Electromechanical coupling dynamics modeling method for propulsion shafting

Abstract

The electromechanical coupling dynamics modeling method comprises the following steps: establishing a current vector control system model according to a permanent magnet synchronous motor structure parameter, a motor rotor displacement and a mechanical rotation angle; motor electromagnetic torque and motor unbalanced magnetic pulling force are calculated through the motor instantaneous inductance parameter and the instantaneous three-phase voltage; calculating and establishing a bearing-rotor dynamical model according to the size parameters of the propulsion shafting; and coupling the calculation equations of the motor electromagnetic torque and the motor unbalanced magnetic pulling force with the bearing-rotor dynamical model to establish a propulsion shafting electromechanical coupling dynamical model. By calculating the influence of the displacement of the permanent magnet synchronous motor rotor on the inductance and the air-gap magnetic field of the permanent magnet synchronous motor, the electromagnetic torque and the unbalanced magnetic pulling force are calculated more accurately, and the propulsion shafting dynamic response characteristic which is more practical is obtained through the propulsion shafting electromechanical coupling dynamic model.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater vehicles, and in particular to an electromechanical coupling dynamics modeling method for a propulsion shaft system. Background Art

[0002] The application of electric propulsion technology has greatly improved the speed range and diving depth of underwater vehicles, but at the same time, the propulsion shaft system of underwater vehicles has also changed from a simple mechanical system to a complex combination of electrical and mechanical subsystems. Nonlinear factors such as non-ideal power sources, electromagnetic torque fluctuations, and unbalanced magnetic pull may aggravate the bending-torsion coupling vibration of the propulsion shaft system, bringing new challenges to the low-vibration design of underwater vehicles.

[0003] The typical propulsion shaft system of an underwater vehicle is mainly composed of an electrical system, a permanent magnet synchronous motor and a mechanical system. The electrical and mechanical systems realize the coupling of the electromechanical system through the air gap magnetic field of the permanent magnet synchronous motor. The current research on the electromechanical coupling dynamics modeling of the propulsion shaft system mainly considers the unidirectional influence of the electrical system on the mechanical system, that is, it is achieved by applying electromagnetic torque and unbalanced magnetic pull to the mechanical system. However, the electrical and mechanical systems affect each other. The lateral vibration displacement of the permanent magnet synchronous motor rotor in the mechanical system will directly change the air gap distribution, thereby causing changes in the inductance and air gap magnetic field of the permanent magnet synchronous motor. This will lead to corresponding changes in the electromagnetic torque and unbalanced magnetic pull applied by the electrical system, and produce new excitation characteristics. The current electromechanical coupling dynamics modeling method for the propulsion shaft system is difficult to fully describe the multiple coupling relationships between the electrical and mechanical systems of the propulsion shaft system, and it is impossible to accurately obtain the dynamic response characteristics of the propulsion shaft system. Summary of the invention

[0004] An embodiment of the present invention provides an electromechanical coupling dynamics modeling method for a propulsion shaft system, which is used to solve the problem that the electromechanical coupling dynamics modeling method for a propulsion shaft system in the prior art is difficult to fully describe the multiple coupling relationships between the electrical and mechanical systems of the propulsion shaft system, and cannot accurately obtain the dynamic response characteristics of the propulsion shaft system.

[0005] On the one hand, an embodiment of the present invention provides a method for electromechanical coupling dynamics modeling of a propulsion shaft system, comprising: The instantaneous inductance parameters of the motor are calculated based on the structural parameters of the permanent magnet synchronous motor, the motor rotor displacement and the mechanical rotation angle; Establishing a current vector control system model according to the instantaneous inductance parameter of the motor and the instantaneous mechanical rotation angular velocity of the motor; Obtaining instantaneous three-phase voltage through the current vector control system model; The electromagnetic torque and the unbalanced magnetic pull of the motor are calculated according to the instantaneous inductance parameter of the motor and the instantaneous three-phase voltage; Calculate the bearing support force and propeller load torque based on the propulsion shafting size parameters; Establishing a bearing-rotor dynamics model according to the bearing support force and propeller load torque; The calculation equations of the electromagnetic torque of the motor, the unbalanced magnetic pull of the motor and the bearing-rotor dynamics model are coupled to establish an electromechanical coupling dynamics model of the propulsion shaft system.

[0006] In a possible implementation, the current vector control system model is established in a Simulink environment.

