Error analysis to minimize cross-axis couplings in 6-DOF motion systems with a single moving part

In multi-axis motion control, cross-axis couplings cause error force and position disturbances in an axis when a desired motion is generated along another axis. Different from the parasitic errors that result from the imperfections of the mechanical bearings and reference surfaces, cross-axis perturbations are caused by errors that occur both statically (geometrical errors) and dynamically (in the transient responses) and are more prevalent in air-bearing and magnetic-levitation (maglev) stages. The parasitic errors are heavily dependent on the sizes of the stage's mechanical components, while the cross-axis perturbations depend significantly on the mover's speed and acceleration. For stages using permanent magnets (PMs) and Lorentz coils, the causes of off-axis forces include 1) errors in the coil turns' straightness, perpendicularity, and parallelism of the motor axes, and 2) errors in the local magnetizations and PMs' fringing effects. The purpose of this paper is to analyze the topologies of 6-degree-of-freedom (6-DOF) single-moving-part stages to minimize cross-axis couplings. The outcome is a stage configuration with reduced couplings and cross-axis perturbations. This is supported by experimental results performed on a newly developed 6-DOF maglev laser-interferometer stage. Its achieved root-mean-square (rms) positioning noise and minimum step size in XY are 3 nm and 10 nm, respectively. Its achieved resolution in out-of-plane rotations is 0.1 μrad. In addition to the analysis supported by these results, this paper introduces a new measure to represent cross-axis perturbations and to compare the effects of couplings in multi-axis positioning. This measure is entitled the cross-coupling quantity (CCQ) and calculated from the displacement of the stage in the axis of interest, the peak time of the response, and the peak-to-peak (p-p) error in the perturbed axis.     

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.     

一种磁悬浮离心式心脏泵刚度与阻尼特性分析

针对一种磁悬浮离心式心脏泵系统的动态特性,需要分析其刚度与阻尼。为此,分析了径向永磁轴承和开关磁阻电机的径向力学特性,得到磁悬浮转子径向运动方程和控制系统框图; 并结合PD控制器,推导出系统径向刚度与阻尼数学表达式,最后通过实例仿真,得到径向刚度与阻尼特性曲线。研究表明,比例和滤波环节对系统动刚度、阻尼比和固有频率均有显著影响,且在低频段,微分系数与阻尼比近似成正比关系。上述研究为磁悬浮离心式心脏泵控制系统的设计和磁悬浮转子径向位移控制提供理论指导。     

A novel long-travel piezoelectric-driven linear nanopositioning stage

This study presents a novel long-travel piezoelectric-driven linear nanopositioning stage capable of operating in either a stepping mode or in a scanning mode. In the stepping mode, the stick–slip friction effect between a linear micropositioner and a sliding stage is used to drive the stage step-by-step through an extended displacement range. The straightness precision of the stage displacement is ensured by running the stage along two high-precision cylindrical guide rails as it moves. The developed linear micropositioner delivers a high amplification of the piezoelectric actuator input and ensures minimum angular deviation. In the scanning mode, the micropositioner acts as an elastic deformation-type linear displacement amplification device and drives the stage through displacements in the micrometer level range. In practical applications, the scanning mode can be utilized to compensate for the final stage positioning error introduced during the stepping motion of the stage. In a series of experiments, a laser interferometer is employed to measure the displacement responses of the stage under the application of input driving voltages with various waveforms. The results demonstrate that in the stepping mode, the stage is capable of performing precision positioning over an extended displacement range in incremental step sizes ranging from 70 nm to 35 μm. Meanwhile, in the scanning mode, the stage can perform a scanning motion over a displacement range of 50 μm with a displacement resolution of less than 10 nm. Finally, it is shown that the high-precision cylindrical guide rails ensure a straightness error of the stage displacement of less than 50 nm within 10 mm motion range.     

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.     

