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In order to diagnose the unbalance of aerostatic guideways, displacement and acceleration sensors were used to measure the vibration signals of the unbalance of the aerostatic guideways caused by the gas fluctuation. The frequency characteristics for the unbalance of aerostatic guideways caused by gas fluctuation has been extracted from the measured signals by power spectral density, and the basic frequencies of the guideway system have been diagnosed according to spectral characteristics, in agreement with the results calculated by the corresponding motion equations and the finite element method.

Due to their low friction and high accuracy of their motion aerostatic bearings and guideways have been successfully applied to various precision devices such as precision machine tools, precision measuring equipment and lithography associated production equipment [

Currently, positioning error analysis [

In 1994, Zhao

Although previous works provide insights into the static and dynamic behaviors of the aerostatic guideway, they seldom mention the gas fluctuations or the hammer phenomenon of the aerostatic slider. In a vertical turning machine tool, gas fluctuation of the cross aerostatic slider of the machine tool will greatly affect the machining quality, but the reasons behind the gas film fluctuation of aerostatic guideways with mass unbalance have not been researched. Therefore, this paper researches the gas film fluctuation of aerostatic guideways with mass unbalance.

Due to the nonlinearity of the gas film pressure, it is very difficult to solve the Reynolds equation analytically. Therefore, motion equations of the aerostatic guideways and finite element methods have been employed to obtain the solution. In order to extract and identify the gas fluctuations of the aerostatic guideways, this paper investigates the relationship between the dynamic characteristic of the aerostatic guideways and the gas fluctuation both mathematically and experimentally, and the main features of the film fluctuation are extracted. The unbalance of aerostatic guideways caused by the fluctuation is identified in the frequency domain.

Aerostatic bearings support objects using air pressure in a non-contact state and thus enable ultra-precise motion of the object without friction. Their life is almost infinite and using these bearings reduces the environmental load because they only consume air, and not lubrication oils. Aerostatic bearings have restriction mechanisms to achieve a high level of stiffness. An aerostatic guideway with an orifice restriction in the laboratory is researched. The guideway is mounted on a granite base, with four air pads, and each pad has six orifices, the restriction type of the X slider is an orifice restriction, and the frame as shown in

For a vertical machine tool, when turning a workpiece, there is a slight fluctuation of the gas film between the cross slider and guideway, and a forced vibration in the slider will be caused by the self-excited oscillation of the gas film fluctuation. In order to study the effect of the vibration on the machining accuracy, the dynamic behavior of the aerostatic guideway system is next analyzed by motion equations and the finite element method, respectively.

The guideway system will be subject to periodic excitation during the machining process. Resonance will occur when an excitation frequency coincides with one of the modal frequencies of the guideway, which will not only reduce the quality of the machined workpiece, but also potentially damage the tool and machine tool. Here the frequency information of the guideway system is analyzed with the transfer matrix method [

Modal analysis is used to understand the natural frequency in order to predict, evaluate and optimize the vibration behavior [

The finite element method (FEM) was used in order to verify the validity of the above method. First, a three-dimensional CAD model is established and imported into the ANSYS software. After modeling, the necessary data of the material properties of guideway are assigned to the beam element (Young's modulus 2.0 × 10^{9} N/m^{2}, Poisson's ratio 0.3 and mass density 8.58 × 10^{3} kg/m^{3}). The natural frequencies are shown in

In order to identify the causes of the gas fluctuation of the guideways, we focused on the airflow in the clearance of the gas pads because the pressure fluctuation due to unsteady airflow may induce the fluctuation. Since the thickness of the gas film of the aerostatic guideway is 10 μm, it corresponds to the micro-scale, therefore, the flow state of the gas film of the guideway is also on the micro-scale. The Navier velocity slip boundary conditions are adopted to the fluid continuous flow equation and the Reynolds equation is modified in the micro-scale. Based on the conservation of oil film flow and the linearization assumption of the oil film pressure distribution, the load capacity of the bearing is gained in the consideration of slip effect. The Reynolds equation for a compressed gas based on the Navier-Stokes equations is used to identify the behavior of the airflow. The basic equation of pressure distribution in the gas film is [

There is no heat exchange in the gas film of the whole process, and the temperature is constant.