[0007] In a possible implementation, the calculation of the bearing support force and the propeller load torque according to the propulsion shaft system size parameters includes: The flexible shaft segment is equivalent to the Timoshenko beam element; The motor rotor and propeller are equivalent to rigid disk units; The bearing support force and propeller load torque are calculated based on the Timoshenko beam unit and the rigid disk unit.

[0008] In a possible implementation, the step of calculating the instantaneous inductance parameters of the motor according to the structural parameters of the permanent magnet synchronous motor and the motor rotor displacement and mechanical rotation angle includes: Calculate the magnetizing inductance of permanent magnet synchronous motor according to the motor stator winding form, motor stator winding parameters and improved winding function method; Calculate the leakage inductance of the permanent magnet synchronous motor based on the geometric dimensions of the motor stator slots; The magnetizing inductance of the permanent magnet synchronous motor and the leakage inductance of the permanent magnet synchronous motor are added to obtain the instantaneous inductance parameter of the motor.

[0009] In a possible implementation, the calculation of the magnetizing inductance of the permanent magnet synchronous motor according to the motor stator winding form, the motor stator winding parameters and the improved winding function method includes: According to the geometric relationship between the vibration displacement and eccentricity of the motor rotor, the Fourier series equation of the non-uniform inverted air gap between the motor stator and the motor rotor under the eccentric state of the motor rotor is established; Establishing a motor stator winding function equation according to the motor stator winding form and motor stator winding parameters; The magnetizing inductance of the permanent magnet synchronous motor is calculated according to the non-uniform inverse air gap Fourier series equation, the motor stator winding function equation and the improved winding function method.

[0010] In a possible implementation, calculating the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator slots includes: Calculate the slot leakage inductance of permanent magnet synchronous motor; Calculate the tooth tip leakage inductance of a permanent magnet synchronous motor.

[0011] In a possible implementation, the current vector control system model is composed of a speed loop PI controller, a current loop PI controller, a space vector pulse width modulation, and a three-phase inverter established according to a Simulink module library; The speed loop and current loop closed-loop control of the current vector control system model are implemented through a maximum torque current ratio control strategy.

[0012] In a possible implementation, calculating the electromagnetic torque of the motor includes: Calculate the permanent magnet flux linkage of permanent magnet synchronous motor according to permanent magnet material and geometric parameters; The electromagnetic torque of the motor is calculated according to the instantaneous inductance parameter of the motor, the permanent magnet flux and the instantaneous three-phase voltage.

[0013] In a possible implementation, calculating the unbalanced magnetic pull of the motor includes: Calculate the magnetomotive force of the stator winding and permanent magnet of the permanent magnet synchronous motor according to Ohm's law of magnetic circuit; Calculate the stress at different positions on the motor rotor surface according to the Maxwell tensor method; The unbalanced magnetic pull of the motor is calculated by integrating the stress tensor along the surface of the motor rotor.

[0014] The electromechanical coupling dynamics modeling method of a propulsion shaft system in the present invention has the following advantages: (1) By calculating the influence of the permanent magnet synchronous motor rotor displacement on the permanent magnet synchronous motor inductance and air gap magnetic field, the electromagnetic torque and unbalanced magnetic pull can be calculated more accurately.