国内衍射光栅刻划机概况

本文介绍了目前国内已制成的衍射光栅刻划机的概况,同时也介绍了它们所刻光栅的质量。国内刻机有机械型、光电型及间歇刻划、连续刻划方式。在正常刻划的刻机共有15台。所刻光栅最大面积到150×180mm²,刻线密度从50到2400线/mm。     

Development of high-precision micro-coordinate measuring machine: Multi-probe measurement system for measuring yaw and straightness motion error of XY linear stage

Today, with the development of microsystem technologies, demands for three-dimensional (3D) metrologies for microsystem components have increased. High-accuracy micro-coordinate measuring machines (micro-CMMs) have been developed to satisfy these demands. A high-precision micro-CMM (M-CMM) is currently under development at the National Metrology Institute of Japan in the National Institute of Advanced Industrial Science and Technology (AIST), in collaboration with the University of Tokyo. The moving volume of the M-CMM is 160 mm × 160 mm × 100 mm (XYZ), and our aim is to achieve 50-nm measurement uncertainty with a measuring volume of 30 mm × 30 mm × 10 mm (XYZ). The M-CMM configuration comprises three main parts: a cross XY-axis, a separate Z-axis, and a changeable probe unit. We have designed a multi-probe measurement system to evaluate the motion accuracy of each stage of the M-CMM. In the measurement system, one autocollimator measures the yaw error of the moving stage, while two laser interferometers simultaneously probe the surface of a reference bar mirror that is fixed on top of an XY linear stage. The straightness motion error and the reference bar mirror profile are reconstructed by the application of simultaneous linear equations and least-squares methods. In this paper, we have discussed the simulation results of the uncertainty value of the multi-probe measurement method using different intervals and standard deviations of the laser interferometers. We also conducted pre-experiments of the multi-probe measurement method for evaluating the motion errors of the XY linear stage based on a stepper motor system. The results from the pre-experiment verify that the multi-probe measurement method performs the yaw and straightness motion error measurement extremely well. Comparisons with the simulation results demonstrate that the multi-probe measurement method can also measure the reference bar mirror profile with a small standard deviation of 10 nm.     

Aspects of scanning microdensitometry. I. Stray light (glare)

A new instrument is described which permits automatic sampling of microscopic fields on sections. For this purpose a motor-driven high-precision specimen stage was fitted to a microscope. The motors are controlled by an electronic unit to permit the following modes of operation: (a) continuous operation by a four-position joy-stick switch for easy and rapid scanning of the preparation; (b) single-step operation, where the specimen is displaced in either the x- or the y-direction by a preselected distance adjustable between 15 μm and 20 mm; (c) automatically repeated step operation, where the steps occur at intervals pre-selectable between 0·5 and 34 sec; (d) scanning operation, where the specimen continuously moves along the x-axis and is shifted to the next line at a preselected distance when the end of the sweep is reached. The details of principle and operation are presented together with a few typical examples of application.     

A compact ultra-precision air bearing stage with 3-DOF planar motions using electromagnetic motors

We designed a novel surface motor stage supported by air bearings and driven by linear electromagnetic motors. This compact and simple planar stage is proposed for compact-sized precision machine systems, such as micro-machine tools or measurement systems requiring minimum X-Y stage height. Four single-phase linear motors with coils and iron cores are located under the base plate, and air bearings and cores with permanent magnets are attached under the moving table. The hard, non-magnetic alumina-ceramic base plate surface acts as a planar guide for the air bearings. The attractive magnetic force between the magnets and motor cores preload the air bearing to increase vertical stiffness. By simultaneously combining actuations of the motors, linear X and Y motion can be controlled, and angular motions can also be generated. A grid encoder is used to control planar motion, and the system is run by a programmable numerical controller. The thrust and attractive force were calculated using a magnetic circuit model. The designed prototype is 220 (L) × 220 (W) × 66 (H) mm³ in size with a 20 mm × 20 mm range of motion. After fabrication, basic aspects of the prototype, such as vertical stiffness and thrust force, were evaluated. Twenty nanometers of positioning resolution was obtained for the X and Y axes, and the three motions could be controlled independently.     

