A method for calculating dynamic displacement response of oil film of static pressure fan-shaped oil pad under impact load working condition

Abstract

The application discloses a kind of static pressure fan-shaped oil pad oil film dynamic displacement response calculation method under impact load working condition, and relates to static pressure supporting technical field.The application includes the following steps:Step one: the oil film of static pressure fan-shaped oil pad is equivalent to single degree of freedom spring-damping system, system parameters are obtained, the system parameters include fan-shaped oil pad bearing capacity, oil film thickness variation after impact load is, oil film stiffness, oil film damping coefficient, the oil film thickness of initial equilibrium position is, supported member mass;Step two: for the form of step load, dynamic equation is established and solved, and the dynamic displacement response of oil film is obtained;Step three: for the form of half-sine function, dynamic equation is established and solved, and the dynamic displacement response of oil film is obtained.The application fully considers the dynamic displacement response of oil film thickness under extreme working condition, and can better reflect the change of oil film thickness.

Description

Technical Field

[0001] This invention relates to the field of hydrostatic bearing technology, and in particular to a method for calculating the dynamic displacement response of the oil film in a hydrostatic sector-shaped oil pad under impact load conditions. Background Technology

[0002] As a key core component of heavy-duty machine tools, the hydrostatic rotary table's support performance directly affects the machine's machining accuracy, dynamic response capability, and reliability. With the increasing weight and complexity of machined parts, the rotary table inevitably encounters extreme conditions during operation, such as impact loads, eccentric loading, and start-stop impacts. These factors cause vibrations in the oil film supporting the rotary table, reducing its support performance and ultimately degrading the machine tool's machining accuracy. Summary of the Invention

[0003] This invention aims to provide a method for calculating the dynamic displacement response of a hydrostatic sector-shaped oil film under impact loading conditions. The main feature of this method is that it considers the influence of the extreme condition of impact loading on the oil film thickness variation when calculating the dynamic displacement response of the hydrostatic sector-shaped oil film.

[0004] The technical solution adopted in this invention is:

[0005] A method for calculating the dynamic displacement response of a hydrostatic sector-shaped oil pad film under impact loading conditions is disclosed. The impact load can be divided into two types: step load and half-sine function impact. The method includes the following steps.

[0006] Step 1: Equivalently represent the oil film as a "spring-damping system". A schematic diagram of the oil film under impact load is shown below. Given the following conditions: the bearing capacity W of the sector-shaped oil pad, and the change in oil film thickness after impact load. , oil film stiffness K, oil film damping coefficient C, oil film thickness at the initial equilibrium position is H0, and the mass of the supported component is M.

[0007] Step 2: Calculate the dynamic displacement response of the oil film under step load. The step load is applied as follows: As shown.

[0008] First, the equation of motion can be obtained according to Newton's second law.

[0009] (1)

[0010] In the formula, y represents the magnitude of the change in oil film thickness, and F impact For impact load. Dividing both sides of the equation by M and introducing standard vibration parameters, we get... The natural frequency is Damping ratio Because hydrostatic bearings have significant compression membrane damping, they are generally overdamped systems. ).

[0011] Secondly, calculate the particular solution of the dynamic displacement response, when When the system is stable, that is .therefore ,but .

[0012] The general solution for the dynamic displacement response is calculated, and the homogeneous equation corresponding to the dynamic equation is:

[0013] (2)

[0014] Solving

[0015] (3)

[0016] because Therefore, the two roots are not equal. The general solution of the equation is: The complete solution is

[0017] (4)

[0018] The initial condition is when t=0 ,Right now

[0019] (5)

[0020] The fluctuation displacement of the oil film is obtained as follows

[0021] (6)

[0022] The displacement of the oil film after stabilization is

[0023] (7)

[0024] Step 3: Calculate the impact load as a half-sine function, as shown in the diagram below. As shown.

[0025] Assuming the applied force is F max This represents the peak impact force. Perform a Fourier series expansion as follows

[0026] (8)

[0027] In engineering calculations, because higher-order terms decay extremely rapidly, using only the first-order AC term (n=1) is sufficient to meet the required accuracy.

[0028] (9)

[0029] The dynamic equations are established based on Newton's second law as follows:

[0030] (10)

[0031] The equations are solved step by step. First, the static response is solved: the average subsidence of the oil film. The oil film will be "compacted" over a certain distance and then oscillate around this new equilibrium position.