[0015] (2) The propulsion shaft system electromechanical coupling dynamics model is used to obtain more realistic dynamic response characteristics of the propulsion shaft system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 A schematic flow chart of a method for electromechanical coupling dynamics modeling of a propulsion shaft system provided in an embodiment of the present application; Figure 2 A schematic diagram of the electromechanical coupling dynamics model of the propulsion shaft system provided in an embodiment of the present application; Figure 3A schematic diagram of the geometric relationship between the vibration displacement and eccentricity of the rotor of a permanent magnet synchronous motor of a propulsion shaft system provided in an embodiment of the present application; Figure 4 A schematic diagram of a double-layer short-pitch winding internal permanent magnet synchronous motor provided in an embodiment of the present application; Figure 5 A schematic diagram of the geometric dimensions of the tooth slots of a permanent magnet synchronous motor provided in an embodiment of the present application; Figure 6 A schematic diagram of the current operating range of a permanent magnet synchronous motor under a maximum torque to current ratio (MTPA) control strategy provided in an embodiment of the present application; Figure 7 A schematic diagram of the geometric dimensions and force conditions of the bearing-rotor dynamics model provided in an embodiment of the present application; Figure 8 A schematic diagram of force analysis of unbalanced mass of a rigid disk in a bearing-rotor dynamics model provided in an embodiment of the present application; Fig. 9 A schematic diagram comparing the self-inductance results of phase A obtained by the finite element method and the method of the present invention under the condition of no eccentricity provided in the embodiment of the present application; Fig.10 A schematic diagram comparing the AB mutual inductance results obtained by the finite element method and the method of the present invention under the condition of no eccentricity provided in the embodiment of the present application; Fig.11 A schematic diagram comparing the self-inductance results of phase A obtained by the finite element method and the method of the present invention when the static eccentricity SE=0.1 and the dynamic eccentricity DE=0.2 provided in the embodiment of the present application; Fig.12 A schematic diagram comparing the AB mutual inductance results obtained by the finite element method and the method of the present invention when the static eccentricity SE=0.1 and the dynamic eccentricity DE=0.2 provided in the embodiment of the present application; Fig.13 A schematic diagram comparing the electromagnetic torque time domain results obtained by the finite element method and the method of the present invention when the static eccentricity SE=0.1 and the dynamic eccentricity DE=0.2 provided in the embodiment of the present application; Fig.14 A schematic diagram comparing the electromagnetic torque frequency domain results obtained by the finite element method and the method of the present invention when the static eccentricity SE=0.1 and the dynamic eccentricity DE=0.2 provided in the embodiment of the present application. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Figure 1 A schematic flow chart of a method for electromechanical coupling dynamics modeling of a propulsion shaft system provided in an embodiment of the present invention; an embodiment of the present invention provides a method for electromechanical coupling dynamics modeling of a propulsion shaft system, comprising: The instantaneous inductance parameters of the motor are calculated based on the structural parameters of the permanent magnet synchronous motor, the motor rotor displacement and the mechanical rotation angle; Establishing a current vector control system model according to the instantaneous inductance parameter of the motor and the instantaneous mechanical rotation angular velocity of the motor; Obtaining instantaneous three-phase voltage through the current vector control system model; The electromagnetic torque and the unbalanced magnetic pull of the motor are calculated according to the instantaneous inductance parameter of the motor and the instantaneous three-phase voltage; Calculate the bearing support force and propeller load torque based on the propulsion shafting size parameters; Establishing a bearing-rotor dynamics model according to the bearing support force and propeller load torque; The calculation equations of the electromagnetic torque of the motor, the unbalanced magnetic pull of the motor and the bearing-rotor dynamics model are coupled to establish an electromechanical coupling dynamics model of the propulsion shaft system.

[0020] For example, Figure 2 As shown in FIG. 1 , the electromechanical coupling dynamics model of the propulsion shaft system provided in the embodiment of the present application is schematically shown. The model is composed of four submodules: the instantaneous inductance calculation method, the current vector control model, the permanent magnet synchronous motor model, and the bearing-rotor dynamics model. The electromechanical coupling dynamics modeling method of the propulsion shaft system in this embodiment is based on Figure 2 The model shown is taken as an example.

[0021] In a possible embodiment, calculating the bearing support force and propeller load torque according to the propulsion shaft system size parameters includes: The flexible shaft segment is equivalent to the Timoshenko beam element; The motor rotor and propeller are equivalent to rigid disk units; The bearing support force and propeller load torque are calculated based on the Timoshenko beam unit and the rigid disk unit.

[0022] The method of calculating the instantaneous inductance parameters of the motor according to the structural parameters of the permanent magnet synchronous motor, the motor rotor displacement and the mechanical rotation angle comprises: Calculate the magnetizing inductance of permanent magnet synchronous motor according to the motor stator winding form, motor stator winding parameters and improved winding function method; Calculate the leakage inductance of the permanent magnet synchronous motor based on the geometric dimensions of the motor stator slots; The magnetizing inductance of the permanent magnet synchronous motor and the leakage inductance of the permanent magnet synchronous motor are added to obtain the instantaneous inductance parameter of the motor.

[0023] The method of calculating the magnetizing inductance of the permanent magnet synchronous motor according to the motor stator winding form, the motor stator winding parameters and the improved winding function method comprises: According to the geometric relationship between the vibration displacement and eccentricity of the motor rotor, the Fourier series equation of the non-uniform inverted air gap between the motor stator and the motor rotor under the eccentric state of the motor rotor is established; Establishing a motor stator winding function equation according to the motor stator winding form and motor stator winding parameters; The magnetizing inductance of the permanent magnet synchronous motor is calculated according to the non-uniform inverse air gap Fourier series equation, the motor stator winding function equation and the improved winding function method.

