KR101420519B1 - Device and Method for Measuring dynamic characteristic of air bearing - Google Patents

Abstract

An apparatus and a method for more accurately measuring the dynamic characteristics of an air bearing are disclosed in the present invention.
For example, an apparatus for measuring dynamic characteristics between a main shaft and an air bearing supporting a load of a main shaft by applying air pressure to the main shaft, comprising: a sinusoidal signal generator for applying an excitation signal in the form of a sinusoidal signal to the main axis; A Fourier transform processor for performing a Fourier transform on the measured displacement and the load on the principal axis; And calculating a coefficient of the equation by substituting the measured displacement and load values into an equation of the applied excitation signal and a displacement signal according to the applied excitation signal, An apparatus for measuring the dynamic characteristics of an air bearing including a dynamic characteristic generator for calculating a dynamic characteristic coefficient by substituting it into an equation is disclosed.

Description

Technical Field [0001] The present invention relates to an apparatus and method for measuring dynamic characteristics of air bearings,

The present invention relates to an apparatus and a method for more accurately measuring the dynamic characteristics of an air bearing.

The air bearing is a type of hydrostatic bearing, and has a form in which compressed air is blown against the main shaft to support the load by floating the shaft by air pressure. These air bearings can measure the dynamic characteristic by measuring the stiffness coefficient and the damping coefficient. This dynamic characteristic is required to measure the reliability of the part because it shows the characteristics of the air bearing time change on the output.

The present invention provides an apparatus and method for more accurately measuring the dynamic characteristics of air bearings.

An apparatus for measuring dynamic characteristics of an air bearing according to the present invention is a device for measuring dynamic characteristics between a main shaft and an air bearing supporting a load of a main shaft by applying air pressure to the main shaft, Sinusoidal signal generator; A Fourier transform processor for performing a Fourier transform on the measured displacement and the load on the principal axis; And calculating a coefficient of the equation by substituting the measured displacement and load values into an equation of the applied excitation signal and a displacement signal according to the applied excitation signal, And a dynamic characteristic generator for calculating the dynamic characteristic coefficient by substituting the equation into the equation.

Here, the above equation of motion can be expressed as follows.

[Equation 1]

(m is the mass of the main shaft, c is the main / ductile damping coefficient of the air bearing, and k is the main / ductile stiffness coefficient of the air bearing)

The equation of the sinusoidal wave and the displacement signal can be expressed as follows.

[Equation 2]

F _x (t) = A _{x c} cos? T + A _xs sin? T

F _y (t) = B _yc cos? T + B _ys sin? T

(Fx (t) is the excitation in the x axis, Fy (t) is the excitation in the y axis, and? Is the angular frequency of the sinusoidal wave applied)

[Equation 3]

x = X X + _1c cosωt _1s sinωt

y = Y _1c cosωt + Y _1s sinωt

(x is a displacement signal generated along the x axis of the main axis, y is a displacement signal generated along the y axis of the main axis, and? is an angular frequency)

The dynamic characteristic generator divides the equation of motion into the following equations to obtain the principal stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, the soft stiffness coefficient kxy, kyx, and the soft damping coefficient Cxy , Cyx) of the air bearing dynamic characteristic measurement device.

[Equation 4]

(Subscripts 1 and 2 are the number of experiments, and ω is the frequency)

Further, the dynamic characteristic verifier further includes a dynamic characteristic verifier that substitutes the measured dynamic characteristic coefficient into the motion equation, numerically obtains a displacement through a Runge-Kutta method, and substitutes it into Equation 3 to verify the dynamic characteristic coefficient Air bearing dynamic characteristics measuring device.

A method of measuring dynamic characteristics of an air bearing according to the present invention is a method of measuring dynamic characteristics between a main shaft and an air bearing supporting a load of a main shaft by applying air pressure to the main shaft, ; Fourier transforming the displacement and the load measured with respect to the main axis; Calculating a coefficient of the equation by substituting the measured displacement and load values into an equation of the applied excitation signal and a corresponding displacement signal; And calculating a dynamic characteristic coefficient by substituting a result of measurement for a plurality of amplitudes and frequencies into an equation of motion.

Here, the above equation of motion can be expressed as follows.

[Equation 1]

(m is the mass of the main shaft, c is the main / ductile damping coefficient of the air bearing, and k is the main / ductile stiffness coefficient of the air bearing)

The equation of the sinusoidal wave and the displacement signal can be expressed as follows.

