Ultraprecision grinding of small-aperture concave aspheric mould insert with tilt axis method

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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 71 (2018) 505–510 www.elsevier.com/locate/procedia

4th CIRP Conference on Surface Integrity (CSI 2018) 4th CIRP Conference on Surface Integrity (CSI 2018)

Ultraprecision of concave aspheric mould Ultraprecision grinding grinding of small-aperture small-aperture concave mould insert insert 28th CIRP Design Conference, May 2018, Nantes,aspheric France with tilt axis method with tilt axis method A new methodology to analyze the functional and physical architecture of a a a,b, Guangpeng Yan a, Kaiyuan Youa, Fengzhou Fanga,b,* Yan , Kaiyuan You , Fengzhou * identification existing productsGuangpeng for an assembly oriented productFang family a State a

Key Laboratory of Precision Measuring Technology & Instruments, Centre of MicroNano Manufacturing Technology, State Key Laboratory of Precision Measuring Instruments, Centre TianjinTechnology University,&Tianjin 300072, Chinaof MicroNano Manufacturing Technology, Tianjin University, Tianjin 300072, China College Dublin, Dublin, Ireland b School of Mechanical & Materials Engineering, MNMT-Dublin, University b School of Mechanical & Materials Engineering,E-mail MNMT-Dublin, University College Dublin, Dublin, Ireland * Corresponding author. Tel.: +86-222-740-7503; fax: +86-222-740-3753; address: [email protected] * Corresponding Tel.:Supérieure +86-222-740-7503; fax: +86-222-740-3753; E-mail address: Écoleauthor. Nationale d’Arts et Métiers, Arts et Métiers ParisTech, [email protected] EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat

* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract Abstract

With the widespread application of various small aspheric optical components, high-precision manufacturing technology of forming molds is With the widespread application of various small aspheric optical components, high-precision manufacturing technology of forming molds is deeply demanded. However, the ultra-precision grinding technology of small-aperture aspheric mould is still undeveloped. An ultraprecision Abstract deeply grinding technology of small-aperture aspheric mould still undeveloped. grindingdemanded. technique However, called tilt the axisultra-precision grinding which is based on the grinding spindle is tilt with the axisisof aspheric surface An andultraprecision profile error grinding technique called tilt axis grinding which is based on the grinding spindle is tilt with the axis of aspheric surface and profile error compensation of aspheric mould are studied. Through constructing geometric model of the tilt axis grinding, the tool path and the interference In today’s business environment, the trend towards more product variety and customization is unbroken. Due to this development, the need of compensation of aspheric mould are studied. Through constructing geometric model of the tilt axis grinding, the tool path and the interference conditions were calculated. The form error was compensated data measured by profiler. experimental testand is conducted to grind an agile and reconfigurable production systems emerged to cope with with the various products and product An families. To design optimize production conditions were calculated.mould The form error was compensated with the data measured by profiler. Anfrom experimental test is conducted grindtwo an aspheric of aperture 5 mm, and theproduct profile accuracy is gradually 0.652 to 89.3 nm methods in PVtoafter systems astungsten well as carbide to choose the optimal product matches, analysis methods are improved needed. Indeed, most μm of the known aim to aspheric tungsten carbide mould of aperture 5 mm, and the profile accuracy is gradually improved from 0.652 μm to 89.3 nm in PV after two compensation cycles. The surface roughness 10 nm inlevel. Ra. Different product families, however, may differ largely in terms of the number and analyze a product or one product family on theisphysical compensation cycles. The surface roughness is 10 nm in Ra. nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production Authors. Published by Elsevier Ltd. is an open access CC BY-NC-ND license © 2018AThe B.V.This system. new methodology is proposed to analyze existing products in article view ofunder theirthe functional and physical architecture. The aim is to cluster © 2018 The Authors. Published by Elsevier B.V. (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity 2018). these productsunder in new assembly oriented product families for the optimization of existing assembly lines and the(CSI creation of future reconfigurable Peer-review responsibility responsibility of the scientific committee of the 4th CIRP onConference Surface Integrity (CSIIntegrity 2018). (CSI 2018). Selectionsystems. andunder peer-review thephysical scientific committee of Conference the 4th CIRP on Surface assembly Based onunder Datum Flow Chain,ofthe structure of the products is analyzed. Functional subassemblies are identified, and Grinding; Tool apath; Formfunctional error compensation a Keywords: functionalAspheric; analysisUltraprecision is performed. Moreover, hybrid and physical architecture graph (HyFPAG) is the output which depicts the Keywords: Aspheric; Ultraprecision Grinding; Tool path; Form error compensation similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. Introduction required as the mould inserts, such as tungsten carbide and ©1.2017 The Authors. Published by Elsevier B.V. 1. Introduction required as the mould inserts, such as tungsten carbide and silicon other cemented carbides. None of these Peer-review under responsibility of the scientific committee of the 28th CIRP Designcarbide Conference 2018.