[0024] For example, Figure 3 As shown, according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, the Fourier series equation of the non-uniform inverted air gap between the motor stator and the motor rotor under the eccentric state of the motor rotor is established, as shown in equations (1) to (3): (1) (2) (3) In the formula, g -1 ( φ , θ m ) is the Fourier series equation of the inverse air gap between the motor stator and the motor rotor under the non-eccentric state; φ is the angular position of the stator winding on the motor stator; θ m The motor rotor rotates mechanically by an angle; ρ m and γ m are the mechanical angles corresponding to the mixed eccentricity and the minimum air gap length position, respectively; p is the pole pair number; τ The polar angle T ig and polar arc angle T lm difference; g 0 is the initial air gap length; g h = g 0 + h m , h m is the thickness of the permanent magnet. k, j All are Fourier series; k max and jmax Fourier series k , j The maximum number of items. Figure 3 As shown in the figure O s and O r They are the symmetry centers of the motor stator and the motor rotor, respectively, and the mixed eccentricity ρ m By static eccentricity ρ s and dynamic eccentricity ρ d Combination is shown in formula (4): (4) Where u, v and θ m The motor rotor rotation center O w along X axis, Y The vibration displacement and rotation of the shaft Z The mechanical rotation angle of the shaft, such as Figure 3 As shown; e is the set eccentricity; γ 0 Static eccentricity ρ s The initial angle of .

[0025] According to Figure 4 The double-layer short-pitch winding internal permanent magnet synchronous motor is shown in the figure. The motor stator winding function equation is established as shown in formula (5): (5) In the formula, M A (φ), M B (φ) and M C (φ) are the function equations of the stator windings of the A-phase, B-phase and C-phase motors respectively; h is the harmonic number, h max To consider the maximum number of harmonics; q and n c are the number of stator slots per pole and per phase of the motor and the number of conductors in a single turn winding, respectively; k d,h and k p,h They are the harmonic distribution factor and pitch factor of the winding respectively.

[0026] According to the non-uniform inverse air gap Fourier series equations described in equations (1) to (4) and the motor stator winding function equation shown in equation (5), the magnetizing inductance of the permanent magnet synchronous motor is calculated based on the improved winding function method, as shown in equation (6): (6) In the formula, L m_wd1,wd2 is the magnetizing inductance between winding wd1 and winding wd2; μ 0 is the air gap permeability; r avg and l ef are respectively the average radius of the outer surface of the permanent magnet, the inner surface of the motor stator and the effective length of the motor stator; n wd1 ( φ )and M wd2 ( φ ) is the turns function equation of winding wd1 and the winding function equation of winding wd2.

[0027] In a possible embodiment, calculating the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator slots includes: Calculate the slot leakage inductance of permanent magnet synchronous motor; Calculate the tooth tip leakage inductance of a permanent magnet synchronous motor.

[0028] For example, according to Figure 5 The geometric dimensions of the motor stator slot are shown in Figure 1, and the permanent magnet synchronous motor slot leakage inductance is calculated as shown in formula (7): (7) In the formula, L sl,self and L sl,mutual They are the self-inductance part and the mutual inductance part in the slot leakage inductance respectively; a and b is an intermediate variable, defined as a = τ p - y 1 , b = q - a ; τ p and y 1 is the pole pitch and winding pitch; z c is the number of conductors in the slot; λ , λ 1 , λ2 and λ m All are intermediate quantities of magnetic permeability; b 0 , b s , h s and h hs are tooth slot size parameters, such as Figure 5 shown.

[0029] Calculate the permanent magnet synchronous motor tooth tip leakage inductance, as shown in formula (8): (8) In the formula, m ph is the number of motor phases; n slot is the number of stator slots of the motor; N ph is the number of series turns of a single-phase winding, defined as N ph = z c n slot / ( a p m ph ),in a p is the number of parallel branches; λ tt is the tooth tip leakage permeability, as shown in formula (9): (9) Specifically, the magnetizing inductance and leakage inductance of the permanent magnet synchronous motor are added to obtain the instantaneous inductance of the motor, as shown in formula (10): (10) In the formula, L s_wd1,wd1 is the synchronous inductance of winding wd1; L m_wd1,wd1 is the magnetizing inductance of winding wd1; L le_self is the leakage inductance of winding wd1, which is composed of the winding wd1 tooth leakage inductance L sl_self and tooth tip inductance L tt composition; L s_wd1,wd2 is the synchronous inductance between windings wd1 and wd2; L m_wd1,wd2 is the magnetizing inductance between windings wd1 and wd2; Lle_mutual is the leakage inductance between windings wd1 and wd2, L sl_mutual is the slot leakage inductance between windings wd1 and wd2.

