Measurement profile of surface revolution by laser scan micrometer method is a non-contact measurement method that allows de-tailed profile measurements with fast measuring speed by using laser scanning and accuracy is much higher than other non-contact scanning methods. This paper presents the mathematical model profile of surface revolution and the application of the laser scan micrometer method for measuring this detailed profile. Fabricating complete equipment model according to the author's proposed method. Compare the results of measuring the profile of surface revolution on a construction measuring device with a roundness meter Jenoptik F315 to prove the feasibility of the construction measurement method

Cam, Le Xuan

Hai, Hoang Hong

Vinh, Nguyen Van

English

American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS)

    36   American Scientific Research Journal for Engineering, Technology,  and Sciences  (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers  http://asrjetsjournal.org/   Measurement Profile of Surface Revolution by Laser Scan Micrometer Method Le Xuan Cama*, Nguyen Van Vinhb, Hoang Hong Haic aMsc. School of machanical  engineering, Hanoi University of Science and Technology, Vietnam bAssoc Prof Dr. School of machanical  engineering, Hanoi University of Science and Technology, Vietnam cPhD. School of machanical  engineering, Hanoi University of Science and Technology, Vietnam aEmail: camlx@mcit.vn bEmail: xuancam.doluongvcn@gmail.com  Abstract Measurement profile of surface revolution by laser scan micrometer method is a non-contact measurement method that allows de-tailed profile measurements with fast measuring speed by using laser scanning and accuracy is much higher than other non-contact scanning methods. This paper presents the mathematical model profile of surface revolution and the application of the laser scan micrometer method for measuring this detailed profile. Fabricating complete equipment model according to the author's proposed method. Compare the results of measuring the profile of surface revolution on a construction measuring device with a roundness meter Jenoptik F315 to prove the feasibility of the construction measurement method. Keywords: Measurement profile; Surface revolution; Profile of surface revolution; Laser scan micrometer; Mathematical model; Roundness; Straightness. 1. Introduction  Details of revolution are common details in mechaning engineering and profile deviations are important factors that greatly affect the quality of the work of this detail, especially for detail that require mounting  accuracy high, participating in rotary movements such as the drive shaft of the processing machine, the tool axis, the axis of the measuring device, the printing device axis, ammuni-tion weapon details, .... Therefore, it is important to determine the profile and  profile deviations of surface revolution in the pro-duction process to better control the quality of the detail after machining. ------------------------------------------------------------------------ * Corresponding author.  American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  37  In recent years, measurement profile method used by scanning lasers has been used extensively in industrial measurement due to the combination of the outstanding advantages of contactless measurement methods and the fast and accurate measurement speed high of laser. Currently, studies focus on profiling instruments by the method of analyzing the laser beam reflected from the surface of the measuring part, such as the measurement method of light wave transmission time, stereo imaging method, light structure method, .... Based on these studies, manufacturers of measuring equipment also offer a wide range of products for quick measure-ment of detailed profiles in industrial production. The above methods give fast measurement speed but the accuracy is limited to a few dozen micrometers. For details of revolution that require high profile accuracy, in addition to fast measurement speed, accuracy is also considered. The measurement profile method using laser scan micrometer is a new solution to overcome the above limitation. 2. Mathematical model profile of surface revolution  Figure 1: Modeling profile of surface revolution. Considering the details in the coordinate system for OXYZ as shown in Figure 1, the profile of surface revolution is formed by the successive pairing of the OXY cross-sections along the Z axis.  