Design, fabrication and measurement of ultra-precision micro-structured freeform surfaces

Computers & Industrial Engineering 61 (2011) 216–225

Contents lists available at ScienceDirect

Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie

Design, fabrication and measurement of ultra-precision micro-structured freeform surfaces q L.B. Kong ⇑, C.F. Cheung State Key Laboratory in Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

a r t i c l e

i n f o

Article history: Received 4 June 2010 Received in revised form 22 March 2011 Accepted 25 March 2011 Available online 3 April 2011 Keywords: Structural freeform surfaces Ultra-precision machining Fast Tool Servo machining Precision surface measurement Integrated platform Pattern analysis

a b s t r a c t Due to the geometry complexity and high precision requirement, there still possess a lot of challenges in the design, manufacturing and measurement of ultra-precision micro-structured freeform surfaces (e.g. microlens array) with submicrometer form accuracy and surface finish in nanometer range. Successful manufacturing of ultra-precision micro-structured freeform surface not only relies on the high precision of machine tools, but also largely depends on comprehensive consideration of advanced optics design, modelling and optimization of the machining process, freeform surface measurement and characterization. This paper presents the theoretical basis for the establishment of an integrated platform for design, fabrication, and measurement of ultra-precision micro-structured freeform surfaces. The platform mainly consists of four key modules, which are Optics Design Module, Data Exchange Module, Machining Process Simulation and Optimization Module and Freeform Measurement and Evaluation Module. A series of experiments have been conducted to evaluate the performance of the platform and its capability is realized through a trial implementation in design, fabricating and measurement of a microlens array. The results predicted by the system are found to agree well with the experimental results. These show that the proposed integrated platform not only helps to shorten the cycle time for the development of microlens array components but also provides an important means for optimization of the surface quality in ultra-precision machining of micro-structured surfaces. With this successful development of the system, optimal machining parameters, the best cutting strategy, and optimization of the surface quality of the ultra-precision freeform surfaces can be obtained without the need for conducting time-consuming and expensive cutting tests. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The high value-added photo-electronic parts currently have been shifted from the traditional symmetrical surfaces to microstructural and non-rotational symmetric complex freeform surfaces. The market for structured freeform optics is huge and also in rapid growth. Structured freeform optics developed based on micro-structural freeform surfaces has become the critical parts in various optical imaging and illumination systems such as digital camera, diffraction optics instrument, broadband fiber coupling, TV of back reflection, collimator and reflector in automotive lamp. Demand for freeform optics drives the development of ultraprecision machining technology of freeform surfaces. However, the achievement of a superior mirror finish and high accurate surface by ultra-precision machining still depends largely on the q

This manuscript was processed by area editor Satish Bukkapatnam.

⇑ Corresponding author. Tel.: +852 2766 6623; fax: +852 2764 7657. E-mail address: [email protected] (L.B. Kong).

0360-8352/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2011.03.014

experience and skills of machine operators through an expensive trial-and-error approach when new materials, new surface design or new machine tools are used. In addition, the cutting strategy in ultra-precision machining is extremely important, with decisions such as whether to cut in only one direction, or both, or, whether to program raster cuts or spiral cuts, or other strategies (Kim & Kim, 1995; Ramos, Relvas, & Simões, 2003; Sun, Guo, & Jia, 2006). Moreover, the machining time cannot be minimized effectively since optimal cutting parameters are difficult to obtain manually using a trial-and-error approach. Relatively little quantitative work has been reported. Although some attempts have been made in the development of geometrical models to simulate surface topography of a workpiece (Bailey, Elbestawi, El-Wardany, & Fitzpatrick, 2002a, 2002b; El-Mounayri, Elbestawi, Spence, & Bedi, 1997; Lai, Lin, Huang, & Zeng, 2001; Lin & Shen, 2003; Weinert, Du, Damm, & Stautner, 2004), most of them focus on the synthesis of surface topography from a number of limit points generated from CAD/CAM system. The effect of cutting mechanics and the materials factors on surface roughness have been overlooked in most of