[0030] In a possible embodiment, the current vector control system model is composed of a speed loop PI controller, a current loop PI controller, a space vector pulse width modulation, and a three-phase inverter established according to a Simulink module library; The speed loop and current loop closed-loop control of the current vector control system model are implemented through a maximum torque current ratio control strategy.

[0031] Exemplarily, according to the current vector control system model, the three-phase inverter module outputs the instantaneous three-phase voltage to the permanent magnet synchronous motor model. Figure 2 As shown, based on the Simulink module library, a speed loop PI controller, a current loop PI controller, a space vector pulse width modulation (SPVWM), and a three-phase inverter are established. The modules are connected as shown in the figure to form a current vector control system model.

[0032] The maximum torque current ratio (MTPA) control strategy is used to realize the closed-loop control of the speed loop and current loop of the current vector control system model. The maximum torque current ratio control strategy should satisfy the constrained optimization problem, as shown in formula (11): (11) In the formula, minimize is the objective function in the optimization function; subject to is the conditional function in the optimization function; I s is the resultant current in the dq rotating coordinate system; I d and I q are the currents along the d-axis and q-axis in the rotating coordinate system respectively; is the reference electromagnetic torque; p is the pole pair number; ψ d and ψ q They are d - q The magnetic flux along the d-axis and along the q-axis in the rotating coordinate system. Using the Lagrange multiplier method, and I d , I q The relationship is shown in formula (12): (12) ψ mis the permanent magnet flux; L d and L q They are d - q Inductance along the d-axis and along the q-axis in the rotating coordinate system; In addition, if Figure 6 As shown, the current I d , I q The operating range can only be within the voltage limit ellipse and current limit circle, as shown in formula (13): (13) In the formula, U d and U q for d - q The voltage along the d-axis and along the q-axis in the rotating coordinate system; U dc is the maximum value of the DC side voltage of the inverter; I lim It is the maximum allowable current value of permanent magnet synchronous motor.

[0033] In a possible embodiment, calculating the electromagnetic torque of the motor includes: Calculate the permanent magnet flux linkage of permanent magnet synchronous motor according to permanent magnet material and geometric parameters; The electromagnetic torque of the motor is calculated according to the instantaneous inductance parameter of the motor, the permanent magnet flux and the instantaneous three-phase voltage.

[0034] Calculating the unbalanced magnetic pull of the motor includes: Calculate the magnetomotive force of the stator winding and permanent magnet of the permanent magnet synchronous motor according to Ohm's law of magnetic circuit; Calculate the stress at different positions on the motor rotor surface according to the Maxwell tensor method; The unbalanced magnetic pull of the motor is calculated by integrating the stress tensor along the surface of the motor rotor.

[0035] Exemplarily, based on the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, a Fourier series equation for the non-uniform inverted air gap between the motor stator and the permanent magnet when the motor rotor is in an eccentric state is established.

[0036] Calculate the permanent magnet flux of the permanent magnet synchronous motor based on the permanent magnet material and geometric parameters; The electromagnetic torque of the permanent magnet synchronous motor is calculated according to the instantaneous inductance parameter of the motor, the instantaneous three-phase voltage and the permanent magnet flux.

[0037] Specifically, according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, the Fourier series equation of the non-uniform inverted air gap between the motor stator and the permanent magnet under the eccentricity state of the motor rotor is established, as shown in formula (14): (14) The permanent magnet flux linkage of the permanent magnet synchronous motor is calculated according to the permanent magnet material and geometric parameters, as shown in formula (15): (15) In the formula, ψ m,A , ψ m,B and ψ m,C They are the permanent magnet flux linkages of phase A, phase B and phase C respectively; B m is the radial magnetic flux density of the permanent magnet; is the Fourier series equation of the non-uniform inverse air gap between the motor stator and the permanent magnet when the motor rotor is eccentric; M A , M B , M C The motor stator winding function equations for phase A, phase B and phase C respectively; r r is the outer diameter of the permanent magnet synchronous motor rotor; H r is the magnetic field intensity of the permanent magnet, and its Fourier series form is shown in formula (16): (16) In the formula, m To consider the number of harmonics, m max is its maximum value; H amp is the coercive force, T lm is the pole arc angle, assuming that the demagnetization curve of the permanent magnet is a straight line, that is, the relative magnetic permeability is 1, then H amp = B r / μ 0 ,in B r For residual magnetism.

