A Precision Grinding Technique for Radome Inner Surfaces. Z.Y. Jia, T. Ji, D.M. Guo and G.H. Bian

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1 Key Engineering Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland A Precision Grinding Technique for Radome Inner Surfaces Z.Y. Jia, T. Ji, D.M. Guo and G.H. Bian School of Mechanical Engineering, Dalian University of Technology, Dalian , China Keywords: Radome, Inner Surface, Measurement, Precision Grinding Abstract. The radome is to ensure the antenna work normally in extreme harsh condition. It not only meets the shape aerodynamics requirement to withstand the thermal and mechanical loads during a high-speed flight, but also satisfies the electromagnetic property requirement. Electric thickness is an important electromagnetic performance index embodying the comprehensive influence of the geometric thickness, the material dielectric constant, and the incidence angle, on the electromagnetic wave transmission characteristics. After semi-finished machining, the electric thickness of the radome that is made of hard and brittle material often fails to meet the requirement owing to geometric error and non-uniformity of the dielectric constant. This electric thickness error has to be compensated through altering geometric thickness by precision grinding of the inner surface. Theoretically, the radome is a solid of revolution with a 3-D complex and curved surface. Therefore, the inner surface precision grinding is, in fact, a machining process for free form surfaces. In this paper, a digitized machining scheme and technical guideline is proposed. Firstly, the inner surface of the radome is precisely measured to set up a grinding datum. Secondly, the finishing grinding is performed based on the real inner surface and the required machining allowance. In addition, to avoid installation errors, the measuring and grinding processes are accomplished on the same machine tool for one-loading and two-operations. It is shown in practice that this technical guideline satisfies all of the performance index requirements for finish machining of the radome, effectively solving the difficult problem existed in finish machining of semi-finished radomes. Introduction The radome is in front of the antenna. It is an assembly to ensure the antenna working normally in an extremely harsh environment. The radome is required to be as transparent as possible to the signal received or radiated by the antenna so as to diminish its impact on the antenna system to the minimal extent. During the high-speed flying, the greater the Mach number, the greater the aerodynamic resistance. The severe friction between the air and the radome wall makes the surface temperature rise quickly, with the rising rate up to 50+C/s or even higher. The surface temperature may reach several hundreds or even several thousands degrees Celsius. Therefore, the radome body should be designed as streamline shape to obtain the least aerodynamic resistance. Meanwhile, it should be made of a special high-temperature resistant material, usually a kind of hard and brittle material. Therefore, it is required for the radome to satisfy not only the aerodynamics requirement for its shape to withstand the heat load and mechanical load during the high-speed flying, but also the electric performance requirements for the antenna system. It is for this reason that the research on its properties is an important task. Although the outer shape and the wall thickness tolerance of the semi-finished radome meet the aerodynamics requirement, the electric performance requirement is not yet satisfied owing to the non-uniformity of the dielectric constant in the material and the influence of manufacturing process. This should be compensated by some method. Presently, the commonly used method is that, first, analyze and determine the non-uniformity caused by the distortion of the electromagnetic wave passing through the radome wall and second, change the thickness of the wall in some location accordingly to make a compensation. In fact, this is a grinding method based on the electric All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (# , Pennsylvania State University, University Park, USA-18/09/16,11:49:39)

2 178 Advances in Abrasive Technology VI thickness index of the radome. For the semi-finished radome, the outer surface already meets the aerodynamics requirement and is not permitted to change. So, only the inner surface can be machined to change the thickness of the wall [1]. For radome, grinding method is specially required owing to the high-stiffness and brittle work material. In order to avoid the grinding liquid used in other methods, it would be better to use dry grinding. In the past, the manual grinding method was adopted for a long time, which was labor-intensive with a high reject rate, being hard to satisfy the quality requirement. To ensure the machining accuracy and efficiency, the precision grinding of the inner surface must be conducted on a special CNC grinding machine tool according to the required machining allowance. The technology discussed in this paper may carry out both the precision measuring of the radome inner surface and the precision grinding according to the required machining allowance at each specified point in the inner surface. Geometry Analysis of the Radome Fig.1 shows the outside view drawing of the radome. The outer surface of the radome is a surface of revolution determined by aerodynamics requirement. Theoretically speaking, its inner surface should be an equidistant surface of the outer surface, also a surface of revolution whose geometric accuracy could be ensured through the semi-finished process. But as mentioned above, it is still necessary to modify the inner surface by finish grinding to ensure the electric thickness satisfying the requirement. When the inner surface is grinded, it will lose its symmetry and become a complex 3-D curved surface. For this reason, precisely grinding of the inner surface of the radome practically is a machining process of a free curved surface [2]. Technology Guideline Fig.1 The outside view drawing of the radome The core technology of the precision grinding of the radome inner surface is to precisely grind the inner surface according to the electric thickness requirement of the radome. In addition, in order to avoid stress concentration influencing the mechanical strength, the ground inner surface should keep smooth. The grinding system should control the grinding wheel to grind the inner surface according to the real inner surface and the theoretical machining allowance at the specified point. (a) The machining allowance of the inner surface is a series of quantity relative to the points in the real inner surface. The real inner surface is a reference datum for determining the required machining allowance at any point. So, it is a key to the finish machining to precisely measure the inner surface at first. It is necessary to perform the digitized tracing measuring and the real-time data acquisition in the real inner surface and to formulate a data file for the point set. (b) Process the obtained data in the point set to reconstruct the pre-machining inner surface and obtain the discrete point set of the inner surface. Determine the normal direction to the inner surface at any point. (c) Reconstruct the post-machining inner surface according to the discrete point set, the normal direction and the required machining allowance in the pre-machining inner surface and obtain the