Mathematical model profile of surface revolution  ,r z  as an extended Fourier function [1,2], shown by the following formula:    01, ( )cos( ) ( )sin( )p ppr z r z a z p b z p        (1) Where: z is the cross-section position, θ is the angle of rotation of details and r0(z) is the medium radius of the cross-sectional profile, ( ) ( )p pa z jb z is the pth harmonic vector of the cross-sectional profile and can be expressed by Legendre interpolation:  0aMjp pjja z a z ;  0bMjp pjjb z b z  (2) Replace equation (2) into (1): American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  38         0 10 10 11 11 1 12 22, cos( ) sin( ) z cos( ) zsin( ) cos( ) sin( )( ) cos( ) ( )sin( )a bM Mj jj jj jp ppr z r z a b a b a z b za z p b z p                            (3) In equation (3), components 2 to 5 are first-order harmonic components that describe the Least Squares Center (LSC) of the cross-sectional profile in the OXYZ coordinate system. Components 2 and 3 are linear components along the Z axis. Although the direction and position of a part can generally vary in different coordinate systems, the detail profile will not change. Therefore, the mathematical model profile of surface revolution can be expressed by equations:        0 1 2, , ,r z r z r z r z      (4) Where:   1 1 1 1 12 2, cos( ) sin( ) ( )cos( ) ( )sin( )a bM Mj jj jj jr z a z b z a z b z                    (5) is the first harmonic component characteristic of the center of the cross-sections and is determined by the least square center (LSC). The second component  2 ,r z   represents the non-roundness of each section and is determined as follows:  22, ( )cos( ) ( )sin( )p ppr z a z p b z p       (6)  Figure 2: Profile of surface revolution. Thus, profile of surface revolution may be considered as a collection of cross sections arranged along a curved centerline. We can use the cross section method to measure the eccentricity, the roundness and the LSC vector of each cross section along the rotating part, then rebuild the profile of surface revolution according to equation (4).   American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  39  3. Measurement profile of surface revolution by laser scan micrometer method  Figure 3: Structure measurement machine Profile of surface revolution. As analyzed above, in order to construct a profile of surface revolution, we need to determine the position of the  cross section and the profile of each section shown by the parameters: radial deviation, roundness and Least Square Centre LSC of the cross section. Therefore, two translational and rotating movements must be created for the measuring device. The translational motion is through a screw - nut movement mechanism and the position is determined by an electronic photometer. Using a rotating angle mechanism connected to the self-centering 4-spoke chuck to clamp the workpiece, the rotation angle is determined through the ecoder. With the diameter parameters determined by the method of laser scan micrometer combined with updated information from electronic optical ruler and ecoder, we can completely build a set of measurement data points at the measurement positions on the profile of surface revolution. Using the formula (4) from the set of measurement data points, we can completely reconstruct the measurement profile of surface revolution and at the same time be able to identify profile errors at different locations.   Figure 4: Machine Laser scan micrometer. The average diameter of detail in a cross section in the position z: 10(z, ) (z, )(z)2ni iiP Hrn  (7) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  40  Determine the centers of sections using the Least Squares Center method (LSC) [4] from the measurement data set. The least square center of coordinates is defined as follows: 112cos2sinni iini iia rnb rn  (8) The profile of the z-section is determined as follows:  Figure 5: Cross section z. 0(z, ) (z, )(z) (z)2i iiP Hr r     (9) 4. Experiment 3.1. Experiment equipment Using the laser scan micrometer of Keyence model LS-5041T / R [3-5] with basic specifications: + The distance between the transmitter and receiver is: 160 ± 40 mm; Measuring range: (0,2 to 40) mm + Resolution: 0,05 µm; Repeatability: Maximum ± 0,3 µm; Accuracy: ± 2 µm + Laser scan speed: 1200 scans/second; Laser scanning speed: 121 m/sec + Laser source: 670 nm red semiconductor laser, 0,8 mW output, type II. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  41   Figure 6: Experimental device model. 