[0038] The electromagnetic torque of the permanent magnet synchronous motor is calculated according to the instantaneous inductance parameter of the motor, the instantaneous three-phase voltage and the permanent magnet flux, as shown in formula (17): (17) In the formula, ψd and ψ q They are d - q The magnetic flux along the d-axis and along the q-axis in the rotating coordinate system is expressed by equation (18): (18) In the formula, L d and L q is the inductance of the d-axis and q-axis. Through the classic Park transformation, the inductance L d , L q and permanent magnet flux ψ m As shown in formula (19) and formula (20): (19) (20) Where, T 3s / 2s and T 2s / 2r They are Clark and Park change matrices respectively; L AA , L BB and L CC They are the self-inductance of phase A, phase B and phase C respectively; L AB , L AC and L BC They are the mutual inductance between phase A and phase B, phase A and phase C, and phase B and phase C; L BA , L CA and L CB They are the mutual inductances between phase B and phase A, phase C and phase A, and phase C and phase B. As shown in formula (10); ψ m,A , ψ m,B and ψ m,C are the permanent magnet flux linkages of phase A, phase B and phase C, respectively, as shown in formula (15).

[0039] According to Ohm's law of magnetic circuit, calculate the magnetomotive force of the stator winding and permanent magnet of the permanent magnet synchronous motor; According to the Maxwell tensor method, the stress at different positions on the motor rotor surface is calculated.

[0040] The stress tensor is integrated along the motor rotor surface to calculate the unbalanced magnetic pull of the permanent magnet synchronous motor.

[0041] Specifically, according to Ohm's law of magnetic circuit, the magnetomotive force of the stator winding and permanent magnet of the permanent magnet synchronous motor is calculated as shown in formula (21): (twenty one) In the formula, F s ( φ , t ) and F r ( φ , t ) are the stator winding magnetomotive force and the permanent magnet magnetomotive force respectively; M A ( φ ), M B ( φ )and M C ( φ ) are the motor stator winding function equations of phase A, phase B and phase C, respectively, as shown in formula (5); I A ( t ), I B ( t )and I C ( t ) are the three-phase winding currents respectively; t To calculate the time.

[0042] According to the Maxwell tensor method, the stress at different positions on the surface of the motor rotor is calculated, as shown in formula (22): (twenty two) In the formula, B r is the radial magnetic flux density in the air gap.

[0043] The stress tensor is integrated along the surface of the motor rotor to calculate the unbalanced magnetic pull of the permanent magnet synchronous motor, as shown in formula (23): (twenty three) In the formula, F x UMP and F y UMP Along X Axis and Edge Y Unbalanced magnetic pull on the shaft.

[0044] like Figure 7The figure shows the geometric dimensions and force of the propulsion shaft system bearing-rotor dynamics model. The propulsion shaft system is divided into lengths by 13 nodes. l 1 to l 12 The propulsion shaft is supported by 4 deep groove ball bearings, and its support force is F b1 to F b4 The motor rotor and propeller are equivalent to two rigid disks with the same mass and moment of inertia.

[0045] According to the propulsion shaft system size parameters, the flexible shaft segment is equivalent to the Timoshenko beam unit, and the motor rotor and propeller are equivalent to the rigid disk unit. The bearing support force and propeller load torque are calculated, and the bearing-rotor dynamic model is established, as shown in formula (24): (twenty four) In the formula, 、M d and M u They are the shaft segment unit mass matrix, rigid disk mass matrix and unbalanced mass matrix respectively; and C b They are the shaft segment unit damping matrix and the bearing damping matrix respectively; and K d are the stiffness matrix of the shaft segment unit and the stiffness matrix of the rigid disk respectively; q is the node displacement vector, which contains 6 degrees of freedom q= [ u , v , w , θ x , θ y , θ z ] T ; and are the node velocity vector and acceleration vector respectively; T L is the propeller load torque; F bj For the j The support force vector of each bearing; F u is the unbalanced mass force vector.

