An electromechanical coupling dynamics modeling method for a propulsion shafting

Abstract

The present invention discloses a method for electromechanical coupling dynamics modeling of a propulsion shafting system, comprising: establishing a current vector control system model according to the structural parameters of a permanent magnet synchronous motor, the displacement of the motor rotor, and the mechanical rotation angle; calculating the electromagnetic torque and the unbalanced magnetic pull of the motor through the instantaneous inductance parameters and the instantaneous three-phase voltage of the motor; establishing a bearing-rotor dynamics model according to the size parameters of the propulsion shafting system; and coupling the calculation equations of the electromagnetic torque and the unbalanced magnetic pull of the motor and the bearing-rotor dynamics model to establish an electromechanical coupling dynamics model of the propulsion shafting system. By calculating the influence of the displacement of the rotor of the permanent magnet synchronous motor on the inductance and the air-gap magnetic field of the permanent magnet synchronous motor, the present invention calculates the electromagnetic torque and the unbalanced magnetic pull more accurately, and obtains more realistic dynamic response characteristics of the propulsion shafting system through the electromechanical coupling dynamics model of the propulsion shafting system.

Description

Technical Field

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

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

[0003] A typical underwater vehicle propulsion shafting system mainly consists of an electrical system, a permanent magnet synchronous motor, and a mechanical system. The electrical and mechanical systems are coupled through the air-gap magnetic field of the permanent magnet synchronous motor. Currently, the research on electromechanical coupling dynamics modeling of the propulsion shafting system mainly considers the unidirectional influence of the electrical system on the mechanical system, that is, by applying the electromagnetic torque and unbalanced magnetic pull force to the mechanical system. However, the electrical and mechanical systems influence each other. The lateral vibration displacement of the rotor of the permanent magnet synchronous motor 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. Furthermore, it will cause corresponding changes in the electromagnetic torque and unbalanced magnetic pull force applied by the electrical system, and generate new excitation characteristics. The current electromechanical coupling dynamics modeling method for the propulsion shafting system is difficult to fully describe the multiple coupling relationships between the electrical and mechanical systems of the propulsion shafting system and cannot accurately obtain the dynamic response characteristics of the propulsion shafting system. Summary of the Invention

[0004] Embodiments of the present invention provide a method for electromechanical coupling dynamics modeling of a propulsion shafting system to solve the problem that the existing electromechanical coupling dynamics modeling method for the propulsion shafting system is difficult to fully describe the multiple coupling relationships between the electrical and mechanical systems of the propulsion shafting system and cannot accurately obtain the dynamic response characteristics of the propulsion shafting system.

[0005] On the one hand, embodiments of the present invention provide a method for electromechanical coupling dynamics modeling of a propulsion shafting system, including:

[0006] Calculating the instantaneous inductance parameters of the motor according to the structural parameters of the permanent magnet synchronous motor, the displacement of the motor rotor, and the mechanical rotation angle;

[0007] Establishing a current vector control system model according to the instantaneous inductance parameters of the motor and the instantaneous mechanical rotation angular velocity of the motor;

[0008] Obtaining the instantaneous three-phase voltage through the current vector control system model;

[0009] The electromagnetic torque and unbalanced magnetic pull of the motor are calculated based on the instantaneous inductance parameters of the motor and the instantaneous three-phase voltage;

[0010] The bearing support force and propeller load torque are calculated according to the dimensions of the propulsion shafting;

[0011] A bearing-rotor dynamic model is established based on the bearing support force and propeller load torque;

[0012] The electromechanical coupling dynamic model of the propulsion shafting is established by coupling the calculation equations of the electromagnetic torque and unbalanced magnetic pull of the motor and the bearing-rotor dynamic model.

[0013] In a possible implementation, the current vector control system model is established in the Simulink environment.

[0014] In a possible implementation, the calculation of the bearing support force and propeller load torque according to the dimensions of the propulsion shafting includes:

[0015] The flexible shaft segment is equivalent to a Timoshenko beam element;

[0016] The motor rotor and propeller are equivalent to rigid disk elements;

[0017] The bearing support force and propeller load torque are calculated based on the Timoshenko beam element and the rigid disk element.