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

the studies of surface generation in freeform machining (Brecher et al., 2006; Duc, Lartigue, Tournier, & Bourdet, 1999; Lartigue, Duc, & Tournier, 1998; Zhu, Kapoor, & DeVor, 2001). As the optimal cutting conditions and cutting strategy depend largely on the machining environment, work materials and the geometry of surfaces being cut, there is a need for the development of an integrated platform which takes into account the processes in the generation of the freeform surface from optics design, ultraprecision machining, measurement of the surface and optical quality evaluation. An integrated platform provides an important means for the optimization of the cutting strategy as well as the prediction of surface generation in ultra-precision machining. The development of the integrated platform demands multidisciplinary knowledge and a considerable amount of research work such as optics design, ultra-precision machining, materials science, surface characterization, freeform surface measurement, etc. Also, it involves a large amount of research work on modelling and simulation and experimental verification. State-of-the-art research only focuses on some of the individual components of the platform such as tool path generator (Elbert & Cohen, 1993; Kim & Jeong, 1995; Zhang, Deng, & Chan, 2000), product data exchange (An, Leep, Parsaei, & Nyaluke, 1995), etc., however, there is a lack of research work which has developed all components and provides their systematic integration. As a result, this paper presents the theoretical basis for the development of an integrated platform for design, fabrication, and measurement of ultra-precision micro-structured freeform surfaces. The results of the experimental verification of the performance of the platform will also be discussed. An application of the platform for the optics design, fabrication and measurement of a microlens array will be used to demonstrate the capability of the platform.

2. Theoretical basis and architecture of the integrated platform An integrated system to develop and produce new optical components requires an optical design which fulfills the desirable optical and functional requirements. Hence, the ultra-precision machining of the optical surface is undertaken based on the results of the optical design. To avoid expensive trail-and-error approach to achieve expected surface quality in ultra-precision machining process, a model-based simulation and optimization system is necessary to determine the optimum machining parameters and to carry out the machining error budgets, as well as the feasibility of the machining process. Due to the need to integrate different software and algorithms, there is a need to develop a data exchange module to realize the data file exchange among different software modules. For example, the designed surface model is exported as Initial Graphics Exchange Specification (IGES) data file from optical design software, and the exported data needs to be transformed into scattered coordinate point data and they are then fitted to polynomial or Non-Uniform Rational B-Spline (NURBS) surface. Hence, tool path is generated and the surface generation is simulated during the ultra-precision machining. After the machining of the workpiece, the measurement and evaluation of the surface quality are necessary to ensure the quality of the machined surface to meet the requirement of the end product. These provide form or surface roughness information as a feedback to the machining process so as to carry out the error compensation and error diagnosis. Therefore, the developed integrated platform consists of four key modules, which are Optics Design Module (ODM), Data Exchange Module (DEM), Machining Process Simulation and Optimization Module (MPSOM) and Freeform Measurement and Evaluation Module (FMEM), as shown Fig. 1. In the ODM, freeform surface is designed and also optimized according to the light

217

distribution requirements; optical simulation and a series of tests are carried out to ensure the designed freeform surface meets the requirements of the applications. Then the standard CAD file is generated and subsequently processed by the DEM. Continuous freeform is reconstructed from scattered points which are obtained from the CAD file by data transformation. Hence, the data are imported to MPSOM. In this module, the tool path is generated after the compensation of cutting path, and simulation of the machining process is done to predict the surface generation and diagnosis of process problems such as tool collision, optimum cutting strategy, and error compensation. Optimized NC tool path is then generated and employed in the real cutting process. The machined microstructured freeform surface is measured and the surface data are processed in the FMEM. Different freeform characterization methods have been developed to evaluate the freeform quality including surface finish and form error. Finally, a comprehensive report is generated to provide the overall information during the complete process. 2.1. Optics design module Due to the limitation of design and optimization process for general optics design software packages (e.g. Zemax, CodeV), it is a time consuming task to adjust and select parameters manually when designing an asymmetrical freeform optical surface, further more, it will take one or even several months to design a more complex freeform surface, sometimes still can not achieve an expected optical performance. During the past decade, significant amount of research work has been carried out in freeform optics design by the research group (Cheung, Lee, Wang, & Jiang, 2007; Jiang, Cheung, To, Cheng, Wang, & Lee, 2006; Jiang, To, Lee, & Cheung, 2005; Lee, Cheung, To, Gao, & Wang, 2005; Lee, To, & Cheung, 2005; Wang, To, Cheung, Jiang, & Wang, 2009). As shown in Fig. 1, optics design module is developed for optics design and simulation of optical performance, and the optics design data can be output as CAD file for further processing. A precise computation algorithm for freeform control knot vectors has been proposed based on the principle of conservation for edge-ray Etendue (Jiang et al., 2006), which can accomplish the design of freeform optical part with optimum efficiency and accuracy light distribution in a short time period (e.g. a few hours or even shorter). 2.2. Data exchange module The aim of surface reconstruction is to find a continuous surface fitted from the scattered points based on a certain criteria, The fitted surface is used as the designed reference surface for the subsequent freeform machining and characterization. Parametric representation of freeform surface includes polynomials, Bezier, B-spline, Non-uniform rational B-spline (Nurbs) and so on. The freeform surface with form accuracy of micrometer or submicrometer is difficult to be described precisely. In this module, the scattered points representing the freeform optical surface are generated from the design CAD data. Fig. 2 shows the flow chart of the freeform reconstruction and optimization. The freeform continuous model is optimized by proper selection of the parameters (e.g. the order of polynomial, order and weight of Nurbs, etc.). 2.3. Machining simulation and optimization module With the development of single point diamond turning technology, one of the supreme methods which are commonly used in fabrication of microstructures is ultra-precision machining with the Fast Tool Servo (FTS). FTS which is independently operated positioning device is usually mounted onto ultra-precision machines