[0046] The dynamic equation of the flexible shaft segment is established, as shown in equations (25) to (28): (25) (26) (27) (28) In the formula, and are the kinetic energy and strain energy of the shaft segment respectively; , and are the axis segment displacement, velocity and acceleration vectors; ρ , and l e are the material density, cross-sectional area and length of the shaft segment respectively; , and For the axis segment x axis, y Axis and z The speed of the axis; , and For the shaft segment x axis, y Axis and z Angular velocity of the axis; , and For the axis segment x axis, y Axis and z Axial stress; , and For the axis segment x axis, y Axis and z Strain of the shaft; V is the unit volume of the shaft segment; and I e Respectively around z Axial polar moment and x Second moment of shaft diameter; m c and n c are the mass matrix damping coefficient and the stiffness matrix damping coefficient; dz is the small change in the length of the shaft segment, d is a differential operator, dt It's about time t The differential of dv is a volume element.

[0047] The dynamic equation of the rigid disk is established, as shown in equation (29) to equation (30): (29) (30) In the formula, is the kinetic energy of the rigid disk; q d , and are the displacement, velocity and acceleration vectors of the rigid disk, which are equal to the displacement, velocity and acceleration vectors of the corresponding axis nodes; m d is the mass of the rigid disk; , and Rigid disc edge x axis, y Axis and z The speed of the axis; Rigid coil z Angular velocity of the axis; For around z Axipolar second moment, I d Rigid coil z Axipolar second moment.

[0048] like Figure 8 As shown, the unbalanced mass dynamic equation is established, which is shown in equation (31) to equation (32): (31) In the formula, Q d is the unbalanced force vector of the rigid disk; , and Rigid disc edge x axis, y Axis and z Unbalanced forces on the shaft; , and Rigid coil x axis, y Axis and z Unbalanced moment of the shaft; and Rigid coil Z Angular displacement and angular acceleration of the axis; Rigid coil z Angular velocity of the axis; (32) Calculate the bearing support force, as shown in equation (33) to equation (34): (33) In the formula, F b is the bearing support force vector; and The bearing support force is X Axis and Y The weight of the axis; N b is the number of bearing rolling elements; φ jFor bearing j The rolling elements are relative to X The angle of the axis; Q j For bearing j The Hertz contact load between the rolling element and the raceway is expressed by formula (34): (34) In the formula, K ci and K co are the Hertz contact stiffness between the bearing rolling element and the inner raceway, and between the rolling element and the outer raceway; χ j and δ j are the contact state determination coefficient and j Each rolling element deforms in contact with the raceway; D aj and D rj The relative distances between the centers of curvature of the inner and outer ring raceways of the bearing in the axial and radial directions; r i and r o are the curvature radii of the inner and outer raceways of the bearing; d b is the rolling element diameter.

[0049] Calculate the propeller load torque as shown in formula (35): (35) In the formula, is the load torque fluctuation percentage; K Q and ρ w are propeller torque coefficient and liquid density in open water condition respectively; θ prop , n prop and D prop are propeller rotation angle, rotation speed and diameter respectively; n blade is the number of propeller blades.

[0050] Specifically, the calculation equations of the electromagnetic torque and unbalanced magnetic pull of the permanent magnet synchronous motor and the bearing-rotor dynamics model are coupled to complete the establishment of the electromechanical coupling dynamics model of the propulsion shaft system, as shown in formula (36): (36) Figures 9 to 12Schematic diagram comparing the results of the self-inductance of phase A and the mutual inductance of phase AB obtained by the finite element method and the method of the present invention provided in the embodiment of the present application, wherein Fig. 9 and Fig.10 To ensure that the shaft system has no eccentricity, Fig.11 and Fig.12 Considering the case of static eccentricity SE=0.1 and dynamic eccentricity DE=0.2. The results show that due to the relative rotation between the stator and the rotor of the permanent magnet synchronous motor, the air gap changes continuously, causing the motor inductance to fluctuate periodically. The inductance curves obtained by the finite element method and the method of the present invention have the same periodicity, and the inductance amplitude error is within 5%, which can verify the correctness of the instantaneous inductance calculation method of the present invention to a certain extent.

[0051] also, Fig.11 and Fig.12 The inductance results considering the eccentricity are shown in Figure 2. Fig. 9 and Fig.10 The inductance results are different when the eccentricity is not considered, and the inductance curve shows additional periodic fluctuations. This proves that the eccentricity caused by the vibration displacement of the motor rotor does affect the inductance of the permanent magnet synchronous motor.