[0018] In a possible implementation, the calculation of the instantaneous inductance parameters of the motor obtained according to the structural parameters of the permanent magnet synchronous motor, the rotor displacement and the mechanical rotation angle of the motor includes:

[0019] The magnetization inductance of the permanent magnet synchronous motor is calculated according to the form of the motor stator winding, the parameters of the motor stator winding and the improved winding function method;

[0020] The leakage inductance of the permanent magnet synchronous motor is calculated according to the geometric dimensions of the motor stator teeth and slots;

[0021] The magnetization inductance of the permanent magnet synchronous motor and the leakage inductance of the permanent magnet synchronous motor are added to obtain the instantaneous inductance parameters of the motor.

[0022] In a possible implementation, the calculation of the magnetization inductance of the permanent magnet synchronous motor according to the form of the motor stator winding, the parameters of the motor stator winding and the improved winding function method includes:

[0023] Based on the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, a non-uniform inverted air-gap Fourier series equation between the motor stator and the motor rotor in the eccentric state of the motor rotor is established;

[0024] According to the form of the motor stator winding and the parameters of the motor stator winding, a motor stator winding function equation is established;

[0025] Calculate the magnetization inductance of the permanent magnet synchronous motor according to the non-uniform inverted air-gap Fourier series equation, the motor stator winding function equation, and the improved winding function method.

[0026] In a possible implementation, the calculating the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator teeth and slots includes:

[0027] Calculate the tooth and slot leakage inductance of the permanent magnet synchronous motor;

[0028] Calculate the tooth tip leakage inductance of the permanent magnet synchronous motor.

[0029] In a possible implementation, the current vector control system model is composed of a speed loop PI controller, a current loop PI controller, space vector pulse width modulation, and a three-phase inverter established according to the Simulink module library;

[0030] The closed-loop control of the speed loop and the current loop of the current vector control system model is realized by the maximum torque current ratio control strategy.

[0031] In a possible implementation, calculating the electromagnetic torque of the motor includes:

[0032] Calculate the permanent magnet flux linkage of the permanent magnet synchronous motor according to the permanent magnet material and geometric parameters;

[0033] Calculate the electromagnetic torque of the motor according to the instantaneous inductance parameters of the motor, the permanent magnet flux linkage, and the instantaneous three-phase voltage.

[0034] In a possible implementation, calculating the unbalanced magnetic pull of the motor includes:

[0035] Calculate the magnetomotive force of the stator winding and the permanent magnet of the permanent magnet synchronous motor according to Ohm's law of the magnetic circuit;

[0036] Calculate the stress on different positions of the motor rotor surface according to the Maxwell tensor method;

[0037] Integrate the stress tensor along the motor rotor surface to calculate the unbalanced magnetic pull of the motor.

[0038] An electromechanical coupling dynamics modeling method for a propulsion shafting in the present invention has the following advantages:

[0039] (1) By calculating the influence of the displacement of the permanent magnet synchronous motor rotor on the inductance and air-gap magnetic field of the permanent magnet synchronous motor, the electromagnetic torque and unbalanced magnetic pull are calculated more accurately.

[0040] (2) Obtain more realistic dynamic response characteristics of the propulsion shafting through the electromechanical coupling dynamics model of the propulsion shafting. Description of the Drawings

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0042] Figure 1 It is a schematic flow chart of a method for electromechanical coupling dynamics modeling of a propulsion shafting provided by an embodiment of the present application;

[0043] Figure 2 It is a schematic diagram of an electromechanical coupling dynamics model of a propulsion shafting provided by an embodiment of the present application;

[0044] Figure 3 It is a schematic diagram of the geometric relationship between the rotor vibration displacement and the eccentricity of a permanent magnet synchronous motor of a propulsion shafting provided by an embodiment of the present application;

[0045] Figure 4 It is a schematic diagram of a double-layer short-pitch winding interior permanent magnet synchronous motor provided by an embodiment of the present application;

[0046] Figure 5 It is a schematic diagram of the tooth-slot geometric dimensions of a permanent magnet synchronous motor provided by an embodiment of the present application;

[0047] Figure 6 It is a schematic diagram of the current operating range of a permanent magnet synchronous motor under the maximum torque per ampere (MTPA) control strategy provided by an embodiment of the present application;

[0048] Figure 7 It is a schematic diagram of the geometric dimensions and force conditions of a bearing-rotor dynamics model provided by an embodiment of the present application;

[0049] Figure 8 It is a schematic diagram of the force analysis of the unbalanced mass of a rigid disk in a bearing-rotor dynamics model provided by an embodiment of the present application;

