Numerical calculation method for temperature field and boundary of static pressure fan-shaped oil pad

Abstract

The invention discloses a numerical calculation method for a temperature field and a boundary of a static pressure fan-shaped oil pad, and aims to solve the problem that the bearing performance is directly influenced by the remarkable change of the viscosity of lubricating oil under high-speed and heavy-load conditions. Based on the principles of fluid mechanics and thermodynamics, a fan-shaped oil pad thermal fluid characteristic analysis model coupled with a pressure field, a temperature field and a viscosity-temperature effect is constructed; discretizing the Reynolds equation by adopting a finite difference method, and calculating the pressure distribution of the oil pad by applying a super-relaxation iteration method; calculating temperature partial differential of each region of the oil pad through a differential difference scheme, and accurately solving a temperature field of the oil pad by combining a sub-relaxation iteration method; the influence of temperature change on viscosity is further included in a viscosity-temperature model, and stable pressure field and temperature field distribution is obtained through multiple times of iterative updating calculation; and finally, solving characteristic parameters such as bearing capacity and friction force of the oil pad.

Description

Technical Field

[0001] The present invention belongs to the field of calculating and analyzing the temperature field of a sector oil pad of a hydrostatic turntable, and particularly relates to a numerical calculation method for the temperature field and its boundary of a single sector oil pad. Background Technique

[0002] The hydrostatic sector oil pad plays a crucial role in supporting and lubricating a high-precision hydrostatic turntable, and its performance directly affects the running accuracy and reliability of the machine tool. In practical applications, due to the high-pressure shear effect and hydrodynamic characteristics of the oil film, significant heat is generated inside the sector oil pad, resulting in uneven temperature field distribution. This temperature rise not only affects the thickness and load-bearing performance of the oil film but also may cause thermal deformation and degradation of lubrication performance, thereby affecting the stability and service life of the turntable. Therefore, the accurate calculation and analysis of the temperature field of the sector oil pad have become an important research content.

[0003] At present, domestic and foreign scholars mainly use the Fluent simulation analysis method to study the temperature field of the sector oil pad. However, since the solution of the temperature field involves many boundary conditions, the calculation process is relatively complex, and the relevant theoretical modeling research is still lacking. In contrast, the theoretical modeling method has significant advantages in revealing the generation mechanism of the temperature field, which can help better understand the basic laws of the temperature field and provide important guidance for engineering design.

[0004] To solve the problem of complex boundary conditions in the temperature field of the hydrostatic sector oil pad, the present invention proposes a numerical calculation method for the temperature field and boundary of the hydrostatic sector oil pad. Summary of the Invention

[0005] The purpose of the present invention is to propose a numerical calculation method for the temperature field and boundary of a hydrostatic sector oil pad in view of the complex geometric boundary conditions in the temperature field of the hydrostatic sector oil pad.

[0006] To achieve the above purpose, the following technical solutions are adopted:

[0007] First, based on the principle of fluid mechanics, the Reynolds equation in cylindrical coordinates considering centrifugal force and viscosity-temperature effect is constructed, the equation is made dimensionless using dimensional parameters, the model is discretized using the five-point difference method, and the pressure distribution of the oil pad is obtained by combining the over-relaxation iteration method.

[0008] Second, based on the principle of thermodynamics, the fluid energy equation in cylindrical coordinates is constructed through the functional relationship of the microelement body. Different difference formats are adopted for different positions and flow velocity directions of the oil pad, and the dimensionless energy equation is discretely solved using the finite difference method combined with the under-relaxation iteration method to obtain the temperature distribution of the oil film.

[0009] Again, consider the variation of the lubricating oil viscosity with temperature through the Reynolds viscosity-temperature model, update the viscosity, and perform cyclic iteration on the oil pad pressure field and temperature field until the convergence condition is met.

[0010] Finally, after obtaining the stable pressure field and temperature field, calculate and solve the characteristic parameters such as the bearing capacity and frictional force.

[0011] A numerical calculation method for the temperature field and boundary of a hydrostatic sector oil pad, characterized by the following steps:

[0012] In the first step, establish and solve the Reynolds equation in the cylindrical coordinate system;

[0013] The present invention constructs a Reynolds equation in the cylindrical coordinate system that takes into account the centrifugal force and the variation of viscosity with temperature:

[0014]

[0015] where r is the radial coordinate of the sector oil pad; θ is the circumferential angle of the oil pad; h is the oil film thickness of the oil pad; η represents the viscosity of the lubricating oil; ω represents the angular velocity of the turntable; ρ represents the density of the lubricating oil; U is the radial velocity of the upper surface of the oil pad; V is the tangential velocity of the upper surface of the oil pad; is the squeeze term of the Reynolds equation.

