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Precision measurement of cylinder straightness using a scanning multi-probe system

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Abstract

This paper describes a scanning multi-probe system for measuring straightness profiles of cylinder workpieces. The system consists of two probe-units, each having three displacement probes. The two probe-units, which are placed on the two sides of the test cylinder, are moved by a scanning stage to scan the two opposed straightness profiles of the cylinder simultaneously. A differential output calculated from the probe outputs in each probe-unit cancels the influence of error motions of the scanning stage, and a double integration of the differential output gives the straightness profile. It is verified that the difference between the unknown zero-values of the probes in each probe-unit (zero-difference) will introduce a parabolic error term in the profile evaluation result, which is the largest error source for straightness measurement of long cylinders. To make zero-adjustment accurately, the cylinder is rotated 180° and scanned by the probe-units again after the first scanning. The zero-differences of the probe-units, as well as the straightness profiles of the cylinder, can be accurately evaluated from the output data of the two measurements. The effectiveness of this method is confirmed by theoretical analysis and experimental results. An improved method, which can measure the variation of the zero-difference during the scanning, is also presented.

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... This study describes a lateral shear self-referencing method for cylindrical surfaces, with a primary application aimed at expanding reliable metrology methods for X-ray telescope mirrors, which have acylindical profiles. Lateral shear type self-referencing methods have been expanded to cylindrical surfaces in the past [8], but a key challenge with using lateral shear methods for measuring 2D non-flat surfaces, such as X-ray telescope mirrors, is accounting for the quadratic ambiguities [9,10] that arise due to rigid body errors-a challenge that ASM addresses. For cylindrical surfaces, two rigid body error rotations affect the quadratic term along the axial profile, namely, pitch (rotations around x ) and roll (rotations around z). ...
... Shearing metrology has its roots in multi-sensor probes [9,10], which are shifted as a group. To our knowledge, the first interferometric lateral shearing technique for measuring optical flats was introduced by Bloemhof [5], which involves taking three measurements, one at a nominal position and then two measurements shifted by one pixel in orthogonal lateral directions. ...
... When this linear term is integrated, it presents itself as a quadratic term in the height information. This can mask a true quadratic term in the surface or reference [9]. This section mathematically describes how this quadratic ambiguity, as named by Huang [24], arises and how it is broken with a known artifact mirror (KAM) in the field of view of the interferometer. ...
Article
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Lateral shearing self-referencing interferometry methods shift the surface under test between measurements to separate its topography from that of the reference surface. However, rigid body errors occur during shifting, creating an ambiguity in the quadratic term of the extracted surfaces. We present axial shift mapping, a lateral shearing self-referencing interferometry method for cylinders, in which the quadratic ambiguity is resolved by measuring the rigid body errors using known artifact mirrors residing in the interferometer’s field of view. First, one-dimensional lines of a flat mirror are measured with 2.8 nm RMS difference compared to a three flat test. Then, axial shift mapping is extended to cylindrical surfaces using a computer generated hologram. We find that axial shift mapping results in full surface extraction of cylindrical optics, along the axial direction, with a repeatability of 4.4 nm RMS. We also find that the reference surface extracted through axial shift mapping is within 4.5 nm RMS of the transmitted wavefront error of the computer generated hologram substrate, which was expected to be the largest contribution of reference wavefront error.
... ASM is a lateral shear type self-referencing method, where we translate the SUT between measurements along the axial direction to extract the axial profile of the SUT without the influence due to the reference surface or null optics, and vice versa. In lateral shear self-referencing tests, rigid body errors during shifting introduce a quadratic ambiguity due to a necessary integration operation [20,21]. For cylindrical surfaces, two rigid body error rotations affect the quadratic term along the axial profile, namely pitch (rotations around ) and roll (rotations around ). ...
... A lateral shearing technique for measuring optical flats was introduced by Bloemhof in 2010 [5] which involves taking three measurements, one at a nominal position and then two measurements shifted by one pixel in orthogonal lateral directions. While this is the first instance to our knowledge this method was described for Fizeau interferometry, shearing metrology has its roots in multi-sensor interferometric probes [20,21]. The technique was expanded upon to show that the system could be shifted by more than a single pixel [6]. ...
... When this linear term is integrated, it presents itself as a quadratic term in the height information. This can mask a true quadratic term in the surface or reference [20]. Here we will mathematically describe how this quadratic ambiguity, as named by Huang [23], arises and how we break the ambiguity with a known artifact mirror (KAM) in the field of view of the interferometer. ...
Preprint
Lateral shearing self-referencing interferometry methods shift the surface under test between measurements to extract the surface under test without contributions due to the reference surface. However, rigid body errors occur during shifting which create an ambiguity in the quadratic term of the extracted surfaces. We present axial shift mapping, a lateral shearing self-referencing method for cylinders where we are able to break this quadratic ambiguity through a known artifact mirror in the field of view of the interferometer. We demonstrate how this quadratic ambiguity arises and how a known artifact mirror is used to eliminate the ambiguity. We show extracted one-dimensional surface lines on a flat mirror with 2.8 nm RMS uncertainty. We discuss how we expand axial shift mapping with known artifact mirrors to cylindrical surfaces using a computer generated hologram. We show our ability to use axial shift mapping to do full surface extraction of cylindrical optics along the axial direction with a repeatability of 4.4 nm RMS and demonstrate how the extracted reference surface is within 4.5 nm RMS of agreement with an external measurement source.
... Theoretically, this EST can eliminate the radial and tilt error motions of the cylinder as well as the carriage straightness error motions. Actually, similarly to the sequential three-point straightness EST, the double integration calculations [15] as Equation (6) are executed for detecting the LSC vectors of each cross-sectional profile of the cylinder, which reduces the anti-interference capacity of the EST. Influences of various interferences on detecting the LSC vectors of each cross-section are amplified, which conduct the large variations in the measured median line profiles. ...
... A reconstructed cylindrical profile ( , )( = 0,1, ⋯ , − 1) can be achieved by taking IDFT to ( , )( = 0,1, , ⋯ , − 1), similarly to Equation(6). However, it is worth noting that Equations (13)-(15) are true if the transfer function ( ) ≠ 0, in addition, the disturbances from the carriage straightness error motions will impact the accuracy of the V-block scan EST. ...
... Therefore, Equations(13) and(15) are not true in this case, the first harmonic suppression occurs in the V-block scan EST. It can be seen that (0, )| =1, −1 and ( , )| =1, −1 , which indicate the first and ( − 1)th harmonic vectors of the = 0, cross-sectional profiles, cannot be accurately extracted. ...
Article
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Cylindricity is a kind of three-dimensional form distortion of a cylinder. An accurate in situ measurement of cylindricity is relatively complex because measuring and reconstructing cylindrical profile and evaluating out-of-cylindricity should be involved. Any method of in situ measuring cylindricity must solve a common issue, i.e., to eliminate spindle error motions and carriage error motions during measurement and reconstruction. Thus, error separation techniques have played an important role in in situ cylindricity measurement through multipoint detections. Although several valuable five-point methods for in situ measurement of cylindrical profile have been proposed up to present, namely the parallel scan, spiral scan, and V-block scan, there are obvious differences in many aspects, such as the arrangement of probes, error separation model, reconstruction method, adaptability to service environment, accuracy and reliability in practical application, etc. This paper presents the evaluation of their advantages and disadvantages in theory and the actual measurement based on the standard ISO 12180. Suggestions for best meeting the requirements of modern manufacturing and the most prospective one for industrial applications are also given.
... Hence, it is a challenge for CMMs to achieve nanometer accuracy. In order to eliminate the motion errors of the stage, multi-sensors with an error separation method have been proposed as a promising approach to address these issues [5][6][7][8][9][10][11][12][13][14][15]. ...
... However, tilt errors of the scanning stage would still be present in the measurement results. A combination of three (or more) sensors offer the opportunity to compensate for the tilt of the scanning stage [7][8][9]. However, the small but systematic offset errors of the utilized sensors can accumulate to a parabolic topography error which can be orders of magnitudes larger than the systematic offset errors [9]. ...
... A combination of three (or more) sensors offer the opportunity to compensate for the tilt of the scanning stage [7][8][9]. However, the small but systematic offset errors of the utilized sensors can accumulate to a parabolic topography error which can be orders of magnitudes larger than the systematic offset errors [9]. Additionally, the resolution is low if using capacitive or other traditional distance sensors. ...
