CN113311710A - Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness - Google Patents
Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness Download PDFInfo
- Publication number
- CN113311710A CN113311710A CN202110586402.4A CN202110586402A CN113311710A CN 113311710 A CN113311710 A CN 113311710A CN 202110586402 A CN202110586402 A CN 202110586402A CN 113311710 A CN113311710 A CN 113311710A
- Authority
- CN
- China
- Prior art keywords
- oil film
- film thickness
- static pressure
- sliding table
- oil
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000003068 static effect Effects 0.000 title claims abstract description 172
- 238000000034 method Methods 0.000 title claims abstract description 42
- 238000013461 design Methods 0.000 claims abstract description 46
- 230000004044 response Effects 0.000 claims abstract description 25
- 238000007789 sealing Methods 0.000 claims abstract description 19
- 230000002706 hydrostatic effect Effects 0.000 claims abstract description 13
- 230000008859 change Effects 0.000 claims abstract description 10
- 238000004364 calculation method Methods 0.000 claims description 31
- 239000007788 liquid Substances 0.000 claims description 26
- 238000010168 coupling process Methods 0.000 claims description 9
- 238000005859 coupling reaction Methods 0.000 claims description 9
- 230000008878 coupling Effects 0.000 claims description 8
- 238000005461 lubrication Methods 0.000 claims description 7
- 238000006073 displacement reaction Methods 0.000 claims description 4
- 239000012528 membrane Substances 0.000 claims description 4
- 238000012546 transfer Methods 0.000 claims description 4
- 238000010276 construction Methods 0.000 claims description 3
- 239000010408 film Substances 0.000 claims 54
- 230000003245 working effect Effects 0.000 claims 2
- 239000010409 thin film Substances 0.000 claims 1
- 230000002277 temperature effect Effects 0.000 abstract 1
- 230000001550 time effect Effects 0.000 abstract 1
- 238000005457 optimization Methods 0.000 description 7
- 238000012360 testing method Methods 0.000 description 7
- 238000004590 computer program Methods 0.000 description 4
- 230000006870 function Effects 0.000 description 3
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 238000003491 array Methods 0.000 description 2
- 238000011156 evaluation Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000011056 performance test Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000001050 lubricating effect Effects 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000008092 positive effect Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
- Sliding-Contact Bearings (AREA)
Abstract
本发明属于静压滑台控制技术领域，公开了一种变油膜厚度的竖直静压滑台工作性能预测与控制方法、系统，构建考虑实际工况的变油膜厚度薄膜式静压支承设计模型，反映油膜厚度的微量变化；构建竖直静压滑台工作性能的预测模型以及综合静压滑台承载力、静刚度、动刚度、快速响应时间和温度影响的油膜厚度微量变化预测模型；基于构建的模型确定变油膜厚度的竖直静压滑台达到最优工作性能的条件；基于确定的条件构建基于等效油膜厚度、供油压力、封油边尺寸和流量比的超精密竖直静压滑台的精度控制模型，进行竖直静压滑台控制。本发明能够有效提高静压滑台的刚性、抗振性，降低响应时间，减少温度波动。
The invention belongs to the technical field of static pressure sliding table control, and discloses a method and system for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness, and constructs a design model of a film type hydrostatic bearing with variable oil film thickness considering actual working conditions , reflecting the slight change of oil film thickness; build a prediction model for the working performance of the vertical hydrostatic sliding table and a prediction model for the slight change of oil film thickness that integrates the bearing capacity, static stiffness, dynamic stiffness, fast response time and temperature effects of the hydrostatic sliding table; based on The constructed model determines the conditions under which the vertical static pressure sliding table with variable oil film thickness can achieve the optimal working performance; based on the determined conditions, an ultra-precision vertical static pressure table based on the equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio is constructed. The precision control model of the pressure slide is used to control the vertical static pressure slide. The invention can effectively improve the rigidity and vibration resistance of the static pressure sliding table, reduce the response time, and reduce the temperature fluctuation.
Description
Technical Field
The invention belongs to the technical field of static pressure sliding table control, and particularly relates to a method and a system for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness.
Background
At present: the oil film is the key of the hydrostatic bearing, the performance of the hydrostatic sliding table is directly influenced by the change of the thickness of the oil film, and the reasonably estimated thickness of the oil film is beneficial to providing larger bearing load, excellent dynamic rigidity and accurate positioning precision for the design of the hydrostatic guide rail. And the shape error and deformation are main factors influencing the thickness of the oil film. The change of the oil film thickness and the control thereof have an important effect on the performance of the hydrostatic sliding table, and are a precondition and guarantee for realizing ultraprecision, large load and high stability of the ultraprecision hydrostatic sliding table. And the scientific calculation of the oil film thickness can provide accurate data for the prediction of the working performance of the static pressure sliding table.