[0016] For the convenience of numerical calculation and highlighting the role of the main factors, the following parameters are used to nondimensionalize the equation:

[0017]

[0018] Substitute each term into Equation (1) and simplify to obtain:

[0019]

[0020] where p0 is the supply pressure; c is the initial oil film thickness between the turntable and the oil sealing edge; R0 is the turntable radius; η0 is the initial viscosity of the lubricating oil;

[0021] The boundary conditions for solving the pressure field are set as the oil cavity pressure being the supply pressure and the pressure at the edge of the oil sealing edge being 0, and the expression is as shown in Equation (3):

[0022]

[0023] where i is the radial grid node; Δr is the radial grid step; j is the circumferential grid node; Δθ is the circumferential grid step; R2 and R4 respectively represent the inner and outer radii of the oil cavity; θ1 represents the central angle of the oil pad; θ2 represents the central angle of the oil cavity; Γ represents the edge where the oil sealing edge meets the environment;

[0024] The equation (2) is discretized by the finite difference method. To accelerate the convergence rate, the over-relaxation iteration method is used to calculate the pressure distribution of the sector oil pad. The iteration formula is as follows:

[0025]

[0026] The pressure convergence judgment condition is:

[0027]

[0028] where α is the over-relaxation iteration factor; δ is the allowable relative error; i and j are the number of radial and circumferential grid nodes respectively; m and n are the number of radial and circumferential grids respectively; k is the number of iterations; is the node pressure value obtained by the k-th iteration; is the node pressure value obtained by the previous (k - 1) iteration.

[0029] In the second step, solve the energy equation and its boundary conditions;

[0030] Based on the functional relationship of the microelement and taking into account the action of the centrifugal force, the energy equation in the cylindrical coordinate system is constructed as follows:

[0031]

[0032] where q r , q θ are the volume flow rates of the radial and circumferential unit-width cross-sections respectively T is the oil film temperature; ρ is the density of the lubricating oil; c v is the specific heat capacity of the lubricating oil.

[0033] The following parameters are taken to make the equation dimensionless:

[0034]

[0035] Substituting each item into equation (6) gives:

[0036]

[0037] The equation (7) is discretized by the finite difference method. Since there is no pressure and temperature distribution outside the oil sealing edge boundary, different difference formats need to be used for different boundaries. The corresponding difference formats at different positions are as follows:

[0038] (1) Inside the oil sealing edge

[0039] The circumferential direction is the main flow direction of the fluid. Its difference format also needs to be judged according to the flow direction of the lubricating oil. The radial direction is the secondary flow direction of the lubricating oil, and the central difference format with higher accuracy can be directly used. The specific expressions are as follows:

[0040] 1) v θ ≥ 0

[0041]

[0042] 2) v θ < 0

[0043]

[0044] (2) Oil cavity edge (four parts)

[0045] The boundary condition of the oil cavity temperature is set to the oil supply temperature, and the dimensionless temperature value is set to 1. The expression is as follows:

[0046]

[0047] (3) Oil pad edge

[0048] The oil pad edge includes four parts: AB, CD, BC, and DA. The difference format needs to be expressed according to the flow velocity direction and geometric position as follows:

[0049] 1) Oil pad edge

[0050] if ν θ ≥ 0

[0051]

[0052] if ν θ < 0

[0053]

[0054] 2) Oil pad edge

[0055] if ν θ ≥ 0

[0056]

[0057] if ν θ < 0

[0058]

[0059] 3) Oil pad edge

[0060]

[0061] 4) Oil pad edge

[0062]

[0063] (4) Endpoint temperature value

[0064] The central difference formula cannot be used in either direction of the endpoint position. To maintain sufficient calculation accuracy, the three-node values within the boundary are used to calculate the first-order partial derivative of temperature.