Feedforward element design using learning controller for precision control of linear synchronous motor with nonlinear characteristics

This study presents a time-invariant feedforward (FF) element design for the high-speed and high-precision tracking control of an ultrahigh-acceleration, high-velocity linear synchronous motor (LSM). The linear motor can generate an acceleration greater than 70 G (= 686 m/s²) and move at a velocity above 10 m/s. To take advantage of this performance and realize high response, the design and usage of suitable FF elements is crucial. However, as the LSM includes highly nonlinear characteristics, it is difficult to provide an exact dynamic model for FF design. To overcome this problem, a control system with a learning controller (LC) as the FF element has been designed previously, demonstrating high-precision and high response motion. However, the motion performance can be achieved only with sufficient pre-learned motions. The integrator and the disturbance observer that were effective in suppressing disturbances were removed from the control system. In addition, the control system has some FF time-invariant elements along with the LC. This study proposes a design method for easy design of all FF elements using an LC. The designed FF elements are time invariant and are used with an integrator and a disturbance observer, without pre-learning. Using the proposed method, two sets of time-invariant FF elements are designed. The performances of two control systems, which include a set of time-invariant FF elements for each, and a simple disturbance observer are experimentally examined and compared with two previously designed control systems. Experimental results demonstrate that the performance of one of the control systems with a set of time-invariant FF elements designed in this study and a disturbance observer is good and almost comparable with that of the previously designed control system with high-precision and high response motion.     

Design evaluation of a single-axis precision controlled positioning stage

This paper presents the design and control of a single-axis positioning stage with a total travel of 50 mm. The single-axis stage is comprised of a long-range slideway, running on ultra-high molecular weight polyethylene (UHMWPE) bearings, and a short-range positioning stage, comprised of a PZT driven flexure. Feedback errors associated with the long-range stage are reduced by the short-range stage, mounted on top of the long-range stage. Within the evaluation of the long-range stage, two alternative drives are assessed; a Roh’lix^® and a feedscrew drive. To determine the effects of dynamic interaction between the two drive systems, a further assessment of the single-axis stage was undertaken with the short-range stage operating at different bandwidths, ranging from 91 Hz to 2188 Hz. At the highest bandwidths, nanometer performance is demonstrated for a sinusoidal displacement demand corresponding to sinusoidal traverses of 1 mm and 5 mm with a maximum velocity of approximately 30 μm s⁻¹ and 150 μm s⁻¹, respectively. Furthermore, a 12 nm RMS controller error over a traverse of 25 mm at a maximum velocity of approximately 330 μm s⁻¹ was observed with the use of the feedscrew drive only.     

Control of an equipment for fabricating periodic nanostructure

This study presents the control for an equipment that is designed for fabricating periodic nanostructures. This equipment can generate the patterns required for nanostructure production using direct writing laser lithography. The equipment incorporates a direct writing laser lithography instrument, a linear motor-driven long-stroke stage (X, Y), a piezoelectric-driven two degrees of freedom (2-DOF) nano-stage (Y, θ_z), a 3-DOF laser interferometer measurement system, and a system control unit. The working stage of this equipment is combined by a long-stroke stage and a nano-stage; therefore, it can provide long-stroke and high-precision positioning. The feedback signal for this stage is obtained using a 3-DOF laser interferometer measurement system. Integral sliding-mode controllers are used to control the linear motor-driven stage and PID controllers are used to control the piezo-stage for precision positioning. This paper presents the design of the controllers and the control results. Experimental results show that satisfactory writing results can be obtained at a 100 mm/s scan speed.     

A 3He cryostat inserted into a refrigerator with an impulse tube

A compact autonomous ³He cryostat inserted into a two-stage refrigerator with an impulse tube is described. The cryostat contains baths filled with ⁴He and ³He and evacuated with cryosorbers to temperatures of ∼1 and ∼0.35 K, respectively. The low temperature is maintained for 6–8 h at an amount of liquid ³He filling the cryostat of ∼0.035 mol. The dimensions of the insert (below the upper flange) are 49 mm (diameter) and 720 mm (length). The insert is introduced into a hermetically sealed tube-well filled with a heat-exchange gas during operation, which promotes the heat removal to levels of 45–50 K (the first stage of the impulse tube) and 3–4 K (the second stage of the impulse tube). The cryostat can be mounted in and extracted from both the warm cryostat and the cryostat cooled to low temperatures.     