3 Key Engineering Materials Vols discrete point set in the post-machining inner surface. Determine the normal direction to the post-machining inner surface at any point. (d) Determine the center position of the grinding wheel according to the normal direction to the post-machining inner surface and the radius of the spherical grinding wheel and obtain the point set of the surface to be traced by the center of the grinding wheel. (e) Make the trajectory planning for the grinding wheel to generate NC machining program. (f) Conduct the NC grinding on the same equipment and carry out the finishing machining of the radome. Fig. 2 The CNC grinding machine tool for the radome (g) Digitized measurement, data acquisition and processing and NC machining are all performed on a special three-coordinate CNC grinding machine tool as shown in Fig. 2. In order to avoid the installing error coming from separate loading operation and to ensure the grinding accuracy, the measuring and grinding of the inner surface are integrated in the same machine tool. The measuring and grinding process are accomplished in a manner of once-loading and two-step-operation. The data obtained during measuring process is processed directly by IPC (Industrial Personal Computer) to plan a grinding locus to perform the grinding. Measuring of the Inner Surface and Data Acquisition The measuring element includes the X and Z direction linear displacement grating sensors, the <-axis angular displacement photoimpact encoder and the gauge head. The gauge head is a special length measuring instrument for micro displacement which is used to measure the micro deviation =x in X-axis direction between the real value and theoretical value [3]. In measuring operation, the real-time data acquisition will be carried out based on such a measuring scheme as comparing the real inner surface with the theoretical one and separating the driving and the measuring. Concretely, the gauge head of the measuring rod is placed on the inner surface of the radome in XOZ plane and the servomechanism drives the gauge head scanning the inner surface according to the locus of the theoretical inner surface. The IPC synchronously collect the feedback value of the micro displacement length-measuring instrument, X-axis direction grating rule, Z-axis direction grating rule and <-axis photoimpact encoder. The coordinate value in X-axis direction is read by the X-axis direction grating and the gauge head jointly as (x+=x). Therefore, the coordinate of the points in the real inner surface can be expressed with (x+=x, z, <). In order to facilitate the data acquisition and processing and to raise the measuring speed, the scanning locus of the gauge head on the inner surface is specified as a circumference in a series of cross-sections perpendicular to the axis of the radome. Meanwhile, in order to reduce the measuring

4 180 Advances in Abrasive Technology VI points and to ensure the measuring accuracy and the fitting accuracy of the curved surface during the data processing, the constant error principle is adopted in data acquisition. Data Processing The data processing is required to complete the reconstruction of the pre-machining inner surface, the post-machining inner surface and generation of the locus surface of the grinding wheel center. In the inner surface measuring operation, the random error among the sample points will result in a unsmooth surface reconstructed, leading to miscalculation of the unit normal vector of the inner surface and the locus error of the grinding wheel center. For this reason, a least-squares method based bi-cubic B-spline function is employed in surface reconstruction, which effectively decreases the impact of the measuring random error and ensures the accuracy of the reconstructed surfaces [4]. Reconstruction of the Pre-Machining Inner Surface. The pre-machining inner surface is the reference surface of the finish grinding. Reconstruction of the pre-machining inner surface is a surface fitting based on the discrete data from measuring of the real inner surface. For example, if there are N=(m+1) (n+1) controlling vertices d i,j,(i=0,1,m,j=0,1,,n), the order of the given parameter u and v are k and l, respectively, and the two node vectors are U = [ u0, u1, L, u m + k+ 1] ; V = [ v0, v1, L, v n + l+ 1]. Then the B-spline surface equation will be [5] m n P ( u, = d N ( u) N ( v, u u u, v v v ), (1) i= 0 j= 0 i, j i, k j, l ) ( k m+ 1 l n+ 1 where N i,k (u) and N j,l ( are B-spline base function; when k=1=3, Eq. (1) is the bi-cubic B-spline surface equation. Suppose the inner surface to be found is P 1 (u,. According to Eq. (1), only if the controlling vertices d i,j are found, the inner surface can be reconstructed. The measured points in the inner surface are P i, i=0,1,2, N. According to the least-squares method, the equation regarding the controlling vertices d i,j that would fit the measured discrete points in the least-squares sense will be obtained as min N i= 0 2 P ( u i, v i ) Pi. (2) Substituting d i,j into Eq. (1), we may complete the reconstruction of the pre-machining inner surface. Reconstruction of the Post-Machining Inner Surface. The purpose of this reconstruction is to obtain the locus surface of the grinding wheel center and to ensure the smoothness of the machined inner surface. The post-machining inner surface P 2 (u, is reconstructed according to the pre-machining inner surface P 1 (u, and the given machining allowance at each point q i in the inner surface. Determine the normal direction to P 1 (u, passing through point q i based on the minimum distance mapping principle. Take off the given machining allowance along the normal direction, the discrete points in the post-machining inner surface will be obtained. Based on these discrete points, the post-machining inner surface P 2 (u, can be reconstructed in a same way as reconstructing the pre-machining inner surface. Generation of the Locus Surface of the Grinding Wheel Center. The locus surface of the grinding wheel center provides a basis for obtaining the grinding path and the final CAM program. The post-machining inner surface and the locus surface of the grinding wheel center are equidistant surfaces. Therefore, the unit normal vector n(u, at arbitrary point in the locus surface of the grinding wheel center is identical to that to P 2 (u,.

