Multi-physical-field coupling viscosity calibration method for large and heavy hydrostatic pressure rotating table

Abstract

The invention discloses a multi-physics coupling viscosity calibration method for a large and heavy hydrostatic pressure rotating table, and belongs to the technical field of fluid mechanics modeling and high-end equipment manufacturing. According to the calibration method, a temperature control / high-pressure rotational rheometer is adopted to obtain experimental data, and experimental verification shows that the average prediction error of the model under the ultrahigh pressure (1000 MPa) and the wide temperature range (20-80 DEG C) is controlled within 10%, and the model is remarkably superior to traditional Arrhenius and Barus models (the error is 40% or above). Theoretical support is provided for oil film dynamic characteristics, bearing capacity optimization and real-time control of a large and heavy hydrostatic pressure system, and the method is suitable for various lubricating media such as mineral oil, synthetic oil and nanofluid and can be widely applied to precision machining and intelligent control in the field of high-end equipment manufacturing.

Description

Technical Field

[0001] This invention belongs to the fields of fluid dynamics modeling and high-end equipment manufacturing, specifically a multi-physics field coupled mathematical calibration method for hydraulic oil viscosity suitable for large and heavy-duty hydrostatic rotary tables. By integrating the multi-field coupling effects of temperature, pressure, and shear rate, this method addresses the insufficient prediction accuracy of traditional viscosity models under high pressure, wide temperature range, and dynamic shear conditions, providing theoretical support for oil film dynamic property analysis, system optimization, and real-time control. Background Art

[0002] The operating conditions of large, heavy-duty hydrostatic rotary tables are essentially a dynamic balance between "heavy-load rigidity" and "precision flexibility" under complex working conditions. These complex operating conditions are particularly evident in the following aspects, particularly under the influence of load, speed, and multi-physics coupling. The worktable carries workpieces or tools weighing tens to thousands of tons. The load distribution can be uneven depending on the workpiece shape and processing position, resulting in a complex hydrostatic oil film pressure field and significant local variations in oil film thickness. Furthermore, cutting forces and impact forces during machining cause periodic load fluctuations, leading to transient changes in oil film pressure, which can cause oil film oscillation or cavitation. Rotary table speeds typically range from 0.1 to 300 rpm. At low speeds, zero creep must be overcome, while at high speeds, oil film temperature rise and centrifugal forces must be controlled. The moment of inertia during startup and shutdown is large, and oil film stiffness can easily cause vibration during speed changes. This series of processes ultimately creates a complex multi-physics coupling operating condition for the rotary table, requiring extremely high heavy-load rigidity and precision flexibility. The oil film's load-bearing capacity and stiffness are directly correlated with viscosity. Under complex operating conditions (such as heavy loads, high speeds, and elevated temperatures), viscosity fluctuations can significantly alter oil film thickness and load-bearing characteristics. Optimizing viscosity formulas accurately quantifies the coupled relationship between temperature rise, load, and speed, ensuring the stability of oil film stiffness and load-bearing capacity. However, the limitations of traditional lubricant viscosity models under complex operating conditions significantly restrict the optimization performance of hydrostatic rotary tables. For example, the Arrhenius equation assumes a constant activation energy, resulting in viscosity prediction errors exceeding 40% in both high and low temperature regions. The Barus equation overestimates temperature at high pressures due to its exponential growth, significantly deviating from the actual value and ultimately failing at high pressures, with errors reaching hundreds of times. The Cross model only describes shear thinning effects, but fails to capture shear thickening at low shear rates, resulting in distorted viscosity predictions during start-up and shutdown phases. These shortcomings directly impact the accuracy of oil film stiffness calculations, leading to deviations in system load-bearing capacity design and potentially incurring risks of local overheating or oil film rupture. Furthermore, existing models lack multiphysics coupling capabilities and struggle to adapt to the interplay of temperature, pressure, and shear rate under dynamic operating conditions, limiting the implementation of high-precision prediction and control strategies.