Article
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In this paper, we present a novel method using an interferometer as a multi-sensor for an absolute profile test. Different from the traditional three flat test, which is complex to implement, the configuration of our method is similar to a classical sub-aperture stitching test but double scanning with different intervals is required. An additional interferometer or auto-collimator is used to measure relative tilt during scanning. The method we propose can eliminate not only systematic error in the interferometer but also the height offset error of the scanning stage, and it can achieve high lateral resolution. We analyze the effect of tilt estimation error on reconstruction accuracy and then propose a way to reduce its effect. The simulation results indicate our method can get exact results when free of noise. Comparisons are made between our method and the previously proposed sub-profile stitching method. The experiment results show that high repeatability and high accuracy can be reached in our method.
... We select the ith (i = 9, 14,19) generatrix data from the reconstructed cylindrical profile r(k, i) (k = 1, 2, . . . , M). ...
... , M). In the same way, the ith (i = 9, 14,19) generatrix data are chosen from the given cylindrical profile r 0 (k, i) (k = 1, 2, . . . , M). ...
... Further, the consistency of the sensitivity of the multiple probes, and the requirements for the overlap of the axial position of one section, rather than two sections [10] in two adjacent measuring positions, are easy to meet during measurements. Although the five-point EST can theor etically eliminate all radial and tilt error motions of the spindle as well as straightness error motions of the probe carriage, its ability to resist interference is relatively weak owing to its double-integration algorithm [19] of separating error motions of the spindle, as shown in the appendix. Because of this, the influence of various interferences on the accurate detection of the LSC vector of each cross-section is amplified, which results in large variations in the measured spatial median line profiles. ...
Article
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A four-point error separation technique integrating three-point roundness and two-point straightness error separations is proposed to measure and reconstruct a cylindrical profile for the accurate evaluation of cylindricity. Four probes mounted onto two sections in the probe carriage target the surface of the cylinder to detect the differential vector of the least-squares centers in two adjacent cross-sectional profiles of the cylinder. The vector of the least-squares center in each cross-sectional profile is extracted by accumulation. The spatial curved median line of the cylinder is determined by fitting the extracted least-squares centers. Theoretical analysis and numerical validation prove that radial error motions of the spindle and straightness error motions of the slider are eliminated during reconstruction of the cylindrical profile. The influence of tilt error motions of the spindle on the accuracy of error separation can be weakened by reducing the distance between the two sections in which the four probes are located. The spatial median line profile of the cylinder is accurately determined even if the error motions of the spindle are not repeatable in each revolution. An experimental system was constructed to perform comparison experiments. The results validate the fact that the technique has higher precision in reconstructing cylindrical profiles owing to its robust anti-interference ability. The technique is suitable for in situ measurement of cylindricity under unrepeatable radial error motions of the spindle and indeterminate straightness error motions of the slider.
... Previous cylindrical form measurements with various ESTs include the multi-step [10][11][12], multi-probe [5,6,[13][14][15][16], and reversal [1,4,13] methods. The multi-probe EST can precisely measure the radial deviations and the out-of-roundness of the crosssectional profile by separating the error motions from the outputs of the probes. ...
... At the same time, the linear motion of the probe carriage will have straightness deviations [ε x (k) , ε y (k)] as well as pitching x (k), yawing y (k) and rolling z (k) motions. Here, [ε x (k) , ε y (k)], will contribute to the outputs of probe 1, 2, and 3, and d × ␥ y (k) and ε x (k) will contribute to probes 4 and 5, as shown in Fig. 4. The influences of x (k) and z (k) are small, which can be neglected [5,6]. ...
... ., N − 1) (m = 4,5) from the 0th and 2nd crosssections, respectively. Taking DFT of t m (1, i) (i = 0, 1, · · ·, N − 1), we can obtain their corresponding 1st harmonic vectors T 4 (1, 1) and T 5 (1, 1). ...
Article
An innovative parallel error separation technique for on-line measurement and reconstruction of cylindrical profile is presented. A five-probe system configured to target three adjacent cross sections of the cylinder is proposed to simultaneously execute the three-probe roundness error separation and three-probe straightness error separation. The curved median line is determined by fitting through the least squares centers of circular cross-sectional profiles. The cylindrical profile conforming to the mathematical definition can then be reconstructed for the cylindricity error evaluation. Theoretical analysis and numerical validation have been performed. The results verify that the spindle’s radial and tilt error motions as well as the probe carriage’s straightness error motions are removed, and the least squares center of each cross-sectional profile of the cylinder is accurately extracted even if the spindle’s error motions are not repeatable in each rotation. This method has thoroughly solved the inherent problem in conventional multi-probe error separation techniques: the suppression of the first-order harmonic in separating the cross-sectional profile of the cylinder and the error motions of the spindle.
... However, the flatness of a conductive surface as the measurement target should be limited within the working range of the capacitance sensors. Moreover, a measurement procedure to identify the zero adjustment difference [21] is proposed. The essential advantages of the proposed system are as follows: (1) no theoretical limitations of measurement range, (2) only a single setup for x-and y-axis measurements, and (3) roll error measurement for the vertical directional moving stage. ...
... The final gaps of every capacitance sensor are derived as shown in Eqs. (19), (20), (21), and 22): ...
... ), and(11) and Eqs.(19),(20),(21), and(22), as shown in Eqs.(23) and (24). Mathematically, either Eq. ...
Article
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In this paper, a measurement system for roll error (angular error of a linear moving stage) is described. The proposed system consists of four capacitance sensors located at four vertices of a tetragon in a fixture. Unnecessary measured data due to global surface roughness on the measuring target is eliminated using a differential method. First, a mathematical model for the proposed system is developed using the error synthesis modeling technique. The zero adjustment difference is a critical parameter for precise measurement. Therefore, an additional measurement procedure is developed to estimate the zero adjustment difference. The x- and y-directional offset errors, which are deviation from the designed position of hole for holding a capacitance sensor, introduce an error in the estimation of roll error. Therefore, a virtual experiment is performed with different values of x- and y-directional offset error to analyze their effect. Then, the roll error is measured using the proposed measurement system. A comparison of the measured data from the proposed method (four capacitance sensors) and the conventional method (two capacitance sensors and a straight-edge) is performed. Finally, the proposed method is verified using a hypothesis test.
... Another way to achieve high-accuracy measurement is to use the multi-sensor error separation method to eliminate the influence of the straightness error of the guideway [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Based on the self-calibration measurement principle, it is not necessary to use a high-accuracy guideway. ...
... (a) Accumulation error. The systematic error in a multi-sensor system will accumulate into a parabolic error, which may be several orders of magnitude larger than the systematic error [15]. Although adding an extra angle sensor can solve this problem, it complicates the measuring system and increases the cost. ...
Article
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This paper proposes a method based on a single-probe scanning system for measuring the profile error of an artifact. Our system employs the movement accuracy of a single sensor to achieve a virtual multi-sensor configuration that can function like a traditional multi-sensor. This novel virtual multi-probe scanning system and its corresponding method have the following benefits: (a) A high-accuracy profile can be reconstructed free of the guidance error of the scanning stage. The reconstructed profile has a very high lateral resolution, depending on the lateral resolution (µm level) of the probe. (b) Sensor drift can be restrained using our method, based on the principle of differential reconstruction. The high steep profile can also be measured with a scanning system moving along the measuring direction, thus extending the measuring range. We developed the measurement system and tested the effects of noise, drift, and other factors on the reconstruction results. Finally, some optical surfaces were measured, and comparisons were made between the results obtained from our method and those of a Zygo interferometer. There was high agreement between the two methods, with a deviation of approximately 0.1 μm.
... This difference could be reduced either by manually aligning the two sensors or post-processing the collected signals [14]. In Ref. [15], Gao proved that in the S-3P, the height differences between the three probes would also introduce a parabolic error term in the profile evaluation result. To solve this issue, he presented a scanning multi-probe system, where 6 probes are employed [15]. ...
... In Ref. [15], Gao proved that in the S-3P, the height differences between the three probes would also introduce a parabolic error term in the profile evaluation result. To solve this issue, he presented a scanning multi-probe system, where 6 probes are employed [15]. This problem was also solved by Dr. Elster, where an additional autocollimator was adopted [16]. ...
Article
To compensate for the straightness error of the slide of a machine tool efficiently and precisely, on-machine self-calibrating measurement of the manufacturing error is critical. The Fourier 3-sensor (F3S) method proposed by Fung is promising in measuring the straightness profile of a workpiece accurately on a machine. However, it still suffers from two main challenges: the height difference between the second and the third probes and the stochastic uncertainty, both of which can significantly decrease the measurement precision. In this paper, we counter these two challenges, respectively, and propose the solutions accordingly. First of all, by resorting to the Laplace transform, an algorithm for the F3S method is proposed. Second, the adverse effect of the height difference between the second and the third probes is demonstrated. An approach is presented for estimating the height difference, and compensating for this. Third, to alleviate the stochastic uncertainty, a hybrid F3S method is developed: several F3S measurements are first performed under different probe spacings; then, the optimal Fourier coefficients of the straightness profile are individually selected from the candidate estimates in accordance to the determinant of the transfer matrix. Finally, practical straightness profile measurements were performed, respectively, on a grinding machine by adopting the hybrid F3S method and on a Taylor Hobson surface profiler. The results show that compared with the conventional F3S method, the hybrid F3S method reduced the measurement uncertainty significantly, and the straightness profiles estimated by the hybrid method and by the surface profiler were consistent with each other.