silicon carbide other cemented carbides. None of these With the increasing of imaging quality of optical devices materials can be machined with ultra-precision diamond With the increasing of imaging quality of optical devices materials can be machined with ultra-precision diamond Keywords: Assembly; Design method;of Family identification and the continuing shrinking imaging system volume, the turning or milling. Ultra-precision grinding is the most and the continuing shrinking of imaging system volume, the turning or milling. Ultra-precision grinding is the most demand for high-precision -aperture aspherical glass lenses is effective machining method for these materials [4]. Cross axis demand for high-precision -aperture aspherical glass lenses is effective machining method for these materials [4]. Cross axis increasing [1, 2]. Small aperture aspherical glass lenses are grinding is the most common grinding method for aspheric increasing [1, 2]. Small aperture aspherical glass lenses are grinding is the most common grinding method for aspheric mainly used in digital cameras, mobile phone lenses, DVD production. As shown in Fig. 1(a), the axis of grinding spindle 1.mainly Introduction of the product characteristics manufactured and/or used in digital cameras, mobile phone lenses, DVD production. Asrange shownand in Fig. 1(a), the axis of grinding spindle laser read heads, fiber optic couplers, and some optical is parallel to the X axis, and axis of workpiece spindle is assembled this context, main challenge laser read heads, fiber optic couplers, and some optical is parallelintothis thesystem. X axis,In and axis of the workpiece spindle in is transmission devices [3-5]. parallel to the Z axis. The trajectory of contact point between Due to the fast[3-5]. development in the domain of modelling analysis is now not only to cope withbetween single transmission devices parallel to and the Z axis. The trajectory of contact point In order to achieve mass production of small-aperture grinding wheel and workpiece is a meridian of the asphere on communication an ongoing trend of ofdigitization and products, a limited range existing of product families, In order to and achieve mass production small-aperture grinding wheel andproduct workpiece is aormeridian the asphere on aspheric lenses, precision glass molding (PGM) technology YOZ plane. If the minimum radius of curvature of the aspheric digitalization, manufacturing enterprises facingtechnology important but also to beIfable analyze radius and to of compare products define aspheric lenses, precision glass moldingare(PGM) YOZ plane. the to minimum curvature of the to aspheric has great advantages over conventional manufacturing surface is small, only small diameter diamond grinding challenges today’s market a continuing new product families.only It can be observed classical grinding existing has great inadvantages over environments: conventional manufacturing surface is small, small diameterthatdiamond methods, such as lapping and polishing. PGM technology wheels can be used for grinding. However, if the concave tendency product development times and product in function of clients or features. methods,towards such asreduction lapping ofand polishing. PGM technology wheels families can be are usedregrouped for grinding. However, if the concave enables one-step processing of ready-to-use optical surface of the part is deep, the grinding wheel shank will shortened In addition, there is an increasing However, families wheel are hardly to find. enables product one-steplifecycles. processing of ready-to-use optical surface ofassembly the partoriented is deep,product the grinding shank will components, which greatly shortens the processing cycle and interfere with the workpiece when the grinding wheel is components, which greatlybeing shortens thesame processing and interfere thefamily workpiece when thediffer grinding wheel is demand of customization, at the time incycle a global On the with product level, products mainly in two saves production costs [6 -9]. However, due to the high placed perpendicular to the work. Therefore, the cross axis competition with competitors all over the world. main characteristics: components (ii)axis the saves production costs [6 -9]. However, due toThis thetrend, high placed perpendicular(i)tothe thenumber work. of Therefore, the and cross temperatures and high pressures in the mold cavity during the grinding method is mainly applied to the manufacturing of temperatures and high in thefrom mold macro cavity during the grinding method is(e.g. mainly applied electrical, to the manufacturing which is inducing the pressures development to micro type of components mechanical, electronical).of molding process, special materials with high hardness, high asphere with convex form or with comparatively large molding results process,inspecial materials with high hardness, high asphere with convex form or withmainly comparatively large markets, diminished lot sizes due to augmenting Classical methodologies considering single products temperature resistance and thermal shock resistance are aperture [10]. Tilt axis grinding using a cylindrical grinding temperature resistance and thermal shock production) resistance [1]. are aperture [10]. Tilt axis grinding using families a cylindrical grinding product varieties (high-volume to low-volume or solitary, already existing product analyze the To cope with this augmenting variety as well as to be able to product structure on a physical level (components level) which identify in the existing causes difficulties regarding an efficient definition and 2212-8271 possible © 2018 The optimization Authors. Publishedpotentials by Elsevier B.V. 2212-8271 2018responsibility The itAuthors. Published Elsevier B.V. of the production system, is important tobyhave a precise knowledge comparison different product families. Addressing this Peer-review©under of the scientific committee 4th CIRP Conference on Surfaceof Integrity (CSI 2018). Peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.05.010

