Compact maglev stage system for nanometer-scale positioning

Semiconductor manufacturing systems and ultra-precise machine tools now require nanometer-scale positioning accuracy. To improve positioning accuracy, it is efficient to support the top table with a noncontact guide system to prevent guide friction and heat transfer from the lower table or base. A magnetic levitation (maglev) stage can accomplish ultra-precise positioning accuracy with six-degrees-of-freedom (6DOF) control even in vacuum conditions. However, if the gravity of the levitated table is supported by the thrust of a linear motor, heat generation from the motor coil dramatically increases. In addition, a larger motor is required, which causes the moving mass to increase and the mechanical response to deteriorate. We aimed to develop a compact maglev stage for which the levitated mass is less than 1 kg and that is dramatically more lightweight than existing maglev stages. This compact feature was enabled by our newly proposed gravity compensation system with repellent force and a planar motor structure. The developed stage system also has long strokes, specifically 200 mm in the X and Y-directions on a horizontal plane. We designed a maglev stage with the following design concepts to create its compact structure: (1) Reduce top-table mass to minimize the motor dimensions and enable a light weight and high responsiveness. (2) Measure the top-table position from the base to eliminate positioning error and isolate vibrations of the coarse stage. (3) Install a motor in a symmetrical layout in view from the Z-axis to enable the same driving characteristics between the X and Y axes. The results of the performance evaluation showed that the developed maglev stage system with a compact structure with 0.81 kg levitated mass has ±10 nm positioning stability.     

Design and precision construction of novel magnetic-levitation-based multi-axis nanoscale positioning systems

This paper presents two novel six-axis magnetic-levitation (maglev) stages capable of nanoscale positioning. These stages have very simple and compact structures, which is advantageous to meet the demanding positioning requirements of next-generation nanomanipulation and nanomanufacturing. Six-axis motion generation is accomplished by the minimum number of actuators and sensors. The first-generation maglev stage, namely the Δ-stage, is capable of generating translation of 300 μm and demonstrates position resolution better than 2 nm root-mean-square (rms). The second-generation maglev stage, namely the Y-stage, is capable of positioning at a resolution better than 3 nm rms over a planar travel range of 5 mm × 5 mm. A novel actuation scheme was developed for the compact structure of this stage that enables six-axis force generation with just three permanent-magnet pieces. This paper focuses on the design and precision construction of the actuator units, the moving platens, and the stationary base plates. The performance of the two precision positioners is compared in terms of their positioning and load-carrying capabilities and ease of manufacture. Control system design for the two positioners is discussed and an experimental plant transfer function model is presented for the Y-stage. The superiority of the developed instruments is also demonstrated over other prevailing precision positioning systems in terms of the travel range, resolution, and dynamic range. The potential applications of the maglev positioners include semiconductor manufacturing, microfabrication and assembly, nanoscale profiling, and nanoindentation.     

Motion control of industrial robots by considering serial two-link robot arm model with joint nonlinearities

This paper presents a model based motion control approach for industrial robots by considering a serial two-link robot arm model with joint nonlinearities. In order to achieve the desired performance using the model based control approaches, it is important to obtain relevant models of both kinematics and dynamics including nonlinear characteristics. Main nonlinear components that lead to trajectory tracking errors of typical multi-axis industrial robot are joint nonlinearities in each axis and dynamic coupling effects between different axes. In this paper, a parametric modeling approach is introduced to reproduce behaviors of a serial two-link robot arm with joint nonlinearities. Nonlinear stiffness, angular transmission errors, and friction in these two links are directly identified as joint nonlinearities. This approach is applied for the serial two-link arm of a typical multi-axis industrial robot, which has low frequency vibration modes and significantly affects to the trajectory performance. Effectiveness of the modeling is verified by comparative studies with numerical simulations and experiments. Finally, a 2-DOF control scheme with the identified two-link dynamic model and a feedback loop-shaping with a variable notch filter are applied to improve the performance of trajectory tracking and residual vibration suppression.     

