A method for quickly calculating the oil film stiffness and damping coefficient of a hydrostatic spindle

Abstract

The present invention provides a method for rapidly calculating the hydrostatic spindle oil film stiffness and damping coefficient, comprising the following steps: Step 1: measuring the axis position coordinates of the hydrostatic bearing and determining the eccentricity of the axis position; Step 2: establishing a mapping relationship between the eccentricity of the hydrostatic bearing and the dynamic pressure ratio; Step 3: measuring and calculating the oil film bearing capacity of the hydrostatic bearing; and Step 4: calculating the hydrostatic bearing oil film stiffness and damping coefficient. This method can conveniently measure the hydrostatic oil film stiffness and damping coefficient.

Description

Technical Field

[0001] The invention relates to the field of machine tool performance calculation, and in particular to a method for quickly calculating the stiffness and damping coefficient of a liquid hydrostatic spindle oil film. Background Art

[0002] The liquid hydrostatic spindle is an important functional component of a precision machine tool. The quality of its performance directly determines the processing capability of the machine tool, and the performance of the liquid hydrostatic spindle is mainly affected by the stiffness and damping coefficient of the hydrostatic oil film. At present, the general method for calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film is to differentiate the Reynolds equation of the hydrostatic oil film with respect to the position and speed of the spindle axis respectively, and then solve the derived Reynolds equation by numerical method to obtain the stiffness and damping coefficient of the hydrostatic oil film. The solution process of this method is time-consuming, and it is impossible to measure the stiffness and damping coefficient of the hydrostatic oil film by this method. In view of this, the present invention proposes a method for quickly calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film based on the determination of the pressure of the hydrostatic oil chamber of the spindle axis trajectory. The application of this method can conveniently realize the measurement of the stiffness and damping coefficient of the hydrostatic oil film. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for quickly calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film, which can conveniently realize the measurement of the stiffness and damping coefficient of the hydrostatic oil film.

[0004] To solve the above technical problems, the technical solution adopted by the present invention is: a method for quickly calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film, comprising the following steps:

[0005] Step 1: measuring the axis position coordinates of the hydrostatic bearing and determining the eccentricity of the axis position; Step 2: establishing a mapping relationship between the eccentricity of the hydrostatic bearing and the dynamic pressure ratio;

[0006] Step 3: Measure and calculate the oil film bearing capacity of the hydrostatic bearing;

[0007] Step 4: Calculate the oil film stiffness and damping coefficient of the hydrostatic bearing.

[0008] In the preferred solution, in step one, two displacement sensors are arranged at 90° on the liquid hydrostatic bearing test bench, and data of the spindle axis position coordinates are collected with Δt as the sampling time interval. When the spindle center coincides with the bearing center, the displacement sensor reading is cleared. After the spindle is running, the displacement sensor reading is the spindle axis position coordinate.

[0009] In the preferred solution, in the step 2, the eccentricity is equally divided in the range of 0 to 1. For each eccentricity value of the bearing, the Reynolds equation and the flow continuity equation are solved simultaneously and iteratively to obtain the static pressure and dynamic pressure of the oil film of the hydrostatic bearing. The dynamic pressure ratio of the bearing corresponding to the eccentricity value can be obtained by dividing the static pressure and dynamic pressure of the oil film. A coordinate system is established to connect the corresponding data to obtain a mapping relationship diagram between the eccentricity and dynamic pressure ratio of the liquid hydrostatic bearing.

[0010] In the preferred scheme, in the step three, a pressure sensor is installed in each oil chamber of the liquid hydrostatic bearing to be tested to measure the static pressure of the liquid hydrostatic bearing. The dynamic pressure ratio when the spindle axis is at this position can be obtained according to the eccentricity determined in step one and the mapping relationship between the eccentricity of the liquid hydrostatic bearing and the dynamic pressure ratio in step two, thereby obtaining the dynamic pressure of the spindle oil film. The dynamic pressure and static pressure of the oil film are multiplied by the area of ​​their respective bearing areas to obtain the static pressure bearing capacity and dynamic pressure bearing capacity of the hydrostatic bearing. The sum of the static pressure bearing capacity and the dynamic pressure bearing capacity is the oil film bearing capacity W of the hydrostatic bearing oil film.