... To eliminate the yaw error three-probe methods are proposed [9]- [10], including the sequential three-probe method (STRP), the combined threeprobe method (CTRP), and the generalized three-probe method (GTEP). Although the three-probe methods can eliminate the yaw error, the zero-adjustment error between the three probes will introduce a parabolic cumulative term in the profile evaluation result, which is the largest error source for straightness measurement of the long workpiece profile [11]. ...
... to(11), after removing the linear trend in (11), we can obtain the ( ) that not have the 1 .Then the output of the N+1th acquisition of the probe is: ...
Article
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We present a novel virtual multi-probe scanning system and a new error separation method for the exact optical profile reconstruction. The system realized the multi-probe function by a single probe that fixed on a flexible hinge stage. The flexible hinge stage has a millimeter-level travel range and driven by a voice coil motor to realize the function of the multi-probe. In this work, a high accuracy profile measurement with a high lateral resolution is realized under the errors of the straightness, zero-adjustment, and yaw. The new method can obtain multiple sets of straightness error of the guideway in one scanning measurement. This novel virtual multi-probe scanning system and its corresponding method has the following benefits: (i) using a single probe to separate straightness error without reversal, and can accurately reconstruct the profile, (ii) the reconstructed profile has a very high lateral resolution, depending on the lateral resolution (μm level) of the probe, (iii) the cumulative amplification effect of zero-adjustment error can be eliminated by our method, (iv) the new method can obtain multiple sets of straightness error with higher reliability and accuracy compared with only one set. These benefits are proved by theoretical derivation and simulation. Experiments also prove that the new method can reconstruct the profile with high accuracy and lateral resolution.
... As in many types of ultra-precision equipment, linear motions are orientated by guide rails or parallel planes, whose accuracies can have a great influence on the smooth operations. On the basis of those mentioned methods, several measuring systems and methods were designed to measure and reconstruct a pair of parallel profiles including the cylinder workpiece and guide rails [18][19][20]. We also designed a four-probe method to reconstruct a pair of profiles, which can eliminate the reference errors and the zero-adjustment error through two scannings [21]. ...
... For multi-probe methods using three or more probes, the zero-adjustment error always has a significant impact on the measurement and reconstruction results [18]. Due to the cumulative effect, using a high precision reference surface to calibrate the zero points of probes is not good enough for eliminating this type of error. ...
Article
Full-text available
To realize the measurement and exact reconstruction of a pair of parallel profiles, a new scanning method using four displacement sensors as probes and different probe spacings has been invented with the advantage of preventing data processing error. The measuring device is placed between the measured objects and moved by a scanning stage to collect measurement data of both measured profiles. Considering many existing methods, the high lateral resolution of the reconstruction result and the rejection of the data processing error cannot always be achieved at the same time. When the measured profiles are in the short wavelength range, data processing errors are often on the same order of magnitude as the height difference of the measured profiles. The new method can eliminate both the straightness error of the measurement reference and the data processing error. The exact reconstruction retaining the high lateral resolution and without data processing error can be realized by rational position arrangement of sensors and corresponding processing method of the measurement data. The new method possesses the following advantages: (i) achievement of the exact reconstruction without data processing error; (ii) high lateral resolution not limited by probe spacing; (iii) concise operation without zero calibration of probes; and (iv) suitability for on-machine measurement. The feasibility and advantages of the new method were demonstrated by theoretical analyses, simulations, and experimental results.
... The sensor configurations of both IF5S and F8S need to be chosen suitably, and the length of the test section is determined by the size of the slider. Based on the reversal method [23] and the generalized threesensor method, Gao et al. [24,25] developed the reversal six-sensor method. By scanning the two opposed surface profiles of a cylinder simultaneously, the method can be used for estimating the profiles and the straightness and tilt errors, with the zero-adjustment values taken into account. ...
... The results related to γ(x) are given in Figure 6(b), showing that �γ max and �γ a max are about 5 × 10 −3 degree and 9 × 10 −4 degree, respectively. The relationships of the residuals induced by PE1 and (24) ...
Article
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Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition. In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to different positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the effects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coefficient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the effects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.
... The three-point method, which uses three displacement probes [13][14][15][16][17][18][19][20][21], can eliminate the influence of both the translational error motion and the yaw error motion. It is widely used for measuring straightness and roundness profiles of cylinder workpieces [19,20]. ...
... The three-point method, which uses three displacement probes [13][14][15][16][17][18][19][20][21], can eliminate the influence of both the translational error motion and the yaw error motion. It is widely used for measuring straightness and roundness profiles of cylinder workpieces [19,20]. However, if the zero-adjustment errors of the probes are not adjusted precisely, it will yield a parabolic error term in the profile evaluation result of the three-point method. ...
Article
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A profile of an X-axis stage mirror results in a phase error of gratings in Scanning Beam Interference Lithography. Traditional methods of measuring the profile require extra probes and another large stage mirror on Y-axis, or requires other operations such as rotating measured object to adjust the zero-adjustment errors. This paper introduces a three-probe system removing the need for Y-axis optical path structure and proposes a bidirectional integration model to solve the problem of zero-adjustment error, simplifying the optical path structure and the measurement process. This method is confirmed by theoretical analysis and experimental results, which is better than traditional methods and can also be used in other application fields of three-point method.
... from the slide error motion, enabling simultaneous measurement of both quantities [10,11]. In 1981, the sequential two-point (S-2P) method was proposed [12]. ...
... Three sensors are arranged on the same cross section of a cylindrical workpiece to measure the roundness according to the three-point method error separation technology [12,13]. Two sensors are arranged on the same busbar to realize the measurement of busbar straightness according to the sequential-two-points method [14,15]. Of all the sensors, one is shared. ...
Article
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The technology of in situ measurement of cylindrical shapes is an important means of improving the surface machining accuracy of cylindrical workpieces. As a method of cylindricity measurement, the principle of the three-point method has not been fully studied and applied, so it is seldom used in the field of high-precision cylindrical topography measurement. Since the three-point method has the advantages of a simpler measurement structure and smaller system error compared with other multi-point methods, the research on it is still of great significance. Based on the existing research results of the three-point method, this paper proposes the in situ measurement and reconstruction technology of the cylindrical shape of a high-precision mandrel by means of a three-point method. The principle of the technology is deduced in detail and an in situ measurement and reconstruction system is built to carry out the experiments. Experiment results are verified using a commercial roundness meter and the deviation of cylindricity measurement results is 10 nm, which is 2.56% of the measurement results of commercial roundness meters. This paper also discusses the advantages and application prospects of the proposed technology.
... This method can only eliminate the effect of repetition motion errors. The last method employs the multiprobe to separate the motion errors of the scanning stage in real-time [3][4][5][6][7][8][9][10][11][12][13][14]. ...
Article
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This study presents a new (to the best of our knowledge) error separation method with a single displacement probe, named as single probe shear scanning (SPSS) method, for the on-machine optical profile measurement to overcome the problems of the existing multiprobe method like the large deviation of probe spacing and the probes’ performance difference. The confocal sensor with superior dynamic range, high lateral resolution, and large measurement angle to surface is applied in this study to fulfill the measurement of the optical aspheric surface. The single probe measurement system, in which the probe fixed on a flexure hinge is driven straight within a millimeter-level travel range, is established to realize the function of the multiprobe. For the established system, a new exact profile reconstruction algorithm is built to eliminate the influences of straightness errors of the scanning stage and the systemic errors of shear stage, and to reduce the effect of the sensor drift. The reconstruction algorithms by difference measurement with two shears are studied to build the bidirectional segment stitching reconstruction method, which reduces the error accumulation and improves the reconstruction accuracy under the condition of measuring errors. A profile reconstruction method with three shears measurement is proposed to make a further improvement on the reconstruction accuracy. The proposed reconstruction method with three shears measurement is successfully employed for the on-machine measurement of an aspheric surface profile, and the evaluation results agree well with those from the Taylor profiler.
... X C Chen [9] studied the straightness measurement of slender rod based on PSD and established a mathematical model. Gao W [10] introduced a scanning multi-probe system for measuring straightness profiles of cylinder workpieces, and the system consists of two probe-units, each having three displacement probes. Although it has been applied in actual production and has achieved relatively good measurement results, there are still some limitations in measurement accuracy and efficiency. ...