[0032] When the system is stable, acceleration and velocity are both zero. , can be obtained

[0033] (11)

[0034] Secondly, the dynamic response is solved, and the main vibration components of the oil film displacement are determined. The dynamic equation is as follows:

[0035] (12)

[0036] The total displacement is

[0037] (13)

[0038] Where static represents the displacement of the system when it first sinks to an equilibrium position.

[0039] dyn: The system vibrates around this equilibrium position at a frequency twice the excitation frequency. )

[0040] Let the excitation force amplitude excitation frequency .

[0041] The above equation simplifies to the form of forced vibration as follows:

[0042] (14)

[0043] Assume the steady-state solution is in the form of Where H is the amplitude, It is the phase lag angle.

[0044] Solving for the amplitude H, according to mechanical vibration theory, the displacement amplitude equals the force amplitude divided by the dynamic stiffness, i.e.

[0045] (15)

[0046] Solving for phase for

[0047] (16)

[0048] Therefore, the expression for the dynamic displacement response is:

[0049] (17)

[0050] The total displacement response is

[0051] (18)

[0052] The advantages and positive effects of this invention are: it fully considers the dynamic displacement response of oil film thickness under extreme working conditions, and the oil film thickness fluctuation under impact load can be calculated using the method described above. Therefore, the dynamic displacement response calculation method for hydrostatic sector-shaped oil film under impact load conditions proposed in this invention can better reflect the changes in oil film thickness. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of an oil film subjected to impact load.

[0054] Figure 2 This is a schematic diagram of a step load.

[0055] Figure 3 This is a schematic diagram of a half-sine load.

[0056] Figure 4 This is a diagram showing the displacement response of the oil film thickness under impact load. Detailed Implementation

[0057] To further understand the invention's content, features, and effects, the following embodiments are provided, and detailed descriptions are given below in conjunction with the accompanying drawings:

[0058] A method for calculating the dynamic displacement response of a static pressure sector-shaped oil film under impact load conditions, comprising the following steps.

[0059] Step 1: Equivalently represent the oil film as a single-degree-of-freedom "spring-damping system". A schematic diagram of the oil film under impact load is shown below. As shown. Given the following conditions: the bearing capacity W of the sector-shaped oil pad, and the change in oil film thickness due to impact load. , oil film stiffness K, oil film damping coefficient C, oil film thickness at the initial equilibrium position is H0, and the mass of the supported component is M.

[0060] Step 2: Calculate the dynamic displacement response of the oil film under step load. The step load is applied as follows: As shown.

[0061] First, the equation of motion can be obtained according to Newton's second law.

[0062] (1)

[0063] In the formula, y represents the magnitude of the change in oil film thickness, and F impact For impact load. Dividing both sides of the equation by M and introducing standard vibration parameters, we get... The natural frequency is Damping ratio Because hydrostatic bearings have significant compression membrane damping, they are generally overdamped systems. ).

[0064] Secondly, calculate the particular solution of the dynamic displacement response, when When the system is stable, that is .therefore ,but .

[0065] The general solution for the dynamic displacement response is calculated, and the homogeneous equation corresponding to the dynamic equation is:

[0066] (2)

[0067] Solving

[0068] (3)

[0069] because Therefore, the two roots are not equal. The general solution of the equation is: The complete solution is

[0070] (4)

[0071] The initial condition is when t=0 ,Right now

[0072] (5)

[0073] The fluctuation displacement of the oil film is obtained as follows

[0074] (6)

[0075] The displacement of the oil film after stabilization under step load is

[0076] (7)

[0077] Step 3: Calculate the impact load as a half-sine function, and apply it as follows: As shown.

[0078] Assuming the applied force is F max This represents the peak impact force. Perform a Fourier series expansion as follows

[0079] (8)

[0080] In engineering calculations, because higher-order terms decay extremely rapidly, using only the first-order AC term (n=1) is sufficient to meet the required accuracy.

[0081] (9)

[0082] The dynamic equations are established based on Newton's second law as follows:

[0083] (10)

[0084] The equations are solved step by step. First, the static response is solved: that is, the average subsidence of the oil film. The oil film will be "compacted" over a certain distance and then oscillate around this new equilibrium position.

[0085] When the system is stable, acceleration and velocity are both zero. , can be obtained

[0086] (11)

[0087] Secondly, the dynamic response is solved, and the main vibration components of the oil film displacement are determined. The dynamic equation is as follows:

[0088] (12)

[0089] The total displacement is

[0090] (13)

[0091] Where static represents the displacement of the system when it first sinks to an equilibrium position.

[0092] dyn: The system vibrates around this equilibrium position at a frequency twice the excitation frequency. )

[0093] Let the excitation force amplitude excitation frequency .