Wear resistant solid lubricant coating made from PTFE and epoxy

A composite coating of polytetrafluoroethylene and epoxy shows 100 × improvements in wear resistance as compared to either of its constituents alone and reduced friction coefficient under testing on a pin-on-disk tribometer. This coating is made by impregnating an expanded PTFE film with epoxy, which provides three unique functions: (1) the epoxy compartmentalizes the PTFE nodes, which is believed to reduce the wear of the PTFE, (2) the epoxy increases the mechanical properties such as elastic modulus and hardness, and (3) the epoxy provides a ready interface to bond the films onto a wide variety of substrates easily and securely. The experimental matrix had normal loads of 1–3 N, sliding speeds from 0.25 to 2.5 m/s, and used a 2.4 mm radius low carbon steel pin in a rotating pin-on-disk tribometer. The skived PTFE films had wear rates on the order of K=10^–3 mm³/Nm and friction coefficients around =0.2. Both the high density films (70 wt%PTFE) and low density films (50 wt% PTFE) had wear rates on the order of K=10^–6 mm³/Nm and friction coefficients around =0.15. The neat epoxy films showed significant scatter in the tribological measurements with wear-rates on the order of K=10^–4 mm³/Nm and friction coefficients around =0.40. The enhanced tribological behavior of these composites is believed to stem from the coatings ability to draw thin PTFE transfer films into the contact from the nodes of PTFE, which act like reservoirs. Nanoindentation mapping of the coatings and the transfer films supports this hypothesis, and accompanies scanning electron microscopy observations of the worn and unworn coatings.     

Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness

This paper presents a two-degree-of-freedom (two-DOF) linear encoder which can measure the position along the moving axis (X-axis) and the straightness along the axis vertical to the moving axis (Z-axis) of a precision linear stage simultaneously. The two-DOF linear encoder is composed of a reflective-type scale grating and an optical sensor head. A reference grating, which is identical to the scale grating except the scale length, is employed in the optical sensor head. Positive and negative first-order diffracted beams from the two gratings are superposed with each other in the optical sensor head to generate interference signals. The optical configuration is arranged in such a way that the direction of displacement in each axis can also be detected. A prototype two-DOF linear encoder is designed and constructed. The size of the optical sensor head is about 50 mm (X) × 50 mm (Y) × 30 mm (Z) and the pitch of the grating is 1.6 μm. It has been confirmed that the prototype two-DOF linear encoder has sub-nanometer resolutions in both the X- and Z-axes.     

In Situ Studies of Cartilage Microtribology: Roles of Speed and Contact Area

The progression of local cartilage surface damage toward early stage osteoarthritis (OA) likely depends on the severity of the damage and its impact on the local lubrication and stress distribution in the surrounding tissue. It is difficult to study the local responses using traditional methods; in situ microtribological methods are being pursued here as a means to elucidate the mechanical aspects of OA progression. While decades of research have been dedicated to the macrotribological properties of articular cartilage, the microscale response is unclear. An experimental study of healthy cartilage microtribology was undertaken to assess the physiological relevance of a microscale friction probe. Normal forces were on the order of 50 mN. Sliding speed varied from 0 to 5 mm/s, and two probes radii, 0.8 and 3.2 mm, were used in the study. In situ measurements of the indentation depth into the cartilage enabled calculations of contact area, effective elastic modulus, elastic and fluid normal force contributions, and the interfacial friction coefficient. This work resulted in the following findings: (1) at high sliding speed (V = 1–5 mm/s), the friction coefficient was low (μ = 0.025) and insensitive to probe radius (0.8–3.2 mm) despite the fourfold difference in the resulting contact areas; (2) the contact area was a strong function of the probe radius and sliding speed; (3) the friction coefficient was proportional to contact area when sliding speed varied from 0.05 to 5 mm/s; (4) the fluid load support was greater than 85% for all sliding conditions (0% fluid support when V = 0) and was insensitive to both probe radius and sliding speed. The findings were consistent with the adhesive theory of friction; as speed increased, increased effective hardness reduced the area of solid–solid contact which subsequently reduced the friction force. Where the severity of the sliding conditions dominates the wear and degradation of typical engineering tribomaterials, the results suggest that joint motion is actually beneficial for maintaining low matrix stresses, low contact areas, and effective lubrication for the fluid-saturated porous cartilage tissue. Further, the results demonstrated effective pressurization and lubrication beneath single asperity microscale contacts. With carefully designed experimental conditions, local friction probes can facilitate more fundamental studies of cartilage lubrication, friction and wear, and potentially add important insights into the mechanical mechanisms of OA.     