The fluid in the gas pad is a Newtonian fluid.

The effect of inertia force on the fluid is ignored (compared with damping and gravity, it is very small).

The pressure variation along the thickness direction of the film is zero.

The momentum equations in

The boundary conditions for the velocity slip are different from conventions, and are:
_{v}_{0}, _{m}_{0} is gas pressure, _{m}_{0}·_{m}

The load capacity of the aerostatic guideway _{a}

The stiffness of the aerostatic guideway is solved with the finite difference method:

Self-excited oscillations are generated during machining due to the slight gas fluctuations of the aerostatic guideway. The air pressure will be increased when the air gap height decreases under the effect of applied loads. The aerostatic slider losses its equilibrium at a certain gap height as the gas film is compressible and it results in a periodical motion [

The vibration direction of the tool in the turning is very important for machining accuracy, this is mainly from the _{d}_{0} and _{0} are the initial disturbance displacement and velocity, respectively.

Gas film fluctuation is a self-excited oscillation, belonging to the class of vibrations with some frequency. A piezoelectric acceleration sensor (LC0101, Qinghuangdao Lance Test Technology Co. Ltd, Qinghuangdao, China) is used to measure the gas fluctuation of the aerostatic slider. Its sensitivity is 100 mV/g, range is 50 g, frequency range is 0.5–15,000 Hz, resolution 0.0002, resonant frequency 40 KHz. A signal conditioning box is used to acquire data. A capacitive displacement sensor (capaNCDT6300/6310, Germany meter iridium (Chinese) Micro-Epsilon Technology Co. Ltd, Beijing, China) is used to measure the displacement (linear range 10 mm, absolute error ≤ ±0.2%, resolution 0.001% (2 Hz), 0.01% (8 kHz), limit frequency 8 kHz (−3 dB)). The equipment is shown in

Power spectral density is a statistical method, defined as the “power” (mean-square value) within the unit frequency band. It is the statistical result of the structure response which is excited by random dynamic loads and is a relationship curve with the values of power spectral density and frequency. In other words, the power spectrum is on the coordinate axis, frequency on the horizontal axis, and power on the vertical axis. Then the power spectral density is the amount changing with the frequency and distributed throughout the spectrum. It is a measurement for the mean square value of the random variable. _{x}_{x}

The random signal _{x}_{x}_{x}(f)

The guideway system will reciprocate around the equilibrium point with some interference. In the time domain, the vibration signal is a series of impulse waveforms. In the frequency domain, it includes the corresponding frequency of the guideway system. When the aerostatic guideway is working, a harmonic vibration may be caused by the fluctuation of gas film between the slide and guideway [

The purpose of the study is to extract the main features and to identify the gas fluctuations caused by the unbalance of aerostatic guideways. Through the dynamic model of the motion sliders, the corresponding frequency of the whole guideway system is obtained. The power spectral density is used to process the measured signal in the frequency domain, and the frequency is shown in

According to the results, the velocity slip method reflects the effect of the rarefied air. Therefore,

The gas flow state is analyzed using the slip velocity method. The dynamic model of the motion slider is established according to the natural frequency. The fluctuation frequency of the gas film of the whole sliders in the

This research was funded by the National Natural Science Foundation of China Grant No. 51105005 and 51275014, Fund for new teachers from Ministry of Education, No.20111103120002.

Dongju Chen adopted the Navier velocity slip boundary conditions to fluid continuous flow equation and modified the Reynolds equation in micro-scale, and established the dynamic model of gas fluctuations of guideway, wrote the whole article. Yanhua Bian measured the signal of the aerostatic guideway system with sensors, and processed the actual signal with power spectral density. Jinwei Fan analyzed the dynamic behavior of the aerostatic guideway system by motion equation and finite element method respectively.

The authors declare no conflicts of interest.

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Frequency of the motion slider.

Measurement equipment of the gas fluctuation.

Measured result of the aerostatic guideway.

Fifth order natural frequencies of guideway system.

Theory (Hz) | 932.68 | 2,570.8 | 5,040.1 | 8,331.6 | 12,446 |

ANSYS (Hz) | 932.68 | 2,571 | 5,040 | 8,330 | 12,440 |