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This paper proposes a synchronous measurement system of four position-independent geometric errors (PIGEs) and two position-dependent geometric errors (PDGEs) for the rotary axis in five-axis machine tools. The measuring instruments used in this system are a touch-trigger probe and two standard calibration spheres. The contribution of this paper is the simultaneous measurement of four PIGEs and two PDGEs (axial and angular positioning errors) can be directly analyzed through only one measuring process. It is expected to improve the shortcomings of previous studies that separately measured PIGEs and PDGEs. This paper analyzed the geometric errors of C-axis of a mill-turn machine tool MT-540. The process of calculation includes the establishment of the mathematical model of the machine and geometric error equations. Using the least squares method to solve the linear overdetermined system and calculate the values of the geometric errors. Before solving the geometric errors, the accuracy of the calculated process is ensured by using the simulated method. The simulation results also confirm the feasibility of this measurement system. Then using the data obtained from the experiment to calculate the geometric errors in the machine tool. During the experiment, the calibration procedure of the touch-trigger probe will be calibrated. After the calibration is completed, the mechanical coordinate values of the two standard calibration balls can be measured. The geometric error equations are programmed on the computer side, and the calibration spheres data obtained from the experimental measurement is substituted into the program to calculate the four PIGEs and two PDGEs.

The positioning error of the moving stage has a significant influence on the machining accuracy of a machine tool. Therefore, the positioning error must be measured accurately. Laser interferometer systems are widely used for positioning error calibration due to their accuracy, but these systems also have many shortcomings in standard procedure and measurement methods. In this study, a positioning error measurement system for a long linear stage by using geometric optics rather than interference principles is proposed. However, as the stage moves, geometric errors apart from the positioning error are produced. Accordingly, the proposed measurement system is designed to not only measure the positioning error but also simultaneously measure the multi-degree-of-freedom (MDOF) geometric errors of the linear stage. The proposed measurement system was characterized numerically by using the commercial software Zemax; the mathematical model of the errors was constructed by using a skew-ray tracing method, a homogeneous transformation matrix, and a first-order Taylor series expansion. The feasibility and effectiveness of the proposed measurement system were experimentally verified by using a laboratory-built prototype. The experimental results demonstrate that compared with conventional laser interferometers, the proposed measurement system has similar accuracy and can simultaneously measure the six-degree-of-freedom (6-DOF) geometric errors of a long linear stage.

With zoom lenses, both the magnification of the camera and the distance between the lens and the object plane can be changed. Changes to zoom lens magnification is accompanied by changes in the depth of field and the distance between the lens and the object plane, complicating the calibration of zoom cameras—specifically, that of each focus and zoom control, for which separate configurations are required. To overcome this problem, a procedure for the calibration of a multifocus zoom lens in a three-dimensional (3D) scanning system was developed in the present study. Specifically, a pragmatic, five-step calibration procedure was proposed. In the first two steps, the characteristics of the zoom lens were obtained. In the third and fourth steps, the calibration was normalized. Finally, the effectiveness of the process was assessed using a laboratory-developed prototype. High reconstruction accuracy was achieved.

In order to simultaneously obtain the thickness and refractive index for each layer of multilayered samples, this paper proposes a novel measurement system with a simple structure by using geometric optics. The key point of the overall structure is that the binary linear equation relation between the upper and lower planes of the layer can be known by the distances between laser spots reflected from the layer. Using two optical paths with different incident angles of laser beams, the CCD sensors capture the spot signal for image processing binarization and data sampling. After the obtained laser spots' spacing is substituted into the equations, the thicknesses and refractive indexes of the multilayered samples can be calculated and measured. The proposed measurement system is characterized numerically using simulations on the commercial software program Zemax and then experimentally tested using a laboratory-built prototype. The experiment results show that the refractive indexes and the thicknesses of three-layer samples were measured with high accuracy (with maximum measurement errors of 2.4% and 2% for a refractive index n and thickness t, respectively).

For automated optical inspection, autofocusing microscopes play an important role in capturing clear images of the measured object. At present, the image processing part of optics-based autofocusing microscopes often has various factors, which makes it impossible to describe the image information of the semicircular (or elliptical) spot with a simple circle-finding method. Accordingly, this study has developed a novel algorithm that can quickly calculate the ideal center of the elliptical spot and effectively compensate the linearity of the focusing characteristic curve. A prototype model was used to characterize and verify the proposed algorithm. The experimental results show that by using the proposed algorithm, the autofocusing accuracy can be effectively improved to less than 1.5 μm.

Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify high-precision control in parallel manipulators, maximum kinematic decoupling is always desired. A constraint map method is used to propose the four required DoF with the consideration of maximum kinematic decoupling. A specific compliant mechanism is presented based on the constraint map, and its kinematics is estimated analytically. Finite element analysis demonstrates the desired qualitative motion and provides some initial quantitative analysis. A normalization-based compliance matrix is finally derived to verify and demonstrate the mobility of the system clearly. In a case study, the results of normalization-based compliance matrix modelling show that the diagonal entries corresponding to the four DoF directions are about 10 times larger than those corresponding to the two-constraint directions, validating the desired mobility.

With the increasing customer demand for high-precision workpieces, the accuracy performance of CNC machine tools has become an increasingly important hot topic for almost all machine tool manufacturers. For fine surface finish workpieces, the performance of multi-axis synchronous motion has a significant impact on lathe processing. Accordingly, it is necessary to calibrate and identify the geometric errors of the workpiece table during multiple-axis synchronous motion. Therefore, this study proposes a novel noncontact optical measurement system for measuring the geometric errors of the workpiece table while the two axes are moving simultaneously. In addition, the horizontal CNC lathe machine iTC-2000LM, produced by Tongtai machine & tool Co., Ltd., was taken as the research vehicle. The proposed measurement system comprises an optics module composed of several reflectors, lenses, and cubic beam splitters; a sensing module composed of multiple two-dimensional position-sensitive detectors (PSDs); and a laser. Based on the principle of geometric optics theory and the optical triangulation method, complete mathematical models that describe the geometric errors of the workpiece table during two-axis synchronous motion were established using the skew-ray tracing method. Additionally, the essential features of the proposed measurement system were verified using the optical design software Zemax. Finally, a laboratory prototype system was constructed to experimentally verify the proposed measurement system. As mentioned above, the main contribution of this study is to design a novel and highly efficient measurement system with established measurement mathematical models and experimental verifications.

For the machining accuracy of five-axis machine tools, it must be emphasized that not only the PIGEs but also the PDGEs of rotary axes influence the machining accuracy. However, until now there is no any commercial measurement system available for identifying the PDGEs in the rotary axes of five-axis machine tools. As a result, this study proposes a robust, efficient, and automatic measurement method to identify and compensate the position-dependent geometric errors (PDGEs) of rotary axes on five-axis machine tools. The proposed measurement method has established an on-machine measurement for the PDGEs of rotary axes by using a touch-trigger probe and three spheres installed on the spindle as well as the tilting rotary table, respectively. For each rotary axis, only a single measuring pattern is implemented to measure the PDGEs with a single setup, which delineates the advantages of efficient and automated identifying procedures in each periodical measurement. By implementing the proposed measurement method, 12 PDGEs can be numerically identified based on the measurement algorithm, which is built through a kinematic error model as well as a least square method. Finally, the proposed measurement method is experimentally conducted on a commercial five-axis machine tool. Moreover, after consequently performing the proposed measurement method, the PDGEs of the rotary axes were quantitatively compensated by the commercial controller to validate its feasibility. The experimental results have clearly delineated that the linear errors and angular errors are reduced from at most 37.81 μm and 10.23 mdeg to 0.9 μm and 0.26 mdeg, respectively. Consequently, the experimental results have demonstrated that the proposed measurement method is efficient and precise.

This study proposed an approach to control voice coil motors (VCMs) installed in smartphone modules as autofocus actuators. The VCM developed in this study comprises guide rods. The magnetic field attraction force between guide rods and movable parts serves as lens restoring force. This study did not use feedback elements to avoid the stick-slip phenomenon between VCM guide rods and movable parts. Instead, this study used a high–low frequency composite signal based on the findings from a mathematical model analysis and VCM dynamic attribute analysis, preventing stick-slip and offering the VCM a more favorable positioning precision.

This paper proposes a 4-degree-of-freedom (DOF) actuator for a fast steer mirror (FSM) compensation system in order to compensate for 4-DOF laser errors. The mathematic system modeling was built to design and predict the performance of the proposed 4-DOF FSM. Finite element analysis was performed by using a commercial software to analyze the characteristics of the electromagnetic structure and mechanical structure for the proposed 4-DOF FSM. This study further verifies the properties of the proposed 4-DOF FSM by using a laboratory-built prototype. The proposed 4-DOF FSM has the travel range of ±5 mrad and ±0.04 mm along X and Y axes with accuracy of 0.025 mrad and 0.0012 mm and the bandwidth of rotational part and translational part are 10 Hz and 39 Hz, respectively.