The static pressure sliding table is a typical implementation case of engineering practice application integrating tribology, mechanics, optimization methods and structural design. The working performance of the ultra-precise static pressure sliding table comprises the rigidity, the motion stability, the reliability and the service life of the sliding table. In the design process of the ultra-precise vertical static pressure sliding table, if the design parameters are not properly selected, the problems of low rigidity, poor movement precision, poor stability and the like of the sliding table can be caused. Different static performance, dynamic performance and thermal performance can be obtained by combining different design parameters of the ultra-precise vertical static pressure sliding table. And the working performance of the static pressure sliding table is analyzed by adopting a finite element analysis method, and the relation between the working performance and all design parameters can be clearly expressed and the optimal design parameters can be selected only by modeling for many times and calculating for a large amount of time. The optimization design method based on experience has high cost, long time consumption and complicated calculation when selecting the design parameter combination, and the optimal design parameter combination is difficult to obtain. Therefore, considering and exploring the change rule of the oil film thickness under the working condition of dynamic change, reasonably selecting the performance evaluation index and establishing the accurate mapping relation between the design parameters and the evaluation index, and is one of the basic theories for developing the ultra-precise, large-load and high-stability hydrostatic pressure sliding table with the rapid dynamic response capability.
Through the above analysis, the problems and defects of the prior art are as follows: the existing method for predicting the working performance of the vertical static pressure sliding table is high in cost, long in time consumption and complex in calculation, and an optimal design parameter combination is difficult to obtain; the control progress of the existing sliding table control method is not high, and the controlled sliding table is low in rigidity, poor in movement precision and poor in stability.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method and a system for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness.
The invention is realized in such a way that the working performance prediction and control method of the vertical static pressure sliding table with variable oil film thickness comprises the following steps:
the working performance of the vertical static pressure sliding table with the variable oil film thickness is predicted and controlled by constructing a variable oil film thickness film type static pressure bearing design model considering the actual working condition, a prediction model of the working performance of the vertical static pressure sliding table and an ultra-precise performance control model of the vertical static pressure sliding table based on the equivalent oil film thickness and other design parameters.
Further, the method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness comprises the following steps:
step one, constructing a variable oil film thickness film type static pressure bearing design model considering actual working conditions, and reflecting the micro-change of the oil film thickness;
constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table;
determining the condition that the vertical static pressure sliding table with variable oil film thickness achieves the optimal working performance based on the models constructed in the first step and the second step;
and fourthly, constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on the determined conditions, and controlling the vertical static pressure sliding table.
Further, the variable oil film thickness film type hydrostatic bearing design model considering the actual working condition comprises: an oil film thickness calculation model considering system errors and a variable oil film thickness film type lubrication theoretical model.
Further, the oil film thickness calculation model considering the system error is as follows:
wherein h (x, z) represents the oil film thickness h (x, z), h0Representing the theoretical oil film thickness, z representing the coordinate variable of the slider motion direction, x representing the coordinate variable of the oil film width direction, a0Represents an initial offset value; a isxmRepresenting the deviation values m times in the x direction; p is a radical ofxRepresents the deviation wavelength in the x direction; phi is axmRepresenting m initial phase angle deviation values in the x direction; a isznRepresenting the deviation value of n times in the z direction; p is a radical ofzRepresents the deviation wavelength in the z direction; phi is aznRepresenting n times of initial phase angle deviation values in the z direction; epsilonmnRepresenting coupling deviation values in x and y directions; thetamnAnd the initial phase angle of coupling deviation in the x and y directions is shown.
Further, the variable oil film thickness film type lubrication theoretical model is as follows:
wherein Q isPRepresenting the flow of the rectangular oil chamber; q. q.sxRepresenting the flow per unit width in the x-direction, qzFlow representing unit width in z direction; l and B respectively represent the length and the width of the oil pad, and L and B respectively represent the length of the oil sealing edge in the length direction and the width direction; mu means hydrodynamic viscosity, pr means maximum oil in the oil chamberThe membrane pressure; r is the hydraulic resistance of the oil cavity, and the calculation formula is as follows:
wherein, cRRepresenting a constant, the calculation formula is as follows:
further, in the second step, the oil film thickness micro-change prediction model integrating the bearing capacity, the static stiffness, the dynamic stiffness, the quick response time and the temperature influence of the static pressure sliding table comprises:
the method comprises the following steps of (1) predicting the bearing capacity of a static pressure sliding table, predicting a static stiffness, predicting a dynamic stiffness, predicting a quick response time and predicting a temperature influence;
the static pressure sliding table bearing capacity prediction model is as follows:
wherein, priDenotes the maximum oil film pressure, p, of the ith oil filmsDenotes the oil supply pressure, q0iDenotes the initial flow rate of the ith oil pad, criRepresenting the flow ratio of the ith oil pad; a. theiThe equivalent oil film bearing area of the ith oil pad is represented, and the calculation formula is as follows:
Ai＝(Li-li)(Bi-bi)；
in the formula, LiAnd BiRespectively representing the length and width of the oil pad; liAnd biRespectively showing the length of the oil sealing edge in the length direction and the width direction;
the static stiffness prediction model is as follows:
wherein, dF is the external load force, dh is the displacement generated after the force is applied;
the dynamic stiffness prediction model is as follows:
wherein G(s) represents the transfer function of the hydrostatic slipway, ω represents the load frequency, Γ0And Γ1The expression of (a) is as follows:
wherein:
(i＝1,2)，Θ1＝-2T1A1，
Θ3＝-2T2A2；
the response time prediction model is as follows:
wherein m represents the slip and its load mass, Δ% represents the percentage of the slip steady state value;
the temperature change prediction model is as follows:
wherein Δ t representsThe amount of temperature fluctuation per unit time; pTRepresents the total power loss; q represents the total flow rate; cp represents specific heat capacity and rho is density;
in the formula, v represents the movement speed of the sliding table, and n represents the number of oil cavities; c. CRRepresents a constant; qiAnd Q respectively represents the flow of a single oil chamber and the flow of all the oil chambers, and the calculation formula is as follows:
further, in the third step, the condition that the vertical static pressure sliding table with the variable oil film thickness achieves the optimal working performance is that the difference between the reciprocal of the oil film liquid resistance and the liquid resistance of the restrictor is positively driven to 0.
