Isoparametric line sampling for the inspection planning of sculptured surfaces
Introduction
Sculptured surfaces are utilised in a wide range of industries. These involve, but are not limited to, aerospace, automotive, biomedical, power generation, and home appliance industries. Sculptured surfaces are applied in product design to serve specific functions, or for aesthetic purposes. The manufacturing of sculptured surfaces involves automatic tool path generation, post-processing, CNC machining and finishing followed by inspection. The final measured accuracy of the manufactured surface is affected by various sources of error. These include CAM system algorithm errors and machine tool drive system errors as well as errors in measurement. In general the manufactured surface is digitised using a coordinate measuring machine (CMM), to test its conformity to the designer's intent as represented by the CAD model.
The output of the CMM is crucial as it is used to assess whether to accept or to reject manufactured parts. The CMM is a complex system that involves hardware, and software components that introduce several error components to the measured data. These errors interact with the work-piece form error to introduce uncertainty in the CMM measurement results [1]. The sampling strategy is a major contributor to the CMM's measurement uncertainty [2]. It may be intuitive that the larger the number of sample points the more accurate the inspection results are. Edgeworth and Wilhelm [3] suggested that the sample period has to be reduced, i.e. more sampled points, in order to reduce the effect of the sinusoidal shape error on the measurement uncertainty. Caskey et al. [4] reached a similar conclusion in their study on the interaction of work-piece form error, sampling strategy, and fitting algorithms. However, increased sample size is associated with longer inspection times, more data processing and data storage and hence, higher overall product cost.
In recent years, sampling of more data has become feasible using probe scanning technology. A scanning probe stays in direct contact with the surface and acquires data as it travels from one surface point to another. The data acquisition rate is inversely proportional to the probe's travelling speed.
The current approach to inspect sculptured surfaces, both in the reported literature as well as in the industrial practices, is to sample discrete points on the manufactured surface, and evaluate their deviations from the surface CAD model. This limits the information on the manufactured surface to these particular points. Furthermore, defining the locations of these points is often left up to the CMM operator.
The work presented in this paper adopts the concept of constructing a substitute geometry for the manufactured surface based on the scanned data. This enables the evaluation of the surface accuracy in a wider domain than that achieved by point-based practices. In order to build an accurate substitute geometry, the surface characteristics have to be taken into consideration in the sampling stage. In this paper, a new approach for the sampling of sculptured surfaces is presented. This approach is based on scanning isoparametric lines on the sculptured surface. These lines are used to construct a substitute geometry of the manufactured surface. The substitute geometry is used to assess the accuracy of the manufactured part.
This paper is organised as follows. Section 2 presents a survey of the related work. Section 3 presents the automatic sampling algorithm. Section 4 presents the curvature change based sampling algorithm. Section 5 presents the implementation of the uniform iso-planar sampling algorithm. Section 6 presents a case study where the three sampling algorithms were applied. Concluding remarks are included in Section 7, together with a discussion of future work.
Section snippets
Related work
The main focus of the reported literature on sampling for CMM inspection planning is the distribution of sample points on the measured surface The approach is threefold [1]. First, simulate the feature to be measured, and superimpose a form error pattern on the nominal data. Second, suggest various sampling patterns. Third, generate the substitute geometry for the measured feature, and compare it to the simulated model. The maximum deviation between the substitute geometry, and the feature
Automatic sampling
This algorithm uses the deviation between the substitute geometry and the CAD model to assess the sampling plan. It depends on the results of the substitute geometry construction algorithm, and does not use the surface features, e.g. surface curvature, directly to decide where to allocate sample lines. A grid of points are evaluated on the substitute geometry. For each point, the shortest distance to the surface CAD model is evaluated. This distance is the deviation of the substitute geometry
Curvature change-based sampling
This algorithm uses the change in the surface mean curvature along the isoparametric lines to determine the locations of the sample lines. The use of curvature change was inspired by considerations related to sculptured surface manufacturing, and substitute geometry construction.
In NC tool path generation, it is crucial to determine the step length λ between two subsequent cutter contact locations (CC-points) along a curved path, as well as the path interval ω between two subsequent tool
Iso-planar sampling
This algorithm divides the surface into a uniform array of iso-planar curves. This is carried out through intersecting the surface with a set of equally spaced infinite planes.
Case study
The algorithms presented in this paper were extensively tested using generic NURBS surfaces, as well as on CAD models for a variety of products with various levels of complexity. This section presents one of these case studies. Fig. 11 shows the surface model for the hood of a 1:18 die-cast car model. In this case study, the minimum distance between subsequent sample isoparametric lines is set to 1.0 mm. The maximum sample sizes used are 23 when sampling v-isoparametric lines, and 29 when
Contributions
The work presented in this paper has the following contributions to research on the inspection planning of sculptured surfaces:
- 1.
A new approach for the inspection planning of sculptured surfaces using the sampling of surface isoparametric lines.
- 2.
Provide the inspection planner with alternate solutions to the sampling plan.
- 3.
Quantify the error due to the sampling plan, and the substitute geometry construction algorithms.
- 4.
Demonstrate the effect of the surface complexity on the accuracy of the sampling
Acknowledgements
Materials and Manufacturing Ontario (MMO) provided financial support for this work. Solid Modeling Solutions (SMS), Bellevue, Washington, contributed the SMLib™ geometric modelling kernel that was used to implement the algorithms developed in this work.
Diaa ElKott is currently a PhD candidate in the Department of Mechanical Engineering, McMaster University, Hamilton, Ont., Canada. His research interests lie in the area of CAD/CAM, geometric modelling, and inspection software development. The focus of his PhD research is the inspection and shape interrogation of sculptured surfaces. He received a BSc in Production Engineering from Mansoura University, Mansoura, Egypt in 1992. He obtained a MASc in Industrial Engineering from the University of
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Diaa ElKott is currently a PhD candidate in the Department of Mechanical Engineering, McMaster University, Hamilton, Ont., Canada. His research interests lie in the area of CAD/CAM, geometric modelling, and inspection software development. The focus of his PhD research is the inspection and shape interrogation of sculptured surfaces. He received a BSc in Production Engineering from Mansoura University, Mansoura, Egypt in 1992. He obtained a MASc in Industrial Engineering from the University of Windsor, Windsor, Ont., Canada in 2001. He has industrial experiences in the fields of machine tool manufacturing, and robot modelling and simulation.
Stephen Veldhuis is currently an assistant professor in the Mechanical Engineering Department, McMaster University, Hamilton, Ont., Canada. His research interests are in high performance manufacturing, specifically in the areas of ultra precision machining, tool design and coatings as well as metrology, geometric modelling, machine tool accuracy, design, controls and machine condition monitoring. He obtained his Undergraduate degree in Mechanical Engineering and Management from McMaster University in 1990 and his Masters of Engineering degree from Carnegie Mellon University in Pittsburgh PA, USA in 1992. In 1998 he completed his Doctorate degree from McMaster University part time.