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Free-form surface inspection techniques state of the art review

Profile image of Peihua GuPeihua Gu

2004, Computer-Aided Design

Abstract

Precision inspection has been widely used in manufacturing to measure the dimensional accuracy of parts and products to meet the quality requirements. For regular geometric features, coordinate-measuring machines (CMM) can be used effectively to assess the accuracy and tolerances. For parts with free-form surfaces, the inspection becomes complex. Therefore, numerous researches have been carried out to tackle both fundamental and application issues concerning free-form surface inspection. In addition to academic research, some commercial packages have also been developed. This paper provides a comprehensive literature review of methodologies, techniques and various processes of inspections of parts with free-form surfaces. The specific topics cover: measurement data acquiring methods including contact and non-contact measurement approaches; inspection planning; geometric description methods of design models or measurement data; and, the free-form surface localization and comparison techniques, which are emphasized in this paper and mainly include the establishment of corresponding relationship, 3D transformation solving, measurement data to design model comparison or surface to surface distance calculations. Other issues, such as the influence factors to the localization/registration process, definition and inspection of free-form surface tolerance, and discussions on the functions of some commercial inspection packages available on market, are also discussed.

Figures (14)
Fig. 1 shows a CMM machine in (a) and _ the inspection of a simple shaped part by CMM in (b). For inspection of parts with free-form surfaces, the relationship between DCS and MCS is complex. Fig. 2 shows the inspection of a part with complex surfaces by Fig. 1. MCS, DCS and a part under inspection (picture modified from Ref. [7]). (a) Measurement Coordinate System (MCS); (b) Part and Design Coordinate System (DCS). A free-form surface is a type of surface, where the shape is not constrained by classical analytical forms and is defined by a set of control points (as with Bézier, b-spline,
Fig. 1 shows a CMM machine in (a) and _ the inspection of a simple shaped part by CMM in (b). For inspection of parts with free-form surfaces, the relationship between DCS and MCS is complex. Fig. 2 shows the inspection of a part with complex surfaces by Fig. 1. MCS, DCS and a part under inspection (picture modified from Ref. [7]). (a) Measurement Coordinate System (MCS); (b) Part and Design Coordinate System (DCS). A free-form surface is a type of surface, where the shape is not constrained by classical analytical forms and is defined by a set of control points (as with Bézier, b-spline,
a contact probe. In this figure, P; is a design model point to be measured, denoted by 7; in the DCS. Due to manufacturing errors, the design coordinate frame does not coincide with the measurement frame. Thus, another point P; is measured as shown in the figure, which is denoted by 7; in the MCS. The difference between these two positions is Ar [91].
a contact probe. In this figure, P; is a design model point to be measured, denoted by 7; in the DCS. Due to manufacturing errors, the design coordinate frame does not coincide with the measurement frame. Thus, another point P; is measured as shown in the figure, which is denoted by 7; in the MCS. The difference between these two positions is Ar [91].
Fig. 4. CMM measurement of a part [7]. fixture and the needs of programming when a different part is inspected [1,8,16,71,70]. There is also a limitation to the size of the part that can be measured. If an object has a very small size (few hundreds of square millimeters), the tip of a slower measuring speed than laser and optical scanners. This single-point measurement technique can generally collect data at a maximum rate of about 50 ~ 60 points per minute, depending on possible requirements of mechanical
Fig. 4. CMM measurement of a part [7]. fixture and the needs of programming when a different part is inspected [1,8,16,71,70]. There is also a limitation to the size of the part that can be measured. If an object has a very small size (few hundreds of square millimeters), the tip of a slower measuring speed than laser and optical scanners. This single-point measurement technique can generally collect data at a maximum rate of about 50 ~ 60 points per minute, depending on possible requirements of mechanical
Fig. 3. Classification of various digitizing devices [55].
Fig. 3. Classification of various digitizing devices [55].