[0003] In large and heavy-duty hydrostatic rotary tables, viscosity formula optimization is the key to resolving the conflict between "heavy-load rigidity" and "precision flexibility." Viscosity formula optimization not only involves modifying fluid parameters but also serves as the underlying technical foundation for improving the robustness, energy efficiency, and reliability of large and heavy-duty hydraulic systems under complex operating conditions. It directly determines the machining accuracy, stability, and intelligence level of high-end equipment. Summary of the Invention

[0004] The core of the present invention is to propose a nonlinear viscosity model based on the coupling of temperature, pressure and shear rate. By introducing dynamic activation energy, nonlinear pressure correction term and segmented shear rate correction function, the viscosity prediction accuracy under extreme working conditions is significantly improved, solving the technical problems raised in the background technology.

[0005] A multi-physics field coupled viscosity calibration method for a large heavy-duty hydrostatic rotary table comprises the following steps:

[0006] Step 1: Modify the Arrhenius equation and introduce the temperature-dependent activation energy E a (T);

[0007] Step 2: Modify the Barus equation and construct the nonlinear pressure-viscosity relationship β(P);

[0008] Step 3: Integrate the Cross model with the shear thickening term to achieve segmented shear rate correction;

[0009] Step 4: Synthesize the final multi-field coupling formula through multiplicative superposition.

[0010] The modified Arrhenius equation is:

[0011]

[0012] Where η0 is the viscosity at the reference temperature and R is the molar gas constant.

[0013] The temperature-dependent activation energy E a (T) is obtained by linear regression fitting of experimental data, and the specific form is:

[0014] E a (T) = k E (T-T0)+E a0 ;

[0015] Among them, k E is the activation energy temperature coefficient, T0 is the reference temperature, E a0 is the activation energy at the reference temperature.

[0016] The nonlinear pressure-viscosity relationship β(P) adopts the nonlinear Barus correction model, which is specifically in the form of:

[0017]

[0018] Where β0 is the viscosity coefficient at normal pressure, and α and d are pressure correction parameters, which are determined by fitting the experimental data using the nonlinear least squares method.

[0019] The shear rate correction takes the form of a piecewise function:

[0020] The low shear rate region is The high shear rate region is Where γ is the shear rate coefficient and m is the nonlinear exponent.

[0021] The multi-field coupling formula is formed by multiplicatively superimposing temperature, pressure, and shear rate correction terms. The specific form is:

[0022] η(T,P,γ)=η T (T)·η P (P)·η γ (γ);

[0023] Among them, η T (T) is the temperature correction term, η P (P) is the pressure correction term, η γ (γ) is the shear rate correction term.

[0024] The temperature-dependent activation energy E a The calibration method of (T) includes: using a temperature-controlled rotational rheometer to measure the viscosity at different temperatures under normal pressure and fixed shear rate, calculating the activation energy at each temperature point based on the Arrhenius equation, and fitting the dynamic activation energy expression by linear regression. The dynamic activation energy expression is E a (T)=E a0 ·[1+k E (T-T0)], where k E is the activation energy temperature coefficient.

[0025] The nonlinear pressure-viscosity relationship β(P) is calibrated using a high-pressure rotational rheometer at constant temperature and fixed shear rate to measure viscosity at different pressure points. The pressure correction coefficients β0, α, and d are fitted using a nonlinear least squares method. The objective function is to minimize the root mean square error between the experimental viscosity and the model prediction value. The pressure correction parameters are optimized using MATLAB lsqnonlin or Python scipy.optimize.curve_fit.

[0026] The calibration method of the shear rate correction includes: measuring the low shear rate region 1-100s respectively -1 and high shear rate zone 100-10 4 s-1 The viscosity data were obtained. The numerator term was used to fit the shear thickening effect in the low shear rate region, and the denominator structure of the Cross model was used to fit the shear thinning effect in the high shear rate region. The parameters λ and m were determined by piecewise fitting.