[0065] 1) Endpoint A

[0066]

[0067] 2) Endpoint B

[0068]

[0069] 3) Endpoint C

[0070]

[0071] 4) Endpoint D

[0072]

[0073] The equation (7) is discretized by the above difference formula. To ensure the stability of the equation convergence, the point-by-point sub-relaxation iteration method is used for solution, and its expression is as follows:

[0074]

[0075] The temperature convergence criterion is:

[0076]

[0077] In the formula, α is the sub-relaxation iteration factor, which can be selected between 0 and 1; δ is the allowable relative error; is the node temperature value obtained by the k-th iteration; is the node temperature value obtained by the previous (k - 1)-th iteration.

[0078] The third step is to iteratively update the lubricating oil viscosity;

[0079] The viscosity of the lubricating oil changes significantly with temperature. According to the pressure distribution and temperature distribution of the oil film obtained in the first and second steps, the viscosity update calculation can be carried out. The Reynolds relationship is used to calculate the change of viscosity with temperature:

[0080]

[0081] In the formula, β is the viscosity-temperature coefficient, which can be taken as 0.03 / °C; η0 is the initial viscosity of the lubricating oil; T0 is the initial temperature of the lubricating oil.

[0082] The viscosity convergence condition is:

[0083]

[0084] In the formula, are the viscosity values of the lubricating oil nodes obtained from the k-th and (k - 1)-th iterations respectively; δ is the allowable relative error.

[0085] Step 4: Calculate the characteristic parameters of the sector oil pad

[0086] (1) Load capacity

[0087] The load capacity is the integral of the oil pad pressure over the entire bearing area. For a sector oil pad, there is the following expression:

[0088]

[0089] In the formula, θ1 is the angle of the sector oil pad; R1 and R4 are the inner and outer radii of the oil pad respectively.

[0090] (2) Frictional force

[0091] The shear stress of the oil pad is obtained according to Newton's law of internal friction, and the frictional force is obtained by integrating over the entire area:

[0092]

[0093] In the formula, F fr , F fy are the radial and circumferential components of the frictional force respectively; F f is the resultant frictional force. Description of the drawings

[0094] Figure 1 Schematic diagram of the structure and boundary of the sector oil pad

[0095] Figure 2 Flow chart for solving the temperature field of the hydrostatic sector oil pad

[0096] Figure 3 Distribution diagram of the pressure field of the hydrostatic sector oil pad

[0097] Figure 4 Distribution diagram of the temperature field of the hydrostatic sector oil pad

[0098] Figure 5 Variation curves of the load capacity of the hydrostatic sector oil pad with the oil film thickness and the oil supply flow rate

[0099] Figure 6 Variation curves of the frictional force of the hydrostatic sector oil pad with the oil film thickness and the oil supply flow rate Detailed implementation manners

[0100] To more clearly illustrate the object and technical solution of the present invention, the following further gives a complete description of the detailed implementation manners of the present invention with reference to the accompanying drawings.

[0101] For the operating conditions of the hydrostatic turntable, the turntable speed set by the present invention is 60 rpm; the angles of a single sector oil pad are θ1 = 26° and θ2 = 36°; the oil pad radii are R1 = 0.85 m, R2 = 0.917 m, R3 = 0.983 m, and R4 = 1.050 m. Figure 2 As the solution flow chart for solving the pressure field and temperature field of the hydrostatic sector oil pad, a numerical calculation method for the temperature field and boundary of the hydrostatic sector oil pad is characterized by including the following steps:

[0102] In the first step, establish and solve the Reynolds equation in the cylindrical coordinate system.

[0103] Based on the principle of fluid mechanics, through the force analysis of the microelement, the present invention constructs the Reynolds equation in the cylindrical coordinate system that simultaneously takes into account the action of centrifugal force and the change of viscosity with temperature:

[0104]

[0105] Among them, r is the radial coordinate of the sector oil pad; θ is the circumferential angle of the oil pad; h is the oil film thickness of the oil pad; η is the viscosity of the lubricating oil; ω is the angular velocity of the turntable; ρ is the density of the lubricating oil; U is the radial velocity of the upper surface of the oil pad; V is the tangential velocity of the upper surface of the oil pad. is the squeeze term of the Reynolds equation;

[0106] For the convenience of numerical calculation and highlighting the role of the main factors, the following parameters are used to nondimensionalize the equation:

[0107]

[0108] Substitute each term into Equation (1) and simplify to obtain:

[0109]

[0110] Among them, p0 is the supply pressure; c is the initial oil film thickness between the turntable and the oil seal edge; R0 is the turntable radius; η0 is the initial viscosity of the lubricating oil.