[Equation 2]

F _x (t) = A _{x c} cos? T + A _xs sin? T

F _y (t) = B _yc cos? T + B _ys sin? T

(Fx (t) is the excitation in the x axis, Fy (t) is the excitation in the y axis, and? Is the angular frequency of the sinusoidal wave applied)

[Equation 3]

x = X X + _1c cosωt _1s sinωt

y = Y _1c cosωt + Y _1s sinωt

(x is a displacement signal generated along the x axis of the main axis, y is a displacement signal generated along the y axis of the main axis, and? is an angular frequency)

The step of calculating the dynamic characteristic coefficient may further include the steps of dividing the equation into the following equations to calculate the main stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, the soft stiffness coefficient kxy, kyx, And to calculate the dynamic coefficient including the damping coefficients Cxy and Cyx.

[Equation 4]

(Subscripts 1 and 2 are the number of experiments, and ω is the frequency)

Further, after the step of calculating the dynamic characteristic coefficient, the measured dynamic characteristic coefficient is substituted into the equation of motion, the displacement is numerically obtained through the Runge-Kutta method, and the displacement is substituted into Equation 3 And a dynamic characteristic verification step of verifying the dynamic characteristic coefficient.

The apparatus and method for measuring the dynamic characteristics of an air bearing according to the present invention are characterized in that a sinusoidal excitation force is applied to a spindle, a displacement and a load are measured at a spindle, a displacement and a load are inputted to an excitation force and a displacement signal, And the dynamic characteristics of the air bearing can be easily grasped by substituting the results measured with different amplitudes and frequencies into the equation of motion.

Also, the apparatus and method for measuring air bearing dynamic characteristics according to the present invention can ensure the reliability of measurement results by verifying the dynamic characteristics of the measured air bearings through the Runge-Kutta method.

Figure 1 is a modeling for the main shaft and air bearing.
2 is a configuration diagram of an air bearing measurement apparatus according to an embodiment of the present invention.
3 is a flow chart for explaining an air bearing measurement method according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings, so that those skilled in the art can easily carry out the present invention.

Figure 1 is a modeling for the main shaft and air bearing.

Referring to FIG. 1, the coupling relationship between the main shaft 10 and the air bearing 20 can be expressed as a displacement value with respect to the main axis 10 in the xx, xy, yy, and yx directions. If the externally applied excitation force is expressed as F _x (t) and F _y (t), the equation of motion of the main shaft 10 and the air bearing 20 can be expressed as follows.

[Equation 1]

Here, m is the mass of the main shaft 10, c is the main / ductile damping coefficient of the air bearing, and k is the main / ductile stiffness coefficient of the air bearing. The apparatus 100 for measuring an air bearing dynamic characteristic according to an embodiment of the present invention calculates the damping coefficient c of the air bearing and the stiffness coefficient k of the air bearing as described later to measure the dynamic characteristics.

Hereinafter, a configuration of an air bearing dynamic characteristic measuring apparatus according to an embodiment of the present invention will be described.

2 is a block diagram of an air bearing dynamic characteristic measuring apparatus according to an embodiment of the present invention.

2, an apparatus 100 for measuring an air bearing dynamic characteristic according to an exemplary embodiment of the present invention includes a sinusoidal signal generator 110, a Fourier transform (FFT) processor 120, a dynamic characteristic generator 130, a dynamic characteristic verifier 140, . ≪ / RTI >

The sinusoidal wave signal generator 110 generates a sinusoidal wave signal which can give an excitation force to the main axis 10. The sinusoidal signal generator 110 generates an excitation force having a required sinusoidal signal form to excite the main axis 10. The excitation force of the sinusoidal signal generator 110 may be generated using hydraulic pressure, air, or magnetic force.

In addition, it is possible to measure the excitation frequency coefficients necessary for the dynamic characteristic measurement according to the sinusoidal wave signal and the measurement result on the main axis 10.

To this end, the sinusoidal signal generator 110 generates an excitation force of the next sinusoidal signal.

[Equation 2]

F _x (t) = A _{x c} cos? T + A _xs sin? T

F _y (t) = B _yc cos? T + B _ys sin? T

Here, Fx (t) denotes an excitation in the x axis with respect to the main axis 10, and Fy (t) denotes an excitation in the y axis with respect to the main axis 10. Further,? Denotes an angular frequency of a sinusoidal wave to be applied.

Accordingly, the displacement signal generated by the main shaft 10 can be expressed as follows.

[Equation 3]

x = X X + _1c cosωt _1s sinωt

y = Y _1c cosωt + Y _1s sinωt

Here, x denotes a displacement signal generated along the x-axis of the main axis 10, and y denotes a displacement signal generated along the y-axis of the main axis 10. Further,? Is an angular frequency coinciding with each frequency of the sinusoidal signal of the applied equation (2).

Also, although not separately shown, the displacement signal and the load of the main shaft 10 are measured using a non-contact displacement sensor and a force sensor.

The Fourier transform (FFT) processor 120 receives the displacement signal and the load information measured by the non-contact displacement sensor and the force sensor, and performs Fourier transform.