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Guangpeng Yan et al. / Procedia CIRP 71 (2018) 505–510 Author name / Procedia CIRP 00 (2018) 000–000

wheel, as shown in Fig. 1(b), can effectively prevent the interference between the grinding wheel shaft and the workpiece. Therefore, it is widely used for machining smallaperture aspheric surfaces [11, 12]. The axis of the grinding wheel and the axis of the workpiece keep an angle α in the XOZ plane in the grinding process. The grinding wheel moves along X, Y, Z axis simultaneously while the contact point between grinding wheel and workpiece always located in YOZ plane. In this study, the tool path generation strategy for tilt axis grinding of small-aperture concave aspheric is proposed. The interference of grinding wheel with the workpiece is analyzed and the criteria for selection of grinding wheel diameter for avoiding the interference is set up. Grinding test with compensation is conducted to verified the proposed tool path generation method.

 y  yo  a2

2

 z   z o   b2

2

 1

(3)

The parametric equation of Eq. (3) can be expressed as：

 y yo  a cos    z zo  b sin 

(4)

where  represents the angle between C ' O ' and the Y ' axis. The coordinates of the projective ellipse centre are：

 yo y  a cos    zo z  b sin 

(5)

Differentiating Eq. (5) ：

dz b cos  b    cot  dy a sin  a

(6)

Fig. 1. Schematic of aspheric grinding mode. (a) cross axis grinding; (b) tilt axis grinding.

2. Tool path planning and interference analysis 2.1. Tool path planning Fig. 2 shows the projection of the cylindrical grinding wheel on XOZ and YOZ plane. According to principle of projective geometry, the projection of the cylindrical grinding wheel edge is an ellipse. Supposing the radius of grinding wheel is a , the length of the major axis semidiameter of ellipse is a and the length of the minor axis semidiameter

(a)

b  a sin  . Where  is the angle between axis of grinding spindle and axis of workpiece spindle. At the contact point C between grinding wheel and workpiece, the ellipse and the aspheric meridian share the same normal vector:

nc '  nc

(1)

Eq. (1) represents that both the ellipse and the aspheric meridian have equal slope:

dzc dzc  dyc dyc

(2)

Setting  yo , zo  to be the centre of the projective ellipse.

(b) Fig. 2. Projection of the cylindrical grinding wheel in tilt axis grinding. (a) projection on XOZ plane; (b) projection on YOZ plane.

The aspheric meridian in YOZ plane can be written as:

 z  y

 y, z is an arbitrary point on the ellipse. The projective ellipse can be given:

y2 R

n

2

1  1  ( K  1) y R

Differentiating Eq. (7) ：

2

  A2i y 2i i 2

(7)



Guangpeng Yan et al. / Procedia CIRP 71 (2018) 505–510 Author name / Procedia CIRP 00 (2018) 000–000

dz df ( y )  dy dy

(8)

The value of  at the contact point by uniting Eq. (2), Eq. (6) and Eq. (8)

c

can be worked out

a df ( yc ) )  c arc cot(  b dyc

(9)

Now, the coordinates of the projective ellipse centre can be obtained:

 yo yc  a cos c   zo zc  b sin  c

(10)

where yc is known quantity, zc and

 c are obtained by

substituting y with yc in Eq. (7) and Eq. (9), respectively. In real machining, the contact point C always stay in the YOZ plane. According to the geometry relationship shown in Fig. 2(a), the X coordinates of point O ' is obtained:

x o

 zo  zc  cot 

(11)

The trace of O ' is the tool path for tilt axis grinding.

where

507 3

d 2 zc can be obtained by differentiating Eq. (6)： dyc 2

d 2 zc d (dzc / dyc ) d (dzc / dyc ) / d  b     2 3 2 dyc dyc dyc / d  a sin  and