systems can be as good as about 0.001” (0.025 mm) [43,70, 44,46], which is sufficient for some applications, such as inspection of products made from rapid prototyping process. However, this level of precision is lower compared with the accuracy of CMM [70,16]. Even though this represents the most common cases, our surveying results show that some producers claim higher accuracy for their laser scanners [45]. the tactile probe will have problems accessing part features. Very small objects often include features with light marks or etchings, on which even the smallest feasible mechanical tip could not reasonably work [7]. Besides, touch probes of CMM are also crash-prone [60].
systems can be as good as about 0.001” (0.025 mm) [43,70, 44,46], which is sufficient for some applications, such as inspection of products made from rapid prototyping process. However, this level of precision is lower compared with the accuracy of CMM [70,16]. Even though this represents the most common cases, our surveying results show that some producers claim higher accuracy for their laser scanners [45]. the tactile probe will have problems accessing part features. Very small objects often include features with light marks or etchings, on which even the smallest feasible mechanical tip could not reasonably work [7]. Besides, touch probes of CMM are also crash-prone [60].
Fig. 6. Three types of standard optical technology [7]. 4 ~ - Based on their characteristics, both contact and non- contact measuring methods have been applied widely to research and manufacturing fields, and will continue to be used for a long period of time. In some applications, solutions of CMM with a non-contact sensor have been used or proposed for the inspection of parts with free-form surfaces [7] and [60]. The literature [60] discussed the integration of vision and touch sensors in a CMM controller used for inspection tasks. This vision-probe system was used in a cooperative interaction integration mode. Global information generated by the vision systems was used to guide the movement of the touch probe. Vision provided information about the positions of part features of interest, and then the probe was guided to the features to make actual measurements. Similar research on integrating multiple sensors and vision probes with CMM in order to achieve high measuring quality and speed can also be found in some other literature such as [83] and [88]. In Ref. [88], a system based on the combination of laser and CMM was used to inspect parts made of soft material. In this research, a laser
Fig. 6. Three types of standard optical technology [7]. 4 ~ - Based on their characteristics, both contact and non- contact measuring methods have been applied widely to research and manufacturing fields, and will continue to be used for a long period of time. In some applications, solutions of CMM with a non-contact sensor have been used or proposed for the inspection of parts with free-form surfaces [7] and [60]. The literature [60] discussed the integration of vision and touch sensors in a CMM controller used for inspection tasks. This vision-probe system was used in a cooperative interaction integration mode. Global information generated by the vision systems was used to guide the movement of the touch probe. Vision provided information about the positions of part features of interest, and then the probe was guided to the features to make actual measurements. Similar research on integrating multiple sensors and vision probes with CMM in order to achieve high measuring quality and speed can also be found in some other literature such as [83] and [88]. In Ref. [88], a system based on the combination of laser and CMM was used to inspect parts made of soft material. In this research, a laser
Fig. 7. Traditional 3—2—1 approach for localization ([{13]). Traditionally, datums are measured to establish a reference frame for the part [66]. This is known as 3-2-1 approach. Three points are measured from the first datum to establish a plane. Two points are measured from the second datum to establish a second plane perpendicular to the first. Finally, one point is measured from the last datum perpendicular to the first two [81,66]. Fig. 7 shows a traditional 3—2-—1 approach for locating DCS. This approach has shortcomings in that the parts are required to have plane surfaces, and the result is very sensitive to measurement and dimensional errors. Besides, because of the manufacturing errors on the datums, the localization quality is sensitive to the selection of those points, there is
Fig. 7. Traditional 3—2—1 approach for localization ([{13]). Traditionally, datums are measured to establish a reference frame for the part [66]. This is known as 3-2-1 approach. Three points are measured from the first datum to establish a plane. Two points are measured from the second datum to establish a second plane perpendicular to the first. Finally, one point is measured from the last datum perpendicular to the first two [81,66]. Fig. 7 shows a traditional 3—2-—1 approach for locating DCS. This approach has shortcomings in that the parts are required to have plane surfaces, and the result is very sensitive to measurement and dimensional errors. Besides, because of the manufacturing errors on the datums, the localization quality is sensitive to the selection of those points, there is