218

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

Data Exchange Module

Optics Design Module Optics Design

CAD File

CAD Data Exchange

Clouds of Points

Freeform Reconstruction

Tool path compensation

Machining Simulation & Optimization Module Cutting Strategy & Condition Optimization

Machining Error Compensation

Machining Process Simulation

Tool Path Generation

Ultra-precision machining

Freeform Measurement & Characterization Module Freeform Measurement

Measured Data

Designed Model

Freeform Characterization

Fig. 1. An integrated system for freeform optics design, fabrication and measurement.

Standard Design of Light CAD file Distribution

CAD Data Exchange

Continuous C Scattered Optimization of Surface S Points Surface Model

Fig. 2. Flow chart of freeform reconstruction and optimization module.

for increasing the tool positioning accuracy in order to fabricate optical microstructures by the rapid actuation of tools with a fine resolution and positioning accuracy and a sufficient high bandwidth. FTS machining process provides an indispensable solution for machining optical microstructures with sub-micrometer form accuracy and a nanometric surface finish without the need for any subsequent processing. Fig. 3 illustrates the motion of axes involved in ultra-precision machining with FTS. The machining simulation and optimization module is based on freeform tool path generator (Lee, Cheung, et al., 2005; Lee, To, et al., 2005) and model-based simulation systems (Cheung, Kong, Lee, & To, 2006; Kong, Cheung, Lee, & To, 2007). Freeform tool path generator is used to generate NC code automatically from the optics design parameters. A model-based simulation system is employed for the prediction, the simulation and the optimization of surface generation in ultra-precision machining process.

2.3.1. Simulation model for surface generation Surface generation by FTS machining is contributed by two major parts which can be presented as

S ¼ ST þ SF

ð1Þ

where ST is the contribution of ultra-precision turning process; SF is the contribution of Fast Tool Servo. The surface generated by turning process is described as following:

8 > < X T ¼ r cosðhÞ ST : Y T ¼ r sinðhÞ > : Z T ¼ f1 ðX T Þ where

Fig. 3. Diagram of diamond turning lathe assembled with FTS.

ð2Þ

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

(

r ¼f t

Z  ðr; uÞ is the non-rotationally symmetric motion which is enabled by activation of FTS. Simulation algorithm of surface generation in ultra-precision FTS machining process is illustrated in Fig. 4. The major variable is time t, which is applied to determine the changes of regional variables, distance in radial direction: r and angles. The surface generation consists of two parts: one of them is the surface generation by FTS which contributes the characteristic profile of fabricated surface and another is contributed by turning process which is the traditional rotational surface such as spherical or aspherical surface.

ð3Þ

V h ¼ x  t ¼ 60 2p  t

And function f1 ðX T Þ defines the surface profile, e.g. for a plane,

f1 ðX T Þ ¼ CðConstantÞ f is the feed rate in mm/min, and V is the spindle speed in rpm. For the surface generated by FTS:

8 > < XF ¼ 0 SF : Y F ¼ 0 > : Z F ¼ f2 ðr; hÞ

ð4Þ

where  h ¼ modðh; 2pÞ, mod(a, b) means the modular after division of a/b. By controlling the motion of diamond tool in the position in Z direction, non-rotationally symmetric (nrs) profiles can be fabricated and derived as

Z nrs ðr; uÞ ¼ Z rot ðrÞ þ Z  ðr; uÞ

2.3.2. Tool path generation Tool path generation which can be described as position to be cut in machining process is the first step for programming CN code of machining. In order to fabricate accurate profile, it is critical to compensate the deviation of tool nose radius involved in tool path generation. The motion axes involved in diamond turning with FTS are X-axis (feed direction) and Z-axis (cutting direction) separately. Compensation of tool nose radius is only necessary in feed profile, which can be illustrated as a 2-D curve as shown in Fig. 5. In the previous section, the cutting locus in the workpiece surface has been derived. That means the trace of cutting point

ð5Þ

where Z rot ðrÞ represents the conventional rotational surface, which can be defined by