In this study, an innovative four-degree-of-freedom (4-DOF) compensation prism is designed for fast steering mirror active laser compensation systems. In addition to improving the disadvantages of the commercially available compensation systems, such as a larger number of components and longer optical paths, the proposed system has further enhanced the shortcoming of high sensitivity to the laser by using double Porro prisms as 4-DOF compensation prisms proposed in a previous study. The prism proposed in this study reduces the sensitivity to the laser while maintaining two translations and two rotations in 4-DOF control characteristic for laser, thereby improving the resolution of the system to control the laser. First, Zemax was used to build the overall system and evaluate the system characteristics. Then, the skew-ray tracing method and homogeneous coordinate transformation matrix were used to build the mathematical model of the compensation prism and analyze the sensitivity of the proposed prism to the laser. Finally, the closed-loop algorithm was established and the system was completely built on the optical table for experiments to compare the results between the laser before and after compensation by the proposed prism. In addition, the resolution of the proposed prism is compared with the double Porro prisms.

In the manufacturing industry, grinding is used as a major process for machining difficult-to-cut materials. Grinding is the most complicated and precise machining process. For grinding machines, continuous generating gear grinding machines are widely used to machine gears which are essential machine elements. However, due to its complicated process, it is very difficult to design a reliable measurement method to identify the grinding wheel loading phenomena during the grinding process. Therefore, this paper proposes a measurement method to identify the grinding wheel loading phenomenon in the grinding process for continuous generating gear grinding machines. In the proposed approach, an acoustic emission (AE) sensor was embedded to monitor the grinding wheel conditions, an offline digital image processing technique was used to determine the loading areas over the surface of Al2O3 grinding wheels, and surface roughness of the ground workpiece was measured to quantify its machining quality. Then these three data were analyzed to find their correlation. The experimental results have shown that there are two stages of grinding in the grinding process and the proposed measurement method can provide a quantitative grinding wheel loading evaluation from the AE signals online.

As a foundation to enhance the machining accuracy of five-axis machine tools, a robust, efficient, and precise method to measure the location errors of rotary axes on five-axis machine tools has been proposed in this study. This precise identification and calibration methodology for on-machine measurement of location errors of rotary axes is achieved by using a touch-trigger probe and a precise sphere installed on a tilting rotary table. Compared to commercially available devices, such as the double ball bar and R-test, the proposed measurement method has the advantages of efficient and automated calibration procedures in each periodical measurement. This proposed calibration algorithm builds a kinematic error model and measurement equations by using a forward and inverse kinematic approach and estimates the location errors by applying the least squares method. Moreover, the proposed calibration algorithm defines the location errors of the two rotary axes so they can be estimated and separated individually to avoid coupling effects. All the location errors of the rotary axes measured using the proposed measurement method were identified after compensation to improve the accuracy of the five-axis machine tool. A simulation was implemented to inspect the influence of uncertainties on the identified location errors of the rotary axes. Finally, an experimental demonstration on a five-axis machine tool with a tilting rotary table validates the feasibility of the proposed measurement method.

In the industrial manufacturing field, machining is a major process. Machining operations involve grinding, drilling, milling, turning, pressing, molding, and so on. Among these operations, grinding is the most precise and complicated process. The surface condition of the grinding wheel plays an important role in grinding performance, and the identification of grinding wheel loading phenomena during the grinding process is critical. Accordingly, this present study describes a measurement method based on the acoustic emission (AE) technique to characterize the loading phenomena of a Si2O3 grinding wheel for the grinding mass production process. The proposed measurement method combines the process-integrated measurement of AE signals, offline digital image processing, and surface roughness measurement of the ground workpieces for the evaluation of grinding wheel loading phenomena. The experimental results show that the proposed measurement method provides a quantitative index from the AE signals to evaluate the grinding wheel loading phenomena online for the grinding mass production process, and this quantitative index is determined via some experiments in advance in the same grinding environment to help the monitoring and controlling of the grinding process.

The function of optical zooming is really rare in smartphone cameras due to its appearances and dimensions now. The manufactures need to provide a better optical performance and make a new gimmick to attract consumers. As a result, a novel VCM actuator with optical zoom for smartphone cameras is proposed in this paper, it has a simpler structure when compared to stepping motor smartphone cameras. The paper presents a segmented magnetic equivalent circuit method to analyze the magnetic characteristics of proposed VCM actuator and further verified by a commercial finite element model software. Furthermore, the performance of the proposed optical zoom VCM actuator was verified by constructing a laboratory-built prototype, the experimental results shows that the proposed VCM actuator has good positioning accuracy and good dynamic response.