A control strategy with motion smoothness and machining precision for multi-axis coordinated motion CNC machine tools

The advanced manufacture technology requires that multi-axis coordinated motion computer numerical control (CNC) machine tools have the capability of high smoothness and high precision. At present, the study of the motion smoothness mainly concentrates on the acceleration and deceleration control method and the look-ahead process of velocity planning in the interpolation stage. The control strategy of the contouring error mainly focuses on tracking error control, cross-coupling control, and optimal control. In order to improve the motion smoothness and contouring precision for multi-axis high-speed CNC machine tools, a multi-axis modified generalized predictive control approach was presented in this paper. In the control strategy, the estimation models of tracking error, contouring error, velocity error, and acceleration error were structured separately. A new improved quadratic performance index was proposed to guarantee the minimum of these errors. Generalize predictive control was also introduced, a multi-axis generalized predictive control model was deduced for motion smoothness and machining precision for multi-axis coordinated motion CNC system, and an approved multi-axis generalized predictive controller based on the model was designed in this paper. The proposed predicted control approach was evaluated by simulation and experiment of circular, noncircular, and space line trajectories, respectively. These simulative and experimental results demonstrated that the proposed control strategy can significantly improve the motion smoothness and contouring precision. Therefore, the new position control method can be used for the servo control system of multi-axis coordinated motion CNC system, which increases motion smoothness and machining precision of CNC machine tools.     

A general strategy for geometric error identification of multi-axis machine tools based on point measurement

Geometric error component identification is needed to realize the geometric error compensation which can significantly enhance the accuracy of multi-axis machine tools. Laser tracker has been applied to geometric error identification of machine tools increasingly due to its high capability in 3D metrology. A general method, based on point measurement using a laser tracker is developed for identifying the geometric error components of multi-axis machine tools in this study. By using this method, all the component errors and location errors of each axis (including the linear axis and rotary axis) of the multi-axis machine tools can be measured. Three pre-described targets are fixed on the stage of the under-test axis which moves step by step. The coordinates of the three targets at every step are determined by a laser tracker based on the sequential multilateration method. The volumetric errors of these three target points at each step can be obtained by comparing the measured values of the target points’ coordinates with the ideal values. Then, nine equations can be established by inversely applying the geometric error model of the axis under test, which can explicitly describe the relationship between the geometric error components and volumetric error components, and then the component errors of this axis can be obtained by solving these equations. The location errors of the axis under test can be determined through the curve fitting. In brief, all the geometric error components of a single axis of multi-axis machine tools can be measured by the proposed method. The validity of the proposed method is verified through a series of experiments, and the experimental results indicate that the proposed method is capable of identifying all the geometric error components of multi-axis machine tools of arbitrary configuration.     

A large range compliant XY nano-manipulator with active parasitic rotation rejection

There is an increasing demand to achieve manipulating operations in nanometric precision and a macro-range (over a millimeter) simultaneously. In principle, it is possible to satisfy both requirements in a compact size taking advantages of flexure-based mechanisms, whereas limitations such as the parasitic rotation, cross-axis coupling, saturation may adversely affect the motion quality in nanometric level practically. Here, we propose a novel design methodology to actively prevent parasitic rotation of XY compliant mechanisms. Further, by means of design synthesis and real-time motion control, the prototype of manipulator is fabricated, which enables large motion range (±3 mm) along each actuation axis. Experimental results demonstrate a travel range of 2 mm × 2 mm with high linearity, small cross-axis coupling (< 0.4%), and low parasitic rotation (< 6.9 μ rad over 0.5 mm × 0.5 mm motion range). Moreover, the high natural frequency (~ 60 Hz) of the manipulator facilitates it to achieve high-precision motion with tracking error < 80 nm (20 Hz sinusoids). The experimental results of the proposed nano-manipulator outperform most of the existing ones.     

Precision design and control of a flexure-based roll-to-roll printing system

This paper presents the design, characterization, and control of a flexure-based roll-to-roll (R2R) printing system that achieves nanometer level precision and repeatability. The R2R system includes an unwinding/rewinding module, a web guide mechanism, and a core positioning stage consisting of two monolithic compliant X–Y stages that control the position/force of the print roller. During the printing process, capacitance probes, eddy current sensors and load cells are used to monitor the displacements of the flexure stage and contact force in real time. Control strategies, including decoupling, PID, and cascade control, have been implemented to decouple the cross-axis and cross-stage motion coupling effect and improve the overall precision and dynamic performance. In actual printing processes, the contact force and roller position can be uniformly controlled within ±0.05 N and ±200 nm respectively across a 4 in. wide PET web. To demonstrate the performance, a positive microcontact printing (MCP) process is adapted to the R2R system, printing various fine metal patterns, e.g., optical gratings and electrodes, in a continuous fashion.     