[0050] Figure 9 It is a schematic diagram of the comparison of 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 by an embodiment of the present application;

[0051] Figure 10 It is a schematic diagram of the comparison of the mutual inductance results of phases AB obtained by the finite element method and the method of the present invention under the condition of no eccentricity provided by an embodiment of the present application;

[0052] Figure 11 It is a schematic diagram of the comparison of the self-inductance results of phase A obtained by the finite element method and the method of the present invention under the condition of static eccentricity SE = 0.1 and dynamic eccentricity DE = 0.2 provided by an embodiment of the present application;

[0053] Figure 12 Schematic diagram for comparing the mutual inductance results of AB obtained by the finite element method and the method of the present invention under the condition that the static eccentricity SE = 0.1 and the dynamic eccentricity DE = 0.2 provided by the embodiments of the present application;

[0054] Figure 13 Schematic diagram for comparing the time-domain results of the electromagnetic torque obtained by the finite element method and the method of the present invention under the condition that the static eccentricity SE = 0.1 and the dynamic eccentricity DE = 0.2 provided by the embodiments of the present application;

[0055] Figure 14 Schematic diagram for comparing the frequency-domain results of the electromagnetic torque obtained by the finite element method and the method of the present invention under the condition that the static eccentricity SE = 0.1 and the dynamic eccentricity DE = 0.2 provided by the embodiments of the present application. Detailed implementation manners

[0056] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0057] Figure 1 Schematic diagram of the process of an electromechanical coupling dynamics modeling method for a propulsion shafting provided by the embodiments of the present invention; The embodiments of the present invention provide an electromechanical coupling dynamics modeling method for a propulsion shafting, including:

[0058] Calculating and obtaining the instantaneous inductance parameters of the motor according to the structural parameters of the permanent magnet synchronous motor, the displacement of the motor rotor, and the mechanical rotation angle;

[0059] Establishing a current vector control system model according to the instantaneous inductance parameters of the motor and the instantaneous mechanical rotation angular velocity of the motor;

[0060] Obtaining the instantaneous three-phase voltage through the current vector control system model;

[0061] Calculating and obtaining the electromagnetic torque and the unbalanced magnetic pull force of the motor according to the instantaneous inductance parameters of the motor and the instantaneous three-phase voltage;

[0062] Calculating the bearing support force and the propeller load torque according to the dimensions of the propulsion shafting;

[0063] Establishing a bearing-rotor dynamics model according to the bearing support force and the propeller load torque;

[0064] Couple the calculation equations of the electromagnetic torque of the motor and the unbalanced magnetic pull of the motor and the bearing-rotor dynamic model to establish the electromechanical coupling dynamic model of the propulsion shafting.

[0065] Exemplarily, as Figure 2 shown, the schematic diagram of the electromechanical coupling dynamic model of the propulsion shafting provided by the embodiment of the present application, this model is composed of 4 sub-modules: the instantaneous inductance calculation method, the current vector control model, the permanent magnet synchronous motor model, and the bearing-rotor dynamic model. The electromechanical coupling dynamic modeling method of this embodiment is all based on Figure 2 the model shown as an example.

[0066] In a possible embodiment, the calculating the bearing support force and the propeller load torque according to the size parameters of the propulsion shafting includes:

[0067] Equivalent the flexible shaft section to a Timoshenko beam element;

[0068] Equivalent the motor rotor and the propeller to rigid disk elements;

[0069] Calculate the bearing support force and the propeller load torque according to the Timoshenko beam element and the rigid disk element.

[0070] The obtaining the instantaneous inductance parameter of the motor according to the structure parameters of the permanent magnet synchronous motor, the displacement of the motor rotor and the mechanical rotation angle includes:

[0071] Calculate the magnetization inductance of the permanent magnet synchronous motor according to the form of the motor stator winding, the parameters of the motor stator winding and the improved winding function method;

[0072] Calculate the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator teeth and slots;

[0073] Add the magnetization inductance of the permanent magnet synchronous motor and the leakage inductance of the permanent magnet synchronous motor to obtain the instantaneous inductance parameter of the motor.