[0011] In a preferred embodiment, in step 4, point B is set as a point on the axis position trajectory measured by the displacement sensor, and a coordinate system is established with the bearing center position as the origin and the vertical direction as the Y axis. The oil film stiffness and damping coefficient when the axis position is at point B can be confirmed by the following steps;

[0012] S1. Calculate the oil film stiffness coefficient of the hydrostatic bearing at a given position:

[0013] Taking the sampling point A immediately before point B, we can get the displacement changes of the axis position in the X and Y directions from point A to point B, which are Δx1=x b -x a , Δy1=y b -y a According to the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at the axis center at points A and B confirmed in step 3, the oil film bearing capacity W when the axis center is at points A and B is obtained. a and W b , decompose the oil film bearing capacity along the X and Y directions to obtain the component forces W of the oil film bearing capacity at points A and B in the X and Y directions ax 、W ay and W bx 、W by Then, according to the definition of the oil film stiffness coefficient, we can get the four stiffness coefficients K of the oil film when the axis position is at point B. xx =(W bx -W ax ) / Δx1,K xy =(W bx -Wax ) / Δy1,K yx =(W by -W ay ) / Δx1,K yy =(W by -W ay ) / Δy1;

[0014] S2. The oil film damping coefficient of the hydrostatic bearing at a given position:

[0015] Take the two sampling points A and C immediately before and after point B, and the coordinates of the midpoint A1 between points A and B are expressed as ((x b +x a ) / 2,(y b +y a ) / 2), the coordinates of the midpoint B1 between points B and C can be expressed as ((x b +x c ) / 2,(y b +y c ) / 2), the components of the speed of the spindle axis at point A1 in the X and Y directions are v a1x =(x b -x a ) / Δt and v a1y =(y b -y a ) / Δt, the components of the speed of the spindle axis at point B1 in the X and Y directions are v b1x =(x c -x b ) / Δt and v b1y =(y c -y b ) / Δt, and the oil film bearing capacity W when the axis is at points A, B, and C is obtained based on the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at points A, B, and C confirmed in step 3. a 、W b and W c The oil film bearing capacity at the axis position at points A1 and B1 is W a1 =(W a +W b ) / 2,W b1 =(W b +W c ) / 2, decompose the oil film bearing capacity along the X and Y directions to obtain the component forces W of the oil film bearing capacity at points A1 and B1 in the X and Y directions a1x 、W a1y and W b1x 、W b1yThen, according to the definition of the oil film damping coefficient, we can get the four damping coefficients of the oil film when the axis position is at point B: Cxx=(W b1x -W a1x ) / (v b1x -v a1x ), Cxy=(W b1x -W a1x ) / (v b1y -v a1y ), Cyx=(W b1y -W a1y ) / (v b1x -v a1x ), Cyy=(W b1y -W a1y ) / (v b1y -v a1y ).

[0016] The present invention provides a method for quickly calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film. In view of the problems that the current method for calculating the stiffness and damping coefficient of the liquid hydrostatic bearing oil film is time-consuming and cannot realize the measurement of the stiffness and damping coefficient, a method for quickly calculating the stiffness and damping coefficient of the liquid hydrostatic spindle oil film is proposed based on the measurement of the static oil chamber pressure of the spindle's axial trajectory. For a measured bearing with a given structure, the mapping relationship between the dynamic pressure ratio and the eccentricity can be obtained by calculation before measurement. This relationship can be stored as basic data in an industrial computer. After the pressure sensor measures the static pressure of the oil film in the oil chamber area, the oil film bearing capacity can be directly determined according to the axial center position measured by the displacement sensor at this time. Then, the stiffness and damping coefficient of the bearing oil film can be obtained according to simple four arithmetic operations, which can conveniently realize the measurement of the stiffness and damping coefficient of the static oil film. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below with reference to the accompanying drawings and examples:

[0018] Figure 1 Schematic diagram of the displacement sensor measuring the axis position;

[0019] Figure 2 It is the plane expansion diagram of the tested hydrostatic bearing;

[0020] Figure 3 Schematic diagram of stiffness and damping coefficient characterization based on axis position;

[0021] Figure 4 is a mapping diagram between the eccentricity and dynamic pressure ratio of a hydrostatic bearing;

[0022] Figure 5 Flowchart for solving the dynamic pressure ratio. DETAILED DESCRIPTION

[0023] A method for quickly calculating the stiffness and damping coefficient of a hydrostatic spindle oil film comprises the following steps:

[0024] Step 1: Measure the axis position coordinates of the hydrostatic bearing and determine the eccentricity of the axis position.

