Static pressure guide rail oil pad rigidity-damping ratio collaborative optimization method based on time domain response

Abstract

The invention discloses a time domain response-based static pressure guide rail oil pad rigidity-damping ratio collaborative optimization method, which comprises the following steps of: firstly, constructing a Reynolds equation of a static pressure oil film under a Cartesian coordinate system, and performing dimensionless operation; according to the dynamic characteristic analysis model and a Reynolds equation, a system damping and rigidity calculation formula is obtained; in order to synergistically improve the two important parameter indexes, namely the rigidity and the damping ratio, multi-objective optimization needs to be carried out. The flow controller structure is mainly selected for optimizing parameters, and an uncertain optimization model is provided; the method is used for optimization, so that the rigidity is better, and the probability that the damping ratio is reduced to be below 1 is extremely low. According to the prior rigidity optimization method, the rigidity is generally improved at the cost of prolonging the stabilization time, and the method can quickly optimize the rigidity and ensure that the stabilization time is in a relatively quick interval at the same time.

Description

Technical Field

[0001] The present invention relates to a dynamic performance design technology for hydrostatic guideways of precision machine tools, and more specifically to a method for evaluating the overshoot / settling time of a hydrostatic oil pad and co-optimizing the stiffness-damping ratio while simultaneously considering the uncertainties of oil supply pressure and cutting force. Background Art

[0002] Traditional hydrostatic guideway design focuses on steady-state load and static stiffness, while transient overshoot (M) and 2% settling time (t) are only tested through calibration tests, lacking a predictable dynamic optimization method. Furthermore, the oil pressure (P) and cutting force (Fc) exhibit random distributions during actual machining, often causing the stiffness-damping ratio (KC) to deviate from the designed value, leading to positioning overshoot or vibration amplification. Existing technologies lack a systematic optimization process that uniformly considers uncertain excitations and targets the stiffness-damping ratio. Summary of the Invention

[0003] While ensuring the dynamic stiffness of the oil pad, the overshoot is minimized and the stabilization time is shortened; by considering the statistical distribution of P and Fc, the damping ratio is within the 95% confidence range and meets the stiffness requirements.

[0004] The technical solution adopted by the present invention is a method for collaboratively optimizing the stiffness and damping ratio of a hydrostatic guide rail oil pad based on time domain response, comprising the following steps:

[0005] Step 1:

[0006] First, construct the Reynolds equation for the static oil film in the Cartesian coordinate system and make it dimensionless:

[0007]

[0008] Where: p0——oil chamber pressure,

[0009] R0——The maximum radius of the fan-shaped oil pad,

[0010] h0——initial oil film thickness,

[0011] μ0——lubricating oil viscosity,

[0012] U is radial velocity, V is axial velocity.

[0013] Simplify the constant pressure closed static oil pad into a parallel spring damping system and perform force analysis:

[0014]

[0015] In the formula: m is the system mass; C1 is the damping of the upper oil pad; C2 is the damping of the upper oil pad; K1 is the stiffness of the upper oil pad; K2 is the stiffness of the lower oil pad; F(t) is the external force.

[0016] The elastic forces W and W can be calculated by the finite difference method, and the dimensionless damping coefficient Dimensionalization can be performed to obtain the damping coefficient. Further simplification can be obtained as follows:

[0017]

[0018] Where: e is the change in oil film thickness (m); h1 is the thickness of the upper oil film; h2 is the thickness of the lower oil film; μ0 is the initial viscosity.

[0019] The steps to obtain the dimensionless damping coefficient of the oil pad are as follows: First, the damping term in the Reynolds equation or the dimensionless damping term in the dimensionless Reynolds equation Different values ​​are set; secondly, the finite difference method is used to repeatedly solve the corresponding relationship between dimensionless bearing capacity and dimensionless damping, and the dimensionless damping coefficient is obtained by fitting this relationship. Finally, the time domain response curve of the oil pad can be solved using the Longo Kutta method.

[0020] Step 2:

[0021] Based on the dynamic characteristics analysis model and Reynolds equation, the calculation formulas for system damping and stiffness are obtained:

[0022]

[0023] Where: Φ(x)——bearing capacity calculation.

[0024] Based on the basic knowledge of control engineering, the solution method for the system natural frequency and damping ratio is established:

[0025]

[0026] Dynamic characteristics such as stabilization time (the minimum time required to reach and stay within the ±2% error range of the stable value) and maximum overshoot can be obtained:

[0027]

[0028] %OS=100M p %

[0029] Step 3:

[0030] In actual machining, there are some uncertainties. For example, the cutting force applied to the workpiece varies with factors such as surface topography inconsistencies and tool wear. Furthermore, during the constant-pressure oil supply process, factors such as cavitation in the hydraulic station or voltage instability can cause fluctuations in oil supply pressure, which also manifests as uncertainty in the data. Therefore, these uncertainties must be considered during the optimization process to ensure that the final results fall within a reliable range.

[0031] To synergistically improve these two key parameters, stiffness and damping ratio, a multi-objective optimization process was required, resulting in greater stiffness and a damping ratio within the 1 to 1.2 range. To optimize the oil pad structure without affecting the overall turntable layout, the optimization parameters were primarily focused on the throttle structure. This allowed the oil circuits on the existing hydrostatic bearings to be reused without affecting the turntable's structural layout.

[0032] Based on this, the following uncertain optimization model is proposed:

[0033]

[0034] Where d s1 ——upper flow edge width (mm); d s2 ——width of lower channeling edge / mm; l Z ——throttle length (mm); L j ——Throttle feedback gap length (mm); L m ——Length of the gap in the middle of the throttle (mm).

