Novel foil aerodynamic bearing and bearing vibration control method

Abstract

The invention belongs to the field of bearings, and particularly relates to a novel foil aerodynamic bearing and a bearing vibration control method.The novel foil aerodynamic bearing comprises a bearing sleeve, and a preload control structure is arranged on the inner wall of the bearing sleeve; the inner wall of the bearing sleeve is elastically connected with a bump foil, the surface of the bump foil is elastically connected with a top foil, the inner wall of the top foil is sleeved with a rotor, and the bearing sleeve is internally provided with a mounting slot position matched with a preload control structure. According to the novel foil gas dynamic pressure bearing and the bearing vibration control method, a preload control structure, a top foil and a bump foil are arranged, when voltage is applied to piezoelectric ceramic, the piezoelectric ceramic deforms due to the inverse piezoelectric effect of the piezoelectric ceramic, so that the input end of a lever amplification mechanism is pushed, the output end of the lever amplification mechanism extrudes the bump foil, and then the piezoelectric ceramic is driven to rotate; and the bump foil deforms, so that the top foil deforms, and real-time adjustment of air pressure distribution, rigidity and damping can be realized.

Description

Technical Field

[0001] This invention relates to the field of bearing technology, specifically to a novel foil gas dynamic bearing and a bearing vibration control method. Background Technology

[0002] Currently, foil gas dynamic bearings are widely used in ultra-high speed rotating equipment due to their advantages such as high speed, long life, oil-free lubrication, and compact structure. Their core principle is to use the cooperation of elastic foils and rigid bearing sleeves to form a supporting gas film to suspend the rotor through the gas dynamic pressure effect, which can significantly improve the DN value (rotor surface linear velocity), energy density and efficiency of rotating machinery.

[0003] In existing technologies, traditional foil gas hydrodynamic bearings are generally "passive" foil gas hydrodynamic bearings. Their performance is mainly improved by optimizing the foil structure (such as corrugated foil, flat foil, cantilever, etc.), adjusting radial clearance, or adding damping elements (such as wire mesh blocks, viscoelastic foil). For example, the corrugated foil bearing developed by the Korea Advanced Institute of Science and Technology (KAIST) in collaboration with other companies improves load-bearing capacity by optimizing the corrugated foil stiffness distribution, but it still has some inherent defects. For instance, it cannot adjust performance according to working conditions; the bearing's structure and performance are fixed after assembly and cannot actively adjust according to equipment conditions (such as changes in speed and load), leading to stability degradation when operating conditions fluctuate. It also suffers from insufficient suppression of subsynchronous vibrations; under high DN values, due to the nonlinearity of the gas film and foil structure, the rotor system is prone to large-amplitude subsynchronous vibrations, weakening the system's high-speed stability and limiting the bearing's application range. Furthermore, it suffers from poor adaptability because the passive design struggles to match the complex dynamic response of rotor systems. For example, it cannot optimize support stiffness and damping in real time when the rotor's unbalanced mass changes or static load fluctuates.

[0004] Furthermore, a few studies have attempted to form hybrid bearings by combining magnetic levitation bearings with gas-dynamic foil bearings. However, the gas-dynamic foil bearings only serve as auxiliary supports, failing to achieve active control, and are structurally complex and costly, making widespread application difficult. Therefore, we propose a novel foil gas-dynamic bearing and a bearing vibration control method. Summary of the Invention

[0005] The main objective of this invention is to provide a novel foil gas dynamic bearing and a bearing vibration control method, which can solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention proposes a novel foil gas dynamic bearing, comprising a bearing sleeve, wherein the inner wall of the bearing sleeve is provided with a preload control structure;

[0007] The inner wall of the bearing sleeve is elastically connected with a corrugated foil, the surface of the corrugated foil is elastically connected with a top foil, and the inner wall of the top foil is fitted with a rotor.

[0008] Preferably, the bearing sleeve has an internal mounting slot adapted to the preload control structure.