[0074] The calculating the magnetization inductance of the permanent magnet synchronous motor according to the form of the motor stator winding, the parameters of the motor stator winding and the improved winding function method includes:

[0075] Establish a non-uniform inverted air-gap Fourier series equation between the motor stator and the motor rotor under the eccentric state of the motor rotor according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity;

[0076] Establish the motor stator winding function equation according to the form of the motor stator winding and the parameters of the motor stator winding;

[0077] Calculate the magnetization inductance of the permanent magnet synchronous motor according to the non-uniform inverted air-gap Fourier series equation, the motor stator winding function equation and the improved winding function method.

[0078] Exemplarily, as Figure 3 shown, according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, a non-uniform inverse air-gap Fourier series equation 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):

[0079] (1)

[0080] (2)

[0081] (3)

[0082] In the formula, g -1 ( φ , θ m ) is the inverse air-gap Fourier series equation 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 is the rotational mechanical angle of the motor rotor; ρ m and γ m are the mechanical angles corresponding to the mixed eccentricity and the position of the minimum air-gap length, respectively; p is the number of pole pairs; τ is the pole pitch angle T ig and the pole 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 are all Fourier series; k max and j max are the maximum number of terms of the Fourier series k 、 j respectively. As Figure 3 shown, in the figure O s and O r are the symmetry centers of the motor stator and the motor rotor respectively, and the mixed eccentricity ρ m is composed of the static eccentricity ρ s and the dynamic eccentricity ρ dCombined as shown in Equation (4):

[0083] (4)

[0084] where u, v, and θ m are the vibration displacements of the center O of the motor rotor along the w axis, the X axis, and the mechanical rotation angle about the Y axis, as shown in Z ; Figure 3 shown; e is the set eccentricity; γ 0 is the static eccentricity ρ s initial angle.

[0085] Based on the double-layer short-pitch winding interior permanent magnet synchronous motor shown in Figure 4 , the function equation of the motor stator winding is established as shown in Equation (5):

[0086] (5)

[0087] where M A (φ), M B (φ), and M C (φ) are the function equations of the motor stator windings of phase A, phase B, and phase C, respectively; h is the harmonic number, h max is the considered maximum harmonic number; q and n c are the number of stator slots per pole per phase and the number of conductors per turn of the winding, respectively; k d,h and k p,h are the harmonic distribution factor and pitch factor of the winding, respectively.

[0088] Based on the non-uniform inverted air-gap Fourier series equation described by Equations (1) to (4) and the function equation of the motor stator winding shown in Equation (5), the magnetization inductance of the permanent magnet synchronous motor is calculated based on the improved winding function method, as shown in Equation (6):

[0089] (6)

[0090] where L m_wd1,wd2 is the magnetization inductance between winding wd1 and winding wd2; μ 0 is the air-gap magnetic permeability; r avg and lef are the average radius of the outer surface of the permanent magnet and the inner surface of the motor stator, and the effective length of the motor stator, respectively; n wd1 ( φ ) and M wd2 ( φ ) are the turn function equation of winding wd1 and the winding function equation of winding wd2.

[0091] In a possible embodiment, the calculation of the leakage inductance of the permanent magnet synchronous motor according to the geometric dimensions of the motor stator slots includes:

[0092] Calculating the slot leakage inductance of the permanent magnet synchronous motor;

[0093] Calculating the tooth tip leakage inductance of the permanent magnet synchronous motor.

[0094] Exemplarily, according to the geometric dimensions of the motor stator slots as shown in Figure 5 , the slot leakage inductance of the permanent magnet synchronous motor is calculated as shown in Equation (7):

[0095] (7)

[0096] In the formula, L sl,self and L sl,mutual are the self-inductance part and the mutual-inductance part in the slot leakage inductance, respectively; a and b are intermediate variables, defined as a = τ p - y 1, b = q - a ; τ p and y 1 are the pole pitch and the winding pitch; z c is the number of conductors in the slot; λ , λ 1, λ 2 and λ m are all magnetic permeability intermediate quantities; b 0, b s , h s and h hs are all slot size parameters, as shown in Figure 5 .