Z rot ðrÞ ¼

n X cr2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ai r i 2 2 1 þ ð1  ðk þ 1ÞÞc r i¼1

ð6Þ

r = f ⋅ t ,θ =

Variable: t

V 2π ⋅ t 60

Region Determination by ( r , θ )

In Microstructure Region? Y

N

FTS Surface:

Turning Surface:

⎧X F = 0 ⎪ S F : ⎨YF = 0 ⎪Z = f ( r , θ ) 2 ⎩ F

⎧ X T = r cos(θ ) ⎪ S T : ⎨YT = r sin(θ ) ⎪Z = f ( X ) 1 T ⎩ T

Surface Generation:

⎧ X = X T + X F = r cos(θ ) ⎪ S = S T + S F : ⎨Y = YT = r sin(θ ) ⎪Z = Z + Z = f ( X ) + f ( r , θ ) T F 1 T 2 ⎩ Fig. 4. Simulation algorithm of surface generation in FTS machining.

Y

Diamond Cutting Tool

Rotation

X'

Central

P

Line

Rp ϕp

219

RT RP

X Z

T rc

nP P

Profile in radial direction

X' Fig. 5. Compensation of tool nose radius for tool path generation.

220

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

P : ðPx ; Py ; P z ÞorðRp ; uP ; Pz Þ has been set and then the tool path is generated by compensating the tool nose radius, which is calculated based on center location of diamond tool nose. Supposing the tool nose center is T : ðT x ; T y ; T z ÞorðRT ; uT ; T z Þ and the radius is rc , the normal vector of the workpiece profile at the point PðRp ; uP Þ is nP : ðnx0 ; nz Þ (Note that nP is not the normal vector of the surface at point P). Referring to Fig. 5, the following relation can be derived:

8 T x ¼ RT  cosðuT Þ > > < T y ¼ RT  sinðuT Þ n x0 > > ffi  rc : T z ¼ Pz þ pffiffiffiffiffiffiffiffiffiffi

ð7Þ

n20 þn2z x

where

(

nz ffi  rc RT ¼ RP þ pffiffiffiffiffiffiffiffiffiffi 2 2 n 0 þnz

ð8Þ

x

uT ¼ uP

To compute the normal vector at a point in a 2D curve line, suppose the 2D curve line is presented as

Fðx; zÞ ¼ 0

ð9Þ

Then the normal vector at point P0 ðx0 ; z0 Þ is

Np0 ¼ ðF x ðP0 Þ; F z ðP0 ÞÞ ¼ ðF x ; F z Þjx¼x0 ;

ð10Þ

z¼z0

where

Fx ¼

@F ; @x

Fz ¼

@F @z

ð11Þ

In the present research, the profile in radial direction is firstly fitted by some methods (e.g. polynomial fitting) as a continuous curve line to obtain the function Eq. (9), and then the normal vector at any point in the curve line can be determined. 2.3.3. Surface roughness model The micro-structured surface is machined by diamond turning process with Fast Tool Servo, therefore the surface roughness can be derived similar to the diamond turning process, as shown in Fig. 6. Some parameters can be derived as follows. Surface residual peak-to-valley is derived as

Rt ¼ r 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2  ðs=2Þ2 ¼

ðs=2Þ2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r þ r 2  ðs=2Þ2

ðs=2Þ2 ¼  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 þ 1  ðs=ð2rÞÞ2

ð12aÞ

Ra ¼ 0:032

f2

ð13Þ

rS2

2.4. Measurement and characterization module The research on the mathematical model of form error is mainly focused on the specifications of straightness, roundness and flatness etc., and some breakthroughs have been found on the theory of surface evaluation, optimization, and evaluation criteria. However, most of the research targets the conic curve and the surface; relatively little research has contributed to the freeform surfaces, and no related international standard has been established for evaluating the form errors. In this module, evaluation algorithms have been developed for the comprehensive characterization of micro-structural surface such as microlens array, such as matching approach base method (MABM) and feature parameter based method (FPBM). Characterization of a single lens surface includes surface finish, form error and dimension feature evaluation and so on. For the whole array evaluation, data processing is first conducted to remove noise, and then the microlens array pattern is identified by pattern recognition analysis. After that a series of grid parameters are derived such as spacing deviations, dislocation angular deviations, profile feature parameters, and other dislocation parameters. Fig. 7 shows the sketch map of metrology for microlens array characterization. Characterization of microlens array consists of two aspects: one is the analysis of the pattern of the array; the other is single lens surface characterization such as roughness and form error. For the characterization of microlens array, one import step is the detection of the boundary of each lens. To detect the boundary, connectivity should be defined first. As shown in Fig. 8, generally there are two types of definition for connectivity, 4-connected neighborhood and 8-connected neighborhood (Huang, An, & Luo, 2005). Different definition of connectivity will generate different boundary and different subsequent area and perimeter calculations. Supposing the boundary edges of each lens are determined as Bi ; i ¼ 0; 1;    ; n; then area and the perimeter will be obtained as follows: (1) Calculation of perimeter P:

for s  r, therefore Eq. (12a) can be simplified as

Rt ¼

where, s is feed rate in mm/rev, r is tool nose radius in mm, f is feed rate in mm/min, S is spindle speed in rpm. Surface roughness (arithmetic mean value) can be presented as follows (Whitehouse, 2003):