High-precision magnetic levitation stage for photolithography

In this paper, we present a high-precision magnetic levitation (maglev) stage for photolithography in semiconductor manufacturing. This stage is the world’s first maglev stage that provides fine six-degree-of-freedom motion controls and realizes large (50 mm × 50 mm) planar motions with only a single magnetically levitated moving part. The key element of this stage is a linear motor capable of providing forces in both suspension and translation without contact. The advantage of such a stage is that the mechanical design is far simpler than competing conventional approaches and, thus, promises faster dynamic response and higher mechanical reliability. The stage operates with a positioning noise as low as 5 nm rms in x and y, and acceleration capabilities in excess of 1 g (10 m/s²). We demonstrate the utility of this stage for next-generation photolithography or in other high-precision motion control applications.     

Three-point method for measuring the geometric error components of linear and rotary axes based on sequential multilateration

The linear and rotary axes are fundamental parts of multi-axis machine tools. The geometric error components of the axes must be measured for motion error compensation to improve the accuracy of the machine tools. In this paper, a simple method named the three-point method is proposed to measure the geometric error of the linear and rotary axes of the machine tools using a laser tracker. A sequential multilateration method, where uncertainty is verified through simulation, is applied to measure the 3D coordinates. Three non-collinear points fixed on the stage of each axis are selected. The coordinates of these points are simultaneously measured using a laser tracker to obtain their volumetric errors by comparing these coordinates with ideal values. Numerous equations can be established using the geometric error models of each axis. The geometric error components can be obtained by solving these equations. The validity of the proposed method is verified through a series of experiments. The results indicate that the proposed method can measure the geometric error of the axes to compensate for the errors in multi-axis machine tools.     

基于激光干涉仪的数控机床运动误差识别与补偿

提出了数控机床运动误差的软件补偿方法。采用刚体运动假设和齐次坐标变换建立了多轴机床空间运动误差的通用模型。该模型把刀具相对于工件的空间误差表示为机床各结构件之间运动误差的位置函数。给出了全部运动误差参数的激光干扰仪识别方法，提出了一种新的roll误差测量措施，在立式加工中心上进行了运动误差的补偿实验，结果证明所提出的运动误差软件联动补偿效果显著。     

Plane kinematic calibration method for industrial robot based on dynamic measurement of double ball bar

A new calibration method is proposed to improve the circular plane kinematic accuracy of industrial robot by using dynamic measurement of double ball bar (DBB). The kinematic model of robot is established by the MDH (Modified Denavit-Hartenberg) method. The error mapping relationship between the motion error of end-effector and the kinematic parameter error of each axis is calculated through the Jacobian iterative method. In order to identify the validity of the MDH parameter errors, distance errors and angle errors of each joint axis were simulated by three orders of magnitude respectively. After multiple iterations, the average value of kinematic error modulus of end-effector was reduced to nanometer range. Experiments were conducted on an industrial robot (EPSON C4 A901) in the working space of 180 mm × 490 mm. Due to the measuring radius of DBB, the working space was divided into 30 sub-planes to measure the roundness error before and after compensation. The average roundness error calibrated by the proposed method at multi-planes decreased about 21.4%, from 0.4637 mm to 0.3644 mm, while the standard deviation of roundness error was reduced from 0.0720 mm to 0.0656 mm. In addition, by comparing the results of positioning error measured by the laser interferometer before and after calibration, the range values of motion errors of end-effector were decreasing by 0.1033 mm and 0.0730 mm on the X and Y axes, respectively.     