Measuring the refractive index and thickness of transparent materials is essential in offline or online automated inspection in the manufacturing and industrial fields. We recently developed a novel optical system with two optical paths for simultaneously measuring the refractive index and thickness (>1 mm) of a transparent plate; the developed system allowed for better thickness measurement with a simpler structure and lower cost (C. S. Liu, R. C. Song, and S. J. Fu, Appl. Phys. B 125, 199, 2019). In the present study, the thickness range that can be measured using the developed optical system is reduced to ≤100 μm by using interference methods instead of triangulation methods. The proposed optical interference system is characterized numerically using simulations on the commercial software program ZEMAX and then experimentally tested using a laboratory-built prototype. The experiment results show that the refractive indexes and the thicknesses of the slim transparent plates (thickness ≤ 100 μm) were measured with high accuracy (with maximum measurement errors of 0.0007 and 3 μm for a refractive index n and thickness d, respectively). Consequently, the proposed optical interference system has the potential to be used in the automated inspection of slim transparent materials.

This study presents a new groove profile using the slant groove depth arrangements to enhance the performance of micro-HGJBs. The computational analysis was based on the steady-state three-dimensional conservation equations of mass and momentum in conjunction with the cavitation model to examine the complex lubricated flow field. The simulated results of load capacity and circumferential pressure distribution of lubricant film are in good agreement with the measurement data and the predictions cited in the literature. Numerical experiments were extended to determine the pressure distribution, load capacity, radial stiffness and friction torque by varying the slant ratio of groove depth, eccentricity ratio, rotational speed and attitude angle. The cavitation extent of lubricant film was also studied for different slant groove patterns.

In order to deal with the free boundary problems occurred in cavitation region, this work incorporates an artificial term in Reynolds equation to stabilize the solution. The current result shows that adding the extra term gives accurate pressure distribution and benefits the selection of the groove shape and size. In addition, this study utilizes herringbone grooves on a reversible rotating journal bearing (RHGJB) and numerically analyzes the characteristics of miniature journal bearings with an inner diameter of 0.6 mm. Miniature journal bearings are limited in that the load capacity is significantly reduced with decreased bearing size, and therefore, the performances (load capacity and side leakage) of miniature RHGJBs are optimized. The optimum geometrical appearance of miniature RHGJBs is calculated by evaluating several groove parameters. Using the Taguchi parameter design methodology greatly reduces the number of full-factorial experimental design tests required to determine the optimal design parameters of the RHGJB from 59 (1,953,125) to 450 runs.

The autofocusing (AF) performance of cell phone cameras is critically dependent on the design of the voice-coil motor (VCM) used to drive the lens module. Also, the metal springs in the AF module should combine high stiffness with a good actuation response and a light weight. The present study utilizes a reverse engineering approach to construct three-dimensional finite element models of the top and bottom springs in the VCM mechanism. Simulations are then performed to investigate the von Mises stress distribution and stiffness characteristics of the two springs given horizontal and vertical orientations of the AF module, respectively. In performing the simulations, the actuation force is computed using two different analysis methods, namely a simplify structure method and a coupled electromagnetic-structural method. It is shown that the simplify structure method has the advantages of a lower computational complexity and a more comprehensive modeling capability. A further series of simulations is thus to examine the effects of the spring shape parameters on the reaction force developed by the spring stiffness. The results show that the spring stiffness increases with an increasing thickness and a decreasing rib length. The simulation results obtained for different spring shape parameter settings are summarized in the form of a parameter design chart for predicting the reaction force given known values of the spring rib length and spring thickness.

In this study, a novel and simple measurement system for simultaneously measuring the geometric errors in six-degree-of-freedom (6-DOF) for a moving linear stage of a machine tool is designed and validated. Compared to laser interferometer and laser Doppler systems, this new measurement system is less expensive and capable of multiple functions. The proposed measurement system comprises an optics module, composed of two reflectors and two cubic beam splitters; a sensing module, composed of three two-dimensional position sensitive detectors (PSDs); and a helium-neon (He-Ne) laser. Using skew-ray tracing and a first-order Taylor series expansion, the 6-DOF geometric errors of the moving linear stage, which include translation and rotation errors, are analyzed. A laboratory prototype system is built to verify the effectiveness and accuracy of the proposed measurement system. The experimental results show that the displacement uncertainty and the angular uncertainty of the proposed measurement system are less than 1.2 µm and 0.4″, respectively. Compared with the Renishaw laser interferometer XL-80 laser system, the translational accuracy and the rotational accuracy of the proposed measurement system are less than ±1 µm and ±0.2″, respectively, when the linear stage travels 6 mm.