[0097] The tooth tip leakage inductance of the permanent magnet synchronous motor is calculated as shown in Equation (8):

[0098] (8)

[0099] Wherein, m ph is the number of phases of the motor; n slot is the number of stator slots of the motor; N ph is the number of turns in series of the single-phase winding, defined as N ph = z c n slot / ( a p m ph ), where a p is the number of parallel branches; λ tt is the magnetic permeability of tooth tip leakage, shown by Equation (9):

[0100] (9)

[0101] Specifically, adding the magnetizing inductance and leakage inductance of the permanent magnet synchronous motor to obtain the instantaneous inductance of the motor, shown by Equation (10):

[0102] (10)

[0103] Wherein, 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 consists of the tooth-slot leakage inductance L sl_self and the tooth tip inductance L tt ; 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; L le_mutual is the leakage inductance between windings wd1 and wd2, L sl_mutual is the tooth-slot leakage inductance between windings wd1 and wd2.

[0104] In a possible embodiment, the current vector control system model is composed of a speed loop PI controller, a current loop PI controller, space vector pulse width modulation, and a three-phase inverter established according to the Simulink module library;

[0105] The closed-loop control of the speed loop and the current loop of the current vector control system model is achieved through the maximum torque per ampere control strategy.

[0106] Exemplarily, according to the current vector control system model, the instantaneous three-phase voltage is output from the three-phase inverter module to the permanent magnet synchronous motor model. As Figure 2 shown, a speed loop PI controller, a current loop PI controller, space vector pulse width modulation (SPVWM), and a three-phase inverter are established based on the Simulink module library, and each module is connected as shown to form a current vector control system model.

[0107] The closed-loop control of the speed loop and the current loop of the current vector control system model is achieved by adopting the maximum torque per ampere (MTPA) control strategy, and the maximum torque per ampere control strategy should satisfy the constrained optimization problem, as shown in Equation (11):

[0108] (11)

[0109] 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 synthesized current in the d-q rotating coordinate system; I d and I q are the currents along the d-axis and the q-axis in the rotating coordinate system, respectively; is the reference electromagnetic torque; p is the number of pole pairs; ψ d and ψ q are respectively d - q the magnetic fluxes along the d-axis and the q-axis in the rotating coordinate system. Using the Lagrange multiplier method, and I d , I q The relationship between them is shown in Equation (12):

[0110] (12)

[0111] ψ m is the permanent magnet flux; L dand L q are respectively d - q the inductances along the d-axis and the q-axis in the rotating coordinate system;

[0112] In addition, as Figure 6 shown, the current I d , I q can only operate within the voltage limit ellipse and the current limit circle, as shown in Equation (13):

[0113] (13)

[0114] wherein, U d and U q are d - q the voltages along the d-axis and the q-axis in the rotating coordinate system; U dc is the maximum value of the DC-side voltage of the inverter; I lim is the maximum allowable current value of the permanent magnet synchronous motor.

[0115] In one possible embodiment, calculating the electromagnetic torque of the motor includes:

[0116] calculating the permanent magnet flux linkage of the permanent magnet synchronous motor according to the permanent magnet material and geometric parameters;

[0117] calculating the electromagnetic torque of the motor according to the instantaneous inductance parameters of the motor, the permanent magnet flux linkage, and the instantaneous three-phase voltages.

[0118] Calculating the unbalanced magnetic pull of the motor includes:

[0119] calculating the magnetomotive forces of the stator winding and the permanent magnet of the permanent magnet synchronous motor according to Ohm's law of magnetic circuits;

[0120] calculating the stresses on different positions of the motor rotor surface according to the Maxwell tensor method;

[0121] integrating the stress tensor along the motor rotor surface to calculate the unbalanced magnetic pull of the motor.

[0122] Exemplarily, according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, a non-uniform inverted air-gap Fourier series equation between the motor stator and the permanent magnet is established under the eccentric state of the motor rotor.

[0123] Calculating the permanent magnet flux linkage of the permanent magnet synchronous motor according to the permanent magnet material and geometric parameters;

[0124] Calculate the electromagnetic torque of the permanent magnet synchronous motor according to the instantaneous inductance parameters of the motor, the instantaneous three-phase voltage, and the permanent magnet flux linkage.