Article
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Straightness is the key geometric accuracy index of the slender rod of key parts of large machinery, which directly affects the manufacturing and installation accuracy, working efficiency and service life of mechanical products. In order to improve the manufacturing precision of the slender rod and overcome the limitations of the existing methods, a method for measuring the straightness of the slender rod based on the time-domain three-point method is proposed. According to the structural characteristics of the slender rod, the measurement principle and the overall scheme of the measurement system are given, and the mathematical model of the straightness measurement is established. Taking the core components of a construction machine as an example, the measurement and comparison of the designed measuring device and the laser tracker are used to prove that the measurement error of the designed measuring device is less than 0.005 mm. The measurement system analysis results show that the R&R of the designed measuring device has less than 10% of the research variation, indicating that its repeatability and reproducibility are good, which further proves that it can be applied to the actual production site.
... Su H et al [6] proposed a two-probe time domain method. Gao W et al [7] describes a scanning multi-probe system for measuring straightness profiles of cylinder workpieces. Vladan Radlovački et al [8] proposed a new method for evaluating minimum zone flatness error. ...
Article
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In order to solve the problem that the flatness error contour curve of the guideway mounting surface on machine tools can not be intuitive description, a novel method is proposed in this paper. The principle is to divide the measured surface with a certain length into several short surfaces with overlapping region, and the segmented surfaces are measured respectively, then the flatness error contours of the segmented surfaces can be obtained, finally, the segmented flatness error contours are spliced together to reconstruct the flatness error contour of the entire surface. On this basis, the detection instrument is designed, the detection principle is given, the benchmark plate is customized to identify the starting position and ending position of measurement, the reference surface and the measured surface are measured respectively in combination with the detection instrument and the benchmark plate. Then, an algorithm is developed to convert the distance difference between the reference surface and the measured surface into the flatness error contours of segmented surfaces. Next, using the geometric relationship between overlapping region of segmented flatness error contours, an algorithm is studied which can splice these segmented flatness error contours and reconstruct the flatness error contour of the entire surface. Meanwhile, mathematical models of the algorithms are established, and the measurement experiment is carried out. The results demonstrate that this method can reconstruct the flatness error contour of long surface accurately.
... Therefore, machine tool kinematic error needs to be mapped for OMSM correction with the proposed kinematics error modelling (based on rigid-body kinematics method) and measurement (based on reversal method) [20]. Gao et al. [21][22][23] conducted extensive research in separation of machine tool motion error (slide straightness and spindle error) and on-machine measured surface error (roundness error and axial profile error) with multiple points and reversal methodology. Calibration of the embedded sensor linearity error is important as well [24]. ...
Article
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Surface measurement is essential to enhance accuracy and efficiency in ultra-precision machining. In order to increase the measurement availability and efficiency, offline lab-based solutions are shifting towards the use of surface metrology upon manufacturing platforms. With the lack of remounting errors, on-machine surface measurement (OMSM) allows the deterministic assessment of manufactured surfaces just-in-time and also provides valuable feedback to the process control of ultra-precision machining. This paper is aimed at reviewing the state-of-the-art OMSM and applications in the ultra-precision machining process. The benefits and considerations on the integration of metrology are discussed. The merits and limitations among different OMSM types are compared as well. Finally, the challenges and outlook of the ultra-precision machining-metrology integration are highlighted.
... This is an even more critical problem when a multiprobe system is used for flatness measurement where more probes are needed and it is necessary to align the probes on different lines of the workpiece surface except some special cases [64]. A self-calibration technique, in which two probe-units of the three-probe method are employed, has been proposed to accurately identify the zero-difference of probes for measurement of cylinder straightness [75]. The technique has been improved to measure and compensate for the variations of the zero-difference caused by thermal drift of the probe outputs during the scanning [71]. ...
Article
On-machine and in-process surface metrology are important for quality control in manufacturing of precision surfaces. The definitions, requirements and tasks of on-machine and in-process surface metrology are addressed. The state-of-the-art on-machine and in-process measurement systems and sensor technologies are presented. Error separation algorithms for removing machine tool errors, which is specially required in on-machine and in-process surface metrology, are overviewed, followed by a discussion on calibration and traceability. Advanced techniques on sampling strategies, measurement systems-machine tools interface, data flow and analysis as well as feedbacks for compensation manufacturing are then demonstrated. Future challenges and developing trends are also discussed.
... In this paper, closed-loop control is also attempted by integrating a Cr-N strain sensor into the fabricated XYZ-micro-stage. In a three-axis XYZ positioning system, the angular motion errors around the X-, Y-, and Z-axes are related to the main X-, Y-, and Z-translational motions [30][31][32]. For high-precision positioning, it is important to design the mechanical structure of the stage to reduce the motion errors of this six-degree-of-freedom. ...
Article
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This paper presents a design study of an XYZ three-axis micro stage which achieves a size of several cubic centimeters, a millimetric travel range, a nanometric driving resolution and three-axis motion at the same time. In addition, unique leaf springs acting not only as guides for a stage table but also as precision displacement sensors are included in the stage system. The XYZ three-axis micro stage is designed and fabricated. The fabricated stage is designed to have a small size of 25 mm (X) × 25 mm (Y) × 6.5 mm (Z). Furthermore, feasibility of the driving principle of the developed XYZ three-axis micro stage is verified in experiments.
... In recent years, nano-CMMs 30,31 have been developed to attain nanoscale accuracy with more number DoFs of measurement and motion, but their measurement range is sacrificed, which is only of several centimeters. Error separation methods have been researched to separate motion errors and form virtual linear datum, such as twoprobe methods, 32-35 three-probe methods, 36,37 and traceable multiple sensor methods. [38][39][40][41] These methods could effectively eliminate the influences of motion errors with complicated data process. ...
Article
In order to further improve the linear datum based geometric measurement accuracy and expand the measurement range, a 6-DoF motion system is developed for realizing a linear datum in the form of motion trajectory of the contact point (CP) of an absolute displacement measurement probe. This linear datum is established based on the concept of coordinate measurement and it does not contain straightness error in theory. The 6-DoF motion system consists of a 6-DoF fine stage and a 1-DoF coarse stage. The probe is moved by the 6-DoF fine stage which is magnetically noncontact supported and parallelly noncontact actuated. A CP-centred 6-DoF metrology model and a CP-centred 6-DoF motion model are established for elimination of Abbe error and on-line compensation of motion error of CP, respectively. 1-DoF coarse stage is controlled with relative position between two stages to extend the limited motion range of 6-DoF fine stage along the linear datum. Effectiveness of the metrology and motion models is verified through experiment. Straightness error of a 91.5 mm long line of an optical flat is measured by the proposed system and a commercial Fizeau interferometer. Comparison shows a consistency with standard deviation of 11 nm. Another experiment indicates that the proposed system could be used to realize a linear datum within a range of 220 mm with a repeatability of standard deviation of 7 nm.
... The lateral resolution of the reconstruction results can be improved by using more than two displacement sensors, which have to be arranged with coprime interspaces [9,10]. In this case, the systematic sensor errors have to be taken into account, otherwise a parabolic error may occur [7,11]. ...
Article
We report on results of high precision straightness measurements of a graduated scale and a comparison of two different error separation methods. One approach is based on the Traceable Multi-Sensor method. For this purpose, a sensor element consisting of three heterodyne interferometers was integrated at PTB's length reference comparator to measure the straightness deviation of structures on scales. For a scale with a grating of 322 mm length a standard uncertainty below 1.5 nm was achieved using this method. A comparison with another method based on reversal technique was realized and revealed a difference below 2.5 nm (PV) between both results.
... Rotary components constitute a large and important group of machine parts. They are common, for instance, in the automotive, power, paper and shipbuilding industries; therefore, one of the most significant metrological tasks today is to ensure maximum accuracy of roundness and cylindricity measurements [1][2][3][4][5][6][7]. ...
Article
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The bird-cage strategy used for measuring cylindricity is reported to be the most effective, as it provides the most detailed information about an analyzed object. The average values of profiles measured with the cross-section and the generatrix strategies may differ slightly, yet this may result from some design imperfections of the measurement instruments used. In this study, the problem of optimal profile matching is formulated and solved. As a result, the differences between the values of the registered profiles at the points of intersection of the scanning trajectories can be minimized.
... Pour séparer le profil de la pièce des défauts de guidage du porte-capteurs, Gao et al [GAO 2002] utilisent une méthode dite de propagation avec plusieurs capteurs. Il s'agit de déplacer 3 capteurs le long du produit à mesurer. ...