[0094] The above equation simplifies to the form of forced vibration as follows:

[0095] (14)

[0096] Assume the steady-state solution is in the form of Where H is the amplitude, It is the phase lag angle.

[0097] Solving for the amplitude H, according to mechanical vibration theory, the displacement amplitude equals the force amplitude divided by the dynamic stiffness, i.e.

[0098] (15)

[0099] Solving for phase for

[0100] (16)

[0101] Therefore, the expression for the dynamic displacement response is:

[0102] (17)

[0103] The total displacement response is

[0104] (18)

[0105] Finally, the following examples are provided, with the oil supply rate set to Q = 0.085 L / min, the peak impact force to be 90 N, the initial film thickness to be 96 μm, the load weight to be 30 kg, and the fan-shaped oil pad structure to have R1 = 0.043 m, R2 = 0.052 m, R3 = 0.061 m, and R4 = 0.070 m. The numerical simulation results based on this method are as follows: As shown.

[0106] The advantages and positive effects of this invention are: it fully considers the dynamic displacement response of oil film thickness under extreme working conditions, and the oil film thickness fluctuation under impact load can be calculated using the method described above. Therefore, the dynamic displacement response calculation method of the hydrostatic sector oil pad oil film under impact load conditions proposed in this invention can better reflect the changes in oil film thickness.

Claims

1. A method for calculating the dynamic displacement response of a hydrostatic sector-shaped oil film under impact loading conditions, characterized in that: The impact load is divided into two types: step load and half-sine function impact; the method includes the following steps: Step 1: Equivalently represent the oil film of the hydrostatic sector-shaped oil pad as a single-degree-of-freedom spring-damping system, and obtain the system parameters. These parameters include the bearing capacity W of the sector-shaped oil pad and the change in oil film thickness after impact load. The oil film stiffness is K, the oil film damping coefficient is C, the oil film thickness at the initial equilibrium position is H0, and the mass of the supported component is M; Step 2: For the impact load as a step load, establish and solve the dynamic equation to obtain the dynamic displacement response of the oil film; Step 3: For the impact load as a half-sine function, establish and solve the dynamic equation to obtain the dynamic displacement response of the oil film.

2. The method for calculating the dynamic displacement response of a static pressure sector-shaped oil film under impact load conditions according to claim 1, characterized in that: Step two includes calculating the dynamic displacement response of the oil film under step load conditions; First, the equation of motion can be obtained according to Newton's second law. (1)； In the formula, y represents the magnitude of the change in oil film thickness, and F impact For impact load; dividing both sides of the equation by M and introducing standard vibration parameters, we get... The natural frequency is Damping ratio ; Secondly, calculate the particular solution of the dynamic displacement response, when When the system is stable, that is ; ,but ; The general solution for the dynamic displacement response is calculated, and the homogeneous equation corresponding to the dynamic equation is: (2)； Solving (3)； because Therefore, the two roots are not equal; the general solution of the equation is... The complete solution is (4)； The initial condition is when t=0 ,Right now (5)； The fluctuation displacement of the oil film is obtained as follows (6)； The displacement of the oil film after stabilization is (7)。 3. The method for calculating the dynamic displacement response of a static pressure sector-shaped oil film under impact load conditions according to claim 1, characterized in that: Step three includes: applying a force of F max Peak impact force; Perform a Fourier series expansion as follows (8)； In engineering calculations, because higher-order terms decay extremely rapidly, taking the first-order AC term n=1 is sufficient to meet the required accuracy. (9)； The dynamic equations are established based on Newton's second law as follows: (10)； The equations are solved step by step. First, the static response is solved: the average subsidence of the oil film. The oil film will be compacted for a certain distance first, and then it will oscillate around the equilibrium position. When the system is stable, acceleration and velocity are both zero. , can be obtained (11)； Secondly, solve for the dynamic response, specifically the main vibration components of the oil film displacement; the dynamic equation is as follows: (12)； The total displacement is (13)； Where static represents the displacement of the system when it first sinks to an equilibrium position; dyn represents the vibration of the system around this equilibrium position, with the vibration frequency being twice the excitation frequency. Let the excitation force amplitude excitation frequency ; The above equation simplifies to the form of forced vibration as follows: (14)； Assume the steady-state solution is in the form of Where H is the amplitude, It is the phase lag angle; Solving for the amplitude H, according to mechanical vibration theory, the displacement amplitude equals the force amplitude divided by the dynamic stiffness, i.e. (15)； Solving for phase for (16)； The dynamic displacement response expression is (17)； The total displacement response is (18)。

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