[0027] The synthesis method of the multi-physics field coupling is to first multiply the temperature correction term with the pressure correction term, and then multiply and superimpose it with the shear rate correction term. The final formula is:

[0028] η(T,P,γ)=η0(T0,P0)×[temperature correction term]×[pressure correction term]×[shear rate correction term].

[0029] Beneficial effects of the present invention:

[0030] The traditional viscosity model is used in high pressure (0.1-1000MPa), wide temperature range (0-100℃) and dynamic shear rate (1-10 4 s -1 ) is insufficient in prediction accuracy under working conditions, a nonlinear viscosity model based on temperature-pressure-shear rate three-field coupling is proposed. a (T) = k E (T-T0)+E a0 , nonlinear pressure correction term 1+α·P d The calibration method uses a temperature-controlled / high-pressure rotational rheometer to obtain experimental data, combines linear regression with nonlinear least squares method to fit model parameters, and finally synthesizes a multi-physics coupling formula through multiplicative superposition.

[0031] η(T, P, γ) = η0 × [temperature correction] × [pressure correction] × [shear correction]. Experimental verification shows that the average prediction error of this model is controlled within 10% under ultra-high pressure (1000MPa) and a wide temperature range (20-80°C), which is significantly better than the traditional Arrhenius and Barus models (error of more than 40%). The present invention provides theoretical support for the dynamic characteristics, load-bearing capacity optimization, and real-time control of the oil film of large and heavy-duty hydrostatic systems. It is applicable to a variety of lubricating media such as mineral oil, synthetic oil, and nanofluids, and can be widely used in precision processing and intelligent control in the field of high-end equipment manufacturing.

[0032] The present invention is achieved step by step by the following steps:

[0033] Step 1: Temperature correction:

[0034] The Arrhenius equation assumes that the activation energy E a The present invention introduces the temperature-dependent activation energy: Ea (T)=E a0 ·[1+k E (T-T0)], where k E <0, this dynamic activation energy formula can show the characteristic that the activation energy decreases with increasing temperature.

[0035] The final corrected temperature-viscosity formula is:

[0036]

[0037] Step 2: Pressure correction:

[0038] The Barus equation is overfitted under high pressure. d The denominator structure can more accurately fit the viscosity changes of materials in different pressure ranges. It is especially suitable for systems where pressure has a nonlinear effect on viscosity, avoiding failure of pressure prediction in high-pressure areas.

[0039] The final corrected compression-adhesion formula is:

[0040]

[0041] Step 3: Shear rate correction:

[0042] The Cross model only describes shear thinning and ignores the low shear rate thickening effect. The present invention introduces the molecular term 1+aγ c , to achieve segmented description.

[0043] Finally, the corrected shear-viscosity formula is obtained:

[0044]

[0045] Step 4: Synthesis of multi-field coupling formula

[0046] In the multi-field coupled model of a hydrostatic rotary table, temperature viscosity, pressure viscosity, and shear viscosity are not completely independent, but their coupling relationship can be modeled through nonlinear superposition in the form of a product. The temperature viscosity and pressure viscosity are first multiplied together, and then multiplied by a correction function for shear viscosity.

[0047] Finally, the revised multi-field coupling viscosity formula is obtained:

[0048] η(T,P,γ)=η0·η temp ·η press ·η shear

[0049] Expanded form:

[0050]

[0051] The verification method of the method includes: measuring viscosity under wide temperature range of 20-100°C and ultra-high pressure of 0.1-1000MPa, calculating the relative error between the model prediction value and the experimental value, verifying the prediction accuracy under extreme working conditions, requiring the average error to be less than 10%, and performing error comparison analysis with traditional models Arrhenius, Barus, and Cross.

[0052] The method is applicable to various lubricating media such as mineral oil, synthetic oil and nanofluid, and the viscosity prediction of different media can be achieved by recalibrating parameters.

[0053] The multi-field coupling formula has been verified through experiments. Under normal working conditions of large and heavy hydrostatic rotary tables, the error is controlled at around 5%. Moreover, under extreme working conditions, the error is significantly lower than that of the traditional Barus formula, and it is still applicable to the precision requirements of hydrostatic rotary tables.