[0009] Preferably, the preload control structure includes a lever amplification mechanism. This mechanism effectively amplifies the minute expansion and contraction deformations of the piezoelectric ceramic actuator, converting them into an effective stroke sufficient to adjust the radial preload and local assembly clearance of the bearing. The lever amplification mechanism is internally fixed to the bearing sleeve via a flexible hinge. This flexible hinge, as a key transmission component of the preload control structure, transmits the minute expansion and contraction deformations of the piezoelectric ceramic actuator without gaps. Combined with the lever amplification mechanism, the deformation is precisely converted into radial preload adjustment amounts for the corrugated foil and top foil, ensuring the accuracy of radial preload and assembly clearance control, thus laying a structural foundation for the precision of vibration control. Motion guidance is achieved through its own elastic deformation, eliminating mechanical friction and gaps, reducing vibration and noise caused by transmission jamming or loosening. The flexible hinge is fixedly connected to the output end of the piezoelectric ceramic actuator. A locking screw is threaded onto the inner wall of the bearing sleeve. The surface of the locking screw is sleeved with one end of the spring, and the other end of the spring is tightly fitted with the surface of the steel ball. The surface of the steel ball is tightly fitted with the surface of the lever amplification mechanism. By adjusting the screw depth, the compression of the spring is changed, thereby adjusting the preload.

[0010] Preferably, the preload control structure is provided in multiple sets and arranged in a circumferential array inside the bearing sleeve.

[0011] Preferably, the procedure includes the following steps:

[0012] S1. Determine the geometric parameters and material properties of the gas dynamic foil bearing, as well as the mass matrix and stiffness matrix of the foil and the initial test conditions;

[0013] S2. Substitute the geometric parameters and material properties determined in S1 into the lubrication motion equation, continuity equation and state equation to derive the Reynolds equation for the gas dynamic foil bearing. Then input the parameters of the corrugated foil and the top foil to establish the gas film thickness equation and calculate the gas film thickness of the foil bearing.

[0014] S3. By using the foil mass matrix and stiffness matrix in S1 and the parameters of the gas film thickness equation in S2, as well as the parameters of the small unbalance disturbance, a mathematical model of the dynamic characteristics of the gas dynamic pressure foil bearing is established, and the differential equation of the dynamic characteristic coefficient is obtained.

[0015] S4. By substituting the geometric parameters and material properties determined in S1 and the system parameters such as bearing dynamic characteristic coefficient, rotor mass, and speed in S3, a dynamic model of the bearing-rotor system is established, and the dynamic characteristics and stability of the system are analyzed.

[0016] S5. Input the foil stiffness matrix of S1, the air film thickness equation of S2, and the preload control substructure parameters to establish a mechanical model of the preload control structure. Combine the equivalent elastic stiffness model of the elastic support structure to obtain the coupling relationship between radial preload, foil deformation and air film thickness.

[0017] Based on the ideal model established by the coupling relationship of input S6 and S5, the system stability analysis results of S4, and the real-time data collected by the sensors, a closed-loop vibration control system is constructed based on the PID algorithm. The convergence condition is solved by the least squares iterative calculation. According to the convergence condition, the gas film pressure distribution, the deformation of the foil structure, and the deviation of the radial preload of the bearing are adjusted to achieve active control of the vibration of the foil gas dynamic pressure bearing.

[0018] Preferably, in step S2, the Reynolds equation for the gas dynamic foil bearing is:

[0019]

[0020] Where x is the circumferential coordinate of the bearing.

[0021] z is the axial coordinate of the bearing.

[0022] p is the film pressure, in Pa.

[0023] h represents the thickness of the lubricating gas film, in meters (m).

[0024] μ is the dynamic viscosity of the gas, with units of Pa·s.

[0025] U is the axial velocity of the journal, in m / s.

[0026] Preferably, the equation for calculating the air film thickness in S2 is:

[0027]

[0028] Where α is the deformation coefficient of the corrugated foil.

[0029] E is the elastic modulus of the corrugated foil, measured in Pa.

[0030] s is the length of the foil, in meters (m).

[0031] l represents the corrugation length of the foil, in meters (m).

[0032] c represents the radius gap, in meters (m).

[0033] The thickness of the corrugated foil is in meters (m).

[0034] v is the Poisson's ratio of the wave foil.