Article
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Long workpieces are characterized by one dimension, usually length is larger than the height and width, for example, railway rails. These products are obtained by hot rolling and then cooling. During manufacturing process, heterogeneity of cooling and plastic deformation induced straightness error. In order to correct this geometrical error, cold straightening process is necessary. Usually, straightening machines are used to correct the straightness of the workpiece center however; the ends' sides were still not straightened. Based on the optical measurement profile, these ends are straightened by mechanical press. The measuring/straightening closed loop is repeated until the straightness of the product is conformed. The process time depends on the knowledge of key parameters related to geometry and material of workpiece. The objective of this research work is to optimize straightening process of the ends of long workpieces. As a first step, the elastic deformation generated during the measurement of long workpiece has been filtered. Then, a coupled analysis of measurement was used to separate error of machine measurement from workpiece measurement, which allowed a better assessment of workpiece straightness profile. Furthermore, based on straightness profile, a semi-automatic straightening methodology has been developed. It is essentially based on an interaction between metrology and mechanics and it is a contribution to the automation of straightening process for ends parts of long workpieces.
... Rotary components constitute a large and important group of machine parts. They are common, for instance, in the automotive, power, paper and shipbuilding industries; therefore, one of the most significant metrological tasks today is to ensure maximum accuracy of roundness and cylindricity measurements [1][2][3][4][5][6][7][8][9]. Currently, the most common methods used for measuring cylindricity and conicity of machine parts are the radial methods, also called radius change methods or nonreference methods. ...
Article
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The paper presents a novel method for the determination of the median line of the cylindrical and conical surfaces. This method can be incorporated into virtually any cylindricity measurement strategy, including the bird-cage strategy and the helical line strategy. In the study, a median line was determined by minimizing the functional made up of two components. The form of the first component results from the classic definition of the median line provided in the corresponding standard. The other, termed the bending energy, is responsible for ensuring appropriate smoothness of the median line. In order to solve this variational problem, the median line was approximated by means of linear combination of cubic B-spline functions. A simulation and experiments were conducted to establish the suitability of the algorithm developed for the determination of the median line using the helical-line and the cross-section measurement strategy.
... [12][13][14] However, the installation error of the probes will introduce an offset in the differential output, if the probes are not initially adjusted or measured (zero-adjustment) precisely, since the error term is proportional to the square of the measurement length, and even a small zero-adjustment error introduced by the flatness error of the reference surface will cause a large profile evaluation error. [15][16][17] The significant constraint of this method is applied for long-range measurement. Nevertheless, in short-range measurement, this method is robust to variations of the measurement circumstances, including humidity, temperature change, and so on. ...
Article
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This article proposes a novel method for identifying the motion errors (mainly straightness error and angular error) of a linear slide, which is based on the laser interferometry technique integrated with the shifting method. First, the straightness error of a linear slide incorporated with angular error (pitch error in the vertical direction and yaw error in the horizontal direction) is schematically explained. Then, a laser interferometry-based system is constructed to measure the motion errors of a linear slide, and an algorithm of error separation technique for extracting the straightness error, angular error, and tilt angle error caused by the motion of the reflector is developed. In the proposed method, the reflector is mounted on the slide moving along the guideway. The light-phase variation of two interfering laser beams can identify the lateral translation error of the slide. The differential outputs sampled with shifting initial point at the same datum line are applied to evaluate the angular error of the slide. Furthermore, the yaw error of the slide is measured by a laser interferometer in laboratory environment and compared with the evaluated values. Experimental results demonstrate that the proposed method possesses the advantages of reducing the effects caused by the assembly error and the tilt angle errors caused by movement of the reflector, adapting to long- or short-range measurement, and operating the measurement experiment conveniently and easily.
Chapter
Straightness measurement needs to be performed before straightening. In this paper, considering the rationality of structural design and protecting the sensor, we used the lever structure to measure the straightness of the regular hexagon section shaft. However, due to lever parameters and the contact mode between the lever and the shaft and between the lever and the sensor, the lever model has measurement errors. Two kinds of lever-type measuring mechanisms are discussed to improve the measuring precision in this paper. The error correction method is proposed through strict mathematical derivation. At the same time, sensitivity analysis of lever parameters was carried out. Finally, the validity of the error correction is proved through experimental verification. The experiments indicate that the error of measurement results of two lever models after error correction is controlled within ± 0.006 mm, which improves the measurement accuracy significantly. At the same time, after correcting the measurement results of deflection of the regular hexagon section shaft, the length error of deflection vector is reduced to 0.01 mm basically.KeywordsLever-typeStraightnessError correctionStraighteningDeflection
Article
Herein, the sequential four-probe method (SFPM), a novel method for obtaining high-density line surface profiles, is proposed. To obtain accurate measurement results using many measurement points, a new surface reconstruction method is developed using the relationship between the existing sequential three-probe method (STPM) and an additional auxiliary probe. The relationship between datasets acquired using the STPM and data acquired from the auxiliary probe is analyzed, and a method for estimating an accurate surface profile using the relationship is described comprehensively. An experiment is conducted using numerical verification to confirm the performance of the proposed method. The result confirms that the proposed method can yield extremely accurate and strict results compared with previously developed error separation techniques.
Article
The hexagonal shaft is often used as the important transmission component. Its bending deflection is a main factor affecting the working capability and fatigue life. In this paper, a contactless continuous measurement method based on contour reconstruction is proposed, which only uses a laser displacement sensor moving at a constant speed to collect the profile information. According to the allowable incident angle, the valid data with high precision is extracted. An algorithm seeking for section center is deduced according to the hexagon edge equations fitted by the least square method, then, the three-dimensions blending axis is obtained. The method precision is analyzed by theoretical error analysis. Finally, the feasibility and high accuracy of the novel method are demonstrated by comparing with ZEISS Calypso scanner results and the repeatability and reproducibility (R&R) analysis.
Article
This paper presents a compact XYZ micro-stage driven by an impact driving mechanism. A moving body is translationally actuated along the X-, Y-, and Z-axes in millimeter-scale range and with nanometer-scale resolution. Cr–N thin-film strain sensors are integrated into the micro-stage for closed-loop positioning. Closed-loop control is also carried out. The motion errors in six degrees of freedom are also investigated for this micro-stage. It is clarified by analysis of finite element method that rotational motion errors around the driving axis are caused by torques due to tensions from the elastic hinges of micro-stage. The mechanical structure of XYZ micro-stage to cancel out the torque generated is proposed and the second prototype is fabricated. Although the rotational motion error is successfully suppressed in the second prototype, a rotational motion error of more than 0.1° remains due to remaining torque and assembly error of the elastic hinges. Then, in order to reduce the rotational motion error, the prototype is designed in which the location of elastic hinges is single-layered. By designing a mechanical structure in which torque is suppressed, all rotational motion errors are successfully reduced to less than 0.05° in the prototype with single-layer hinges.
Article
Inner/outer cylindrical surface parts are often applied into all kinds of machines. The bending deformation of these parts will affect the working performance and service life of the machine. A non-contact measuring method only using a displacement sensor and a guide rail for bending deflection is proposed in this paper. A peak-valley enveloping algorithm derived through rigorous mathematical molding and analysis can be utilized to obtain the eccentricity, direction and the corresponding cross-section position, and then the axis deflection curve can be determined. The error analysis of numerical simulation results shows that the method proposed in this paper can feature a high accuracy by setting appropriate operation parameters. Then, a specialized experiment is carried out to prove the correctness and reliability of the measuring method proposed by comparing with commercial instrument results. Finally, a parameter design method is provided to match the algorithm calculation time and measuring accuracy.
Article
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A novel system and its corresponding method for the measurement and the exact reconstruction of a pair of parallel profiles are designed. There are six sensors installed on the measuring device and they are divided into two groups with different sensor spacings. The exact reconstruction can be realized under the condition of a high lateral resolution, as the straightness error, the yaw error, the zeroadjustment error, and the data processing error can be all eliminated through two scannings and certain data processing method. The measurement error of the displacement sensors can also be suppressed. The new method has the following advantages: (i) the realization of the exact reconstruction, (ii) a high lateral resolution of the reconstruction result which is independent of the sensor spacings, (iii) the skip of the zero calibration before the measurement process, and (iv) the suppression of the sensor random error. These advantages are demonstrated by the theoretical analyses and the simulations. Experiments are also conducted to prove some of these characteristics.
