Freeform Surface Profile Research Articles

Freeform measurement method based on differential confocal and real-time comparison

To meet the need for the high-precision contactless measurement of the freeform surface profile during the manufacturing, we propose a high-precision measurement method that combines the laser differential confocal trigger sensor (LDCTS) and the real-time comparison method using reference planes (RCMRP). LDCTS is used to measure the freeform surface under test (FSUT), which enables the high-precision measurement of the surface profile with the large roughness and local inclination. Through the real-time comparisons of the coordinate changes of the reference planes and FSUT, the dominant straightness and rotation errors can be separated based on the error model and thus the spatial motion errors can be significantly reduced along all three axes. Combing these two strategies, we find that the inclination measurement capacity becomes larger than 25° and the repeated measurement accuracy is improved to be better than 10 nm within the horizontal scanning range of 150 mm × 150 mm. Compared with the non-RCMRP method, the repeated measurement accuracy is improved by at least 5 times. We believe the proposed method provides a strategy for the high-precision measurement of freeform surface profile with large local inclination and roughness during different manufacturing periods.

A novel 3D radius compensation method of probe stylus tip in the free-form surface profile curve scanning measurement

The normal vectors of the free-form surface profile curve are generally not in the same plane, even if the profile curve is generated from the interaction between a plane and a surface. If the 2D compensation vector is adopted to reduce the cosine error, the accuracy is limited because the normal direction of the curve plane is not considered. In this paper, a novel radius compensation method adopts the 3D compensation vector instead of the 2D compensation vector like most existing works. An approximating method is proposed to estimate the 3D compensation vector, which is composed of two parts. One is the projection of the 3D vector in the curve plane that is calculated by the normal vector of the non-uniform rational Bézier spline fit curve. The other is the normal vector of the curve plane passing the measuring point. In addition, the deviation between the workpiece and CAD model may degrade the accuracy of the radius compensation. Through theoretical analysis, the influence of the deviation cannot be ignored when the deviation is larger than 0.2 mm. By setting up this threshold, under various levels of torsion angles and deviations for the free-form surface, the results show that the compensation accuracy of the proposed method has a better performance than traditional 2D compensation methods, which decreases the maximum error from 70.8 to 2.6 μm.

A study of a priori knowledge-assisted multi-scopic metrology for freeform surface measurement

The traditional multi-scopic metrology system makes use of a micro lens array to capture a raw 3D-image of the target surface in a single snapshot through a CCD camera under normal illumination. However, the resolution of the system depends on the matching precision and efficiency of disparity information during the processing of the 3D raw data. In this paper, the a priori knowledge-assisted multi-scopic metrology is studied and an a priori knowledge-assisted multi-scopic metrology system is established which makes use of patterned illumination custom-designed based on the a priori knowledge of the target freeform surface profile. The a priori knowledge provides abundant versatile known information for a precise and efficient matching process so as to enhance the measuring performance. A customized disparity matching process based on the a priori knowledge is developed accordingly for high-resolution 3D surface reconstruction. An experimental study for measuring freeform surface is conducted to verify the feasibility of the proposed a priori knowledge-assisted multi-scopic metrology system through the comparison between that using normal illumination and a priori knowledge-assisted patterned illumination.

Surface generation of freeform surfaces in diamond turning by applying double-frequency elliptical vibration cutting

A new freeform surface generation method for the difficult-to-cut materials is proposed in this paper. Fast tool servo and slow slide servo diamond turning are the main generation technologies for freeform surfaces, whereas they cannot machine the freeform surfaces of difficult-to-cut materials very effectively. On the other hand, elliptical vibration cutting has demonstrated its excellent performance in material processing, especially for the difficult-to-cut materials. Nevertheless, it is unable to generate the freeform surfaces very successfully. Therefore, this paper proposes the double-frequency elliptical vibration cutting method for the freeform surface diamond machining on the difficult-to-cut materials, which provides the high-frequency elliptical vibration to improve the machinability in material removal and the low-frequency reciprocating movements for the freeform surface profile generation. The relative movements between the tool and the workpiece are analyzed, and because of the Y direction elliptical vibration, the cutting plane does not always cross the workpiece center, which makes the tool path generation, the tool geometry selection and the surface topography prediction very different from those in the conventional fast tool servo or slow slide servo diamond turning. A new tool path generation method is proposed, and the selection of the tool geometry parameters is discussed. The surface generation process is analyzed, based on which the topography model for the machined surfaces is constructed. Three typical freeform surfaces are machined on the die steel workpieces, which verifies the feasibility of the proposed tool path generation strategies. In addition, the experimental results agree well with the surface topography predictions, which validates the effectiveness of the topography model. This model also applies to the diamond turning processes with tool motion in the Y direction, such as turning with EVC.

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%–22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.

Freeform Surface Measurement from a Single Encoded Image Captured by a Camera with Varying Parameters

In this paper, we present a method of measuring a freeform surface profile from a single image taken by a vision system consisting of a digital camera and a pattern projector. The measurement can be implemented without calibrating the camera’s parameters, provided that the intrinsic and extrinsic parameters of the projector are known. The method enables the camera to have much more adaptability for measuring a stationary or moving object with complex shape of surface.

Intermittent Process Measurement of a Freeform Surface Profile with a Circular Triangulation Laser Probe on a Machining Centre

μm. In this case, the tolerance of the designed part is about 50 μm, so the developed system can be applied to the inspection of mould production in bakelite according to the experimental results.