[0125] Specifically, according to the geometric relationship between the vibration displacement of the motor rotor and the eccentricity, establish the non-uniform inverted air-gap Fourier series equation between the motor stator and the permanent magnet under the eccentric state of the motor rotor, as shown in Equation (14):

[0126] (14)

[0127] Calculate the permanent magnet flux linkage of the permanent magnet synchronous motor according to the permanent magnet material and geometric parameters, as shown in Equation (15):

[0128] (15)

[0129] In the formula, 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; B m is the radial magnetic flux density of the permanent magnet; is the non-uniform inverted air-gap Fourier series equation between the motor stator and the permanent magnet under the eccentric state of the motor rotor; M A , M B , M C are the motor stator winding function equations of phase A, phase B, and phase C respectively; r r is the outer diameter of the rotor of the permanent magnet synchronous motor; H r is the magnetic field strength of the permanent magnet, and its Fourier series form is shown in Equation (16):

[0130] (16)

[0131] In the formula, m is to consider the number of harmonics, m max is its maximum value; H amp is the coercivity, T lm is the pole arc angle. Assuming that the demagnetization curve of the permanent magnet is a straight line, that is, the relative permeability is 1, then H amp = B r / μ 0, where B r is the remanence.

[0132] The electromagnetic torque of the permanent magnet synchronous motor is calculated based on the instantaneous inductance parameter of the motor, the instantaneous three-phase voltage, and the permanent magnet flux linkage, as shown in Equation (17):

[0133] (17)

[0134] In the formula, ψ d and ψ q are respectively d - q the flux linkages along the d-axis and the q-axis in the rotating coordinate system, as shown in Equation (18):

[0135] (18)

[0136] In the formula, L d and L q are the inductances of the d-axis and the q-axis. Through the classical Park transformation, the inductances L d 、 L q and the permanent magnet flux linkage ψ m are shown in Equations (19) and (20):

[0137] (19)

[0138] (20)

[0139] In the formula, T 3s / 2s and T 2s / 2r are the Clark and Park transformation matrices respectively; L AA , L BB and L CC are the self-inductances of phase A, phase B, and phase C respectively; L AB , L AC and L BC are the mutual inductances between phase A and phase B, phase A and phase C, and phase B and phase C respectively; L BA , L CA and L CB are the mutual inductances between phase B and phase A, phase C and phase A, and phase C and phase B respectively. As shown in Equation (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 Equation (15).

[0140] According to Ohm's law of magnetic circuits, calculate the magnetomotive forces of the stator winding and the permanent magnet of the permanent magnet synchronous motor;

[0141] According to Maxwell's tensor method, calculate the stress on different positions of the motor rotor surface.

[0142] Integrate the stress tensor along the motor rotor surface to calculate the unbalanced magnetic pull of the permanent magnet synchronous motor.

[0143] Specifically, the calculation of the magnetomotive forces of the stator winding and the permanent magnet of the permanent magnet synchronous motor according to Ohm's law of magnetic circuits is shown in Equation (21):

[0144] (21)

[0145] In the formula, F s ( φ , t ) and F r ( φ , t ) are the magnetomotive forces of the stator winding and the permanent magnet, respectively; M A ( φ ), M B ( φ ) and M C ( φ ) are the function equations of the motor stator windings of phase A, phase B, and phase C, respectively, as shown in Equation (5); I A ( t ), I B ( t ) and I C ( t ) are the three-phase winding currents; t is the calculation time.

[0146] The calculation of the stress on different positions of the motor rotor surface according to Maxwell's tensor method is shown in Equation (22):

[0147] (22)

[0148] In the formula, B r is the air-gap radial magnetic flux density.

[0149] 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):

[0150] (twenty three)

[0151] In the formula, F x UMP and F y UMP Along X Axis and Edge Y Unbalanced magnetic pull on the shaft.

[0152] like Figure 7 The 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.

[0153] 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):

[0154] (twenty four)

[0155] 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 is the j support force vector of the u th bearing; F

[0156] Establish the dynamic equation of the flexible shaft section, as shown in Equations (25) to (28):

[0157] (25)

[0158] (26)

[0159] (27)

[0160] (28)

[0161] In the formula, and are the kinetic energy and strain energy of the shaft section respectively; 、 and are the displacement, velocity and acceleration vectors of the shaft section; ρ , and l e are the material density, cross-sectional area and length of the shaft section respectively; 、 and are the velocities of the shaft section along the x axis, y axis and z axis; 、 and are the angular velocities of the shaft section around the x axis, y axis and z axis; 、 and are the stresses of the shaft section along the x axis, y axis and z axis; 、 and are the strains of the shaft section along the x axis, y axis and z axis; V is the unit volume of the shaft section; and I e are the polar second moment around the z axis and the polar second moment around thex Second moment of shaft diameter; m c and n c are the damping coefficients of the mass matrix and the stiffness matrix; dz is the small change in the shaft segment length, d is the differential operator, dt is the differentiation with respect to time t ; dv is the volume element.