[0111] The boundary conditions for solving the pressure field are set as the oil cavity pressure being the supply pressure and the pressure at the edge of the oil seal being 0, and the expressions are as follows:

[0112]

[0113] Among them, i is the radial grid node; Δr is the radial grid step; j is the circumferential grid node; Δθ is the circumferential grid step; R2 and R4 respectively represent the inner and outer radii of the oil cavity; θ1 represents the central angle of the oil pad; θ2 represents the central angle of the oil cavity; Γ represents the edge of the intersection between the oil seal and the environment.

[0114] The finite difference method is used to discretize Equation (2). To accelerate the convergence rate, the over-relaxation iteration method is adopted to calculate the pressure distribution of the sector oil pad. The iteration formula is as follows:

[0115]

[0116] The pressure convergence judgment condition is:

[0117]

[0118] where α is the over-relaxation iteration factor, generally selected between 1 and 2; δ is the allowable relative convergence error; i and j are the number of radial and circumferential grid nodes respectively; m and n are the number of radial and circumferential grids respectively; k is the number of iterations; is the node pressure value obtained by the k-th iteration; is the node pressure value obtained by the previous (k - 1) iteration; The oil film pressure distribution of the static pressure sector oil pad is as Figure 3 shown.

[0119] The second step is to solve the energy equation and its boundary conditions;

[0120] Based on the thermodynamic principle, according to the functional relationship of the microelement body and taking into account the action of the centrifugal force, the energy equation in the cylindrical coordinate system is constructed as follows:

[0121]

[0122] where: q r , q θ are the volume flow rates of the radial and circumferential unit-width cross-sections respectively T is the oil film temperature; ρ is the density of the lubricating oil; c v is the specific heat capacity of the lubricating oil.

[0123] The following parameters are taken to make the equation dimensionless:

[0124]

[0125] The finite difference method is used to discretize Equation (7). Since there is no pressure and temperature distribution outside the oil seal edge boundary, different difference formats need to be used for different boundaries. Figure 1 is the structure and geometric boundary position of the static pressure sector oil pad. The corresponding difference formats at different positions are as follows:

[0126] (1) Inside the oil seal edge

[0127] The circumferential direction is the main flow direction of the fluid. Its difference format also needs to be judged according to the flow direction of the lubricating oil. The radial direction is the secondary flow direction of the lubricating oil, and the central difference format with higher accuracy can be directly adopted. The specific expressions are as follows:

[0128] 1) v θ ≥ 0

[0129]

[0130] 2) v θ < 0

[0131]

[0132] (2) Oil cavity edge (four parts)

[0133] The boundary condition of the oil cavity temperature is set to the oil supply temperature, and the dimensionless temperature value is set to 1. The expression is as follows:

[0134]

[0135] (3) Oil pad edge

[0136] The oil pad edge includes a total of four parts: AB, CD, BC, and DA. The difference format represented according to the flow velocity direction and geometric position is as follows:

[0137] 1) Oil pad edge

[0138] if ν θ ≥ 0

[0139]

[0140] if ν θ < 0

[0141]

[0142] 2) Oil pad edge

[0143] if ν θ ≥ 0

[0144]

[0145] if ν θ < 0

[0146]

[0147] 3) Oil pad edge

[0148]

[0149] 4) Oil pad edge

[0150]

[0151] (4) Endpoint temperature value

[0152] The central difference format cannot be used in both directions of the endpoint position. To maintain sufficient calculation accuracy, the first-order partial derivative of temperature is expressed by the values of three nodes within the boundary.

[0153] 1) Endpoint A

[0154]

[0155] 2) Endpoint B

[0156]

[0157] 3) Endpoint C

[0158]

[0159] 4) Endpoint D

[0160]

[0161] The equation (7) is discretized by the above difference format. To ensure the stability of the equation convergence, the point-by-point sub-relaxation iteration method is used to solve it, and its expression is as follows:

[0162]

[0163] The convergence criterion is:

[0164]

[0165] In the formula, α is the sub-relaxation factor, which can be selected between 0 and 1; δ is the allowable relative error; is the node temperature value obtained by the k-th iteration; is the node temperature value obtained by the previous (k - 1)-th iteration; Figure 4 is the distribution contour map of the temperature field of the sector oil pad obtained by iterative calculation.