ðs=2Þ2 s2 f2 f2 ¼ 0:125 2 ¼ ¼ 2 2r 8r 8rS rS

P¼ ð12bÞ

n X

li

ð14Þ

i¼1

Surface Finish Measurement Instrument

Feed rate per revolution: s

Single Microlens Characterization

Dimension Features

Microlens Data Measurement

Feed direction Tool nose radius: r Rt

Form Accuracy

Microlens Array Characterization

Spacing Deviation

Surface Data Processing Angular Deviation Pattern Recognition

Lattice Parameters

Profile Roundness Other Dislocations

Fig. 6. Surface roughness produced by turning process (round tool nose).

Fig. 7. Sketch map of microlens array characterization.

221

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

1

2

3

2

0

where (i) 4-connectivity, li ¼ Bi Bi1 ¼ 1; ei ¼ 0; 1; 2; 3 (ii) 8-connectivity, pffiffiffi li ¼ Bi Bi1 ¼ f1 : ei ¼ 0; 2; 4; 6; 2 : ei ¼ 1; 3; 5; 7g

1

0

4

ei is the connectivity sequence, as shown in Fig. 8. (2) Calculation of area A

7

5

3

6

(a)

(b)

Fig. 8. Two definitions of connectivity for the regions: (a) 4-connected neighborhood; (b) 8-connected neighborhood.

λh11 λh12

λh1,n−1

...

There are two definitions for area; one is defined as number of the pixels inside the boundary, and the other is number of the grids formed by the pixels inside the boundary. In the present study, the second definition is employed to calculate the area enclosed by the boundary. Assume the starting point is ðx0 ; y0 Þ;then the y coordinate of ending point of jth pixel is.

yj ¼ y0 þ

A4 ¼

λv21

φ

λvm−1,n−1 φ

λvm−1,1 λhm−1,n−1

i¼1

v m −1

8 > < 1 : ei ¼ 0 Dxi ¼ 0 : ei ¼ 1; 3 > : 1 : ei ¼ 2

8 > < 1 : ei ¼ 1 Dyi ¼ 0 : ei ¼ 0; 2 > : 1 : ei ¼ 3

ð17Þ

For 8-connectivity, the area is

A8 ¼

n i X X ððy0 þ Dyj ÞDxi þ ai Þ i¼1

j¼1

where

φ nh−1

ð16Þ

j¼1

where

v ij

λijh

n n i X X X ðyi1 Dxi Þ ¼ ððy0 þ Dyj ÞDxi Þ i¼1

v 2

...

...

λ

φ 2h

ð15Þ

Then for 4-connectivity, the area is

φ1v

φ1h

Dy i

i¼1

λv11

...

j X

Fig. 9. Microlens array lattice parameter characterization.

Introduction

Optics Design

Machining Process

Measurement

Reports

Exit

Fig. 10. A snapshot of the developed software interface.

ð18Þ

222

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

8 > < 1 : ei ¼ 1; 2; 3 Dyi ¼ 0 : ei ¼ 0; 4 ; > : 1 : ei ¼ 5; 6; 7 8 1=2 : ei ¼ 1; 5 > < ai ¼ 0 : ei ¼ 0; 2; 4; 6 > : 1 : ei ¼ 3; 7

8 > < 1 : ei ¼ 0; 1; 7 Dxi ¼ 0 : ei ¼ 2; 6 ; > : 1 : ei ¼ 3; 4; 5 ð19Þ

Lattice Dislocation (LD) parameters have been developed to characterize the relative position errors among the microlens as shown in Fig. 9. The centers of the lens profiles are obtained by

the least-squared circle fitting from the boundaries detected in the previous section. It is assumed that the microlens is an m  n array, so the horizontal distance between the lens can be derived as khij ði ¼ 1; 2;    ; m  1; j ¼ 1; 2;    ; n  1Þ while the vertical distance as kvij (ði ¼ 1; 2;    ; m  1; j ¼ 1; 2;    ; n  1Þ). All the lens centers form a grid, and the grid dislocations are defined as horizontal dislocation (angular deviation) /hk ðk ¼ 1; 2;    ; m  1Þ and vertical dislocation /vl ðl ¼ 1; 2;    ; n  1Þ,which can be obtained by grid lines fitting from the centers of the lens profiles. 3. Experimental verification and implementation results

Table 1 Experimental design for surface roughness study (workpiece material: Al6061). Sample no.