The dynamic characteristic generator 130 substitutes the values converted in the Fourier transform processor 120 into F _x (t), F _y (t), x and y in Equation 2 and Equation 3, A _xc , A _xs , B _yc , B _ys , X _1c , X _1s , Y _1c, and Y _1s , respectively.

In addition, the sinusoidal signal generator 110 may repeat the operation of applying an excitation force having a different amplitude and frequency at a rotational speed to be tested, and when the Fourier transform processor 120 performs the conversion, The dynamic characteristic generator 130 receives this and separates the sine term and the cosine term as shown in the following Equation 4 to generate the dynamic characteristic.

[Equation 4]

Here, subscripts 1 and 2 are the number of experiments, and ω is the frequency of excitation.

The dynamic characteristic generator 130 calculates the main stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, the soft stiffness coefficient kxy, kyx and the soft damping coefficients Cxy, Cyx from Equation 4, can do. Therefore, the air bearing dynamic characteristic measuring apparatus 100 according to the embodiment of the present invention can measure the dynamic characteristics of the entire system by calculating the above coefficients.

The dynamic characteristics verifier 140 performs verification of the calculated coefficients through an algorithm stored therein. The dynamic characteristics verifier 140 calculates the dynamic stiffness coefficients kxx and kyy, the main damping coefficients Cxx and Cyy, the soft stiffness kxy and kyx, and the soft damping coefficients Cxy and Cyy, which are calculated from the dynamic characteristic generator 130, ) Is substituted into the equation of motion of equation (1), and the displacement x and y are numerically calculated through the Runge-Kutta method.

Further, the dynamic characteristics verifier 140 substitutes the calculated displacements x and y into the equation 4 to verify the dynamic characteristic coefficient.

For example, when the main shaft rotation frequency is 83 [Hz] and the excitation frequency is 100 [Hz], the measured stiffness / damping coefficient is shown in Table 1 below.

[Table 1]

Table 2 below shows the stiffness / damping coefficient verified by the Runge-Kutta method in the dynamic characteristics verifier 140.

[Table 2]

Therefore, comparing Table 1 and Table 2, the dynamic characteristic verifier 140 can determine that the result of the dynamic characteristic generator 130 is correct It can be verified that it is a numerical value.

Hereinafter, an air bearing measurement method according to an embodiment of the present invention will be described.

3 is a flow chart for explaining an air bearing measurement method according to an embodiment of the present invention.

Referring to FIG. 3, an air bearing measurement method according to an exemplary embodiment of the present invention includes steps S 1, S 2, S 3, S 3, S4), and a dynamic characteristic algorithm verification step (S5).

The step S 1 of exciting the sinusoidal wave signal is a step in which the sinusoidal wave signal generator 110 applies an excitation signal composed of a sinusoidal signal to the main axis 10. The excitation signal has the form of Equation 2 as described above.

The displacement and load measuring step S2 measures the displacement signal and the load information of the main shaft 10. The measurement may be performed by a non-contact displacement sensor and a force sensor (not shown).

The excitation frequency coefficient calculation step S3 calculates the excitation frequency coefficient by Fourier transforming the displacement signal and the load information measured by the non-contact displacement sensor and the force sensor through the Fourier transform processor 120, and in the formula _{3 F x (t), F} y (t), a frequency coefficient by substituting x and y, with _{a xc, a xs, B yc} , B ys, x 1c, x 1s, y 1c and y _1s Respectively.

In the step S 4, the sinusoidal signal generator 110 repeats the operation of applying an excitation force having a different amplitude and frequency at a rotational speed to be tested. When the Fourier transform processor 120 transforms the sinusoidal signal, The dynamic characteristic generator 130 separates the sine term and the cosine term as shown in Equation (4) to generate dynamic characteristics.

Accordingly, the method for measuring the dynamic characteristics of the air bearing according to the embodiment of the present invention is characterized in that the main stiffness coefficient (kxx, kyy), the main damping coefficient (Cxx, Cyy), the soft stiffness coefficient (kxy, kyx) and the ductility attenuation coefficients (Cxy, Cyx), respectively, to measure the dynamic characteristics of the system.

In the dynamic characteristic algorithm verification step S5, the dynamic characteristics verifier 140 calculates the main stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, and the soft stiffness coefficient kxy, kyx calculated from the dynamic characteristic generator 130, And a soft damping coefficient (Cxy, Cyx), substituting this into the equation of motion of Equation 1, numerically calculating displacements x and y through a Runge-Kutta method, and verifying the values to be. Therefore, other measurement results can be verified in the air bearing dynamic characteristic measuring method according to the embodiment of the present invention.

As described above, the present invention is not limited to the above-described embodiment, but rather may be applied to a method of measuring the dynamic characteristics of an air bearing according to the present invention It will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention.