Article
A three-probe error separation technique with a novel V-block for measuring and reconstructing a cylindrical profile is presented. The V-block has two tandem V-shaped planes and three displacement probes mounted in one section. During the measurement, the V-block is put onto the measured cylinder, and the two V-shaped planes contact with the cylinder when the cylinder rotates, which make the measurement of cylindrical profile immune to the radial error motions of the spindle. Three probes target each cross-section of the cylinder to collect the data. From the outputs of the probes, the least squares circle center vector of each cross-section is determined via an error separation model built in accordance with the respective relationships of the cross-sectional profiles of the cylinder and error motions of the V-block. Theoretical analysis and numerical validations proved that this technique can accurately detect the median line profile of the cylinder, and the anti-interference capability can be moderately improved by the modified error separation models based on two measuring strategies. This technique realized theoretically full harmonic error separation with the minimum number of probes, accurately detected the spatial median line of the cylinder. Further, high-precision reconstruction of the cylindrical profile was achieved. Integrating the V-block with a laser measurement system can yield a portable system for in-situ measurement cylindricity. It is foreseeable that this technique will garner more attention for future applications.
Article
This study focuses on developing a new error separation technique for the in situ measurement and reconstruction of cylindrical profile. Based on a five-point system proposed, the center vectors of the least squares circle in the cross-sectional profile of the cylinder can are accurately extracted by the error separation model. The vectors are based on a spatial straight line that connects two least squares centers of the fixed cross-sectional profiles, which makes the double integration calculations avoided and the ability to resist interference improved. A cylindrical profile conforming to the mathematical definition can be reconstructed for cylindricity error evaluation. Theories, numerical validations and experiments verified that the spindle’s radial and tilt error motions as well as the probe carriage’s straightness deviations are all removed. This innovative technique solved a crucial problem regarding the accurate and high-precision reconstruction of a cylindrical profile in the in situ measurement.
Article
We present a four-probe scanning system to reconstruct a pair of parallel profiles which are the foundation of the straightness and parallelism measurement. The system, which is placed between two profiles to be measured and mainly used for on-machine measurement, consists of four displacement sensors. As the scanning stage moves along the profiles, the sensors collect measurement data of both profiles simultaneously. The reconstruction result is obtained by a double differential and a double integral, and the data processing eliminates the influence of the stage motion errors during the scanning. It is known that the zero-adjustment error of three sensors placed abreast in the system causes a parabolic reconstruction error, which can be removed by rotating the device 180° for a second scanning. Using the measurement data of the two scannings, straightness error and yaw error of the scanning motion, as well as the zero-adjustment error can be removed, and the reconstruction result can be utilized to evaluate straightness. In addition, the relative position of two measured profiles can also be calculated, which means the reconstruction result can be used to evaluate the parallelism of them. The new method possesses these following advantages: (i) reconstruction result is affected by neither motion error of the scanning stage nor the zero-adjustment error of sensors, (ii) reconstruction result can be utilized to evaluate both straightness and parallelism of the measured profiles, (iii) zero calibration of sensors is not required. The effectiveness and advantages of this method are demonstrated by theoretical analyses and simulations. And an experimental system was constructed to confirm its ability to eliminate errors.
Article
We present a compensation method for the sensor gain difference when a mixed sequential two-probe method (MTPM) is applied for precision measurements of straightness error. According to theoretical analysis of the effect of sensor gain error, much of the measurement error comes from the sensor gain difference. Also, measurement error caused by misalignment of the straight-edge is dramatically amplified by the sensor gain difference. Therefore, the measurement error in MTPM can be significantly reduced by compensating for the sensor gain difference. To compensate for sensor gain difference, we propose a very simple approach that uses sensor outputs for two different alignment conditions of the straight-edge. To verify the proposed compensation method, experiments were performed with a hydrostatic linear motion table. Experimental results show that the gain difference of the two sensors used in the experiments was about 3.4%. Before compensation, the deviation in the calculated straightness error depending on the alignment conditions was 1.30 μm, which was reduced to 0.08 μm after compensation. The compensated measurement results were compared with results obtained by a reversal method. The maximum deviation between the two methods was 0.22 μm. These results demonstrate that the proposed compensation method is very effective for the measurement of straightness error with sub-micron accuracy and in addition it is practical because compensation can be performed on the actual measurement setup.
Article
An on-machine measurement method, called the square-layout four-point (SLFP) method with angle compensation, for evaluating two-dimensional (2-D) profiles of flat machined surfaces is proposed. In this method, four displacement sensors are arranged in a square and mounted to the scanning table of a 2-D stage. For measuring the 2-D profile of a target plane, height data corresponding to all measuring points are acquired by means of the raster scanning motion. At the same time, pitching data of the first primary scan line and rolling data of the first subsidiary scan line are monitored by means of two auto-collimators to compensate for major profile errors that arise out of the posture error. Use of the SLFP method facilitates connection of the results of straightness-measurements results obtained for each scanning line by using two additional sensors and rolling data of the first subsidiary scan line. Specifically, the height of a measuring point is calculated by means of a recurrence equation using three predetermined height data for adjacent points in conjunction with data acquired by the four displacement sensors. Results of the numerical simulation performed in this study demonstrate higher efficiency of the SLFP method with angle compensation. During actual measurement, however, it is difficult to perfectly align inline the origin height of each displacement sensor. With regard to the SLFP method, zero-adjustment error is defined as the relative height of a sensor’s origin with respect to the plane comprising origins of the other three sensors. This error accumulates in proportion to number of times the recurrence equation is applied. Simulation results containing the zero-adjustment error demonstrate that accumulation of the said error results in unignorable distortion of measurement results. Therefore, a new self-calibration method for the zero-adjustment error has been proposed. During 2-D profile measurement, two different calculation paths – the raster scan path and orthogonal path – can be used to determine the height of a measurement point. Although heights determined through use of the two paths must ideally be equal, they are observed to be different because accumulated zero-adjustment errors for the two paths are different. In view of this result, the zero-adjustment error can be calculated backwards and calibrated. Validity of the calibration method has been confirmed via simulations and experiments.
Article
This paper presents a precision measurement of the Z-slide vertical error motion of an ultra-precision lathe based on a three-probe measurement method. The vertical error motion of the Z-slide, which is composed of the vertical parallelism error motion and the vertical straightness error motion, is measured by utilizing three displacement measuring probes to scan a self-cut roll workpiece and an accurate straightedge, respectively. A series of factors which could influence the measurement of the vertical error motion, including the error motion of the spindle, the surface form error of the reference object and the horizontal error motion of the Z-slide, are all successfully removed by using the proposed three-probe measurement system with an error separation method. The influence of the gravity induced deflection of the roll workpiece on the measurement of the Z-slide vertical parallelism error motion is also discussed. Experiments were carried out to verify the feasibility of the proposed methods on a three-axis ultra-precision lathe. The vertical straightness error motion was evaluated to be 133 nm with a measurement repeatability of 21 nm and the vertical parallelism error motion was evaluated to be 12.1 μm with a measurement repeatability of 38 nm.
Article
With the development of new materials and ultra-precision processing technology, the sizes of measured objects increase, and the requirements for machining accuracy and surface quality become more exacting. The traditional measurement method based on reference datum is inadequate for measuring a high-precision object when the quality of the reference datum is approximately within the same order as that of the object. Self-referenced measurement techniques provide an effective means when the direct reference-based method cannot satisfy the required measurement or calibration accuracy. This paper discusses the reconstruction algorithms for self-referenced measurement and connects lateral shearing interferometry and multi-probe error separation. In lateral shearing interferometry, the reconstruction algorithms are generally categorized into modal or zonal methods. The multi-probe error separation techniques for straightness measurement are broadly divided into two-point and three-point methods. The common features of the lateral shearing interferometry method and the multi-probe error separation method are identified. We conclude that the reconstruction principle in lateral shearing interferometry is similar to the two-point method in error separation on the condition that no yaw error exists. This similarity may provide a basis or inspiration for the development of both classes of methods.
Chapter
The straightness is another fundamental geometric parameter of precision workpieces. The straightness of a workpiece surface can be measured by scanning a displacement sensor or a slope sensor over the workpiece surface by a linear stage (slide). Because the axis of motion of the linear stage functions as the reference for the measurement, any out-of-straightness error motion of the slide will cause a measurement error. Because the out-of-straightness error of a precision linear slide (slide error) is typical on the order of 100 nm over a 100 mm moving stroke [1], it is necessary to separate the error motion for precision nanometrology of the workpiece straightness. The influence of the straightness error of a straightedge surface, which is employed as the reference for measurement of slide error, should also be removed. Similar to the roundness measurement described in Chapter 5, error separation can be carried out by the multi-sensor method and the reversal method. This chapter provides solutions to some key issues inherent in conventional error separation methods for measurement of workpiece straightness and slide error.
Conference Paper
This paper presents nanometrology of an ultraprecision machined surface by using optical sensors. To verify the feasibilities of optical sensors on the measurement of surface profile, different types of fiber-optic sensor and laser micro interferometer are employed to measure the roundness of a ultraprecision machined cone in this paper. Experiments confirmed that the fiber-optic sensor can measure not only the roundness but also the surface roughness of the cone. Experiments also confirm that the measurement of the laser micro interferometer is highly affected by the surface roughness of the cone because of the relative measurement principle of the laser micro interferometer.
