Recently, freeform surfaces are widely used in optical field. Fabrication of freeform surface optics needs high machining accuracy and high efficiency simultaneously. Using the present ultraprecision manufacturing technologies, the form accuracy of freeform surfaces can reach submicrometric or even nanometer range but at the cost of low efficiency; moreover, the form accuracy cannot be predicted; the number and the position of cutter points cannot be accurately controlled before practical machining. A novel strategy of cutter points distribution is proposed in the paper, which is based on the required accuracy of the freeform surface and the machining efficiency can be improved by eliminating redundant cutter points on the processing trajectory. The new idea is detailed, simulations are conducted, and experiments are done to verify the feasibility of the proposed method in fabricating two sinusoidal ring surfaces.

With the development of high-technology, the optical freeform components have become more and more widely applied in recent years, especially in advanced optical system. For such system, the freeform components can minimize system sizes, lower weight, enhance imaging quality, and provide some other advantages [

There are many literatures analyzing the efficiency issue from different topics, such as optimizing machining parameters [

For cutter point, the commonly used generation methods are getting the point equally spaced angles and equally spaced chords in plane spiral tool path [

In this paper, the cutter point generation method based on form accuracy control in whole surface is studied, and the single point diamond turning (SPDT) technology is adopted to analyze the improved method. The main purpose is to generate the effective cutter point according to the given form accuracy requirement, which can both increase the machining efficiency and predict the precision ahead of machining. To verify the novel cutter points’ generation method, experiments are done for machining two sinusoidal ring surfaces with different required form accuracy.

For SPDT, the trajectory of diamond tool is composed by a series of cutter points. Generally, the model of the ultraprecision diamond turning machining tool is shown in Figure

The model of the ultraprecision diamond turning machining tool.

Equally spaced angles is the most common method used to generate cutter points on

Schematic diagram of equally spaced angles.

The form accuracy of machined surface can be seen as a measure which is used to evaluate the effective of the adopted cutter points. Since the ideal curve is approximated by polylines which composed by cutter points, the chord error must be existent between ideal curve and approximated polylines. So, the form accuracy can be reflected by chord error of cutter tool path, and the smaller chord error is, the higher form accuracy is.

To further analyze the characteristic of equally spaced angle points, the sinusoidal ring surface is taken as the example. The equation of sinusoidal ring surface is presented as

The cutter points of equally spaced angles in

The change of chord error for two adjacent points of equally spaced angles in

It can be found that the equally spaced angles cannot achieve the prediction of form accuracy when generating the cutter points, which not only lower the efficiency, but also lower the quality of whole surface, so it is very necessary to research a method that generates the cutter point according to the limitation of form accuracy in whole surface.

The main idea of form accuracy control proposed in this paper is generating cutter point based on the given requirement for form accuracy rather than confirmation about the range of accuracy after generating the point. This new method can predict form accuracy and increase the harmoniousness of accuracy in whole surface.

The schematic diagram of the proposed method is indicated in Figure

The schematic diagram of proposed method for cutter point generation.

To verify the effectiveness of the proposed cutter point generation method, cutter points of sinusoidal ring surface are generated under the condition of two kinds of form accuracy, which are 1

Two kinds of generated cutter points with proposed method (a) chord error is 1

To test the practicability of the proposed method, the chord error for produced tool path composed of calculated cutter points is computed, and the result is demonstrated in Figure

The error between theoretical curve and polyline constituted of cutter points with proposed method; (a) the predefined chord error is 1

Based on the above theory, two sinusoidal ring surfaces with the corresponding parameters given above were fabricated in ultraprecision machining system, the Nanoform250. Material of the workpieces is Al-6061. A diamond tool with the nose radius of 0.506 mm, including angle of 120° and clearance angle of 10°, was applied. Figure

Machining process (a) chord error is 1

Diagram of measurement (a) chord error is 1

Analysis figures of the 1

Analysis figures of the 0.1

Figure

Figure

In real machining process, the PVT interpolating mode is used. Usually, execution time of each instruction is a constant, then total executing time of the program for predefined 0.1

Based on the theoretical analysis and experimental verification, the following conclusions can be drawn.

A novel cutter point generation method is presented based on the required form accuracy of the machining surface; this method can eliminate redundant cutter points, improve the machining efficiency, and predict the number and locations of the cutter points.

Simulations are conducted for two sinusoidal ring surfaces with 0.1

Two Al-6061 workpieces with sinusoidal ring surfaces are machined which are based on the cutter points generated by the novel method. The profiles of the two machined sinusoidal ring surfaces are measured and analyzed. It can be found that, under different required form accuracy, different practical machined surfaces will be obtained. The practicability of the proposed method can be verified.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the National Key Basic Research and Development Program (973 Program) of China (Grant no. 2011CB706702), Natural Science Foundation of China (Grants nos. 51305161 and 51135006), and Jilin province science and technology development plan item (Grant no. 20130101042JC).