[0054] The method formula is applicable to a real-time monitoring system, which dynamically adjusts the oil supply strategy of the lubrication system by online monitoring of temperature, pressure and shear rate parameters to optimize oil film stability and load-bearing capacity.

[0055] The method is applicable to the following working conditions: large heavy-duty hydrostatic rotary table (load capacity ≥ 10 tons), speed range 0.1-300rpm, temperature fluctuation range 0℃ to 100℃, oil supply pressure range 0.1-30MPa, shear rate range 1-10 4 s -1 .

[0056] Parameter expansion methods for new lubrication media such as nanofluids, parameter update strategies for multi-physics field coupling formulas, real-time calculation modules for oil film stiffness, and system stability evaluation index systems.

[0057] The application of the method in the hydrostatic rotary table includes: dynamic compensation of oil film thickness, load-bearing capacity optimization design, vibration suppression during start-up and shutdown phases, temperature rise control strategy specification, and system performance optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described below with reference to the accompanying drawings, in which:

[0059] Figure 1 Build a flow chart for a multiphysics coupled viscosity model.

[0060] Figure 2 is the fitting curve of the temperature-corrected activation energy formula.

[0061] Figure 3 This is a comparison chart of the viscosity predicted by the temperature-corrected temperature-viscosity formula, the viscosity predicted by the Arrhenius formula, and the actual viscosity.

[0062] Figure 4 This is a comparison chart of the viscosity at ultra-high pressure (1000 MPa) predicted by the pressure-corrected pressure-viscosity formula, the viscosity at ultra-high pressure (1000 MPa) predicted by Barus, and the actual viscosity at 1000 MPa. DETAILED DESCRIPTION

[0063] Before using the formula of the present invention, it can be calibrated and used directly. If reliable data is available, the data can be used directly for calibration. If no reliable data is available, it needs to be obtained through experimental measurement. The following are the specific experimental and calibration steps.

[0064] Step 1: Temperature correction item calibration (E a (T))

[0065] The fluid was subjected to constant pressure (P = 0.1 MPa) and fixed shear rate (γ = 100s -1 The viscosity of the sample was measured at a temperature range of 273K to 373K (0℃~100℃). The reference viscosity was measured at a reference temperature T0=313K, and the viscosity η(T) was recorded at every 10K temperature rise. The activation energy E at each temperature point was calculated according to the Arrhenius equation. a (T i ), Finally, the dynamic activation energy E was calculated based on the experimental data. a (T), and obtained by linear regression fitting

[0066] Step 2: Pressure correction term calibration (β(P))

[0067] The fluid was subjected to constant temperature (313K) and fixed shear rate (γ=100s -1 ) under a pressure range of 0.1 MPa to 100 MPa. The reference viscosity is measured at a reference pressure P0 = 0.1 MPa. The viscosity η(P) at each pressure point is recorded at every 10 MPa pressure increase. β0, α, d are fitted by the nonlinear least squares method. The objective function is: minimize The fitting tool is MATLAB lsqnonlin or Python scipy.optimize.curve_fit.

[0068] Step 3: Calibration of shear rate correction term (segmented correction)

[0069] The viscosity of the fluid was measured at constant temperature (T = 313K) and constant pressure (P = 0.1MPa) using a rotational rheometer. -1 ~100s-1 ) and high shear rate region (γ=100s -1 ~10 4 s -1 ) Viscosity at different shear rates, testing shear thickening and shear thinning effects. Segmented fitting based on experimental data. Low shear rate region: Fitting the molecular term 1+aγ c , describing the slight thickening effect, the objective function is (Fixed λγ<<1, the denominator is approximately 1) High shear rate area: fitting denominator 1+(λγ) m , describing shear thinning. The objective function is (Fixed numerator is 1).