Article
Flatness tolerance of mirror is usually determined for a particular manufactured product based on the user’s requirement. To help meet this requirement, we here propose a high-accuracy microscale flatness-measuring machine (micro-FMM) that consists of a multi-beam angle sensor (MBAS). We review the techniques and the sensors predominantly used in the industry to quantify flatness. Compared with other methods, the MBAS can eliminate zero-difference error by circumferential scan and automatically eliminates the tilt error caused by the rotation of a workpiece. Our optical probe uses the principle of an autocollimator, and the flatness measurement of the mirror comprises two steps. First, the MBAS is designed to rotate around a circle with a given radius. The workpiece surface profile along this trajectory is then measured by the micro-FMM. Experimental results, confirming the suitability of the MBAS for measuring flatness are also presented.
Article
This paper researches on the non-contact online detection of concentricity error, which mainly focus on the structural principle of the measurement system and the concentricity error evaluation methods. The paper using the method of projection, converting the three-dimensional model to a two-dimensional model and evaluating coaxially error. And it is validated by the simulation of MATLAB. In theory, the proposed measurement system can measure geometric tolerance, including coaxially error, cylindricity error, circularity error, etc.
Article
Full-text available
The first uses of Nomarski differential interference contrast imaging with the real time confocal scanning optical microscope are described. The advantage of differential interference contrast imaging in a confocal scanning microscope is that both the height and width of an edge can be measured without ambiguity, even if the edge is taller than half of a wavelength. Imaging modes are described in which (1) average reflectivity changes of the sample have been eliminated but the resulting edge enhanced images are nonlinear in phase, or (2) linear phase images are superimposed on an average reflectivity image of the sample. A third method has been developed which both eliminates the reflectivity image of the sample and generates edge enhanced images which are linear in phase for small phase changes. Applications to box-in-box overlay targets, imaging the passivation layer of an integrated circuit, and the measurement of sidewall slope are described.
Article
Full-text available
Interferometry of wave fronts reflected off conical surfaces requires new interferometric schemes. The pencil beam interferometer is proposed as a metrology tool for conical as well as for spherical optical surfaces. The instrument employs two narrow pencil beams which scan the optical surface to be measured. An electronic fringe position readout system, which measures the location of the fringes that develop through interference of the pencil beams, provides high accuracy surface information. Metrology on a waxicon indicates a measurement precision of ±6 nm. Due to the differential nature of the instrument, alignment requirements are relatively modest.
Article
Full-text available
In scanning systems for surface profile measurement, e.g., stylus systems, the profile of a surface is generally determined by measuring the distance of the surface relative to a reference plane. This can be either a plane defined by a moving stage under a rigid stylus or a plane defined by a moving stylus if a fixed stage is used. In both cases, the measurement precision is limited by the straightness of a linear motion. This paper presents a new interferometric profile measurement technique based on using a rigid differential interferometer probing the test object which is moved by a stage. Information on the surface profile is obtained by scanning the surface with two laser spots simultaneously and measuring the optical path difference between the reflected light beams. This makes the profile measurement largely insensitive to flatness errors of the mechanical stage and enables extremely precise measurements. Data processing is done digitally using a storage scope and a microprocessor. The suitability of this method for measuring the profiles of magnetic sliders and SIMS sputter craters has been investigated. The experimental work includes long- and short-term repeatability tests and an extensive investigation of the temperature dependent behavior of the measuring instrument.
Article
The authors describe techniques used to measure straightness errors of precision machines. These measurements employ a dimensionally stable mechanical reference surface that is sampled with a laser interferometer hence the term optical straightedge. The figure error of the reference surface and the straightness error motion of a coordinate measuring machine carriage in a horizontal plane are each measured with an estimated accuracy of 0. 5 mu in. (13 nm) over 40 in. (1 m) of travel. When measuring straightness error in a vertical plane, the results are complicated by deformation of the reference surface by gravitational forces. The authors use a computational algorithm, based upon simple beam theory, to correct straightness data for this distortion. While inadequate for accuracies better than about 2 mu in. (50 nm), they believe that the algorithm, which may be tested using an uncalibrated straightedge, may be improved using finite-element calculations of gravitational sag.
Article
The purpose of the paper is to realize precise measurement of straight motion accuracy over long travel. The reversal method as well as the sequential three-point method is conventional. However, it is difficult to measure motion accuracy over long travel precisely using either method. The paper proposes a new precise measuring method which will be called the improved sequential three-point method. In this method, the principles of the reversal method and the sequential three-point method are introduced. Straight motion accuracy of a slide table was measured over 850mm travel using the improved sequential three-point method. The standard deviations from 12times measurements were 1.0μm in horizontal position and 2.0arc sec in yaw angle.
Article
A new method of roundness measurement of machine elements based on the three-point method is studied. In this method a workpiece is surrounded with three detectors M1, M2 and M3, each of which is different in its detective magnification, and is able to rotate freely in them. The outputs of detectors are summed together and are indicated on a indicator.The rotational error of a workpiece (eccentric motion or play of rotating centre) does not appear on the indicator if the relative angular positions of the detectors r (between M1 and M2) and φ (between M1 and M3) are adequately arranged. Let the ratios of the detective magnifications of the detectors M1, M2 and M3 be 1 : a : b, then the combinations of (τ, φ) or (a, b) can be selected as follows so as to cancel the rotational error of a workpiece.1 + a cos τ b cos φ = 0 asinτ-sinbφ=0These equations correspond to the magnifying power of the Fourier coefficient of first order of workpiece profile Under these conditions the combinations of (τ, φ) and (a, b) are calculated numerically in which the magnifying powers of the Fourier coefficients of the higher order of workpiece profile are as large as possible.It is proved experimentally, that this method can be used practically for measuring roundness without any high precision turn device.
Article
The combined 3-point method, which combines the generalized 3-point method with the sequential 3-point method, is described in the present paper. The combined 3-point method can not only measure profiles that include high-frequency components whose spatial wavelengths are shorter than the probe distance, but also cancel the influence of the z-directional error and the pitching error in the scanning motion. In the combined 3-point method, some data points from a profile evaluated by the generalized 3-point method are chosen as reference points of the standard area and are used to determine the relative heights among the data groups of the sequential 3-point method. An automatic selection method was used to select the standard area correctly and quickly. Theoretical analyses and computer simulations were performed to confirm the effectiveness of the combined 3-point method. Experimental profile measurements were also carried out using three capacitance-type displacement probes.
Article
The combined method, which combines the generalized 2-point method with the inclination method, has been developed to measure profiles that include high-frequency components whose spatial wavelengths are shorter than the probe interval. It is suitable for measuring discontinuous profiles that include step-wise variations and abrupt changes. In this paper, we discuss the influences of the setting error of the probe interval, and the positioning error of sampling when we use the combined method to measure a step-wise profile. Results of theoretical analyses show that these errors cause the same kind of evaluation errors in the profile measured with the combined method, and large profile evaluation errors are caused by the edge part of a step-wise profile. The value of the profile evaluation error is concerned with the aperture size of the displacement probe and the height of the step-wise profile. The influence of the gain errors of the probe is also investigated. An automatic selection method that can select the standard area properly and quickly is developed to improve the accuracy of the combined method. A machined surface with a step-wise profile is measured by using two capacitance-type displacement probes. Experimental results that confirm the effectiveness of the combined method are also presented.
Article
Conventional measuring methods for evaluating error motion of spindle rotation are inadequate to meet the current needs of ultra precision spindle bearing systems.In this paper, therefore, a new measuring method for spindle rotational accuracy based on a three points method was proposed. This method made it possible to reduce considerably the time and effort required in measuring the spindle rotational accuracy. Measurement of error motion to the nano-meter order was attained. Furthermore, this method was proved to be an effective method for measuring the out-of-roundness of a testpiece.
Article
Characteristics of errors which might occur in the straightness measurement method due to sequential-two-points were investigated. The investigation made it clear that the slight discrepancies of alignment at the tip between two displacement sensors would be accumulated onto the portion of linear increment generally observed when the straightness is measured; the method of compensation is analytically shown. It is theoretically proposed that the error which might be introduced by the yaw of the tool post and is neglected by the present system can be evaluated by the measurement using sequential-three-points.
Article
In this paper, we describe a new differential method for on-machine roundness measurement of cylindrical workpieces, which is called the combined three-point method. This method combines the advantages of the generalized three-point method and the sequential three-point method and can accurately measure roundness profiles including stepwise variations. In the combined three-point method, some data points in the roundness profile evaluated by the generalized three-point method are chosen as the reference points of the standard area and used to determine the relationships among the data groups of the sequential three-point method. An interpolation technique is employed in the data processing of the generalized three-point method to improve the accuracy of the standard area. Theoretical analyses and computer simulations confirming the feasibility of the combined three-point method are shown in this paper. A roundness measurement system using three capacitance-type displacement probes is constructed. The measurement system and the experimental results are also presented.