Further, the precision control model of the ultra-precise vertical static pressure sliding table based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio comprises:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio.
Further, the control model of oil film liquid resistance and the control model of film flow controller liquid resistance based on equivalent oil film thickness and other design parameters include:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are both equal to the equivalent oil film thickness haIs inversely proportional to the third power of the flow rate, and the hydraulic resistance control model of the membrane restrictor is directly proportional to the flow rate ratio cr and inversely proportional to the oil supply pressure ps as follows:
further, the performing vertical static pressure slip control includes:
selecting the minimum oil supply pressure value, and simultaneously making the difference f between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictoruThe forward direction is towards 0, and the vertical static pressure sliding table is controlled;
namely:
ps→ps min；
another objective of the present invention is to provide a system for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness, which includes:
the static pressure support design model building module is used for building a variable oil film thickness film type static pressure support design model under the actual working condition and reflecting the micro-change of the oil film thickness;
the prediction model construction module is used for constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table;
the optimal working performance determining module is used for determining the condition that the vertical static pressure sliding table with variable oil film thickness achieves the optimal working performance;
and the vertical static pressure sliding table control module is used for constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on determined conditions and controlling the vertical static pressure sliding table.
Another object of the present invention is to provide a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the computer program causes the processor to execute the method for predicting and controlling the working performance of the vertical static pressure sliding table with variable oil film thickness.
Another object of the present invention is to provide an information data processing terminal comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to execute the method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness.
By combining all the technical schemes, the invention has the advantages and positive effects that: according to the invention, the working performance of the variable oil film thickness vertical static pressure sliding table is predicted and controlled by constructing a variable oil film thickness film type static pressure bearing design model considering the actual working condition, a prediction model of the working performance of the vertical static pressure sliding table and an ultra-precise vertical static pressure sliding table performance control model based on equivalent oil film thickness and other design parameters. The invention can effectively improve the rigidity and the vibration resistance of the static pressure sliding table, reduce the response time and reduce the temperature fluctuation.
The invention builds a static pressure sliding table working performance test experimental platform on the basis of a basic part of an ultra-precise curved surface numerical control machine tool, namely an ultra-precise vertical static pressure sliding table. In order to ensure the accuracy of the test result of the ultra-precise vertical static pressure sliding table, experiments are required to be carried out in constant temperature, constant humidity, constant pressure and clean environments.
The independently developed ultraprecise vertical static pressure sliding table of the ultraprecise curved surface numerical control machine tool is taken as an example to predict and control the working performance of the vertical static pressure sliding table, and a test platform is shown in fig. 3. The size of the oil seal edge, the oil film gap and the flow ratio are all unchangeable and are respectively 11mm, 19 mu m and 2.5. When the design is based on experience, the oil supply pressure is usually selected to be 3MPa, the oil supply pressure is 2.8MPa according to the working performance prediction and control method of the vertical static pressure sliding table with variable oil film thickness, and the oil film pressure, the response time and the temperature fluctuation obtained by comparing the tests before and after the optimization of the static pressure sliding table are shown in the table 1. As can be seen from the table, after optimization, the rigidity of the static pressure sliding table is improved by 17%, the vibration resistance is improved by 9.3%, the response time is reduced by 40%, and the temperature fluctuation is reduced by 20%.
Drawings
Fig. 1 is a flow chart of a method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness, provided by the embodiment of the invention.
Fig. 2 is a schematic view of a static pressure oil film structure provided by the embodiment of the invention.
Fig. 3 is a schematic view of a platform for testing performance of an ultra-precise vertical static pressure sliding table provided by an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness, and the invention is described in detail below by combining the attached drawings.
The method for predicting and controlling the working performance of the vertical static pressure sliding table with variable oil film thickness, provided by the embodiment of the invention, comprises the following steps:
the working performance of the vertical static pressure sliding table with the variable oil film thickness is predicted and controlled by constructing a variable oil film thickness film type static pressure bearing design model considering the actual working condition, a prediction model of the working performance of the vertical static pressure sliding table and an ultra-precise performance control model of the vertical static pressure sliding table based on the equivalent oil film thickness and other design parameters.
As shown in fig. 1, the method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness provided by the embodiment of the invention comprises the following steps:
s101, constructing a variable oil film thickness film type static pressure bearing design model considering actual working conditions, and reflecting the micro-change of the oil film thickness;
s102, constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static stiffness, dynamic stiffness, quick response time and temperature influence of the static pressure sliding table;
s103, determining the condition that the vertical static pressure sliding table with the variable oil film thickness achieves the optimal working performance based on the models constructed in the S101 and the S102;
and S104, constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on the determined conditions, and controlling the vertical static pressure sliding table.