[0035] Preferably, the differential equation for the dynamic characteristic coefficient in S3 is:

[0036]

[0037] in, It is the stiffness coefficient, which reflects the elastic restoring force characteristics of the system.

[0038] It is the damping coefficient, which reflects the energy dissipation characteristics of the system.

[0039] For acceleration,

[0040] For speed,

[0041] For displacement.

[0042] Preferably, the differential equation for the dynamic characteristic coefficients in S4 is:

[0043]

[0044] in, The unbalanced mass of the rotor, expressed in kg.

[0045] e is the eccentricity of the unbalanced mass, in meters (m).

[0046] ω represents the angular velocity of the rotor, expressed in rad / s.

[0047] The excitation angular frequency, in rad / s.

[0048] The initial phase angle of the unbalanced excitation, in rad.

[0049] This represents the stiffness coefficient of the bearing-rotor system. This represents the damping coefficient of the bearing-rotor system.

[0050] This invention provides a novel foil gas dynamic bearing and a method for controlling bearing vibration. It has the following beneficial effects:

[0051] (1) The novel foil gas dynamic pressure bearing, through the preload control structure, top foil and wave foil: when current is applied to the piezoelectric ceramic actuator, the piezoelectric ceramic actuator deforms due to its own inverse piezoelectric effect, thereby pushing the input end of the lever amplification mechanism, causing the output end of the lever amplification mechanism to squeeze the wave foil, and the deformation of the wave foil causes deformation of the top foil, thereby realizing real-time adjustment of air pressure distribution, stiffness and damping.

[0052] (2) The novel foil gas dynamic pressure bearing vibration control method establishes a parameter analysis model of the foil gas dynamic pressure bearing, inputs the known parameters into the parameter analysis model, and then obtains the ideal foil gas dynamic pressure bearing model. Based on the deviation between the ideal foil gas dynamic pressure bearing model and the actual situation, it makes data-driven adjustments, thereby saving a lot of repetitive and disorderly adjustment time. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0054] Figure 1 This is a schematic diagram of the bearing structure of the present invention;

[0055] Figure 2 This is a schematic diagram of the preload control structure of the present invention;

[0056] Figure 3 This is a diagram illustrating the control effect of the present invention;

[0057] Figure 4 This is the control flowchart of the present invention.

[0058] Explanation of reference numerals: 1. Bearing sleeve; 2. Rotor; 3. Corrugated foil; 4. Preload control structure; 5. Top foil; 401. Lever amplification mechanism; 402. Piezoelectric ceramic actuator; 403. Flexible hinge; 404. Locking screw; 405. Spring; 406. Steel ball.

[0059] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Please see Figures 1-4This invention proposes a novel foil gas dynamic bearing, comprising a bearing sleeve 1, wherein the bearing sleeve 1 has an installation groove adapted to a preload control structure 4, and the inner wall of the bearing sleeve 1 is provided with the preload control structure 4; the preload control structure 4 includes a lever amplification mechanism 401; through the provided lever amplification mechanism 401, the lever amplification mechanism 401 can effectively amplify the minute extension and contraction deformation of the piezoelectric ceramic actuator 402, converting it into an effective stroke sufficient to adjust the radial preload and local assembly clearance of the bearing.

[0062] The lever amplification mechanism 401 is fixedly connected to the inside of the bearing sleeve 1 via a flexible hinge 403, which is also fixedly connected to the output end of the piezoelectric ceramic actuator 402. The flexible hinge 403, as a key transmission component of the preload control structure 4, can transmit the minute expansion and contraction deformation of the piezoelectric ceramic actuator 402 without gaps. In conjunction with the lever amplification mechanism 401, the deformation is precisely converted into radial preload adjustment of the corrugated foil 3 and the top foil 5, ensuring the accuracy of radial preload and assembly gap control, thus laying a structural foundation for the precision of vibration control. Motion guidance is achieved through its own elastic deformation, eliminating mechanical friction and gaps, reducing vibration and noise caused by transmission jamming or loosening.