[0166] The third step is to iteratively update the lubricating oil viscosity;

[0167] The viscosity of the lubricating oil changes significantly with temperature. According to the pressure distribution and temperature distribution of the oil film obtained in the first and second steps, the viscosity update calculation can be carried out. The Reynolds relationship is used to calculate the change of viscosity with temperature:

[0168]

[0169] In the formula, β is the viscosity-temperature coefficient, which can be taken as 0.03 / °C; η0 is the initial viscosity of the lubricating oil; T0 is the initial temperature of the lubricating oil.

[0170] The viscosity convergence condition is as follows:

[0171]

[0172] In the formula, are the viscosity values of the lubricating oil nodes obtained from the k-th and (k - 1)-th iterations respectively; δ is the allowable relative error.

[0173] Step 4: Calculate the characteristic parameters of the sector oil pad;

[0174] (1) Load capacity

[0175] The load capacity is the integral of the oil pad pressure over the entire bearing area. For the sector oil pad, there is the following expression:

[0176]

[0177] In the formula, θ1 is the angle of the sector oil pad; R1 and R4 are the inner and outer radii of the oil pad respectively. Figure 5 is the curve of the load capacity of the sector oil pad varying with the oil film thickness and the supply oil flow rate.

[0178] (2) Frictional force

[0179] The shear stress of the oil pad is obtained according to Newton's law of internal friction, and the frictional force is obtained by integrating over the entire area:

[0180]

[0181] In the formula, F fr , F fy are the radial and circumferential components of the frictional force respectively; F f is the resultant frictional force. Figure 6 is the curve of the frictional force of the sector oil pad varying with the oil film thickness and the supply oil flow rate.

Claims

1. A numerical calculation method for the temperature field and boundary of a hydrostatic sector oil pad, characterized in that It includes the following steps: Based on the principles of fluid mechanics and thermodynamics, construct a sector oil pad thermal fluid characteristics analysis model that couples the pressure field, temperature field, and viscosity-temperature effect; Use the finite difference method to discretize the Reynolds equation, and use the successive over-relaxation iteration method to calculate the pressure distribution of the oil pad; calculate the temperature partial differential of each region of the oil pad through a differential difference format, and combine the under-relaxation iteration method to accurately solve the temperature field of the oil pad; consider the influence of temperature change on viscosity by the viscosity-temperature model, and iteratively update the calculation multiple times to obtain the stable pressure field and temperature field distributions; finally, solve the bearing capacity and friction characteristic parameters of the oil pad.

2. The numerical calculation method for the temperature field and boundary of a static pressure sector oil pad according to claim 1, characterized in that, The implementation steps for establishing and solving the Reynolds equation in the cylindrical coordinate system are as follows: The Reynolds equation in the cylindrical coordinate system considering the action of centrifugal force and the variation of viscosity with temperature: where, r is the radial coordinate of the sector oil pad; θ is the circumferential angle of the oil pad; h represents the oil film thickness of the oil pad; η represents the viscosity of the lubricating oil; ω represents the angular velocity of the turntable; ρ is the density of the lubricating oil; U is the radial velocity of the upper surface of the oil pad; V is the tangential velocity of the upper surface of the oil pad; is the squeeze term of the Reynolds equation; For the convenience of numerical calculation and highlighting the role of main factors, the following parameters are taken to make the equation dimensionless: Substitute each term into Equation (1) and simplify to obtain: Among them, p0 is the supply oil pressure; c is the initial oil film thickness between the turntable and the oil sealing edge; R0 is the turntable radius; η0 is the initial viscosity of the lubricating oil; The boundary conditions for solving the pressure field are set as the oil chamber pressure being the supply oil pressure and the pressure at the edge of the oil sealing edge and the environment being 0, and the expressions are as follows: In the formula, i is the radial grid node; Δr is the radial grid step; j is the circumferential grid node; Δθ is the circumferential grid step; R2 and R4 respectively represent the inner and outer radii of the oil chamber; θ1 represents the central angle of the oil pad; θ2 represents the central angle of the oil chamber; Γ represents the edge of the oil sealing edge and the environment.