[0070] Step 4: Comprehensive verification and reliability analysis

[0071] The temperature-corrected temperature-viscosity formula, the pressure-corrected pressure-viscosity formula, and the correction terms after shear rate correction obtained by calibration are synthesized into a multi-field coupling formula according to step four in the implementation steps of the invention. The final formula obtained is the viscosity formula after multi-field coupling correction for the specific experimental material. The viscosity under each working condition calculated by this formula is compared with the actual viscosity to analyze the reliability of the calibration.

[0072] Example 1

[0073] The formula calibration and error analysis are performed using VG46 mineral oil, a common oil used in hydrostatic rotary tables. Since reliable measurement data for the shear rate and viscosity of VG46 mineral oil is currently unavailable, this patent only calibrates and verifies the temperature and pressure correction terms.

[0074] In Chapter 4 of "High-Pressure Rheology for Quantitative Elastohydrodynamics," Bair measured the viscosity of VG46 oil at various temperatures and pressures using a capillary rheometer. The table below shows the experimentally measured values for the temperature-viscosity relationship of VG46 oil.

[0075]

[0076]

[0077] Step 1: Preprocess the experimental data to obtain data that can be directly calibrated.

[0078] Step 2: Take the point where the pressure is 0.1MPa and the temperature is 313.15K as the reference point, and calculate the activation energy E at each temperature point according to the modified Arrhenius equation. a (T i ), Among them, R = 8.314 J / (mol·K), T0 = 313.15 K, η0 = 0.046 Pa·s. This patent uses a manual fitting method for linear regression to obtain the temperature-corrected activation energy: Ea(T) = 86.07-0.8255(T-313.15) KJ / mol

[0079] Step 3: Integrate to obtain the temperature-corrected viscosity formula:

[0080]

[0081] Step 4: Calculate the temperature-corrected viscosity value and compare it with the actual viscosity. It is found that the viscosity formula after temperature correction has a low-temperature (20°C) viscosity prediction error of less than 5%, and a high-temperature (60°C) viscosity prediction error of about 10%.

[0082] Step 5: Calculate the fixed value E of the Arrhenius formula a , in the original Arrhenius equation, the activation energy E a Usually it is a constant obtained by fitting based on experimental data. This patent will recalculate a fixed E based on the above data through linear regression. a The regression equation is: The slope is calculated using the least squares method, Among them, x i =1 / T i ,y i =ln(η i ), n = 4. Fitting result E a =72.06KJ / mol.

[0083] Step 6: Calculating the viscosity predicted by the Arrhenius equation and comparing it to the actual viscosity revealed an error of over 40%. Ultimately, the conclusion was reached that the original Arrhenius equation, assuming a constant activation energy, resulted in large prediction errors over a wide temperature range (especially low and high temperatures). The temperature-dependent activation energy proposed in this patent significantly improves viscosity prediction accuracy by dynamically adjusting the activation energy, particularly within the turntable's operating range (20-60°), achieving a 3-5x improvement in accuracy, meeting the operational requirements of a hydrostatic turntable.

[0084] Step 7: Define the nonlinear Barus correction model: The parameters that need to be fitted are: β0, α, d.

[0085] Step 8: Use Matlab's lsqcurvefit function to complete the curve fitting. The fitting result is: β0=1.8116×10 -8 , α=3.2811×10 -6, d = 0.6547, goodness of fit R 2 =0.9922, the fitting effect is very good.

[0086] Step 9: Get the final pressure correction formula:

[0087] Step 10: Calculate the pressure-corrected viscosity value and compare it with the actual viscosity. It is found that after the pressure correction, the viscosity prediction error is controlled at about 5% at high pressure (500MPa) and at about 10% at ultra-high pressure (1000MPa).

[0088] Step 11: Calculate the fixed value β of the Barus formula, and use the viscosity values at various temperatures under 0.1 MPa and 500 MPa as the reference viscosity η0.

[0089] Step 12: Calculate the viscosity value predicted by the Barus formula and compare it with the actual viscosity. It is found that the Barus formula fails to predict the viscosity directly under ultra-high pressure (1000 MPa), and the error reaches hundreds of times.