The invention also provides a system for predicting and controlling the working performance of the vertical static pressure sliding table with variable oil film thickness, which comprises:
the static pressure support design model building module is used for building a variable oil film thickness film type static pressure support design model under the actual working condition and reflecting the micro-change of the oil film thickness;
the prediction model construction module is used for constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table;
the optimal working performance determining module is used for determining the condition that the vertical static pressure sliding table with variable oil film thickness achieves the optimal working performance;
and the vertical static pressure sliding table control module is used for constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on determined conditions and controlling the vertical static pressure sliding table.
The variable oil film thickness film type static pressure bearing design model considering the actual working condition provided by the embodiment of the invention comprises the following steps: an oil film thickness calculation model considering system errors and a variable oil film thickness film type lubrication theoretical model.
The oil film thickness calculation model considering the system error provided by the embodiment of the invention is as follows:
wherein h (x, z) represents the oil film thickness h (x, z), h0Coordinate variable representing theoretical oil film thickness and z representing slide block movement directionX represents a coordinate variable in the oil film width direction, a0Represents an initial offset value; a isxmRepresenting the deviation values m times in the x direction; p is a radical ofxRepresents the deviation wavelength in the x direction; phi is axmRepresenting m initial phase angle deviation values in the x direction; a isznRepresenting the deviation value of n times in the z direction; p is a radical ofzRepresents the deviation wavelength in the z direction; phi is aznRepresenting n times of initial phase angle deviation values in the z direction; epsilonmnRepresenting coupling deviation values in x and y directions; thetamnAnd the initial phase angle of coupling deviation in the x and y directions is shown.
The film type lubricating theoretical model with variable oil film thickness provided by the embodiment of the invention is as follows:
wherein Q isPRepresenting the flow of the rectangular oil chamber; q. q.sxRepresenting the flow per unit width in the x-direction, qzFlow representing unit width in z direction; l and B respectively represent the length and the width of the oil pad, and L and B respectively represent the length of the oil sealing edge in the length direction and the width direction; μ represents the hydrodynamic viscosity, pr represents the maximum oil film pressure within the oil chamber; r is the hydraulic resistance of the oil cavity, and the calculation formula is as follows:
wherein, cRRepresenting a constant, the calculation formula is as follows:
the oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table provided by the embodiment of the invention comprises:
the method comprises the following steps of (1) predicting the bearing capacity of a static pressure sliding table, predicting a static stiffness, predicting a dynamic stiffness, predicting a quick response time and predicting a temperature influence;
the static pressure sliding table bearing capacity prediction model is as follows:
wherein, priDenotes the maximum oil film pressure, p, of the ith oil filmsDenotes the oil supply pressure, q0iDenotes the initial flow rate of the ith oil pad, criRepresenting the flow ratio of the ith oil pad; a. theiThe equivalent oil film bearing area of the ith oil pad is represented, and the calculation formula is as follows:
Ai＝(Li-li)(Bi-bi)；
in the formula, LiAnd BiRespectively representing the length and width of the oil pad; liAnd biRespectively showing the length of the oil sealing edge in the length direction and the width direction;
the static stiffness prediction model is as follows:
wherein, dF is the external load force, dh is the displacement generated after the force is applied;
the dynamic stiffness prediction model is as follows:
wherein G(s) represents the transfer function of the hydrostatic slipway, ω represents the load frequency, Γ0And Γ1The expression of (a) is as follows:
wherein:
(i＝1,2)，Θ1＝-2T1A1，
Θ3＝-2T2A2；
the response time prediction model is as follows:
wherein m represents the slip and its load mass, Δ% represents the percentage of the slip steady state value;
the temperature change prediction model is as follows:
where Δ t represents the amount of temperature fluctuation per unit time; pTRepresents the total power loss; q represents the total flow rate; cp represents specific heat capacity and rho is density;
in the formula, v represents the movement speed of the sliding table, and n represents the number of oil cavities; c. CRRepresents a constant; qiAnd Q respectively represents the flow of a single oil chamber and the flow of all the oil chambers, and the calculation formula is as follows:
the condition that the vertical static pressure sliding table with variable oil film thickness provided by the embodiment of the invention achieves the optimal working performance is that the difference between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictor is positively driven to 0.
The precision control model of the ultra-precise vertical static pressure sliding table based on the equivalent oil film thickness, the oil supply pressure, the oil sealing edge size and the flow ratio, provided by the embodiment of the invention, comprises the following steps:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio.
The embodiment of the invention provides an oil film liquid resistance control model and a film restrictor liquid resistance control model based on equivalent oil film thickness and other design parameters, which comprises the following steps:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are both equal to the equivalent oil film thickness haIs inversely proportional to the third power of the flow rate, and the hydraulic resistance control model of the membrane restrictor is directly proportional to the flow rate ratio cr and inversely proportional to the oil supply pressure ps as follows:
the vertical static pressure sliding table control method provided by the embodiment of the invention comprises the following steps:
selecting the minimum oil supply pressure value, and simultaneously making the difference f between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictoruThe forward direction is towards 0, and the vertical static pressure sliding table is controlled;
namely:
ps→ps min；
the technical solution of the present invention is further described with reference to the following specific embodiments.
Example 1:
the invention provides a method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness. The method comprises a variable oil film thickness film type static pressure bearing design model considering actual working conditions, a prediction model of the working performance of the vertical static pressure sliding table, and an ultra-precise vertical static pressure sliding table performance control model and method based on design parameters such as equivalent oil film thickness.