5 Key Engineering Materials Vols Suppose r p is the radius of the grinding wheel. The locus surface P 3 (u, of the grinding wheel center can be obtained as p 3 2 ( u, = p ( u, rpn( u,. (3) NC Machining An unequally-spaced sectional ring-cutting approach is adopted in NC machining of the inner surface of the radome. This approach plans the cutting locus in such a way that the width of the machining belt along the generator direction is determined by the constant scallop-height method and the step size along the circumferential direction is determined by an isoparametric method. The curvature of the generator of the radome varies continuously and so, the constant scallop-height method is adopted along the generator to increase the machining efficiency. In the cross-section, however, the sectional curve is a closed curve approaching to a circle. Therefore, using the isoparametric method is simple in calculation, without loss in machining efficiency. Based on the constant scallop-height method, the distance between the two consecutive machining belt along Z-axis direction are determined by [6] L i * R i-1 2 2hR, (4) * R i-1 R where h is the given scallop height, R * i-1 is the radius of curvature of the generator at Z i-1, R is the radius of the grinding wheel and L i is the distance between the center lines of the two consecutive machining belts in Z-axis direction. The next sectional position is obtained as Z i =Z i-1 +L i. (5) A series of unequally-spaced cross-sections at positions perpendicular to Z-axis can then be obtained by recursion method. The radius of curvature R * i-1 of the generator increases along with increasing of Z and, hence, the distance L i will decrease accordingly. In other words, the machining belts in the inner surface will gradually get dense from the cone tip to the large end of the radome. At each cross-section obtained above, a series of discrete points are obtained on the sectional curve approaching to a circle by the isoparametric method, which is a basis for generating a CAM program. According to this CAM program, the NC machining is performed on the special 3-axis inner surface grinding system. Conclusions Based on the technology guideline proposed in this paper, all the software and hardware of the grinding control system and the machine tool are developed. On the developed special precision measuring and grinding system for radome inner surface, the grinding test was performed using the radome of some type. The test results demonstrate that all the performance indexes, such as the machining accuracy and the smoothness of the surface etc., meet the requirements, reaching the expected objective. The system has been appraised and accepted by an authentic group of experts and is also appreciated by its user. The precision grinding technology discussed in this paper has effectively solved the difficult problem existed in finish machining of the semi-finished radome, capable of rapidly and precisely measuring and grinding the inner surface of the radome according to the required machining allowance. As a result, the manufacturing accuracy of the electric thickness of the radome is ensured. It fills up the gap in that field in China.

6 182 Advances in Abrasive Technology VI Acknowledgment The authors are very grateful to the Hi-Tech Research and Development Program of China for its financial support for this project under grant No.2001AA References [1] W.Z. Peng: Anti-aircraft Missile Radome (Astronavigation Press, China 1993). [2] D.M. Guo, X. Lou, X.M. Wang and Z.Y. Jia: Chinese Journal of Mechanical Engineering, Vol. 37 (2001), p. 92. [3] D.M. Guo, X.J. Sheng, Z.X. Xu, Z.Y. Jia and X.M. Wang: Journal of Dalian University of Technology, Vol. 42 (2002), p [4] C.C. Liang and G.C.T. Lin: CTMS, Vol. 10 (1997), p. 49. [5] F.Z. Shi: CAGD & NURBS (Higher Education Press, China 2001). [6] B.Y. Ren and Y.Y. Tang: Theory and Application of Geometry Modeling in NC Machining (Harbin Institute of Technology Press, China 2000).

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