[0090] The final conclusion is that the exponential form of the Barus formula causes the viscosity to increase exponentially with pressure, while the actual viscosity increases more slowly, which causes the Barus formula to fail to predict viscosity under high pressure. The nonlinear correction of the pressure term proposed in the patent effectively suppresses the phenomenon of excessive viscosity growth under high pressure, significantly improves the viscosity prediction accuracy, and controls the average error to about 5% under ultra-high pressure (1000MPa).

Claims

1. A multi-physics field coupled viscosity calibration method for a large heavy-duty hydrostatic rotary table, characterized in that The steps include: Step 1: Modify the Arrhenius equation and introduce the temperature-dependent activation energy E a (T); Step 2: Modify the Barus equation and construct the nonlinear pressure-viscosity relationship β(P); Step 3: Integrate the Cross model with the shear thickening term to achieve segmented shear rate correction; Step 4: Synthesize the final multi-field coupling formula through multiplicative superposition.

2. The method according to claim 1, characterized in that The modified Arrhenius equation is: Where η0 is the viscosity at the reference temperature and R is the molar gas constant.

3. The method according to claim 1, wherein the temperature-dependent activation energy E a (T) is obtained by linear regression fitting of experimental data, and the specific form is: E a (T)=k E ·(T-T0)+E a0 ; in, k E is the activation energy temperature coefficient, T0 is the reference temperature, E a0 is the activation energy at the reference temperature.

4. The method according to claim 1, wherein: The nonlinear pressure-viscosity relationship β(P) adopts the nonlinear Barus correction model, which is specifically in the form of: Where β0 is the viscosity coefficient at normal pressure, and α and d are pressure correction parameters, which are determined by fitting the experimental data using the nonlinear least squares method.

5. The method according to claim 1, wherein: The shear rate correction takes the form of a piecewise function: The low shear rate region is The high shear rate region is Where γ is the shear rate coefficient and m is the nonlinear exponent.

6. The method according to claim 1, characterized in that The multi-field coupling formula is formed by multiplicatively superimposing temperature, pressure, and shear rate correction terms. The specific form is: η(T,P,γ)=η T (T)·h P (P)·h γ (c); Among them, η T (T) is the temperature correction term, η P (P) is the pressure correction term, η γ (γ) is the shear rate correction term.

7. The method according to claim 1, characterized in that The temperature-dependent activation energy E a The calibration method of (T) includes: using a temperature-controlled rotational rheometer to measure the viscosity at different temperatures under normal pressure and fixed shear rate, calculating the activation energy at each temperature point based on the Arrhenius equation, and fitting the dynamic activation energy expression by linear regression. The dynamic activation energy expression is E a (T)=E a0 ·[1+k E (T-T0)], where k E is the activation energy temperature coefficient.

8. The method according to claim 1, characterized in that The calibration method of the nonlinear pressure-viscosity relationship β(P) includes: using a high-pressure rotational rheometer to measure the viscosity at different pressure points at a constant temperature and fixed shear rate, using a nonlinear least squares method to fit the pressure correction coefficients β0, α, and d, with the objective function being to minimize the root mean square error between the experimental viscosity and the model prediction value, and the pressure correction parameters are optimized using MATLAB lsqnonlin or Python scipy.optimize.curve_fit.

9. The method according to claim 1, characterized in that The calibration method of the shear rate correction includes: measuring the low shear rate region 1-100s-1 and the high shear rate region 100-10 4 s -1 The viscosity data were obtained. The numerator term was used to fit the shear thickening effect in the low shear rate region, and the denominator structure of the Cross model was used to fit the shear thinning effect in the high shear rate region. The parameters λ and m were determined by piecewise fitting.

10. The method according to claim 1, characterized in that The synthesis method of the multi-physics field coupling is to first multiply the temperature correction term with the pressure correction term, and then multiply and superimpose it with the shear rate correction term. The final formula is: η(T,P,γ)=η0(T0,P0)×[temperature correction term]×[pressure correction term]×[shear rate correction term].

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