[0035] This method allows for optimization that results in optimal stiffness with a very low probability of the damping ratio dropping below 1. Previous stiffness optimization methods typically increased stiffness at the expense of increased stabilization time. This method allows for rapid stiffness optimization while ensuring a relatively fast stabilization time. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Internal feedback oil pad structure diagram.

[0037] Figure 2 Equivalent diagram of the dynamic model of the internal feedback oil pad.

[0038] Figure 3 Oil pad time domain response diagram. DETAILED DESCRIPTION

[0039] The technical solution adopted by the present invention is a method for collaboratively optimizing the stiffness and damping ratio of a hydrostatic guide rail oil pad based on time domain response, comprising the following steps:

[0040] Step 1: Modeling and Linearization

[0041] First, construct the Reynolds equation for the static oil film in the Cartesian coordinate system and make it dimensionless:

[0042]

[0043] Simplify the constant pressure closed static oil pad into a parallel spring damping system and perform force analysis:

[0044]

[0045] The elastic forces W and W can be calculated by the finite difference method, and the dimensionless damping coefficient Dimensionalization can be performed to obtain the damping coefficient. Further simplification can be obtained as follows:

[0046]

[0047] The steps to obtain the dimensionless damping coefficient of the oil pad are as follows: First, the damping term in the Reynolds equation or the dimensionless damping term in the dimensionless Reynolds equation Different numerical values ​​are set; secondly, the finite difference method is used to repeatedly solve the corresponding relationship between dimensionless bearing capacity and dimensionless damping; finally, the dimensionless damping coefficient is obtained by fitting this relationship.

[0048] Finally, the time domain response curve of the oil pad can be solved by the Longo Kutta method.

[0049] Step 2:

[0050] Based on the dynamic characteristics analysis model and Reynolds equation, the calculation formulas for system damping and stiffness are obtained:

[0051]

[0052] Based on the basic knowledge of control engineering, the solution method for the system natural frequency and damping ratio is established:

[0053]

[0054] Dynamic characteristics such as stabilization time (the minimum time required to reach and stay within the ±2% error range of the stable value) and maximum overshoot can be obtained:

[0055]

[0056] %OS=100M p %

[0057] Step 3:

[0058] In actual machining, there are some uncertainties. For example, the cutting force applied to the workpiece varies with factors such as surface topography inconsistencies and tool wear. Furthermore, during the constant-pressure oil supply process, factors such as cavitation in the hydraulic station or voltage instability can cause fluctuations in oil supply pressure, which also manifests as uncertainty in the data. Therefore, these uncertainties must be considered during the optimization process to ensure that the final results fall within a reliable range.

[0059] To synergistically improve these two key parameters, stiffness and damping ratio, a multi-objective optimization process was required, resulting in greater stiffness and a damping ratio within the 1 to 1.2 range. To optimize the oil pad structure without affecting the overall turntable layout, the optimization parameters were primarily focused on the throttle structure. This allowed the oil circuits on the existing hydrostatic bearings to be reused without affecting the turntable's structural layout.

[0060] Based on this, the following uncertain optimization model is proposed:

[0061]

Claims

1. A method for collaborative optimization of the stiffness and damping ratio of a hydrostatic guide rail oil pad based on time domain response, characterized in that: The steps include: Step 1: First, construct the Reynolds equation for the static oil film in the Cartesian coordinate system and make it dimensionless: Where: p0 - oil chamber pressure, R0 - maximum radius of fan-shaped oil pad, h0 - initial oil film thickness, μ0 - lubricating oil viscosity, U - radial velocity, V is axial velocity; Simplify the constant pressure closed static oil pad into a parallel spring damping system and perform force analysis: Where: m - system mass; C1 - upper oil pad damping; C2 - upper oil pad damping; K1 - upper oil pad stiffness; K2 - lower oil pad stiffness; F(t) - external force; The elastic forces W and W are calculated by the finite difference method, and the dimensionless damping coefficient The damping coefficient is obtained by dimensionalization; further simplified to: Where: e - oil film thickness change; h1 - upper oil film thickness; h2 - lower oil film thickness; μ0 - initial viscosity; The steps to obtain the dimensionless damping coefficient of the oil pad are as follows: First, the damping term in the Reynolds equation or the dimensionless damping term in the dimensionless Reynolds equation Set different values; secondly, use the finite difference method to repeatedly solve and obtain the corresponding relationship between dimensionless bearing capacity and dimensionless damping, and obtain the dimensionless damping coefficient by fitting this relationship; finally, the time domain response curve of the oil pad can be solved by the Longo Kutta method; Step 2: Based on the dynamic characteristics analysis model and Reynolds equation, the calculation formulas for system damping and stiffness are obtained: Where: Φ(x)——bearing capacity calculation; Based on the basic knowledge of control engineering, the solution method for the system natural frequency and damping ratio is established: Calculate the minimum time required to reach and stay within the ±2% error range of the stable value, that is, the stabilization time, and the dynamic characteristics such as the maximum overshoot: Step 3: In order to optimize the oil pad structure without affecting the overall layout of the turntable, the optimization parameters are selected on the throttle structure, and the oil circuit on the original hydrostatic bearing is directly used without affecting the structural layout of the turntable; The following uncertain optimization model is proposed: Where d s1 ——upstream flow edge width; d s2 ——width of the lower channeling edge; l Z ——throttle length; L j ——Throttle feedback gap length; L m ——The length of the gap in the middle of the throttle.

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