The variable oil film thickness film type static pressure bearing design model comprises an oil film thickness calculation model considering the actual working condition and a variable oil film thickness film type lubrication theoretical model. Assuming that the oil film thickness h (x, z) considering the actual condition is the theoretical oil film thickness h0The sum of the error and the system error e (x, z) is shown in formula (1).
h(x,z)＝h0+e(x,z) (1)
In the formula (1), h0For theoretical oil film thickness, z is the coordinate variable of the slider motion direction, x is the coordinate variable of the oil film width direction, and e (x, z) is the guide rail offset, as shown in fig. 2.
And respectively expressing the guide rail offset on the length and the width by using a first-order Fourier series, and expressing the coupling error in the length direction and the width direction by using a second-order Fourier series, wherein e (x, z) is expressed by the formula (2).
In the formula (2), a0Is an initial offset value; a isxmIs the deviation value of m times in the x direction; p is a radical ofxIs the offset wavelength in the x direction; phi is axmThe initial phase angle deviation value is m times in the x direction; a isznIs the deviation value of n times in the z direction; p is a radical ofzIs the deviation wavelength in the z direction; phi is aznThe initial phase angle deviation value is n times in the z direction; epsilonmnCoupling deviation values in the x direction and the y direction; thetamnIs the initial of the coupling deviation in the x and y directionsThe phase angle.
In summary, the oil film thickness h (x, z) considering the actual working condition is shown as formula (3).
The flow calculation formula of the rectangular oil cavity in the variable oil film thickness film type lubrication theoretical model considering the actual working condition is shown as a formula (4).
In the formula (4), qxFlow rate per unit width in the x direction, qzL and B are the length and width of the oil pad, respectively, for a unit width flow in the z direction. l and b represent the length and the length of the bank in the width direction, respectively. μ is the hydrodynamic viscosity. pr is the maximum oil film pressure within the oil chamber.
Wherein, R is the hydraulic resistance of the oil chamber, and the calculation formula is shown as (5).
In the formula (5), cRIs a constant value, and the calculation formula is shown in formula (6).
The oil film thickness-variable static pressure sliding table working performance prediction model comprises a static pressure sliding table bearing capacity, static stiffness, dynamic stiffness, quick response time and temperature prediction model considering oil film thickness change.
Single oil film bearing capacity WiThe calculation model of (2) is shown in equation (7).
In the formula (7), psFor supply pressure, priThe maximum oil film pressure of the ith oil film. c. CriThe flow ratio of the ith oil pad. q. q.s0iThe initial flow rate of the ith oil pad. A. theiThe equivalent oil film bearing area of the ith oil pad is shown as the formula (8).
Ai＝(Li-li)(Bi-bi) (8)
In the formula (8), LiAnd BiRespectively the length and width of the oil pad. liAnd biThe length and the length of the oil seal in the width direction are shown.
The calculation model of the oil film static stiffness ju is shown as formula (9).
In the formula (9), dF is the external load force, and dh is the displacement generated after the external load force.
The calculation model of the dynamic stiffness J of the oil pad is shown in the formula (10).
In the formula (10), G(s) is a transfer function of the static pressure slip, ω is a load frequency, and Γ is0And Γ1Is represented by the formulae (11) and (12).
In formulae (11) and (12): theta1＝-2T1A1，
Θ3＝-2T2A2，
The calculation model of the response time is:
in equation (13), m is the slip and its load mass, and Δ% is the percentage of the slip steady state value (typically 5% or 2% is chosen).
The calculation model of the temperature fluctuation amount Δ t per unit time is shown in the formula (14).
Wherein Cp is the specific heat capacity; rho is density; pTIs the total power loss, as shown in equation (15); q is the total flow, as shown in equation (17).
In the formula (16), v is the moving speed of the sliding table, and n is the number of oil chambers; c. CRIs a constant value, as shown in formula (6); qiThe flow rate for a single oil chamber is as shown in equation (16).
And the performance control model of the ultra-precise vertical static pressure sliding table is based on design parameters such as equivalent oil film thickness. The method is characterized by mainly relating to a control model of oil film liquid resistance based on design parameters such as equivalent oil film thickness and the like and a control model of liquid resistance of a film restrictor, which are respectively shown as a formula (18) and a formula (19).
An oil film liquid resistance control model and a liquid resistance control model of a film restrictor. It is characterized in that the equivalent oil film thickness h is mainly relatedaThe control method comprises four main design parameters of control performance, namely oil supply pressure ps, oil seal edge size l and flow ratio cr. The control model of the oil film liquid resistance and the liquid resistance control model of the film restrictor are both equal to the equivalent oil film thickness haIs inversely proportional to the third power of the pressure, and the hydraulic resistance control model of the diaphragm restrictor is also directly proportional to the flow ratio cr and inversely proportional to the oil supply pressure ps.
A performance control method for an ultra-precise vertical static pressure sliding table based on design parameters such as equivalent oil film thickness and the like. Characterized in that the value of the pressure (p) of the oil supply is chosen as small as possibles) And the difference f between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictor is madeuThe forward direction goes towards 0. The calculation expression method is shown in formulas (20) and (21).
ps→ps min (20)
The invention provides a method for predicting and controlling the working performance of a vertical static pressure sliding table with variable oil film thickness. The method is characterized by comprising a variable oil film thickness film type static pressure bearing design model considering actual working conditions, a prediction model of the working performance of the vertical static pressure sliding table, and an ultra-precise vertical static pressure sliding table performance control model and method based on design parameters such as equivalent oil film thickness.