Parameters Spindle speed (S: rpm)

Feed rate (f: mm/min)

Tool nose radius (r: mm)

Depth of cut (DOC: lm)

S1 S2 S3 S4 S5 S6 S7 S8 S9

50 50 50 75 75 75 100 100 100

0.5 1 1.5 0.5 1 1.5 0.5 1 1.5

0.2 0.3 0.4 0.2 0.3 0.4 0.2 0.3 0.4

5 10 15 5 10 15 5 10 15

Table 2 Design specification of microlens array.

A prototype of the integrated platform is established by MatlabÒ and MicrosoftÒ Visual C++. Fig. 10 shows a snapshot of the developed system software interface. The software mainly consists of five functional modules, which are Introduction module, Optics Design module, Machining Process module, Measurement module and Report module. The optics design interface includes the link to commercial optics design software, standard CAD file (e.g. IGES file) view and data exchanges. The machining process has the sub-functional module such as simulation of machining and surface generation, optimization of cutting conditions and cutting strategies, tool path generator and other tools (e.g. machine dynamic monitoring and cutting force analysis, etc.). Measurement module consists of freeform characterization methods for the freeform surface. Finally, reports on the overall production flow are generated. 3.1. Experimental studies

Pattern

Dot spacing

Depth

Radius

Angles

Diameter

13  13

1 mm

0.03 mm

1.1705 mm

13°

0.5266 mm

Two experimental studies were undertaken to verify the developed model-based simulation system and structured surface

Fig. 11. Comparisons between the predicted surface roughness and the measured results.

Fig. 12. Case study: microlens array, (a) microlens array mould insert manufactured by FTS; (b) 3D topography of horizontal spacing deviation.

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

characterization method in the integrated platform. One of the experimental studies was conducted to validate the surface roughness model. The workpiece samples were made of Al6061, and they were machined by using Nanoform 200 equipped with Fast Tool Servo (FTS) from Precitech Inc. of USA. The surface being machined is a tilted flat surface with a diameter of 10 mm. The machined surface was measured by Wyko NT 8000 from Veeco Inc. of USA. Table 1 shows the experimental design which involves nine samples. The

223

cutting speeds were selected based on the considerations: (1) to achieve good surface quality; (2) to produce tilted flat surface by using FTS process, during which low cutting speeds are usually used due to the characteristics of the Tool Servo such as the servo bandwidth. The other experiment was the measurement for a microlens array, which is used in light guide panel for mobile phone, PDF, TV, etc. One 13  13 spherical microlens array was machined by the

Fig. 13. Form error pattern of the tilted plat machined by FTS (under the same cutting conditions): (a) Wyko NT8000; (b) error pattern of the tilted plat.

Optics Design & Simulation

Machining Process Simulation

Microlens Array Form Error Analysis Tool Path & NC Code Generation

Results Report Generation Fig. 14. Snapshots of result of the application of the proposed integrated system for design, fabrication and measurement of a microlens array.

224

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225

Nanoform 200 diamond turning tool assembled with Fast Tool Servo (FTS). The design specifications of the microlens array are shown in Table 2. The workpiece was made of Al6060. The machining parameters include spindle speed: 100 rpm; feed rate: 1 mm/ min; depth of cut: 5 lm. 3.2. Results and discussions Fig. 11 shows a comparison between the predicted surface roughness and the measured results for the machining of the tilted flat surfaces. From the experimental results, it is found that the predicted values agree well with the measured results. This further validates the developed model in the proposed integrated platform. There exist some deviations between the predicted and measured results, which might be caused by some factors such as material factors (material swelling, etc.), Fast Tool Servo hysteresis, etc. These factors are not included in the current study and they will be studied in the future work. Fig. 12a shows the microlens array mould insert, which was measured by Talysurf CCI 3000 from Taylor-Hobson Ltd of UK. Fig. 12b is the horizontal spacing deviations characterized by the proposed FPBM. It is interesting to note that the spacing deviation is almost centrosymmetric, which reveals the important fact that the dislocation of the microlens varies with the relative position of the microlens to the rotational center. A significant phenomenon observed from the experimental results is that the overall deviation exhibits a regular pattern which is possibly due to the systematic errors of the Fast Tool Servo. To verify this phenomenon, a tilted plate was machined under the same cutting conditions. The workpiece surface was measured by an optical profiler, Wyko NT8000 from Veeco Inc. USA. This is shown in Fig. 13a while the measured form error of the 3D topography, after tilting, is shown in Fig. 13b. It is interesting to note that the form error exhibits a similar pattern to the experimental results produced in FTS machining of the microlens array. This further confirms the validity and efficiency of the proposed characterization method for the characterization of surface generation in optical microstructures. Fig. 14 shows a snapshot of the process flow for the application of the proposed integrated system for design, fabrication and measurement of the microlens array. As shown in Fig. 14, it starts with optics design, surface generation and process simulation of machining by FTS, the generation of the machine tool path and NC program, measurement and characterization of the machined microlens array by the matching approach and feature parameter based method, respectively. Finally, the report for overall machining process is provided.