3.2. Experimental results - Sample for experiment: Cylindrical with diameter of 20,004 mm; length 80 mm. Measure the profile at points 5 mm apart. - The measurement results determine the detailed center position and the profile at some positions: + Measurement position 1: Table 1: Measurement data at position 1.   Angle Diameter (mm) Error profile ri1 (µm) ri1 (mm) a1 (µm) b1 (µm) r01 (mm) 300 20,0038 0,017 10,0040 1,49 - 0,54 10,0019 600 20,0038 0,017 10,0026 900 20,0038 0,017 10,0012 1200 20,0047 0,467 10,0002 1500 20,0038 0,017 9,9999 1800 20,0037 -0,033 10,0004 2100 20,0036 -0,083 10,0010 2400 20,0037 -0,033 10,0020 2700 20,0039 0,067 10,0025 3000 20,0036 -0,083 10,0031 3300 20,0032 -0,283 10,0028 3600 20,0036 -0,083 10,0025   Figure 7:  The cross-sectional profile is at position 1 with the roundness measured as 0,75 µm. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  42  + Measurement position 2: Table 2: Measurement data at position 2.  Angle Diameter (mm) Error profile ri1 (µm) ri1 (mm) a1 (µm) b1 (µm) r01 (mm) 300 20,0041 0,129 10,0022 1,57 -0,49 10,0019 600 20,0048 0,479 10,0003 900 20,0038 -0,021 9,9992 1200 20,0038 -0,021 10,0024 1500 20,0037 -0,071 9,9986 1800 20,0031 -0,371 9,9987 2100 20,0038 -0,021 9,9993 2400 20,0040 0,079 10,0005 2700 20,0039 0,029 10,0017 3000 20,0035 -0,171 10,0021 3300 20,0040 0,079 10,0026 3600 20,0037 -0,071 10,0024   Figure 8:  The cross-sectional profile is at position 2 with the roundness measured as 0,85 µm. + Measurement position 3: Table 3: Measurement data at position 3. Angle Diameter (mm) Error profile ri1 (µm) ri1 (mm) a1 (µm) b1 (µm) r01 (mm) 300 20,0044 0,129 10,0029 1,42 -0,90 10,0021 600 20,0046 0,229 10,0019 900 20,0044 0,129 10,0011 1200 20,0047 0,279 9,9998 1500 20,0041 -0,021 9,9996 1800 20,0041 -0,021 10,0006 2100 20,0042 0,029 10,0012 2400 20,0041 -0,021 10,0020 2700 20,0040 -0,071 10,0027 3000 20,0031 -0,521 10,0031 3300 20,0040 -0,071 10,0030 3600 20,0040 -0,071 10,0031   Figure 9:  The cross-sectional profile is at position 3 with the roundness measured as 0,80 µm. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  43   Figure 10: Cylindrical profile on straight line 15mm, Straightness is 2,1 µm. The measured sample is defined on the JENOPTIK F135 roundness meter as a basis for comparison with the method of author construction. The result of the roundness at the three positions is respectively: 0,51 µm; 0,87 µm; 0,93 µm. Straightness is 1,95 µm.    Figure 11: Roundness meter JENOPTIK F135. Experimental results  measurement the roundness and straightness on construction equipment compared with the measurement on the roundness meter JENOPTIK F135 are relatively similar. 4. Conclusion The content of the paper presented the mathematical basis for building a profile of surface revolution. Analyze the components to determine whether a complete profile of surface revolution can be measured. Application of the laser scan micrometer method in combination with the rotation and translational movement of details in the profile measurement of these details. Building equipment models and experimenting in measuring the detailed contour of cylinders with diameter of 20,004 mm, length of 80 mm at different positions. Compare measurement results when measuring on JENOPTIK F135 circular measuring machine to prove the feasibility of the method of measuring the profile of surface revolution of the author proposed. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2020) Volume 67, No  1, pp 36-44  44  References [1]. W. Liu, P. Hu, and K. Fan, “Comparison of current five-point cylindricity error separation techniques,” Applied Sciences (Switzerland), vol. 8, no. 10. MDPI AG, 16-Oct-2018, doi: 10.3390/app8101946. [2]. K. Endo, W. Gao, and S. Kiyono, “A new multi-probe arrangement for surface profile measurement of cylinders,” JSME Int. Journal, Ser. C Mech. Syst. Mach. Elem. Manuf., vol. 46, no. 4, pp. 1531–1537, 2003, doi: 10.1299/jsmec.46.1531. [3].  “1-s2.0-S2351978917307151-main.pdf.” . [4]. B. Muralikrishnan and J. Raja, “Computational surface and roundness metrology,” Computational Surface and Roundness Metrology. pp. 1–263, 2009, doi: 10.1007/978-1-84800-297-5. [5]. Laser Scan Micrometer– Keyence. Available online:https://www.keyence.com/ss/  products/measure/measurement_library/type/optical/ (accessed on 02 May 2019).  

Measurement Profile of Surface Revolution by Laser Scan Micrometer Method

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Measurement Profile of Surface Revolution by Laser Scan Micrometer Method

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