[0025] like Figure 1 As shown in the figure, two displacement sensors are arranged at 90 degrees on a hydrostatic bearing test bench. Data on the spindle center position coordinates is collected at a sampling interval of Δt. When the spindle center coincides with the bearing center, the displacement sensor reading is reset to zero. Once the spindle is running, the displacement sensor reading is the spindle center position coordinate. The spindle center position coordinates can be used to calculate the distance A between the spindle center and the bearing center. Dividing A by the reduction in the bearing oil film gives the eccentricity of the spindle center position.

[0026] Step 2: Establish a mapping relationship between the eccentricity of the liquid hydrostatic bearing and the dynamic pressure ratio.

[0027] The eccentricity is divided equally into 50 parts within the range of 0 to 1. For each eccentricity value of the bearing, the following Reynolds equation and flow continuity equation are jointly established:

[0028]

[0029]

[0030] Among them, θ and z are the circumferential and axial coordinates respectively, R and L are the bearing radius and length respectively, P is the oil film pressure, Ps is the oil supply pressure, P ir is the oil chamber pressure (i = 1, 2, 3, 4, representing four oil chambers), η is the viscosity of the lubricating oil, ω is the angular velocity of the spindle, h is the oil film thickness, C is the throttling coefficient of the throttle, and Γ1-Γ4 represent the four sides of the rectangular oil chamber.

[0031] The static and dynamic pressures of the oil film in the hydrostatic bearing can be obtained by the finite element method. The specific iterative solution process is as follows: Figure 5 shown.

[0032] Dividing the oil film static pressure and dynamic pressure can get the bearing dynamic pressure ratio corresponding to the eccentricity value. Establishing a coordinate system and connecting these 50 sets of corresponding data can obtain the mapping relationship diagram between the eccentricity and dynamic pressure ratio of the hydrostatic bearing, as shown in Figure 4 shown.

[0033] Step 3: Measure and calculate the oil film bearing capacity of the hydrostatic bearing.

[0034] In step 3, a pressure sensor is installed in the oil cavity of each hydrostatic bearing to be tested to measure the static pressure of the hydrostatic bearing. Figure 2As shown, three pressure sensors are installed in each oil chamber, and the average value of their readings is taken as the static pressure value of the oil chamber.

[0035] In this embodiment, the bearing is a four-oil-cavity bearing with a rectangular oil cavity structure. The specific parameters are as follows:

[0036] Geometric parameters and operating parameters Numerical Bearing diameter (D) 150mm Bearing length (L) 100mm Lubricant viscosity (η) <![CDATA[0.0087N·s·m -2 ]]> Lubricant density (ρ) <![CDATA[870kg·m -3 ]]> Radius clearance (c) 0.050mm Oil supply pressure (ps) <![CDATA[2.3N·mm -2 ]]> Circumferential width of oil sealing edge 8mm Axial width of oil seal edge 8mm Oil cavity wrap angle 60° Restrictor type Capillary throttling Capillary diameter 0.5mm Capillary length 50mm Bearing speed 1500r / min

[0037] According to the mapping relationship between the eccentricity determined in step one and the eccentricity and dynamic pressure ratio of the liquid hydrostatic bearing in step two, the dynamic pressure ratio when the spindle axis is at this position can be obtained, thereby obtaining the dynamic pressure of the spindle oil film. The dynamic pressure and static pressure of the oil film are multiplied by the area of ​​their respective bearing areas to obtain the static pressure bearing capacity and dynamic pressure bearing capacity of the hydrostatic bearing. The sum of the static pressure bearing capacity and the dynamic pressure bearing capacity is the oil film bearing capacity W of the hydrostatic bearing oil film. The static pressure bearing area is the oil cavity area, and the dynamic pressure bearing area is the oil sealing edge area.