more comprehensive model-based simulation system will be established to predict, simulate and optimize the surface generation; (3) Different characterization methods and parameters will be developed for the measurement and evaluation of structured freeform surfaces. For example, the evaluation of the pattern of the structured surfaces, functional parameters for microstructural freeform surfaces, etc.; (4) The integrated platform will be packaged into user friendly software which provides different interfaces with machining equipments and metrology instruments. Hence, the surface data can be acquired and tool path can be generated more conveniently and interactively. 5. Conclusions Currently, the high value-added photo-electronic parts have been shifted from the traditional symmetrical surfaces such as spherical and aspheric surfaces to micro-structural and nonrotational complex freeform surfaces such as microlens arrays, pyramid, etc. They are fabricated by Fast-Tool-Servo (FTS) technology with submicrometer form accuracy and surface finish in nanometer range. However, the achievement of a superior mirror finish of ultra-precision machining still depends largely on the experience and skills of machine operators through an expensive trialand-error approach when new materials, new surface design or new machine tools are used. Moreover, there is lack of integrated platform which can cater for bridging the technological gaps in design, fabrication and measurement in FTS machining of optical micro-structured surfaces. In this paper, the technological development of an integrated system for optical design, ultra-precision machining and precision measurement of optical microstructures are presented. The platform has been built based on different core technologies such as data interchange from optics design to the reconstruction of the microstructured surfaces, tool path generation, modeling and simulation, and hence the measurement and characterization of the surface quality of the workpiece. With the successful development of the platform, the optimal machining parameters and strategies can be obtained. The machining and measuring process can be simulated on the computer and the verified data can then be input into the advanced CNC ultra-precision machine equipped with Fast Tool Servo for machining the components. This results in shortening the cycle time for product development and in improving the quality of the product without the need for time-consuming and expensive trial cutting tests. Acknowledgement

4. Suggestions for future work The development of an integrated platform involves considerable amount of research work. Some research work will be done in the future to make the developed integrated platform more comprehensive. They include: (1) A study of the relationship between optical performance and geometry features, and hence a mathematic model or data base will be established, which will provide suggestions during the optical design and machining process such as machining tolerance settings, etc.; (2) More factors affecting the machining process and the generation of the structured freeform surface will be investigated. These include the study of material effect on surface roughness, the effect of machine tool vibration and the hysteresis of the Fast Tool Servo, etc. Hence, a

The authors would like to express their sincere thanks to the Research Grants Council of the Government of the Hong Kong Special Administrative Region of the People’s Republic of China for financial support of the research work under the Project no. PolyU 5141/08E. References An, D., Leep, H. R., Parsaei, H. R., & Nyaluke, A. P. (1995). A product data exchange integration structure using PDES/STEP for automated manufacturing applications. Computers & Industrial Engineering, 29(1–4), 711–715. Bailey, T., Elbestawi, M. A., El-Wardany, T. I., & Fitzpatrick, P. (2002a). Generic simulation approach for multi-axis machining, part 1: Modeling methodology. Journal of Manufacturing Science and Engineering, 124(3), 624–633. Bailey, T., Elbestawi, M. A., El-Wardany, T. I., & Fitzpatrick, P. (2002b). Generic simulation approach for multi-axis machining, part 2: Model calibration and feed rate scheduling. Journal of Manufacturing Science and Engineering, 124(3), 634–642.