[0063] The inner wall of the bearing sleeve 1 is threaded with a locking screw 404. The surface of the locking screw 404 is sleeved with one end of the spring 405, and the other end of the spring 405 is in close contact with the surface of the steel ball 406. The surface of the steel ball 406 is in close contact with the surface of the lever amplification mechanism 401. The preload control structure 4 is provided in multiple sets and arranged in a circumferential array inside the bearing sleeve 1. By adjusting the screw depth of the locking screw 404, the compression of the spring 405 is changed, thereby adjusting the magnitude of the preload force.

[0064] The inner wall of the bearing sleeve 1 is elastically connected with a corrugated foil 3, the surface of the corrugated foil 3 is elastically connected with a top foil 5, and the inner wall of the top foil 5 is sleeved with a rotor 2.

[0065] In this invention, the following steps need to be followed during operation:

[0066] S1. Determine the geometric parameters and material properties of the gas dynamic foil bearing, as well as the mass matrix and stiffness matrix of the foil and the initial test conditions;

[0067] S2. Substituting the geometric parameters and material properties determined in S1 into the lubrication motion equation, continuity equation, and state equation, the Reynolds equation for the gas dynamic foil bearing is derived:

[0068] In S2, the Reynolds equation for the gas dynamic foil bearing is:

[0069]

[0070] Where x is the circumferential coordinate of the bearing.

[0071] z is the axial coordinate of the bearing.

[0072] p is the film pressure, in Pa.

[0073] h represents the thickness of the lubricating gas film, in meters (m).

[0074] μ is the dynamic viscosity of the gas, with units of Pa·s.

[0075] U is the axial velocity of the journal, in m / s.

[0076] Next, input the parameters for the corrugated foil and the top foil, establish the air film thickness equation, and calculate the air film thickness of the foil bearing:

[0077]

[0078] Where α is the deformation coefficient of the corrugated foil.

[0079] E is the elastic modulus of the corrugated foil, measured in Pa.

[0080] s is the length of the foil, in meters (m).

[0081] l represents the corrugation length of the foil, in meters (m).

[0082] c represents the radius gap, in meters (m).

[0083] The thickness of the corrugated foil is in meters (m).

[0084] v is the Poisson's ratio of the wave foil;

[0085] S3. Using the foil mass matrix and stiffness matrix from S1, and the parameters of the gas film thickness equation and small unbalance disturbance parameters from S2, a dynamic characteristic mathematical model of the gas dynamic pressure foil bearing is established, yielding the differential equations for the dynamic characteristic coefficients:

[0086] The differential equation for the dynamic characteristic coefficient in S3 is:

[0087]

[0088] in, It is the stiffness coefficient, which reflects the elastic restoring force characteristics of the system.

[0089] It is the damping coefficient, which reflects the energy dissipation characteristics of the system.

[0090] For acceleration,

[0091] For speed,

[0092] For displacement;

[0093] S4. By substituting the geometric parameters and material properties determined in S1 and the system parameters such as bearing dynamic characteristic coefficients, rotor mass, and rotational speed from S3, a dynamic model of the bearing-rotor system is established, and the dynamic characteristics and stability of the system are analyzed:

[0094] Differential equations for dynamic characteristic coefficients in S4:

[0095]

[0096] in, The unbalanced mass of the rotor, expressed in kg.

[0097] e is the eccentricity of the unbalanced mass, in meters (m).

[0098] ω represents the angular velocity of the rotor, expressed in rad / s.

[0099] The excitation angular frequency, in rad / s.

[0100] The initial phase angle of the unbalanced excitation, in rad.

[0101] This represents the stiffness coefficient of the bearing-rotor system. This represents the damping coefficient of the bearing-rotor system;

[0102] S5. Input the foil stiffness matrix of S1, the air film thickness equation of S2, and the preload control substructure parameters to establish a mechanical model of the preload control structure. Combine the equivalent elastic stiffness model of the elastic support structure to obtain the coupling relationship between radial preload, foil deformation and air film thickness.

[0103] Based on the coupling relationship of input S6 and S5, the system stability analysis results of S4, and the ideal model established by the real-time data collected by the sensors, a closed-loop vibration control system is constructed based on the PID algorithm. The convergence condition is solved by least squares iterative calculation. According to the convergence condition, the gas film pressure distribution, foil structure deformation, and bearing radial preload deviation are adjusted to achieve active control of the vibration of the foil gas dynamic bearing.