(15)

d 2 zc can be obtained by differentiating Eq. (8). dyc 2

2.3. Case study In this example, two cylindrical grinding wheels with diameter of 5mm and 4mm were used to analyze the interference conditions for a designed aspheric surface with parameters shown in Table 1 Fig 3. demonstrates the curvature curves of aspheric meridian in YOZ plane, projective ellipses of grinding wheels with diameter of 5mm and 4mm. From this figure, the grinding wheel with diameter of 5mm will interfere to the aspheric surface at the distance to center around 2mm in grinding process, but the grinding wheel with diameter of 4mm will not. Fig 4 show the tool path generated for grinding wheel with diameter of 4mm. With the Y coordinate of point O ' increasing from the ordinate origin, both the X and Z coordinate increase. Table 1. Parameters of the aspheric surface

2.2. Interference analysis In grinding of concave surface, an interference between the grinding wheel and the workpiece will caused by choosing improper diameter of grinding wheel. In order to avoid possible interference, Ineq. (11) has to be satisfied.

RCurv ( yc , zc )  RCurv ( yc , zc )

(12)

Parameters

Values

R

10.71094

K

-104.9144

A4

1.0506696E-02

A6

-8.7250859E-05

A8

3.5132180E-06

A10

-1.8052060E-08

Aperture /(mm)

5.0

where RCurv ( yc , zc ) and RCurv ( yc , zc ) are the radius of curvature of the projective ellipse and the radius of curvature of the aspheric meridian in YOZ plane at the contact point C.

RCurv ( yc , zc ) and RCurv ( yc , zc ) can be got via the

formula of radius of curvature of curve: 3

RCurv ( yc , zc ) 

  dz 2  2 1   c     dyc   d 2 zc  dyc 2

(13)

3

  dz 2  2 1   c     dyc   RCurv ( yc , zc )   d 2 zc dyc 2

(14)

Fig. 3. Comparison of the curvatures of aspheric surface and projective curve of grinding wheels with different diameter.

Guangpeng Yan et al. / Procedia CIRP 71 (2018) 505–510 Author name / Procedia CIRP 00 (2018) 000–000

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Table 2. Conditions and process parameters used in the grinding experiments Rough grinding

Fine grinding

Machine

650FG, Nanotechnology System, USA

Workpiece

Tungsten carbide

Grinding wheel

Fig. 4. Tool path for grinding wheel with diameter of 4mm

3. Grinding experiments As shown in Fig. 5, a simultaneous 5-axis (X, Y, Z, B, C) controlled grinding machine (650FG, Nanotechnology System, USA) was used to conduct grinding experiments. The grinding wheel actuated in X, Y and Z-axes by the linear scale feedback system of 1 nm positioning resolutions. In the grinding test, the workpiece was vacuum chucked to the workpiece spindle. The diamond wheel was adjusted to grinding spindle with collet chuck on the Y-axis table. Table 2 shows the grinding conditions and process parameters. Two resinoid bonded diamond wheels of #325 and #2000 was used to conduct the rough and fine grinding tests, respectively. Wheels were trued to a cylindrical shape with sharp edge by the on-machine truer. Tungsten carbide was used as the material of workpiece. Aspheric surface with parameters shown in Table 1 was tested and the material of workpiece was tungsten carbide. workpiece spindle

nozzle

grinding wheel

Y

grinding spindle truer X

workpiece

Z

Fig. 5. Photo of the experimental setup.

After every fine grinding, the ground surface was measured by contact type of profiler (Form Talysurf) with a 2 μm radius stylus. Form error of the aspheric surface was analyzed by the measured data and used to compensation grinding.

Diameter /(mm)

3.985

Abrasive

Diamond

Bond

resinoid

Grit size

#325

3.993

#2000

Title angle α /(°)

45

Rotation speed of grinding wheel /(rpm)

45000

45000

Rotation speed of workpiece /(rpm)

157

157

Depth of cut /(μm)

2

0.5

Feedrate /(mm/min)