Article
This article presents a new differential method for surface profile measurement called the combined method. This method, which combines the generalized two-point method with the inclination method, is developed to measure profiles that include high-frequency components whose spatial wavelengths are shorter than the distance between the probes. Differential methods, such as the generalized two-point method and the inclination method, have been used to measure profiles under on-machine conditions. The inclination method can determine relative heights rigoursly among discrete points whose interval is equal to the probe interval. Even though the correctness of the relative heights is not influenced by high-frequency components in the profile, the method cannot provide information about points not included in the data group. On the other hand, the generalized two-point method can measure relatively smooth surfaces accurately with a sampling period as short as necessary. The proposed combined method features the advantages of both methods and is capable of rigorously expressing the relative heights of sampled points with a period shorter than the probe interval. Experimental results confirming the effectiveness of the combined method are also presented in this article.
Article
This paper presents a new multiprobe method for roundness measurements called the mixed method. In this method, displacements at two points on a cylindrical workpiece and an angle at one of the two points are simultaneously monitored by two probes. The differential output of the probes cancels the effect of the spindle error, and deconvolving the differential data yields the correct roundness error. The mixed method is compared to the traditional 3-point method with respect to the transfer function and resolution. Unlike the 3-point method, the mixed method can completely separate the roundness error and the spindle error, and can measure high-frequency components regardless of the probe distance. Resolution can also be improved throughout the entire frequency domain by increasing angular separation of the probes. An optical sensor specifically suited to the mixed method is designed and used to make roundness measurements. A fiber coupler and single-mode fibers are used in the sensor to divide a light beam from a laser diode into two beams, resulting in a compact sensor with good thermal drift characteristics. The displacement meter of the sensor is based on the imaging system principle and has a resolution of 0.1 μm. The angle meter is based on the principle of autocollimation and has a resolution of 0.5 in. A measurement system is constructed to realize measurements of roundness by using the optical sensor. Experimental results confirming the effectiveness of the mixed method for roundness measurements are also presented in this paper.
Article
An optical probe based on the principle of differential laser autocollimation has been developed for the purpose of on-machine measurement of mirror shapes. The probe is so compact that it can be mounted on diamond lathes. It can be rotated by a stepping motor about an axis perpendicular to the optical axis of measurement, and has been used to measure mirror shapes on an apparatus that imitates the conditions of an on-machine measurement system. The probe can reduce remarkably the measurement errors due to vibrational and thermal noises that could not be avoided previously in on-machine measurement. Estimating from repeatability, accuracy is better than 0.1 μm in measurement of a parabolic curve whose depth is >1 mm and length is ≈ 100 mm.
Article
An optical probe for profile measurement of mirror surfaces is developed. This probe, consisting of a displacement meter and an angle meter, can detect the displacement and surface slope at one point simultaneously. Both the displacement meter and the angle meter of the probe employ position-sensing detectors (PSDs) as detecting devices. An optical fiber output is used as the light source so that the probe is made compact and has good characteristics. To eliminate influences of light disturbance the light intensity of the light source is modulated by a sine wave of 20 kHz, and only the position signal is removed from signals obtained from the PSDs. Calibration results show that the displacement meter and the angle meter can measure larger than plus or minus 500 micrometer and plus or minus 60 arcmin with good linearity, respectively. Estimating from the SNR of the system, the displacement resolution and angle resolution are plus or minus 10 nm and plus or minus 0.1 arcsec, respectively.
Article
A new measurement method of straightness which will be called TSP method in the paper is applied to a larage horizontal boring and Milling machine for the purpose of developing its practical use. Principle of the method is that: the straightness can be obtained due to an algorithm using series of a pair of relative displacements between tool and objective which are measured at successive two points fed with the distance of two sensors. The algorithm was programmed in a micro-processor and the Method was compared with conventional ones such as laser instrumentation and collimator. It was shown that the measurement system satisfactorily works in easy adjustment, no need of skill, good repetitive accuracy, and simultaneous measurement for both tool motion and objective including cut surface. The errors which might be introduced by feed pitch, distance of the probes, the surface roughness, characteristics of the probes, and other factors are discussed. The analysis also shows that parallelness and flatness can be obtained simultaneously. The straightness of the cut surface could be improved by tool notion compensated with NC function. This made it possible to apply the method to combinations of different tool motions and objectives. The measurement for these combinations verified reliability of the method; the straightness obtained for a cut surface using two different tool motions agreed well each other.
Article
There is an increasing demand for more accurate surface metrology instruments and for techniques which will allow complicated or large parts to be measured in situ. An analysis is presented of existing and new multi-orientation and multiprobe techniques and it is shown how they can be used to remove systematic and variable errors.
Article
The author examines current practice in the multiprobe method of roundness measurements, and derives design strategies for improved measurement accuracy and reliability. The multiprobe method eliminates variable centring errors by combining displacement measurements made simultaneously at several points about the periphery of the workpiece. Discrete signal processing methods for reconstruction of the workpiece profile are described, and design guidelines are established to eliminate the detrimental effects of aliasing from the reconstruction process. The harmonic response of a three-probe arrangement is investigated, and methods are developed to avoid the unwanted suppression of harmonics. The advantages of a more complex multiprobe arrangement are discussed, and a novel harmonic reconstruction method used to avoid suppression, and to allow the detection of incorrect measurements by a redundancy technique.
Article
This paper presents an automated instrument for high-precision roundness measurement of spheres. Instead of a rotating spindle, the surface of the sphere itself is used as a geometrical reference. The measurement method is based on the well-established three-point method. In our design, two points are realized as mechanical contacting points and one as a capacitive gauge that directly faces the surface of the sphere. By this simple design—without any moving parts involved in the probing process—we measured the roundness of 1-inch steel spheres with nanometer resolution. After a short introduction into the basic mathematics of the three-point method, the design of the instrument is presented, including the automation of the measuring process and the means used to minimize environmental effects in an industrial environment. Results are presented that prove the outstanding repeatability and accuracy of the instrument. In a comparison with conventional methods, the advantages and limitation of the method are discussed.
Article
The long trace profiler (Takacs et al.) has found significant applications in measuring the surfaces of synchrotron optics. However, requirements of small slope errors at all spatial wavelengths of the synchrotron optics mandate more accurate slope measurements. A straightness reference for the long trace profiler greatly increases the accuracy of the instrument. Methods of using the straightness reference by interpreting the sequential interference patterns are discussed and results of measurements are presented.
Article
This paper presents a new error separation method for accurate roundness measurement called the orthogonal mixed method. This method uses the information of one displacement probe and one angle probe to separate roundness error from spindle error. This method was developed from the mixed method, which uses the information of two displacement probes and one angle probe to carry out the error separation. In the present paper, the relationship between the characteristics of the mixed method and the probe arrangement is analyzed. Well-balanced harmonic response of the mixed method is verified to be obtainable for the case where the angular distance between the displacement probe and the angle probe is set at 90°. This orthogonal mixed method also had the simplest probe arrangement, because it requires only one displacement probe and one angle probe to realize the error separation. Optical probes were used to construct an experimental measurement system that employs the orthogonal mixed method. The displacement probe and the angle probe both use the principle of the critical angle method of total reflection, and they have stabilities of 1 nm and 0.01 in., respectively. The measurement results show that roundness measurement can be performed with a repeatability on the order of several nanometers.
Article
A novel self-calibration method is proposed for calibrating differential interferometers with subnanometer resolution, and the basic characteristics of the method are discussed. Analysis shows that without using any external reference, the calibration accuracy approaches the resolution limit of the interferometer, which is determined by the signal-to-noise ratio (SNR) and the stability of the measurement system. A compact differential interferometer that uses a laser diode as the light source has been developed in order to demonstrate the viability of the proposed calibration method. The conventional fringe-counting and phase modulation methods are combined in order to extend the measurement range and improve the resolution of the interferometer. The developed interferometer was calibrated using the new method, and the calibration results were compared to those obtained by a comparison calibration method that uses a capacitance displacement sensor as the reference.
Article
Over the years many techniques have been developed for accurate measurement of part features without reference to an externally calibrated artefact. This paper presents a partial survey of such methods for dimensional metrology, their ranges of application, and their limits. Finally, the paper attempts to distil the common features of the various methods in the hope that this may provide the basis, or inspiration, for development of “new” methods.
Handbook of dimensional measurement
  • Farago
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In situ self-calibration of metrological sensors
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