[0038] Step 4: Calculate the oil film stiffness and damping coefficient of the liquid hydrostatic bearing, that is, the spindle oil film stiffness and damping coefficient.

[0039] Assume that point B is a point on the axis position trajectory measured by the displacement sensor. Establish a coordinate system with the bearing center as the origin and the vertical direction as the Y axis. The oil film stiffness and damping coefficient when the axis is at point B can be confirmed by the following steps:

[0040] S1. Calculate the oil film stiffness coefficient of the hydrostatic bearing at a given position:

[0041] Taking the sampling point A immediately before point B, we can get the displacement changes of the axis position in the X and Y directions from point A to point B, which are Δx1=x b -x a , Δy1=y b -y a According to the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at the axis center at points A and B confirmed in step 3, the oil film bearing capacity W when the axis center is at points A and B is obtained. a and W b , decompose the oil film bearing capacity along the X and Y directions to obtain the component forces W of the oil film bearing capacity at points A and B in the X and Y directions ax 、W ay and W bx 、W by Then, according to the definition of the oil film stiffness coefficient, we can get the four stiffness coefficients K of the oil film when the axis position is at point B. xx =(W bx -W ax ) / Δx1,K xy =(Wbx -W ax ) / Δy1,K yx =(W by -W ay ) / Δx1,K yy =(W by -W ay ) / Δy1.

[0042] S2: The oil film damping coefficient of the hydrostatic bearing at a given position:

[0043] Take the two sampling points A and C immediately before and after point B, and the coordinates of the midpoint A1 between points A and B are expressed as ((x b +x a ) / 2,(y b +y a ) / 2), the coordinates of the midpoint B1 between points B and C can be expressed as ((x b +x c ) / 2,(y b +y c ) / 2), the components of the spindle axis velocity at point A1 in the X and Y directions are v a1x =(x b -x a ) / Δt and v a1y =(y b -y a ) / Δt, the components of the speed of the spindle axis at point B1 in the X and Y directions are v b1x =(x c -x b ) / Δt and v b1y =(y c -y b ) / Δt, and the oil film bearing capacity W when the axis is at points A, B, and C is obtained based on the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at points A, B, and C confirmed in step 3. a 、W b and W c The oil film bearing capacity at the axis position at points A1 and B1 is W a1 =(W a +W b ) / 2,W b1 =(W b +W c ) / 2, decompose the oil film bearing capacity along the X and Y directions to obtain the component forces W of the oil film bearing capacity at points A1 and B1 in the X and Y directions a1x 、W a1y and W b1x 、W b1yThen, according to the definition of the oil film damping coefficient, we can get the four damping coefficients of the oil film when the axis position is at point B: Cxx=(W b1x -W a1x ) / (v b1x -v a1x ), Cxy=(W b1x -W a1x ) / (v b1y -v a1y ), Cyx=(W b1y -W a1y ) / (v b1x -v a1x ), Cyy=(W b1y -W a1y ) / (v b1y -v a1y ).

Claims

1. A method for quickly calculating the stiffness and damping coefficient of a hydrostatic spindle oil film, characterized in that: The steps include: Step 1: Measure the axis position coordinates of the hydrostatic bearing and determine the eccentricity of the axis position. The specific operations are as follows: Two displacement sensors are arranged at 90 degrees on the hydrostatic bearing test bench. The spindle center position coordinates are collected with a sampling interval of Δt. When the spindle center coincides with the bearing center, the displacement sensor reading is reset to zero. After the spindle is running, the displacement sensor reading is the spindle center position coordinate. The distance A between the spindle center and the bearing center is calculated from the spindle center position coordinates. Dividing A by the reduction in the bearing oil film gives the eccentricity of the spindle center position. Step 2: Establish a mapping relationship between the eccentricity and dynamic pressure ratio of the hydrostatic bearing. The specific operations are as follows: The eccentricity is divided equally into the range of 0 to 1. For each eccentricity value of the bearing, the Reynolds equation and the flow continuity equation are solved iteratively to obtain the static pressure and dynamic pressure of the hydrostatic bearing oil film. The dynamic pressure ratio of the bearing corresponding to the eccentricity value can be obtained by dividing the static pressure and dynamic pressure of the oil film. A coordinate system is established to connect the corresponding data to obtain a mapping diagram between the eccentricity and dynamic pressure ratio of the hydrostatic bearing. Step 3: Measure and calculate the oil film bearing capacity of the hydrostatic bearing; Step 4: Calculate the oil film stiffness and damping coefficient of the hydrostatic bearing.