100; An air bearing dynamic characteristic measuring device 110; Sinusoidal signal generator
120; A Fourier transform processor 130; Dynamic characteristic generator
140; Dynamic characteristic verifier

Claims (10)

An apparatus for measuring dynamic characteristics between a main shaft and an air bearing supporting a load of a main shaft by applying air pressure to the main shaft,
A sinusoidal signal generator for applying an excitation signal in the form of a sinusoidal signal to the main axis;
A Fourier transform processor for performing a Fourier transform on the measured displacement and the load on the principal axis; And
Calculating a coefficient of the equation by substituting the measured displacement and load values into an equation of the applied excitation signal and a displacement signal according to the applied excitation signal and calculating a coefficient of the equation by using the sinusoidal signal generator with respect to a plurality of amplitudes and frequencies, And calculates a dynamic characteristic coefficient,
Wherein the equation of the sinusoidal wave and the displacement signal is expressed as follows.
[Equation 1]
F _x (t) = A _{x c} cos? T + A _xs sin? T
F _y (t) = B _yc cos? T + B _ys sin? T
(Fx (t) is the excitation in the x axis, Fy (t) is the excitation in the y axis, and? Is the angular frequency of the sinusoidal wave applied)
[Equation 2]
x = X X + _{1s 1c} cosωt sinωt
y = Y + Y _{1s 1c} cosωt sinωt
(x is a displacement signal generated along the x axis of the main axis, y is a displacement signal generated along the y axis of the main axis, and? is an angular frequency) The method according to claim 1,
Wherein the equation of motion is expressed as: < RTI ID = 0.0 >
[Equation 3]

(m is the mass of the main shaft, c is the main / ductile damping coefficient of the air bearing, and k is the main / ductile stiffness coefficient of the air bearing) delete The method according to claim 1,
The dynamic characteristic generator divides the equation of motion into the following equations to obtain the main stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, the soft stiffness coefficient kxy, kyx and the soft damping coefficients Cxy, Cyx Wherein the dynamic characteristic coefficient calculating means calculates the dynamic characteristic coefficient including the dynamic characteristic coefficient.
[Equation 4]

(Subscripts 1 and 2 are the number of experiments, and ω is the frequency) 5. The method of claim 4,
And a dynamic characteristic verifier that substitutes the measured dynamic characteristic coefficient into the equation of motion and numerically obtains a displacement through a Runge-Kutta method and substitutes the numerical value into the equation 4 to verify the dynamic characteristic coefficient. Bearing dynamic characteristics measuring device. A method of measuring dynamic characteristics between a main shaft and an air bearing supporting a load of a main shaft by applying air pressure to the main shaft,
Applying an excitation signal in the form of a sinusoidal signal to the main axis;
Fourier transforming the displacement and the load measured with respect to the main axis;
Calculating a coefficient of the equation by substituting the measured displacement and load values into an equation of the applied excitation signal and a corresponding displacement signal;
Calculating a dynamic characteristic coefficient by substituting a result of measurement for a plurality of amplitudes and frequencies into an equation of motion,
Wherein said sinusoidal and displacement signal expressions are expressed as:
[Equation 1]
F _x (t) = A _{x c} cos? T + A _xs sin? T
F _y (t) = B _yc cos? T + B _ys sin? T
(Fx (t) is the excitation in the x axis, Fy (t) is the excitation in the y axis, and? Is the angular frequency of the sinusoidal wave applied)
[Equation 2]
x = X X + _{1s 1c} cosωt sinωt
y = Y + Y _{1s 1c} cosωt sinωt
(x is a displacement signal generated along the x axis of the main axis, y is a displacement signal generated along the y axis of the main axis, and? is an angular frequency) The method according to claim 6,
Wherein the equation of motion is expressed as: < EMI ID = 17.1 >
[Equation 3]

(m is the mass of the main shaft, c is the main / ductile damping coefficient of the air bearing, and k is the main / ductile stiffness coefficient of the air bearing) delete The method according to claim 6,
Wherein the step of calculating the dynamic characteristic coefficient comprises the steps of dividing the equation into the following equations to calculate the main stiffness coefficient kxx, kyy, the main damping coefficient Cxx, Cyy, the soft stiffness coefficient kxy, kyx, (Cxy, Cyx) of the air bearing.
[Equation 4]

(Subscripts 1 and 2 are the number of experiments, and ω is the frequency) 10. The method of claim 9,
Subsequently to the step of calculating the dynamic characteristic coefficient, the measured dynamic characteristic coefficient is substituted into the equation of motion, and the displacement is numerically obtained through the Runge-Kutta method. Then, the dynamic characteristic coefficient is substituted into the equation (4) And a dynamic characteristic verifying step of verifying the dynamic characteristic of the air bearing.

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