2

0.5

Coolant

ISO-PARH

4. Results and discussions Fig. 6 shows the profile error curves of the mould insert ground with the tilt axis grinding mode The first fine grinding was done without error compensation, which has a profile error of 651.9 nm in peak-to-valley (PV) value, as shown in Fig. 6(a). The V-shape profile in error curve is obvious, indicating that the setting offset of the wheel was inward. Thus in the next grinding cycle, the position of the wheel was adjusted in X-axis and the wear error in Z-axis was compensated in the new tool path. After the first fine compensation grinding with error compensation, the profile accuracy was improved to 288.9 nm in PV. From the error curve shown in Fig. 6(b), the tool setting error is not obvious, but the form error fluctuated with a magnitude of less than 0.3 μm along the radial direction. To further improve the accuracy, the compensation procedure was repeated. After the second fine compensation grinding, the profile accuracy was improved to 89.3 nm in PV. Fig. 7 shows the profile roughness of the ground aspheric surface measured by Form Talysurf. The average surface roughness values (Ra) obtained after the final grinding process was 10nm, which is sufficient for the following polish process [13]. Fig. 8 shows the morphology of the final ground aspheric surface measured by scanning electron microscope (SEM, FEI, Nova 200 Nanolab). At central area, the grinding occurred primarily in the ductile regime, resulting in the ground surface being fracture free, as shown as Fig. 8(a). The surface was very smooth. There was no crack on the surface. At the off central area, the material was removed mainly in the ductile regime. However, some small crack pits occurred. These crack pits may be caused by a relatively smaller relative velocity out of center.



Guangpeng Yan et al. / Procedia CIRP 71 (2018) 505–510 Author name / Procedia CIRP 00 (2018) 000–000

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(a)

(a)

(b)

(b) Fig. 8. SEM images of the final ground aspheric surface (a) central area; (b) off central area.

5. Conclusions (c) Fig. 6. Form error after (a)first fine grinding; (b)first fine compensation grinding; (c)second fine compensation grinding.

Tool path planning and interference of a cylindrical grinding wheel with the workpiece in tile axis grinding of small concave surface was studied and the criteria for selection of diameter of grinding wheel for avoiding the interference was set up. The experimental results showed that the grinding process was capable to generate small-aperture concave aspheric surfaces on tungsten carbide material that has high accuracy with a profile error of less than 100 nm in PV value and surface roughness 10nm in Ra value. Acknowledgements

Fig. 7. Roughness of the final ground aspheric surface.

The authors would like to acknowledge the financial support of the National Natural Science Foundation (No. 61635008, 51320105009 & 91423101), the National Key

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Research & Development Program (No. 2016YFB1102200), and the ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (No. B07014). References [1] Chen WK, Huang H, Yin L. Machining of micro aspherical mould inserts. Precis Eng 2005;29:315-323. [2] Chen FJ, Yin SH, Ohmori H, Yu JW. Form error compensation in singlepoint inclined axis nanogrinding for small aspheric insert. Int. J Adv Manufact Technol 2012;65:433-441. [3] Chen FJ, Yin SH, Huang H, Ohmori H, Wang Y, Fan YF, et al. Profile error compensation in ultra-precision grinding of aspherical surfaces with on-machine measurementInt. J Mach Tools Manufact 2010;50:480-486. [4] Brinksmeier E, Mutluguenes Y, Klocke F, Aurich JC, Shore P, Ohmori H. Ultra-precision grinding. CIRP Ann Manufact Technol 2010;59:652-671. [5] Meiners, Brinksmeier E, Riemer O, et al. Kinematics in ultra-precision grinding of WC moulds. International Journal of Nanomanufacturing 2011;7(3/4):199-213. [6] Yin SH, Jia HP, Zhang GH, Chen FJ, Zhu KJ. Review of small aspheric glass lens molding technologies. Frontiers of Mechanical Engineering 2017;12(1):66-76.

[7] Lee DK, Oh JG, Jang WG, Kim YG, Lee K, Park A, Yang YS. Thermal deformation compensation in the molding of aspheric glass lenses. Opt. Eng. 2014;53(6):065106.. [8] Cha DH, Kim HJ, Lee JK, Kim HU, Kim SS, Kim JK. A study of mould grinding and pressing conditions in the moulding of aspherical glass lenses for camera phone module. Mater Manufact Process 2008;23:683689. [9] Kim HJ, Kim HU, Kim SS, et al. Fabrication and optical evaluation of aspheric glass lenses for 3 megapixel zoom camera phone module. Optical Review 2007;14(3):145.. [10] Tohme YE. Grinding aspheric and freeform micro-optical molds. Proc Spie 2007; 6462:64620K-64620K-8.. [11] Chen FJ, Yin SH, Huang H, et al. Fabrication of small aspheric moulds using single point inclined axis grinding. Precision Engineering 2015;39:107-115. [12] Suzuki H, Kodera S, Maekawa S, et al. Study on Precision Grinding of Micro Aspherical Surface. Feasibility Study of Micro Aspherical Surface by Inclined Rotational Grinding. Journal of the Japan Society for Precision Engineering 1998;64(4):619-623. [13] Brinksmeier E, Riemer O, Gläbe RM. Fabrication of Complex Optical Components. Berlin Heidelberg: Springer; 2013.