The invention is implemented by taking a basic part of an ultra-precise curved surface numerical control machine tool, namely an ultra-precise vertical static pressure sliding table as a basis to build a static pressure sliding table working performance test experimental platform. In order to ensure the accuracy of the test result of the ultra-precise vertical static pressure sliding table, experiments are required to be carried out in constant temperature, constant humidity, constant pressure and clean environments.
The independently developed ultraprecise vertical static pressure sliding table of the ultraprecise curved surface numerical control machine tool is taken as an example to predict and control the working performance of the vertical static pressure sliding table, and a test platform is shown in fig. 3. The size of the oil seal edge, the oil film gap and the flow ratio are all unchangeable and are respectively 11mm, 19 mu m and 2.5. When the design is based on experience, the oil supply pressure is usually selected to be 3MPa, the oil supply pressure is 2.8MPa according to the working performance prediction and control method of the vertical static pressure sliding table with variable oil film thickness, and the oil film pressure, the response time and the temperature fluctuation obtained by comparing the tests before and after the optimization of the static pressure sliding table are shown in the table 1. As can be seen from the table, after optimization, the rigidity of the static pressure sliding table is improved by 17%, the vibration resistance is improved by 9.3%, the response time is reduced by 40%, and the temperature fluctuation is reduced by 20%.
TABLE 1 Performance comparison table for ultra-precise vertical static pressure slipway before and after optimization
Description of the main symbols
It should be noted that the embodiments of the present invention can be realized by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using dedicated logic; the software portions may be stored in a memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those skilled in the art will appreciate that the apparatus and methods described above may be implemented using computer executable instructions and/or embodied in processor control code, such code being provided on a carrier medium such as a disk, CD-or DVD-ROM, programmable memory such as read only memory (firmware), or a data carrier such as an optical or electronic signal carrier, for example. The apparatus and its modules of the present invention may be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of hardware circuits and software, e.g., firmware.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. The method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness is characterized by comprising the following steps of:
the working performance of the vertical static pressure sliding table with the variable oil film thickness is predicted and controlled by constructing a variable oil film thickness film type static pressure bearing design model under the actual working condition, a prediction model of the working performance of the vertical static pressure sliding table and an ultra-precise performance control model of the vertical static pressure sliding table based on the equivalent oil film thickness and other design parameters.
2. The method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness as claimed in claim 1, wherein the method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness specifically comprises the following steps:
constructing a variable oil film thickness film type static pressure bearing design model under actual working conditions, and reflecting the micro-change of the oil film thickness;
constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table;
determining the condition that the vertical static pressure sliding table with variable oil film thickness achieves the optimal working performance based on the models constructed in the first step and the second step;
and fourthly, constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on the determined conditions, and controlling the vertical static pressure sliding table.
3. The method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness according to claim 2, wherein the variable oil film thickness film type static pressure bearing design model considering the actual working condition comprises the following steps: an oil film thickness calculation model considering system errors and a variable oil film thickness film type lubrication theoretical model.
4. The method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness as claimed in claim 3, wherein the oil film thickness calculation model considering the system error is as follows:
wherein h (x, z) represents the oil film thickness h (x, z), h0Representing the theoretical oil film thickness, z representing the coordinate variable of the slider motion direction, x representing the coordinate variable of the oil film width direction, a0Represents an initial offset value; a isxmRepresenting the deviation values m times in the x direction; p is a radical ofxRepresents the deviation wavelength in the x direction; phi is axmRepresenting m initial phase angle deviation values in the x direction; a isznRepresenting the deviation value of n times in the z direction; p is a radical ofzRepresents the deviation wavelength in the z direction; phi is aznRepresenting n times of initial phase angle deviation values in the z direction; epsilonmnRepresenting coupling deviation values in x and y directions; thetamnAnd the initial phase angle of coupling deviation in the x and y directions is shown.