L.B. Kong, C.F. Cheung / Computers & Industrial Engineering 61 (2011) 216–225 Brecher, C., Lange, S., Merz, M., Niehaus, F., Wenzel, C., & Winterschladen, M. (2006). NURBS based ultra-precision free-form machining. CIRP Annals-Manufacturing Technology, 55(1), 547–550. Cheung, C. F., Kong, L. B., Lee, W. B., & To, S. (2006). Modelling and simulation of freeform surface generation in ultra-precision raster milling. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 220(B11), 1787–1802. Cheung, C. F., Lee, W. B., Wang, B., & Jiang, J. B. (2007). Design and fabrication of electronic and optical systems for advanced automotive lighting. Advanced optics (1st ed., Vol. 2). Hong Kong: The Hong Kong Polytechnic University Press (ISBN978-962-367-569-7). Duc, E., Lartigue, C., Tournier, C., & Bourdet, P. (1999). A new concept for the design and the manufacturing of free-form surfaces: The machining surface. CIRP Annals-Manufacturing Technology, 48(1), 103–106. Elbert, G., Cohen, E. (1993). Tool path generation for freeform surface models. In 2nd ACM solid modeling ‘93-5/93/Montreal. Canada (pp. 419–428). El-Mounayri, H., Elbestawi, M. A., Spence, A. D., & Bedi, S. (1997). General geometric modelling approach for machining process simulation. International Journal of Advanced Manufacturing Technology, 1, 237–247. Huang, A. M., An, X. J., & Luo, L. (2005). ShuZi TuXiang ChuLi: FenXi JiChu. Beijing: China WaterPower Press, pp. 256–258 (in Chinese). Jiang, J. B., Cheung, C. F., To, S., Cheng, K., Wang, H., Lee, W. B. (2006). Design and fabrication of freeform reflector for automotive headlamp. In Proc. 2nd ICPESA, November 12-14, Hong Kong (pp. 220–224). Jiang, J. B., To, S., Lee, W. B., & Cheung, B. (2005). Design of the freeform V-cut optics in the cell phone backlight system. Chinese Journal of Liquid Crystals and Displays, 20(3), 178–184. Kim, K. I., & Kim, K. (1995). A new machine strategy for sculptured surfaces using offset surface. International Journal of Production Research, 33(6), 1683–1697. Kim, K., & Jeong, J. (1995). Tool path generation for machining free-form pockets with Islands. Computers & Industrial Engineering, 28(2), 399–407. Kong, L. B., Cheung, C. F., Lee, W. B., & To, S. (2007). A framework of an integrated platform for modelling and measurement of freeform surface generation in ultra-precision raster milling. Key Engineering Materials, 339, 422–426.

225

Lai, X. M., Lin, Z. Q., Huang, T., & Zeng, Z. P. (2001). A study of a reverse engineering system based on vision sensor for free-form surfaces. Computers & Industrial Engineering, 40, 215–227. Lartigue, C., Duc, E., & Tournier, C. (1998). Machining of free-form surfaces and geometrical specifications. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 213, 21–27. Lee, W. B., Cheung, C. F., To, S., Gao, D., & Wang, S. J. (2005). An investigation of fast tool servo machining of optical microstructures. Nanotechnology and Precision Engineering, 3(3), 216–221. Lee, W. B., To, S., & Cheung, C. F. (2005). Design and advanced manufacturing technology for freeform optics. Hong Kong: The Hong Kong Polytechnic University Press (ISBN-962-367-476-7). Lin, Y., & Shen, Y. (2003). Modelling of five-axis machine tool metrology models using the matrix summation approach. International Journal of Advanced Manufacturing Technology, 21, 243–248. Ramos, A. M., Relvas, C., & Simões, J. A. (2003). The influence of finishing milling strategies on texture, roughness and dimensional deviations on the machining of complex surfaces. Journal of Materials Processing Technology, 136, 209–216. Sun, Y. W., Guo, D. M., & Jia, Z. Y. (2006). Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach. Journal of Materials Processing Technology, 180, 74–82. Wang, W. K., To, S., Cheung, C. F., Jiang, J. B., & Wang, B. (2009). A new method to test the photometric characteristics of lamps for motor vehicles. Optik – International Journal for Light and Electron Optics, 120(11), 549–552. Weinert, K., Du, S. J., Damm, P., & Stautner, M. (2004). Swept volume generation for the simulation of machining processes. International Journal of Machine Tools and Manufacture, 44(6), 617–628. Whitehouse, D. J. (2003). Handbook of surface and nanometrology. Bristol and Philadephia: Institute of Physics Publishing, p. 708. Zhang, L., Deng, J., & Chan, SC-F. (2000). A next generation nc machining system based on NC feature unit and real-time tool-path generation. International Journal of Advanced Manufacturing Technology, 16, 889–901. Zhu, R., Kapoor, S. G., & DeVor, R. E. (2001). Mechanistic modeling of the ball end milling process for multi-axis machining of free-form surfaces. Journal of Manufacturing Science and Engineering, 123(3), 369–379.