A parallel link end effector for scanning electrical discharge machining process

Because a parallel mechanism has a high-frequency response, multiple degrees of freedom (DOF), and high stiffness, it can be applied to an end effector for electrical discharge machining (EDM) with a scanning motion. A prototype has 3 DOF: two tilting angles around the x- and y-axes, and the movement in the z-direction. It consists of, a base plate, a stage, a constraint link, and three inchworm devices that act as links. The inchworm devices are connected with the stage and the base plate. The z-position and inclination of the stage are changed by adjusting the length of the inchworm devices. The electrode feeding is controlled by the combination of the steplike movement with the inchworm devices and continuous extension of piezos. The frequency response of the stage by the continuous extension of the piezos is up to 200 Hz. The positioning accuracy of the end effector is less than 30 μm in height and 0.04° in inclination. Some examples of EDM by the scanning motion are demonstrated.     

Multichannel wire gas electron multipliers with 1- and 3-mm gaps

The operation of multichannel wire gas electron multipliers (MWGEMs) with gaps between electrodes δ = 1 and 3 mm, when the chamber is filled with commercial neon under a 0.4- and 1.0-atm (abs.) pressure and irradiated with α and β particles, is studied. The following maximal proportional electron multiplication coefficients are obtained: 6 × 10³ (α, irradiation, δ = 3 mm, 1 atm, and 20% streamers), 1.2 × 10⁴ (β⁻, 3 mm, 1 atm, and 50% streamers), 6 × 10³ (α, 3 mm, 0.4 atm, and 20% streamers), and 10⁵ (β⁻, 3 mm, 0.4 atm, and 50% streamers). The maximal proportional electron multiplication coefficients are obtained in the MWGEM and its anode (induction) gap in the sequential electron multiplication mode: 1.08 × 10⁵ (β⁻, 1 mm, 0.4 atm, 50% streamers), 2 × 10⁶ (β⁻, 3 mm, 0.4 atm, 20% streamers), and 1.12 × 10⁵ (α, 3 mm, 0.4 atm, 50% streamers).     

Effects of Environment on Friction and Wear of Al-Si Alloy Impregnated Graphite Composite

Pin-on-disk-type wear experiments for an Al-Si alloy impregnated graphite composite (pin) in contact with a bearing steel (disk) were conducted at 100N normal load (100 Newtons) in air, argon, and deionized water to investigate the effects of environment on the tribological characteristics of the composite. The friction and wear behavior and the pin-lifting phenomenon due to wear particle ingress into the contact surfaces were continuously measured during the experiments. At low relative humidity (RH) levels, the friction coefficients in air and argon are high (0.32 to 0.39) and decrease with increasing RH to values around 0.2. The friction coefficients in air have reached a minimum of 0.15 to 0.17 between 50 and 70% RH and increased slightly at 80% RH. The friction coefficients in argon are constant at about 0.2 between 10 and 80% RH. Because of the lubricating action of a water film, the friction coefficient in deionized water is slightly lower (0.1 to 0.17) than that in air. The mean wear rate of 10^?4 to 8 × 10^?4 mm ³ /mm (specific wear rate; w _s = 10 ^?6 to 8 × 10^{? 6} mm ² /N) is very high in a severe wear regime at RH levels lower than 10% in air, decreases with increasing RH to a minimum in the middle RH range (30 to 60%), and increases slightly at RH levels higher than 70%. Although the mean contact pressure is very high (31.8 MPa), mild wear with the rates of 10^?8 to 10^?7 mm ³ /mm (w _s = 10^?10 to 10^?9 mm ² /N) occurs in the middle RH range. The same change in wear with RH as that in air is found in argon but the wear rate in argon is slightly lower than the wear rate in air. The height of the pin-lifting, having a wear reduction effect, is greater in argon than in air over almost the whole RH range. The wear rate in deionized water is nearly equal to the rate at 70% RH in air and argon.