-line implementation to the sphericity evaluation. Using the GA-based computational techniques, the accuracy of sphericity assessment and the efficiency of sphericity feasibility analysis are agreeable.

Analysis of Spherical Form Errors to Coordinate Measuring Machine Data

This paper considers the sensitivity of three sphere-fitting algorithms to real-world measurement errors. It pays particular attention to nominally spherical surfaces, such as those typically measured by tactile and optical profilometers, addressing the limitations of sensor gauge range and angular tolerance. A recently proposed linear circle-fitting algorithm is extended to a sphere-fitting algorithm and its performance compared to two long standing sphere-fitting algorithms; namely linear and non-linear least-squares. Sources of measurement error in optical profilometers are discussed, and user defined scan parameters are optimised based on the results of a designed experiment. The performance of all three sphere-fitting algorithms are tested on a sphere superimposed with varying degrees of surface irregularities in a Monte Carlo simulation; this study shows that both linear routines display a negative skewness in their radius error distribution. Finally, a method of predicting radius uncertainty is offered that considers the surface residual that remains after sphere-fitting and relates this to the radius uncertainty of the chosen algorithm.

The uncertainty of radius estimation in least-squares sphere-fitting, with an introduction to a new summation based method

Measurement and characterisation of 3D form to maintain manufacturing quality has particular problems in cases such as lenses which do not generally have a clear measurement datum. A 3D-form measurement includes information about the form, the orientation and the position of the surface under test. Orientation and position can be design parameters or may result from misalignment of the test specimen on a measurement table. In either case, it is necessary to separate form from orientation and position if the data-set is to be fitted and compared with an “ideal” surface. In this paper two pre-processing algorithms are presented and examples given of the separation of form from orientation and position. The algorithm is applied to simulated data-sets consisting of up to 26,000 discrete points on a square grid, simulating the measurement of an aspheric lens in 3D. The rotationally symmetric data-set is translated for a distance x 0 , y 0 and z 0 and rotated about two axes, x and y , to simulate misalignment. To simulate inaccuracies from a manufacturing process, normally distributed random noise is superimposed on the ideal surface. An application of pre-processing using a real data-set is also shown. Furthermore, form fitting is addressed and the interpretation of form by decomposition of the data into error types is discussed.

Separation of form from orientation in 3D measurements of aspheric surfaces with no datum

Recent developments in high precision machining have allowed for the design and manufacture of precision aspheric lenses. These have the advantage over conventional spherical lenses in that a multiple element lens can be replaced by a single aspheric lens. There are however difficulties both in the measurement of the lens surface after machining and the assessment of the quality of the lens. In this paper an aspheric lens surface is measured using a 3D Form Talysurf. The data are then analysed using an analytical least-squares technique to fit the points to an exponential function. The methods developed show that the machining methods can now be complemented by an analysis technique.

/pdf/the-analysis-of-the-form-of-aspheric-lens-surfaces-9u6mch80zc.pdf

The Analysis Of The Form Of Aspheric Lens Surfaces

Two aspects of a surface are of interest: surface form and surface irregularity.
The form is the geometry of an object.
Superimposed on the form and usually of much finer detail is surface irregularity.
The irregularity can be a combination of symmetrical and non-symmetrical deviations from nominal form and conclusions about the manufacturing process or the environmental and operating conditions under which a body has been used can be drawn from it.
In this paper the reconstruction of surfaces for computer aided surface assessment (CASA) is discussed

/pdf/surface-reconstruction-from-discrete-data-obtained-by-a-3d-18qzsiylyq.pdf

Surface reconstruction from discrete data obtained by a 3D surface measurement system

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Papers

A method for the selection of algorithms for form characterization of nominally spherical surfaces

Separation of form from orientation in 3D measurements of aspheric surfaces with no datum

The Analysis Of The Form Of Aspheric Lens Surfaces

Surface reconstruction from discrete data obtained by a 3D surface measurement system