[0104] In this invention, when a current is applied to the piezoelectric ceramic actuator 402, the piezoelectric ceramic actuator 402 deforms due to its own inverse piezoelectric effect, thereby pushing the input end of the lever amplification mechanism 401, causing the output end of the lever amplification mechanism 401 to squeeze the corrugated foil 3. The deformation of the corrugated foil 3 causes deformation of the top foil 5, thereby enabling the adjustment of air pressure distribution, stiffness, and damping.

[0105] Example:

[0106] S1、

[0107] Basic parameter definition and matrix determination:

[0108]

[0109] S2,

[0110] Reynolds equations (after substituting parameters)

[0111]

[0112] in: For the bearing circumferential coordinates, For axial coordinates, For film pressure, The thickness of the air film;

[0113] Substituting the foil deformation coefficient into the air film thickness formula... ,have to:

[0114]

[0115] Simplified relationship between film thickness and pressure: .

[0116] S3. Combining the foil mass matrix, stiffness matrix, and air film parameters, the dynamic characteristic coefficients are obtained through finite element simulation:

[0117]

[0118] The corresponding dynamic characteristic differential equation:

[0119]

[0120] S4

[0121] Substitute rotor unbalance excitation Calculate the unbalanced excitation amplitude:

[0122]

[0123] System dynamic equations:

[0124]

[0125] It is the equivalent stiffness / damping coefficient of the bearing-rotor system, obtained by coupling the bearing characteristics and the rotor structure.

[0126] S5: A piezoelectric ceramic preload actuator is used as the control unit, and its parameters and coupling relationship are as follows:

[0127]

[0128] Through finite element coupled analysis, we obtained:

[0129] 1. Preload-foil deformation coupling relationship: ( (This refers to the deformation of the foil).

[0130] 2. Coupling relationship between preload and film thickness: .

[0131] S6

[0132] Control algorithm and parameters:

[0133] The PID control algorithm is adopted, and the parameters are tuned as follows:

[0134]

[0135] Control process:

[0136] 1. Deploy displacement sensors to collect real-time vibration displacement of the rotor;

[0137] 2. Input the vibration signal into the PID controller, and combine it with the system stability results of the original method S4 to output the preload control quantity;

[0138] 3. The convergence conditions for air film pressure and foil deformation are solved iteratively using the least squares method;

[0139] 4. The preload actuator adjusts the air film parameters according to the control quantity to suppress vibration.

[0140] Control effect:

[0141]

[0142] This embodiment fully demonstrates the accuracy of the idealized model established by this method, thereby saving a lot of repetitive and disordered adjustment time and enabling targeted control of bearings.

[0143] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A novel foil gas dynamic bearing, comprising a bearing sleeve (1), characterized in that: The inner wall of the bearing sleeve (1) is provided with a preload control structure (4). The inner wall of the bearing sleeve (1) is elastically connected with a corrugated foil (3), the surface of the corrugated foil (3) is elastically connected with a top foil (5), and the inner wall of the top foil (5) is fitted with a rotor (2).

2. The novel foil gas dynamic bearing according to claim 1, characterized in that: The bearing sleeve (1) has an installation slot inside that is adapted to the preload control structure (4).

3. The novel foil gas dynamic bearing according to claim 1, characterized in that: The preload control structure (4) includes a lever amplification mechanism (401), which is fixedly connected to the inside of the bearing sleeve (1) via a flexible hinge (403). The flexible hinge (403) is fixedly connected to the output end of the piezoelectric ceramic actuator (402). The inner wall of the bearing sleeve (1) is threaded with a locking screw (404). The surface of the locking screw (404) is sleeved with one end of the spring (405), and the other end of the spring (405) is tightly fitted with the surface of the steel ball (406). The surface of the steel ball (406) is tightly fitted with the surface of the lever amplification mechanism (401).