2. A method for rapidly calculating the oil film stiffness and damping coefficient of a hydrostatic spindle according to claim 1, characterized in that: In the step three, a pressure sensor is installed in the oil cavity of each tested liquid hydrostatic bearing to measure the static pressure of the liquid hydrostatic bearing. The dynamic pressure ratio when the spindle axis is at this position can be obtained according to the eccentricity determined in step one and the mapping relationship between the eccentricity of the liquid hydrostatic bearing and the dynamic pressure ratio in step two, thereby obtaining the dynamic pressure of the spindle oil film. The dynamic pressure and static pressure of the oil film are multiplied by the area of ​​their respective bearing areas to obtain the static pressure bearing capacity and dynamic pressure bearing capacity of the hydrostatic bearing. The addition of the static pressure bearing capacity and the dynamic pressure bearing capacity is the oil film bearing capacity of the hydrostatic bearing oil film. W .

3. The method for rapidly calculating the oil film stiffness and damping coefficient of a hydrostatic spindle according to claim 1, characterized in that: In step 4, let point B be a point on the axis position trajectory measured by the displacement sensor, establish a coordinate system with the bearing center position as the origin and the vertical direction as the Y axis, and the oil film stiffness and damping coefficient when the axis position is at point B can be confirmed by the following steps; S1. Calculate the oil film stiffness coefficient of the hydrostatic bearing at a given position: Taking the sampling point A immediately before point B, we can get the displacement changes of the axis position in the X and Y directions from point A to point B, which are Δx1=x b -x a , Δy1= y b -y a According to the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at the two points A and B confirmed in step 3, the oil film bearing capacity when the axis is at the two points A and B is obtained. W a and W b , decompose the oil film bearing capacity along the X and Y directions to obtain the components of the oil film bearing capacity at points A and B in the X and Y directions W ax 、 W ay and W bx 、 W by Then, according to the definition of the oil film stiffness coefficient, we can get the four stiffness coefficients K of the oil film when the axis position is at point B. xx =( W bx - W ax ) / Δx1, K xy =( W bx - W ax ) / Δy1,K yx =( W by - W ay ) / Δx1,K yy =( W by - W ay ) / Δy1; S2. The oil film damping coefficient of the hydrostatic bearing at a given position: Take the two sampling points A and C immediately before and after point B, and the coordinates of the midpoint A1 between points A and B are expressed as ((x b + x a ) / 2,(y b + y a ) / 2), the coordinates of the midpoint B1 between points B and C can be expressed as ((x b + x c ) / 2,(y b + y c ) / 2), the components of the speed of the spindle axis at point A1 in the X and Y directions are v a1x =(x b -x a ) / Δt and v a1y =(y b -y a ) / Δt, the components of the speed of the spindle axis at point B1 in the X and Y directions are v b1x =(x c -x b ) / Δt and v b1y = (y c -y b ) / Δt, based on the static pressure of the oil film in the oil chamber area measured by the pressure sensor and the dynamic pressure ratio at the three points A, B, and C when the axis is located in step 3, the oil film bearing capacity when the axis is located at points A, B, and C is obtained. W a 、 W b and W c The oil film bearing capacity at the axis position at points A1 and B1 is W a1 =( W a + W b ) / 2, W b1 =( W b + W c ) / 2, decompose the oil film bearing capacity along the X and Y directions to obtain the components of the oil film bearing capacity at points A1 and B1 in the X and Y directions W a1x 、 W a1y and W b1x 、 W b1y Then, according to the definition of the oil film damping coefficient, we can get the four damping coefficients of the oil film when the axis is at point B: Cxx = ( W b1x - W a1x ) / ( v b1x - v a1x ),Cxy=( W b1x - W a1x ) / ( v b1y - v a1y ),Cyx =( W b1y - W a1y ) / ( v b1x - v a1x ),Cyy =( W b1y - W a1y ) / ( v b1y - v a1y )。

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