A novel parallel-kinematics mechanism for integrated, multi-axis nanopositioning: Part 2: Dynamics, control and performance analysis

In this paper, we discuss the dynamics, controls and performance of a parallel-kinematics, integrated, multi-axis nanopositioner, the PKXYZNP [Yao Q, Dong J, Ferreira PM. A novel parallel-kinematics mechanisms for integrated, multi-axis nano-positioning. Part 1: Kinematics and design for fabrications]. The paper focuses on computing the workspace of the stage, characterization of its dynamic behavior, synthesis of a controller for it, and the testing of its contour tracking and positioning performance. For this system, because of the coupled nature of the axes, a MIMO control scheme is adopted to directly close the loop around the kinematics of the stage, i.e., the position of the table/end-effector is fed back to control the actuators. This scheme has the added advantage of not requiring complex and fragile kinematic calibration of the stage as the accuracy becomes a function of only the accuracy of the sensing system and the servo performance. To make the MIMO control scheme tractable by reducing its order, the controller design is performed in the modal space of the system. A resolution of 2–4 nm is achieved from this stage. Linear and circular tests were performed to evaluate the contouring performance of the PKXYZ stage. In spite of a relatively heavy load condition (the weight of a solid target), the linear and circular contouring errors are less than 40 and 150 nm, respectively, with contouring speeds ranging up to 40 μm/s.     

Feedforward compensation of back electromotive force for suppressing rotational motion errors in a magnetically levitated system

The magnetically levitated system, so called maglev system, has been researched and developed with the purpose of vacuum compatibility in the semiconductor industry. In the maglev system, the back electromotive force is inevitably generated when the system moves. The back electromotive force causes force/moment disturbances. Especially, the moment disturbances have negative effect on controlling the rotational motions (θ _x , θ _y , θ _z ) whose control bandwidth is low. Therefore, the back electromotive force causes rotational motion errors. The rotational motion errors should be suppressed since they prevent high speed motion of the maglev system due to the rotational motion allowance of sensors. The rotational motion errors are suppressed by compensating the back electromotive force. In this paper, the back electromotive force, the cause of the rotational motion errors, is mathematically found in terms of the mover velocity and element of force-current matrix. A maglev system without the compensation was simulated and the rotational motion errors due to back electromotive force were found. Then, a feedforward compensated system using a mathematically modeled back electromotive force was simulated. It was verified that the feedforward compensation method with the modeled equation could be useful for suppressing rotational motion errors.     

Comprehensive analysis of the influence of structural and dynamic parameters on the accuracy of nano-precision positioning stages

Nano-precision positioning stages are characterized by rigid-flexible coupling systems. The complex dynamic characteristics of mechanical structure of a stage, which are determined by structural and dynamic parameters, exert a serious influence on the accuracy of its motion and measurement. Systematic evaluation of such influence is essential for the design and improvement of stages. A systematic approach to modeling the dynamic accuracy of a nano-precision positioning stage is developed in this work by integrating a multi-rigid-body dynamic model of the mechanical system and measurement system models. The influence of structural and dynamic parameters, including aerostatic bearing configurations, motion plane errors, foundation vibrations, and positions of the acting points of driving forces, on dynamic accuracy is investigated by adopting the H-type configured stage as an example. The approach is programmed and integrated into a software framework that supports the dynamic design of nano-precision positioning stages. The software framework is then applied to the design of a nano-precision positioning stage used in a packaging lithography machine.     

A linear air bearing stage with active magnetic preloads for ultraprecise straight motion

In this paper, we propose a linear motion stage designed with magnetically preloaded air bearings. The magnetic actuators for preloading air bearings were combined with permanent magnets and coils to adjust the air bearing clearance by actively controlling the magnetic force. The system was designed to achieve a simplified configuration of air bearing stage while providing ultraprecise straight motion by actively compensating for the motion errors. The porous aerostatic bearings and magnetic preload actuators were designed and analyzed numerically for a single-axis prototype linear stage driven by a coreless linear motor. A magnetic circuit model was derived for the magnetic actuators. The static stiffness and load capacity of the air bearing stage in the vertical (magnetically preloaded) direction were experimentally measured and compared with the results from the numerical analysis. Motion control laws for three degrees of freedom (i.e., vertical, pitch, and roll motions) were obtained with a high linearity and independence for each axis. The active compensation of three motion errors, the vertical, pitch and roll motion errors were performed through curve-fitting the three errors measured with combination of capacitive gap sensors and a laser interferometer. The errors were reduced from 1.09 to 0.11 μm for the vertical straightness error, from 9.42 to 0.18 arcsec for the pitch motion, and from 2.42 to 0.18 arcsec for the roll motion as level of measured repeatability.     