5. The method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness as claimed in claim 3, wherein the variable oil film thickness thin film type lubrication theoretical model is as follows:
wherein Q isPRepresenting the flow of the rectangular oil chamber; q. q.sxRepresenting the flow per unit width in the x-direction, qzFlow representing unit width in z direction; l and B respectively represent the length and the width of the oil pad, and L and B respectively represent the length of the oil sealing edge in the length direction and the width direction; μ represents the hydrodynamic viscosity, pr represents the maximum oil film pressure within the oil chamber; r is the hydraulic resistance of the oil cavity, and the calculation formula is as follows:
wherein, cRRepresenting a constant, the calculation formula is as follows:
6. the method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness according to claim 2, wherein in the second step, the oil film thickness micro-change prediction model integrating the bearing capacity, the static stiffness, the dynamic stiffness, the quick response time and the temperature influence of the static pressure sliding table comprises the following steps:
the method comprises the following steps of (1) predicting the bearing capacity of a static pressure sliding table, predicting a static stiffness, predicting a dynamic stiffness, predicting a quick response time and predicting a temperature influence;
the static pressure sliding table bearing capacity prediction model is as follows:
wherein, priDenotes the maximum oil film pressure, p, of the ith oil filmsDenotes the oil supply pressure, q0iDenotes the initial flow rate of the ith oil pad, criRepresenting the flow ratio of the ith oil pad; a. theiThe equivalent oil film bearing area of the ith oil pad is represented, and the calculation formula is as follows:
Ai＝(Li-li)(Bi-bi)；
in the formula, LiAnd BiRespectively representing the length and width of the oil pad; liAnd biRespectively showing the length of the oil sealing edge in the length direction and the width direction;
the static stiffness prediction model is as follows:
wherein, dF is the external load force, dh is the displacement generated after the force is applied;
the dynamic stiffness prediction model is as follows:
wherein G(s) represents the transfer function of the hydrostatic slipway, ω represents the load frequency, Γ0And Γ1The expression of (a) is as follows:
wherein:
Θ1＝-2T1A1，
Θ3＝-2T2A2；
the response time prediction model is as follows:
wherein m represents the slip and its load mass, Δ% represents the percentage of the slip steady state value;
the temperature change prediction model is as follows:
where Δ t represents the amount of temperature fluctuation per unit time; pTRepresents the total power loss; q represents the total flow rate; cp represents specific heat capacity and rho is density;
in the formula, v represents the movement speed of the sliding table, and n represents the number of oil cavities; c. CRRepresents a constant; qiAnd Q respectively represents the flow of a single oil chamber and the flow of all the oil chambers, and the calculation formula is as follows:
7. the method for predicting and controlling the working performance of the vertical static pressure sliding table with the variable oil film thickness according to claim 2, wherein in the third step, the condition that the vertical static pressure sliding table with the variable oil film thickness achieves the optimal working performance is that the difference between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictor is positive and tends to 0;
the precision control model of the ultra-precise vertical static pressure sliding table based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio comprises:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio;
the control model of oil film liquid resistance and the control model of film flow controller liquid resistance based on equivalent oil film thickness and other design parameters include:
the control model of the oil film liquid resistance and the control model of the liquid resistance of the film restrictor are both equal to the equivalent oil film thickness haIs inversely proportional to the third power of the flow rate, and the hydraulic resistance control model of the membrane restrictor is directly proportional to the flow rate ratio cr and inversely proportional to the oil supply pressure ps as follows:
the performing vertical static pressure slip table control comprises:
selecting the minimum oil supply pressure value, and simultaneously making the difference f between the reciprocal of the oil film hydraulic resistance and the hydraulic resistance of the restrictoruThe forward direction is towards 0, and the vertical static pressure sliding table is controlled;
namely:
ps→ps min；
8. the utility model provides a vertical static pressure slip table working property prediction and control system of variable oil film thickness which characterized in that, vertical static pressure slip table working property prediction and control system of variable oil film thickness includes:
the static pressure support design model building module is used for building a variable oil film thickness film type static pressure support design model under the actual working condition and reflecting the micro-change of the oil film thickness;
the prediction model construction module is used for constructing a prediction model of the working performance of the vertical static pressure sliding table and an oil film thickness micro-change prediction model integrating the bearing capacity, static rigidity, dynamic rigidity, quick response time and temperature influence of the static pressure sliding table;
the optimal working performance determining module is used for determining the condition that the vertical static pressure sliding table with variable oil film thickness achieves the optimal working performance;
and the vertical static pressure sliding table control module is used for constructing an ultra-precise vertical static pressure sliding table precision control model based on equivalent oil film thickness, oil supply pressure, oil sealing edge size and flow ratio based on determined conditions and controlling the vertical static pressure sliding table.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110586402.4A CN113311710B (en) | 2021-05-27 | 2021-05-27 | Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110586402.4A CN113311710B (en) | 2021-05-27 | 2021-05-27 | Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113311710A true CN113311710A (en) | 2021-08-27 |