Fig. 8. Block diagram of the inspection system [65].
Fig. 8. Block diagram of the inspection system [65].
Minimum number of primitives needed to establish the transformation [17] Table 1 as a least-square minimization problem. If the estimation of the rotational elements of the transformation matrix was not a straightforward minimization, quaternion might be used. Improvements were made in this approach based on the method introduced in Ref. [17]. However, it has short- coming that only planer primitives were used for the localization, this requires a number of planer primitives on the object studied for the localization.
Minimum number of primitives needed to establish the transformation [17] Table 1 as a least-square minimization problem. If the estimation of the rotational elements of the transformation matrix was not a straightforward minimization, quaternion might be used. Improvements were made in this approach based on the method introduced in Ref. [17]. However, it has short- coming that only planer primitives were used for the localization, this requires a number of planer primitives on the object studied for the localization.
Fig. 9. Point to NURBS surface distance [65]. where k, and k, are the principle curvatures at the measurement point; while k, and k, denote the principle curvatures of the corresponding design point. A matching rate function was designed to evaluate the local errors. The global evaluation was to extract and evaluate the surface features such as a bend or twist. The relationship between the aggregate normal vectors of the surface features was decomposed into a bent angle and a twisted angle. The differences of bent and twisted angles constituted the global evaluation results.
Fig. 9. Point to NURBS surface distance [65]. where k, and k, are the principle curvatures at the measurement point; while k, and k, denote the principle curvatures of the corresponding design point. A matching rate function was designed to evaluate the local errors. The global evaluation was to extract and evaluate the surface features such as a bend or twist. The relationship between the aggregate normal vectors of the surface features was decomposed into a bent angle and a twisted angle. The differences of bent and twisted angles constituted the global evaluation results.
In previous Sections 4.1 and Section 4.2, we mentioned some techniques for solving the rigid body transformation for localization process, such as the method of solving non- linear equations introduced in Refs. [49,80] and the pseudo- inverse method discussed in Ref. [13]; the minimization method illustrated in Refs. [54,63,74]; the minimization approached solved by a self-learning neural network by Ref. [4]; the modified pseudo-inverse approach developed in Refs. [92,93]; the method of using quaternion in Refs. [17,65,73], etc. For above approaches, the method of solving non-linear equations normally is costly regarding the computation time, especially when more points are involved. The pseudo-inverse approach and the self- learning neural network assisted method improve the processing speed, while the modified pseudo-inverse further reduced the processing cost in solving the transformation. The methods by using quaternion or unit quaternion have obvious advantages and this will be covered below together with some other techniques.
In previous Sections 4.1 and Section 4.2, we mentioned some techniques for solving the rigid body transformation for localization process, such as the method of solving non- linear equations introduced in Refs. [49,80] and the pseudo- inverse method discussed in Ref. [13]; the minimization method illustrated in Refs. [54,63,74]; the minimization approached solved by a self-learning neural network by Ref. [4]; the modified pseudo-inverse approach developed in Refs. [92,93]; the method of using quaternion in Refs. [17,65,73], etc. For above approaches, the method of solving non-linear equations normally is costly regarding the computation time, especially when more points are involved. The pseudo-inverse approach and the self- learning neural network assisted method improve the processing speed, while the modified pseudo-inverse further reduced the processing cost in solving the transformation. The methods by using quaternion or unit quaternion have obvious advantages and this will be covered below together with some other techniques.
Comparison of four closed-form solutions for solving 3D transformation [58]
Comparison of four closed-form solutions for solving 3D transformation [58]
Fig. 11. Calculation procedure for localization with datum [91].
Fig. 11. Calculation procedure for localization with datum [91].

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