3. The numerical calculation method for the temperature field and boundary of a hydrostatic sector oil pad according to claim 2, characterized in that Use the finite difference method to discretize Equation (2). To accelerate the convergence speed, use the successive over-relaxation iteration method to calculate the pressure distribution of the sector oil pad, and the iteration formula is: The pressure convergence judgment condition is: In the formula, β is the over-relaxation iteration factor; δ is the allowable relative error, i and j are the number of grid nodes in the radial and circumferential directions respectively; m and n are the number of grids in the radial and circumferential directions respectively; k is the number of iterations; is the node pressure value obtained from the k-th iteration; is the node pressure value obtained from the previous iteration, i.e., the (k - 1)-th iteration.

4. A numerical calculation method for the temperature field and boundary of a hydrostatic sector oil pad according to claim 2, characterized in that, Solve based on the energy equation and its boundary conditions: According to the functional relationship of the microelement body and considering the action of centrifugal force at the same time, the energy equation in the cylindrical coordinate system is: where q r , q θ are the volume flow rates of the radial and circumferential unit-width cross-sections, respectively T is the oil film temperature; ρ is the density of the lubricating oil; c v is the specific heat capacity of the lubricating oil; the meanings of the remaining characters are the same as above; Take the following parameters to make Equation (6) dimensionless: Substitute into Equation (6) to obtain the dimensionless energy equation:

5. The numerical calculation method for the temperature field and boundary of a static pressure sector oil pad according to claim 4, wherein Use the finite difference method to discretize Equation (7). Different differential formats are used for different boundaries, and the corresponding differential formats at different positions are as follows: (1) Inside the oil sealing edge; The circumferential direction is the main flow direction of the fluid. Its differential format also needs to be judged according to the flow direction of the lubricating oil. The radial direction is the secondary flow direction of the lubricating oil and can directly adopt the central difference format with higher accuracy. The specific expressions are as follows: 1) When v θ ≥ 0 2) When v θ <0 (2) Edge of the oil chamber; The oil chamber temperature boundary condition is set as the supply oil temperature, and the dimensionless temperature value is set to 1. The expression is as follows: (3) Edge of the oil pad; The edge of the oil pad includes four edges AB, CD, BC, and DA in total. The temperature differential formats represented according to the flow velocity direction and different geometric positions are as follows: 1) Oil pad edge if ν θ ≥ 0 if ν θ <0 2) Oil pad edge if ν θ ≥ 0 if ν θ <0 3) Oil pad edge 4) Oil pad edge (4) Endpoint temperature value; The central difference format cannot be used in both directions at the endpoint position. To maintain sufficient calculation accuracy, use the three-node values within the boundary to represent the first-order partial derivative of temperature; 1) Endpoint A 2) Endpoint B 3) Endpoint C 4) Endpoint D Discretize Equation (7) through the above differential formats. To ensure the convergence stability of the equation, use the point-by-point under-relaxation iteration method to solve, and its expression is as follows: The temperature convergence criterion is: where α is the sub-relaxation iteration factor, which can be selected between 0 and 1; δ is the allowable relative error; is the node temperature value obtained by the k-th iteration; is the node temperature value obtained by the previous (i.e., k-1)-th iteration.

6. A numerical calculation method for the temperature field and boundary of a static pressure sector oil pad according to claim 4, characterized in that, Iterative update of lubricating oil viscosity; The viscosity of the lubricating oil changes significantly with temperature. Based on the obtained pressure distribution and temperature distribution of the oil film, the update calculation of the lubricating oil viscosity is carried out, and the Reynolds relationship is used to calculate the change of viscosity with temperature: In the formula, β is the viscosity-temperature coefficient; η0 is the initial viscosity of the lubricating oil; T0 is the initial temperature of the lubricating oil; The viscosity convergence judgment condition is: wherein, are the lubricating oil node viscosity values obtained from the k-th and (k-1)-th iterations respectively; δ is the relative error allowed for iteration.

7. A numerical calculation method for the temperature field and boundary of a static pressure sector oil pad according to claim 6, characterized in that The process of calculating the characteristic parameters of the sector oil pad is as follows: (1) Load capacity; The load capacity is the integral of the oil pad pressure over the entire bearing area. For the sector oil pad, there is the following expression: In the formula, θ2 is the angle of the sector oil pad; R1 and R4 are the inner and outer radii of the oil pad respectively; (2) Frictional force; The shear stress of the oil pad is obtained according to Newton's law of internal friction, and the frictional force is obtained by integrating over the entire area: where, F fr , F fy are the radial and circumferential components of the frictional force respectively; F f is the resultant frictional force.

Images