[0162] The dynamic equation of the rigid disk is established as shown in Eqs. (29) to (30):

[0163] (29)

[0164] (30)

[0165] In the equations, 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 shaft nodes; m d is the mass of the rigid disk; , and are the velocities of the rigid disk along the x axis, y axis, and z axis; is the angular velocity of the rigid disk about the z axis; is the polar second moment about the z axis, I d is the polar second moment of the rigid disk about the z axis.

[0166] As shown in Figure 8 , the dynamic equation of the unbalanced mass is established as shown in Eqs. (31) to (32):

[0167] (31)

[0168] In the equations, Q d is the unbalanced force vector of the rigid disk; , and are the unbalanced forces of the rigid disk along the x axis, y axis, and z axis; , and is the unbalanced moment of the rigid disk about x axis, y axis and z axis; and are the angular displacement and angular acceleration of the rigid disk about Z axis; is the angular velocity of the rigid disk about z axis;

[0169] (32)

[0170] Calculate the bearing support force, as shown in Equations (33) to (34):

[0171] (33)

[0172] In the formula, F b is the bearing support force vector; and are the components of the bearing support force along X axis and Y axis respectively; N b is the number of bearing rolling elements; φ j is the angle of the j th rolling element of the bearing relative to X axis; Q j is the Hertz contact load between the j th rolling element of the bearing and the raceway, as shown in Equation (34):

[0173] (34)

[0174] 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 respectively; χ j and δ j are the contact state determination coefficient and the contact deformation between the j th rolling element and the raceway respectively; D aj and D rj are the relative distances of the curvature centers of the inner and outer raceways of the bearing along the axial and radial directions; r i and r o are the curvature radius of the inner raceway and the curvature radius of the outer raceway of the bearing; db is the rolling element diameter.

[0175] Calculate the propeller load torque as shown in Equation (35):

[0176] (35)

[0177] where is the percentage of load torque fluctuation; K Q and ρ w are the propeller torque coefficient and the liquid density under open water conditions, respectively; θ prop , n prop and D prop are the propeller rotation angle, rotation speed, and diameter, respectively; n blade is the number of propeller blades.

[0178] Specifically, couple the electromagnetic torque and unbalanced magnetic pull calculation equations of the permanent magnet synchronous motor, and the bearing-rotor dynamic model to complete the establishment of the electromechanical coupling dynamic model of the propulsion shafting as shown in Equation (36):

[0179] (36)

[0180] Figures 9 to 12 is a schematic diagram comparing the results of the self-inductance of phase A and the mutual inductance of phases AB obtained by the finite element method provided in the embodiments of the present application and the method of the present invention, where Figure 9 and Figure 10 are the cases where there is no eccentricity in the propulsion shafting, Figure 11 and Figure 12 are the cases considering the static eccentricity SE = 0.1 and the 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, resulting in periodic fluctuations in the motor inductance. The periodicity of the inductance curve fluctuations obtained by the finite element method and the method of the present invention is consistent, 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.

[0181] In addition, Figure 11 and Figure 12 the inductance results considering eccentricity shown are different from the inductance results without considering eccentricity shown in Figure 9 and Figure 10 , and their inductance curves show additional periodic fluctuations. This proves that the eccentricity caused by the vibration displacement of the motor rotor does indeed affect the inductance of the permanent magnet synchronous motor.

[0182] Figures 13 to 14Schematic diagram of the comparison of the time-domain and frequency-domain results of the electromagnetic torque obtained by the finite element method and the method of the present invention under the condition that the static eccentricity SE = 0.1 and the dynamic eccentricity DE = 0.2 provided by the embodiments of the present application. Figure 13 It shows that the amplitudes of the time-domain waveforms of the electromagnetic torque obtained by the finite element method and the method of the present invention are close, and the amplitude error is within 5%; Figure 14 It shows that the characteristic frequencies of the electromagnetic torque spectra obtained by the finite element method and the method of the present invention coincide. The electromagnetic torque results can further verify the accuracy of the method of the present invention.

[0183] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred examples as well as all changes and modifications falling within the scope of the present invention.

[0184] 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 equivalent technologies, 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 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.

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 includes: 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 the permanent magnet synchronous motor based on the 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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