[0052] Figure 13 to Figure 14 A schematic diagram for comparing the time domain and frequency domain results of electromagnetic torque obtained by the finite element method and the method of the present invention when considering the static eccentricity SE=0.1 and the dynamic eccentricity DE=0.2 provided in the embodiment of the present application. Fig.13 It is shown that the amplitudes of the electromagnetic torque time domain waveforms obtained by the finite element method and the method of the present invention are close, and the amplitude error is within 5%; Fig.14 It shows that the characteristic frequencies of the electromagnetic torque spectrum obtained by the finite element method and the method of the present invention are consistent. The electromagnetic torque results can further verify the accuracy of the method of the present invention.

[0053] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0054] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for electromechanical coupling dynamics modeling of a propulsion shaft system, characterized in that: include: The instantaneous inductance parameters of the motor are obtained by calculation according to the structural parameters of the permanent magnet synchronous motor, the motor rotor displacement and the mechanical rotation angle; Establishing a current vector control system model according to the instantaneous inductance parameter of the motor and the instantaneous mechanical rotation angular velocity of the motor; Obtaining instantaneous three-phase voltage through the current vector control system model; The electromagnetic torque and the unbalanced magnetic pull of the motor are calculated according to the instantaneous inductance parameter of the motor and the instantaneous three-phase voltage; Calculate the bearing support force and propeller load torque based on the propulsion shafting size parameters; Establishing a bearing-rotor dynamics model according to the bearing support force and propeller load torque; The calculation equations of the electromagnetic torque and unbalanced magnetic pull of the motor and the bearing-rotor dynamics model are coupled to establish an electromechanical coupling dynamics model of the propulsion shaft system.

2. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 1 is characterized in that: The current vector control system model is established in the Simulink environment.

3. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 1 is characterized in that: The calculation of the bearing support force and propeller load torque according to the propulsion shaft system size parameters includes: The flexible shaft segment is equivalent to the Timoshenko beam element; The motor rotor and propeller are equivalent to rigid disk units; The bearing support force and propeller load torque are calculated based on the Timoshenko beam unit and the rigid disk unit.

4. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 1 is characterized in that: The method of calculating the instantaneous inductance parameters of the motor according to the structural parameters of the permanent magnet synchronous motor, the motor rotor displacement and the mechanical rotation angle comprises: Calculate the magnetizing inductance of permanent magnet synchronous motor according to the motor stator winding form, motor stator winding parameters and improved winding function method; Calculate the leakage inductance of the permanent magnet synchronous motor based on the geometric dimensions of the motor stator slots; The magnetizing inductance of the permanent magnet synchronous motor and the leakage inductance of the permanent magnet synchronous motor are added to obtain the instantaneous inductance parameter of the motor.

5. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 4 is characterized in that: The method of calculating the magnetizing inductance of the permanent magnet synchronous motor according to the motor stator winding form, the motor stator winding parameters and the improved winding function method comprises: According to the geometric relationship between the vibration displacement and eccentricity of the motor rotor, the Fourier series equation of the non-uniform inverted air gap between the motor stator and the motor rotor under the eccentric state of the motor rotor is established; Establishing a motor stator winding function equation according to the motor stator winding form and motor stator winding parameters; The magnetizing inductance of the permanent magnet synchronous motor is calculated according to the non-uniform inverse air gap Fourier series equation, the motor stator winding function equation and the improved winding function method.

6. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 4 is characterized in that: Calculating the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator slots comprises: Calculate the slot leakage inductance of permanent magnet synchronous motor; Calculate the tooth tip leakage inductance of a permanent magnet synchronous motor.

7. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 1 is characterized in that: The current vector control system model is composed of a speed loop PI controller, a current loop PI controller, a space vector pulse width modulation, and a three-phase inverter established according to the Simulink module library; The speed loop and current loop closed-loop control of the current vector control system model are implemented through a maximum torque current ratio control strategy.

8. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 5, characterized in that: Calculating the electromagnetic torque of the motor includes: Calculate the permanent magnet flux linkage of permanent magnet synchronous motor according to permanent magnet material and geometric parameters; The electromagnetic torque of the motor is calculated according to the instantaneous inductance parameter of the motor, the permanent magnet flux and the instantaneous three-phase voltage.

9. The electromechanical coupling dynamics modeling method of a propulsion shaft system according to claim 1, characterized in that: Calculating the unbalanced magnetic pull of the motor includes: Calculate the magnetomotive force of the stator winding and permanent magnet of the permanent magnet synchronous motor according to Ohm's law of magnetic circuit; Calculate the stress at different positions on the motor rotor surface according to the Maxwell tensor method; The unbalanced magnetic pull of the motor is calculated by integrating the stress tensor along the surface of the motor rotor.

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