Positioning error correction using virtual coordinate system for mMTs

In this paper, a new calibration and correction method is proposed to effectively improve positioning accuracy of practical 3-DOF positioning devices of miniaturized machine tools (mMTs). The method is composed of correction of the machine’s coordinate system, which is distorted due to the effects of various error components, and correction of positioning errors at arbitrary points in workspace using this corrected coordinate system. If only positioning results could be measured and assessed three-dimensionally, squareness and scale errors of the mMTs’ coordinate system can be corrected using this method without any additional device or jig. The proposed method was applied to correct the positioning errors of a serial-type 3-DOF precision positioning device used for a micro/nano-pattering system. After correction of over 40 μm × 40 μm × 40 μm of its workspace, the positioning accuracy was successfully improved by about 98%.     

Geometric error compensation for multi-axis CNC machines based on differential transformation

As the geometric errors of motion axis can be equivalent to the differential movement, regarded as a differential operator based on its ideal position, a new modeling method for multi-axis CNC machines based on differential transform theory is proposed in this paper. First, the workpiece coordinates is selected to observe the errors of the tool pose. Then, a general geometric error model for multi-axis machines is established. Moreover, the Jacobian matrix is applied to describe the relationship between the tool pose error vector and the compensation error vector. All the elements of the matrix are obtained by computing the differential operators instead of computing the partial derivatives. The compensation errors vector is solved using the pseudo-inverse Jacobian matrix. Finally, an automatic modeling procedure is developed to construct the geometric errors for multi-axis machine tools. An experiment on a five-axis machine tool is conducted to test and verify the proposed method. The results show that the proposed method dramatically improves the overall position accuracy of the test tool path.     

Assessing geometrical errors of multi-axis machines by three-dimensional length measurements

In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.     

Design and control of a decoupled two degree of freedom translational parallel micro-positioning stage

This paper presents a novel decoupled two degrees of freedom (2-DOF) translational parallel micro-positioning stage. The stage consists of a monolithic compliant mechanism driven by two piezoelectric actuators. The end-effector of the stage is connected to the base by four independent kinematic limbs. Two types of compound flexure module are serially connected to provide 2-DOF for each limb. The compound flexure modules and mirror symmetric distribution of the four limbs significantly reduce the input and output cross couplings and the parasitic motions. Based on the stiffness matrix method, static and dynamic models are constructed and optimal design is performed under certain constraints. The finite element analysis results are then given to validate the design model and a prototype of the XY stage is fabricated for performance tests. Open-loop tests show that maximum static and dynamic cross couplings between the two linear motions are below 0.5% and -45 dB, which are low enough to utilize the single-input-single-out control strategies. Finally, according to the identified dynamic model, an inversion-based feedforward controller in conjunction with a proportional-integral-derivative controller is applied to compensate for the nonlinearities and uncertainties. The experimental results show that good positioning and tracking performances are achieved, which verifies the effectiveness of the proposed mechanism and controller design. The resonant frequencies of the loaded stage at 2 kg and 5 kg are 105 Hz and 68 Hz, respectively. Therefore, the performance of the stage is reasonably good in term of a 200 N load capacity.     

Note: Rotaphone, a new self-calibrated six-degree-of-freedom seismic sensor

We have developed and tested (calibration, linearity, and cross-axis errors) a new six-degree-of-freedom mechanical seismic sensor for collocated measurements of three translational and three rotational ground motion velocity components. The device consists of standard geophones arranged in parallel pairs to detect spatial gradients. The instrument operates in a high-frequency range (above the natural frequency of the geophones, 4.5 Hz). Its theoretical sensitivity limit in this range is 10(-9) m/s in ground velocity and 10(-9) rad/s in rotation rate. Small size and weight, and easy installation and maintenance make the instrument useful for local-earthquake recording and seismic prospecting.