4. The novel foil gas dynamic bearing according to claim 1, characterized in that: The preload control structure (4) is provided in multiple sets and arranged in a circumferential array inside the bearing sleeve (1).

5. A novel vibration control method for foil gas dynamic bearings, characterized in that, Includes the following steps: S1. Determine the geometric parameters and material properties of the gas dynamic foil bearing, as well as the mass matrix and stiffness matrix of the foil and the initial test conditions; S2. Substitute the geometric parameters and material properties determined in S1 into the lubrication motion equation, continuity equation and state equation to derive the Reynolds equation for the gas dynamic foil bearing. Then input the parameters of the corrugated foil and the top foil to establish the gas film thickness equation and calculate the gas film thickness of the foil bearing. S3. By using the foil mass matrix and stiffness matrix in S1 and the parameters of the gas film thickness equation in S2, as well as the parameters of the small unbalance disturbance, a mathematical model of the dynamic characteristics of the gas dynamic pressure foil bearing is established, and the differential equation of the dynamic characteristic coefficient is obtained. S4. By substituting the geometric parameters and material properties determined in S1 and the system parameters such as bearing dynamic characteristic coefficient, rotor mass, and speed in S3, a dynamic model of the bearing-rotor system is established, and the dynamic characteristics and stability of the system are analyzed. S5. Input the foil stiffness matrix of S1, the air film thickness equation of S2, and the preload control substructure parameters to establish a mechanical model of the preload control structure. Combine the equivalent elastic stiffness model of the elastic support structure to obtain the coupling relationship between radial preload, foil deformation and air film thickness. Based on the ideal model established by the coupling relationship of input S6 and S5, the system stability analysis results of S4, and the real-time data collected by the sensors, a closed-loop vibration control system is constructed based on the PID algorithm. The convergence condition is solved by the least squares iterative calculation. According to the convergence condition, the gas film pressure distribution, the deformation of the foil structure, and the deviation of the radial preload of the bearing are adjusted to achieve active control of the vibration of the foil gas dynamic pressure bearing.

6. The novel foil gas dynamic bearing vibration control method according to claim 5, characterized in that, In S2, the Reynolds equation for the gas dynamic foil bearing is: Where x is the circumferential coordinate of the bearing. z is the axial coordinate of the bearing. p is the film pressure, in Pa. h represents the thickness of the lubricating gas film, in meters (m). μ is the dynamic viscosity of the gas, with units of Pa·s. U is the axial velocity of the journal, in m / s.

7. The novel foil gas dynamic bearing vibration control method according to claim 5, characterized in that, The equation for calculating the thickness of the air film in S2 is: Where α is the deformation coefficient of the corrugated foil; E is the elastic modulus of the corrugated foil, measured in Pa. s is the length of the foil, in meters (m). l represents the corrugation length of the foil, in meters (m). c represents the radius gap, in meters (m). The thickness of the corrugated foil is in meters (m). v is the Poisson's ratio of the wave foil.

8. The novel foil gas dynamic bearing vibration control method according to claim 5, characterized in that, The differential equation for the dynamic characteristic coefficient in S3 is: in, It is the stiffness coefficient, which reflects the elastic restoring force characteristics of the system. It is the damping coefficient, which reflects the energy dissipation characteristics of the system. For acceleration, For speed, For displacement.

9. The novel foil gas dynamic bearing vibration control method according to claim 5, characterized in that, The differential equation for the dynamic characteristic coefficients in S4 is as follows: in, The unbalanced mass of the rotor, expressed in kg. e is the eccentricity of the unbalanced mass, in meters (m). ω represents the angular velocity of the rotor, expressed in rad / s. The excitation angular frequency, in rad / s. The initial phase angle of the unbalanced excitation, in rad. This represents the stiffness coefficient of the bearing-rotor system. This represents the damping coefficient of the bearing-rotor system.

10. A novel method for vibration control of a foil gas dynamic bearing according to claim 5, characterized in that, In S5, the preload control substructure parameters include: piezoelectric ceramic voltage input extension amount, lever amplification factor of lever amplification mechanism, and spring preload force; In step S6, the real-time data collected by the sensor includes: air film pressure, foil deformation, and rotor displacement.

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