| CN113311710B CN113311710B (en) | 2022-08-02 |
Family
ID=77375680
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110586402.4A Active CN113311710B (en) | 2021-05-27 | 2021-05-27 | Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113311710B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2614287Y (en) * | 2001-12-28 | 2004-05-05 | 哈尔滨电机厂有限责任公司 | A hydrostatic bearing variation constant-current oil supply system |
| JP2006266456A (en) * | 2005-03-25 | 2006-10-05 | Nsk Ltd | Hydrostatic air-cushion bearing straight line guide |
| CN102767568A (en) * | 2012-06-29 | 2012-11-07 | 中国工程物理研究院总体工程研究所 | Composite hydrostatic oil film slide table with large bearing capacity for centrifuge vibration table |
| CN104036079A (en) * | 2014-06-09 | 2014-09-10 | 北京工业大学 | Quantitative type static pressure turntable optimization design method based on sensitivity analysis |
| CN108591260A (en) * | 2018-05-03 | 2018-09-28 | 哈尔滨理工大学 | A kind of ramp type double square lubricating pad bearing capacity computation method considering dynamic pressure effect |
| CN110968966A (en) * | 2019-11-28 | 2020-04-07 | 北京工业大学 | A Method for Determining the Maximum Reasonable Speed of the Hydrostatic Rotary Table of Heavy-duty Machine Tools |
-
2021
- 2021-05-27 CN CN202110586402.4A patent/CN113311710B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2614287Y (en) * | 2001-12-28 | 2004-05-05 | 哈尔滨电机厂有限责任公司 | A hydrostatic bearing variation constant-current oil supply system |
| JP2006266456A (en) * | 2005-03-25 | 2006-10-05 | Nsk Ltd | Hydrostatic air-cushion bearing straight line guide |
| CN102767568A (en) * | 2012-06-29 | 2012-11-07 | 中国工程物理研究院总体工程研究所 | Composite hydrostatic oil film slide table with large bearing capacity for centrifuge vibration table |
| CN104036079A (en) * | 2014-06-09 | 2014-09-10 | 北京工业大学 | Quantitative type static pressure turntable optimization design method based on sensitivity analysis |
| CN108591260A (en) * | 2018-05-03 | 2018-09-28 | 哈尔滨理工大学 | A kind of ramp type double square lubricating pad bearing capacity computation method considering dynamic pressure effect |
| CN110968966A (en) * | 2019-11-28 | 2020-04-07 | 北京工业大学 | A Method for Determining the Maximum Reasonable Speed of the Hydrostatic Rotary Table of Heavy-duty Machine Tools |
Non-Patent Citations (10)
| Title |
|---|
| DYI-CHENG CHEN: "Study of membrane restrictors in hydrostatic bearing", 《MECHANICAL ENGINEERING》 * |
| ENBING QI: "A method for predicting hydrostatic guide error averaging effects based on three-dimensional profile error", 《TRIBOLOGYINTERNATIONAL》 * |
| HUA LU: "Design and Application on the Composite Rail of Column-Beams in Gantry Machine", 《IC3ME 2015》 * |
| SHUMING YANG: "Hydrostatic worktable performance of an ultra-precision optical aspheric machine tool", 《SCIENCEDIRECT》 * |
| 刘佳源: "液体静压导轨静动态特性研究", 《中国优秀硕博士学位论文全文数据库》 * |
| 张方杰: "液体静压导轨实验平台的设计与关键技术研究", 《中国优秀硕博士学位论文全文数据库》 * |
| 武鹏飞: "考虑节流形式的液体静压导轨油膜动刚度建模研究", 《机床与液压》 * |
| 董婉娇: "Prediction of different design conditions on comprehensive performance of hydrostatic slide and experimental verification", 《ORIGINAL ARTICLE》 * |
| 董婉娇: "纳米级精度的竖直液体静压滑台设计", 《光学精密工程》 * |
| 郭鹏阁: "定量式液体静压回转台的机械特性分析与参数识别", 《中国优秀博硕士论文全文数据库》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113311710B (en) | 2022-08-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP2107439B1 (en) | Method and system for the design and implementation of optimal multivariable model predictive controllers for fast-sampling constrained dynamic systems | |
| WO2020155228A1 (en) | Spindle thermal error compensation method insensitive to disturbance of cooling system | |
| CN109063404B (en) | Dynamic prediction method for rigidity of aerostatic thrust bearing | |
| Zhuang et al. | Effect of surface waviness on the performances of an aerostatic thrust bearing with orifice-type restrictor | |
| CN113311710A (en) | Method and system for predicting and controlling working performance of vertical static pressure sliding table with variable oil film thickness | |
| Gong et al. | Degradation index construction and learning-based prognostics for stochastically deteriorating feedback control systems | |
| Dhande et al. | Implementation of CFD–FSI technique coupled with response surface optimization method for analysis of three-lobe hydrodynamic journal bearing | |
| Oyama et al. | Computational fluid dynamics modeling of a wafer etch temperature control system | |
| Nicodemus et al. | Performance characteristics of micropolar lubricated membrane-compensated worn hybrid journal bearings | |
| CN116777010B (en) | A model training method and task execution method and device | |
| CN112560361A (en) | Centrifugal pump head value prediction method based on simulation result correction | |
| Barthwal et al. | Construction of solutions of a two‐dimensional Riemann problem for a thin film model of a perfectly soluble antisurfactant solution | |
| Wenkler et al. | Analysing the Impact of Process Dependent Thermal Loads on the Prediction Accuracy of Thermal Effects in Machine Tool Components | |
| Leva et al. | Model-based Proportional− Integral/Proportional− Integral− Derivative (PI/PID) autotuning with fast relay identification | |
| Dahlem et al. | Hybrid model approaches for compensating environmental influences in machine tools using integrated sensors | |
| Shen et al. | Intelligent CNC control with improved adaptive thermal error compensation model | |
| Goodyer et al. | Adaptive timestepping for elastohydrodynamic lubrication solvers | |
| Naumann et al. | Hybrid Thermal Error Compensation Combining Integrated Deformation Sensor and Regression Analysis Based Models for Complex Machine Tool Designs | |
| Gou et al. | Design and analysis methods for aerostatic bearings: The past, the present, and the future | |
| Chang et al. | Solving wave dispersion equation for dissipative media using homotopy perturbation technique | |
| Wang et al. | Stopping criterion in iterative solution methods for Reynolds equations | |
| Xia et al. | A novel method for fast identification of a machine tool selected point temperature rise based on an adaptive unscented Kalman filter | |
| Zhang et al. | Refined Hydrodynamic Lubrication Model with a High-Accuracy Numerical Algorithm for Starved Lubrication with Free Surfaces | |
| Pfeil et al. | SBFEM with reduced modal basis for hydrodynamic bearings | |
| Jang | Deterministic surface roughness effects on elastic material contact with shear thinning fluid media |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |