Mechanical system analysis and experimental method based on circuit analogy

Abstract

The application provides a mechanical system analysis and experiment method based on circuit analogy, which provides two kinds of circuit analogy methods for two kinds of mechanical systems of rotation and translation, can satisfy simulation of mechanical systems with different complexity, specifically, variables in the circuit are analogous to variables in the mechanical system, the mechanical system is converted into an equivalent circuit, the equivalent circuit is analyzed by using a circuit analysis method, and an analysis result of the mechanical system can be directly mapped to obtain an analysis result. In terms of analysis and calculation, the circuit calculation method is mature, loop current method and node voltage method can be used to solve the circuit steady state; the circuit theorem is complete, the equivalent transformation principle is clear, the circuit can be simplified; the circuit time-frequency domain analysis method is mature, the network function method can be used to analyze the small signal dynamic characteristics; the circuit element has no rotating part, the variable direction is easy to understand and represented in a plane. In terms of experiment, the circuit element is rich in types and easy to obtain; the circuit element parameter is easy to measure, and the element with the required parameter can be obtained through series and parallel connection.

Description

Technical Field

[0001] This invention belongs to the field of mechanical system analysis technology, specifically relating to a mechanical system analysis and experimental method based on circuit analogy. Background Technology

[0002] Conventional methods for analyzing mechanical systems involve establishing dynamic mathematical models, solving differential equations, linearizing the equations, and performing small-signal analysis. However, these methods encounter several challenges, including difficulties in solving the problems, analyzing local components of the mechanical system, and deriving small-signal transfer functions. Taking a transmission system as an example, the rotational speed and torque in a transmission system are rotational in nature, which is not readily apparent in existing analytical methods. Simulation methods also present difficulties. For instance, conducting a scaled-down experiment on the shaft system of a MW-level wind turbine presents significant challenges. Simulating the moment of inertia disk, transmission shaft stiffness, and transmission shaft damping is extremely difficult and impractical for later modifications. Torque synthesis requires complex mechanical devices such as pulleys and gearboxes, and simulation devices capable of generating controllable torque are needed at both ends of the shaft system. Summary of the Invention

[0003] This invention addresses the aforementioned problems by providing a method for simplifying the analysis and experimentation of mechanical systems based on circuit analogy and circuit analysis techniques. The invention employs the following technical solution:

[0004] This invention provides a method for analyzing and experimenting with mechanical systems based on circuit analogy, characterized by comprising:

[0005] Step S1: Convert the mechanical system analogy into the corresponding equivalent circuit according to the predetermined analogy rules;

[0006] Step S2: Simplify the equivalent circuit using circuit equivalence transformations and / or circuit theorems;

[0007] Step S3: Perform circuit analysis on the equivalent circuit to obtain the circuit analysis results;

[0008] Step S4: Map the circuit analysis results to the mechanical system analysis results according to the analogy rule.

[0009] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features: the mechanical system is a transmission system composed of several mechanical rotors and several flexible transmission shafts interconnected, and its basic components include three types:

[0010] The mechanical rotor has the parameter of rotational inertia;

[0011] The mechanical rotor is self-damped, and its parameters are the friction torque coefficient; and

[0012] The flexible drive shaft has the following parameters: drive shaft stiffness and drive shaft mutual damping.

[0013] In step S1, the analogy rules are as follows: voltage is used to analogize the torque of the mechanical rotor, current is used to analogize the rotational speed of the mechanical rotor, resistance is used to analogize the self-damping of the mechanical rotor and the mutual damping of the transmission shaft, inductance is used to analogize the moment of inertia, capacitance is used to analogize the stiffness of the transmission shaft, a controlled voltage source is used to analogize the control of the torque, and Kirchhoff's voltage law is used to analogize the torque synthesis on the mechanical rotor. The motion equation of any one of the mechanical rotors is analogous to:

[0014]

[0015] In the formula, J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, ΔT is the resultant torque acting on the mechanical rotor, L is the inductance used to analogize the moment of inertia of the mechanical rotor, and i L For the inductance used to analogize the rotational speed of the mechanical rotor, u L The voltage across the inductor is given, and the frictional torque coefficient generated by the self-damping of any one of the mechanical rotors is analogous to:

[0016]

[0017] In the formula, D is the self-damping of the mechanical rotor, and R D For analogy to the self-damping resistance of the mechanical rotor, ω is the rotational speed of the mechanical rotor, i is the current for analogy to the rotational speed of the mechanical rotor, and T D u is the frictional torque generated by the self-damping of the mechanical rotor. D For the voltage used as an analogy to the frictional torque, the torque analogy on any of the flexible drive shafts is as follows:

[0018]

[0019] In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft, respectively, and K s D is the stiffness of the drive shaft. s C is the mutual damping of the drive shaft, and C is the capacitance used to analogize the stiffness of the drive shaft, the value of which is equal to 1 / K. s R s The resistance is analogous to the mutual damping of the drive shaft.

[0020] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features: the mechanical system is a transmission system composed of several mechanical rotors and several flexible transmission shafts interconnected, and its basic components include three types:

[0021] The mechanical rotor has the parameter of rotational inertia;

[0022] The mechanical rotor is self-damped, and its parameters are the friction torque coefficient; and

[0023] The flexible drive shaft has the following parameters: drive shaft stiffness and drive shaft mutual damping.

[0024] In step S1, the analogy rules are as follows: Current is used to analogize the torque of the mechanical rotor; voltage is used to analogize the rotational speed of the mechanical rotor; conductance is used to analogize the self-damping of the mechanical rotor and the mutual damping of the transmission shaft; capacitance is used to analogize the moment of inertia; inductance is used to analogize the stiffness of the transmission shaft; a controlled current source is used to analogize the control of the torque; Kirchhoff's current law is used to analogize the torque synthesis on the mechanical rotor; and the equation of motion for any one of the mechanical rotors is analogous to:

[0025]

[0026] In the formula, J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, ΔT is the resultant torque on the mechanical rotor, C is the capacitance used to represent the moment of inertia of the mechanical rotor, and i c The frictional torque generated by the self-damping of any one of the mechanical rotors, representing the current flowing into the capacitor, is analogous to:

[0027]

[0028] In the formula, D is the self-damping of the mechanical rotor, G is the conductance used to analogize the self-damping of the mechanical rotor, u is the voltage used to analogize the rotational speed of the mechanical rotor, and the torque analogy on any of the flexible transmission shafts is:

[0029]

[0030] In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft, respectively, and K s D is the stiffness of the drive shaft. s L is the mutual damping of the drive shaft. s The inductance used to analogize the stiffness of the drive shaft is equal to 1 / K. s G s The conductance is used to analogize the mutual damping of the drive shaft.

[0031] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features, wherein the mechanical system is a translational system with thrust, velocity, damping, mass, and stiffness. In step S1, the analogy rules are as follows: the thrust is analogized by voltage, the velocity by current, the damping by resistance, the mass by inductance, the stiffness by capacitance, the control of the thrust by a controlled current source, and the synthesis of the thrust by Kirchhoff's voltage law.

[0032] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features, wherein the mechanical system is a translational system with thrust, velocity, damping, mass, and stiffness. In step S1, the analogy rules are as follows: the thrust is analogized by current, the velocity by voltage, the damping by conductance, the mass by capacitance, the stiffness by inductance, the control of the thrust by a controlled current source, and the synthesis of the thrust by Kirchhoff's current law.

[0033] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features, wherein step S3 includes dynamic analysis of the equivalent circuit, comprising the following sub-steps:

[0034] Step S3-1: Use Laplace transform to obtain the operational circuit of the equivalent circuit;

[0035] Step S3-2: Decompose the operational circuit into a steady-state sub-circuit and a small-signal dynamic sub-circuit;

[0036] Step S3-3: For the small-signal dynamic sub-circuit, obtain the network function of interest, i.e., the transfer function, for dynamic response analysis.

[0037] The mechanical system analysis and experimental method based on circuit analogy provided by the present invention may also have the following technical features, wherein, in step S3-3, Thevenin's theorem is applied to simplify the small-signal dynamic sub-circuit during the process of obtaining the network function.

[0038] The mechanical system analysis and experimental method based on circuit analogy provided by this invention may also have the following technical features, wherein step S3 further includes:

[0039] Step S3-4: Perform steady-state analysis on the steady-state sub-circuit using the loop current method or the nodal voltage method.

[0040] The mechanical system analysis and experimental method based on circuit analogy provided by the present invention may also have the following technical features, including: step S5, constructing an actual circuit based on the equivalent circuit, the steady-state sub-circuit, or the small-signal dynamic circuit for conducting simulation experiments of the mechanical system.

[0041] Invention Function and Effect

[0042] According to the mechanical system analysis and experimental method based on circuit analogy of the present invention, variables in a circuit are analogous to variables in a mechanical system, thereby converting the mechanical system into an equivalent circuit. The equivalent circuit is then analyzed using circuit analysis methods, and the analysis results can be directly mapped to the analysis results of the mechanical system. In terms of analysis and calculation, the method of the present invention has the following advantages: First, circuit calculation methods are mature; therefore, the steady-state condition of the circuit can be easily obtained using existing methods such as loop current method and nodal voltage method. Second, circuit theorems are complete, and the equivalent transformation principle is clear; therefore, the circuit can be simplified, thereby simplifying the calculation. Third, time-domain dynamic analysis and complex frequency-domain analysis methods for circuits are very mature; methods such as network functions can be used to analyze the dynamic characteristics of small signals. Fourth, circuit elements have no rotating parts, the direction of circuit variables is easy to understand, and it is easy to represent them on a plane, thus facilitating analysis. In summary, the method of the present invention has the advantages of intuitive and simple analysis. Attached Figure Description

[0043] Figure 1 This is a flowchart of the mechanical system analysis and experimental method based on circuit analogy in an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the dynamic model of the two mass block shaft system in this embodiment;

[0045] Figure 3 This is a circuit structure diagram of the equivalent circuit in Embodiment 1 of the present invention;

[0046] Figure 4 This is a circuit analysis diagram of the equivalent circuit in Embodiment 1 of the present invention;

[0047] Figure 5 This is a circuit structure diagram of the equivalent circuit in Embodiment 2 of the present invention. Detailed Implementation

[0048] To make the technical means, creative features, objectives and effects of this invention easier to understand, the following describes in detail the mechanical system analysis and experimental method based on circuit analogy of this invention with reference to embodiments and accompanying drawings.

[0049] <Example 1>

[0050] This embodiment provides a mechanical system analysis and experimentation method based on circuit analogy. The mechanical system is analogized to a corresponding circuit, and the analysis and experimentation are carried out using circuit analysis methods. In this embodiment, the mechanical system is a transmission system composed of several mechanical rotors and several flexible transmission shafts connected to each other, specifically a two-mass block shaft system dynamic model.

[0051] Figure 2 This is a schematic diagram of the dynamic model of the two mass block shaft system in this embodiment.

[0052] like Figure 2 As shown, the shaft system dynamics model is usually composed of three basic components: 1) a mechanical rotor, whose parameter is the moment of inertia, denoted by J, and whose unit is usually kg*m. 2 2) Self-damping of the mechanical rotor, characterizing the frictional torque of the mechanical rotor, denoted by D; 3) Flexible transmission shaft, connecting two mechanical rotors, with the parameter being the transmission shaft stiffness K. s Mutual damping D of the drive shaft s The number of mechanical rotors and flexible drive shafts can be one or more.

[0053] The equation of motion for any mechanical rotor is:

[0054]

[0055] In the formula, ω is the rotational speed of the mechanical rotor, and ΔT is the resultant torque on the mechanical rotor, which can be determined by the external driving torque T1, the external resistance torque T2, and the self-damping torque T. D You get what you deserve by doing bad things.

[0056] The self-damping torque generated by the self-damping friction effect of any mechanical rotor can be expressed as:

[0057] T D =Dω

[0058] The torque on any flexible drive shaft can be expressed as:

[0059] T s =K s (θ1-θ2)+D s (ω1-ω2)=K s ∫(ω1-ω2)dt+D s (ω1-ω2)

[0060] In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft.

[0061] Based on the mathematical equations of the three basic components mentioned above, these components can be analogized to corresponding circuit components, and then circuit analysis methods can be used to conduct analysis experiments. The method will be explained in detail below.

[0062] Figure 1 This is a flowchart of the mechanical system analysis and experimental method based on circuit analogy in this embodiment.

[0063] like Figure 1 As shown, the mechanical system analysis and experimental method based on circuit analogy specifically includes the following steps:

[0064] Step S1: Convert the transmission system into a corresponding equivalent circuit according to a predetermined analogy rule.

[0065] In this embodiment, based on the aforementioned mathematical equations, the analogy rules are specifically as follows: voltage u is used as an analogy for torque T, current i as an analogy for rotational speed ω; resistance R is used as an analogy for damping (including self-damping of the mechanical rotor or mutual damping of the transmission shaft), inductance L is used as an analogy for moment of inertia, and capacitance Cs is used as an analogy for the stiffness of the flexible shaft (capacitance value 1 / C). s =K s The torque synthesis is analogous to Kirchhoff's current law. Furthermore, the control portion can be represented by a controlled power source; in this embodiment, the controlled power source is a voltage-controlled current source used to represent torque control based on speed detection.

[0066] Based on the analogy of the above components, the equation of motion for any mechanical rotor can be compared as follows:

[0067]

[0068] In the formula, J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, ΔT is the resultant torque acting on the mechanical rotor, L is the inductance used to analogize the moment of inertia of the mechanical rotor, and i L For the inductance used to analogize the rotational speed of a mechanical rotor, u L This is the voltage difference across the inductor L. Taking this equation as an example, the relationship between the parameter values ​​is: the moment of inertia J of the mechanical rotor is equal to the value of the inductance L. Because the two halves of the equation are in one-to-one correspondence, after this selection, by analogy to a circuit, the voltage in SI units is equal to the torque in SI units, and other values ​​can be deduced similarly.

[0069] The frictional torque coefficient generated by the self-damping of any mechanical rotor can be compared to:

[0070]

[0071] In the formula, D is the self-damping of the mechanical rotor, and R D Let i be the resistance used to analogize the self-damping of the mechanical rotor, and let T be the current used to analogize the rotational speed of the mechanical rotor. D u is the frictional torque generated by the self-damping of the mechanical rotor. D This is the voltage used to analogize frictional torque.

[0072] The torque on any flexible drive shaft can be compared to:

[0073]

[0074] In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft, respectively, and R s K is used to simulate the resistance of a flexible drive shaft with mutual damping. s For the stiffness of the drive shaft, D s For mutual damping of the drive shaft, C is a capacitor used to analogize the stiffness of the drive shaft, and its value is equal to 1 / K. s R s This is a resistor used for analog transmission shaft mutual damping.

[0075] Figure 3 This is a circuit structure diagram of the equivalent circuit in this embodiment.

[0076] like Figure 3 As shown, based on the analogy method described above, Figure 2 The two-mass block shaft system model shown can be equivalent to: Figure 3 The circuit diagram shown.

[0077] In this embodiment, an analogy transformation was performed using a two-mass-block shaft system model as an example. In fact, any transmission system model of varying complexity composed of the three basic components described above can be transformed into an equivalent circuit using the same method. This includes the three parts mentioned above: 1) determining which circuit element represents the transmission system element; 2) determining the correspondence between the circuit element parameters and the transmission system parameters; and 3) determining the connection relationship of the circuit elements based on the transmission system structure. Through this analogy transformation, circuits can be easily simplified using equivalent circuit transformations and circuit theorems, or analyzed using loop current methods or nodal voltage methods.

[0078] Step S2: Simplify the above equivalent circuit using circuit equivalent transformations and / or circuit theorems.

[0079] Specifically, it refers to existing technology, which will not be elaborated further.

[0080] Step S3: Perform circuit analysis on the above equivalent circuit to obtain the circuit analysis results.

[0081] Figure 4 This is a circuit analysis diagram of the equivalent circuit in an embodiment of the present invention.

[0082] like Figure 4 As shown, in this embodiment, the circuit analysis includes steady-state analysis and dynamic analysis, and specifically includes the following sub-steps:

[0083] Step S3-1: Use Laplace transform to obtain the operational circuit of the equivalent circuit;

[0084] Step S3-2: Decompose the operational circuit into a steady-state sub-circuit and a small-signal dynamic sub-circuit;

[0085] Step S3-3: For the decomposed small-signal dynamic sub-circuit, obtain the network function of interest, i.e., the transfer function, for dynamic response analysis. In the process of obtaining the network function, Thevenin's theorem can also be applied to simplify the small-signal dynamic sub-circuit.

[0086] Step S3-4: Perform steady-state analysis on the decomposed steady-state sub-circuit using the loop current method or the nodal voltage method.

[0087] Step S4: Map the circuit analysis results back to the analysis results of the transmission system according to the analogy rules described above. This involves replacing the corresponding components and parameters in reverse order.

[0088] Step S5: Based on the above equivalent circuit, the decomposed steady-state sub-circuit or small-signal dynamic circuit, construct the actual circuit for conducting simulation experiments of the corresponding mechanical system.

[0089] Among them, circuit elements with the required parameters can be formed by connecting them in series or in parallel.

[0090] As described above, the two-mass-block axis model is converted into a corresponding circuit through circuit analogy using the method of this embodiment, and a circuit analysis experiment is conducted using mature circuit analysis methods in the prior art. Finally, the results of the circuit analysis are mapped back to the analysis experimental results of the two-mass-block axis model.

[0091] In this embodiment, the parts not described in detail are well-known technologies in the art.

[0092] <Example 2>

[0093] This embodiment provides a mechanical system analysis and experimental method based on circuit analogy. The difference between this embodiment and the first embodiment is that different analogy rules are used to perform circuit analogy of the transmission system.

[0094] In step S1 of this embodiment, the analogy rule is specifically as follows: based on the above mathematical equations, current is analogized to torque, voltage to rotational speed; conductance to damping, capacitance to moment of inertia, and inductance to the stiffness of a flexible shaft (inductance value 1 / L). s =K s The torque synthesis is represented by Kirchhoff's current law. The part involving control can be represented by a controlled power source. In this embodiment, the controlled power source is a voltage-controlled current source, which is used to represent torque control based on speed detection.

[0095] Following the analogy rules of this embodiment, the motion equation of any mechanical rotor can be compared to:

[0096]

[0097] In the formula, ΔT is the resultant torque acting on the mechanical rotor, C is the capacitance used to analogize the rotational inertia of the mechanical rotor, and i c This is the current flowing into the capacitor.

[0098] The frictional torque coefficient generated by the self-damping of any mechanical rotor can be analogized as follows:

[0099]

[0100] In the formula, G is the conductance used to analogize the self-damping of the mechanical rotor, and u is the voltage used to analogize the rotational speed of the mechanical rotor.

[0101] The torque on any flexible drive shaft can be compared to:

[0102]

[0103] In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft, respectively, and L s The inductance used to analogize the stiffness of the drive shaft is equal to 1 / K. s G s For the conductance used in analog transmission shaft mutual damping.

[0104] Figure 5 This is a circuit structure diagram of the equivalent circuit in this embodiment.

[0105] like Figure 5 As shown, according to the analogy rules of this embodiment, Figure 2 The transmission system shown is analogous to Figure 5 The equivalent circuit shown.

[0106] In this embodiment, the further analysis and simulation experimental methods are the same as in Embodiment 1, so they will not be described again.

[0107] <Example 3>

[0108] This embodiment provides a mechanical system analysis and experimentation method based on circuit analogy. The difference between this embodiment and the first embodiment is that this embodiment analyzes and experiments on a translational system, specifically a spring oscillator on a plane.

[0109] According to common knowledge, there is the following correspondence between translational motion in a translational system and rotational motion in a transmission system:

[0110] Table 1. Correspondence between variables of the transmission system and the translation system

[0111] Physical quantity - rotation Physical quantity - translation Torque thrust Moment of inertia quality rotational speed speed stiffness stiffness Damping Damping

[0112] Table 1 lists the physical quantities of rotational motion in the transmission system on the left and the corresponding physical quantities of translational motion in the translational system on the right, showing a one-to-one correspondence between the two. Therefore, the method of Embodiment 1 can also be mapped to the translational system, that is, the translational system can be analogized to obtain an equivalent circuit, and analysis and experiments can be conducted based on the equivalent circuit.

[0113] According to the correspondence in Table 1, in this embodiment, for the translational system, the thrust is analogous to voltage, the velocity to current, the damping to resistance, the mass to inductance, the stiffness to capacitance, the control of the thrust to a controlled voltage source, and the synthesis of the thrust to Kirchhoff's voltage law, thereby converting the translational system into an equivalent circuit.

[0114] In this embodiment, the further analysis and simulation experimental methods are the same as in Embodiment 1, so they will not be described again.

[0115] <Example 4>

[0116] This embodiment provides a mechanical system analysis and experimentation method based on circuit analogy. The difference between this embodiment and embodiment two is that this embodiment analyzes and experiments on a translational system. In this embodiment, the translational system is specifically a spring oscillator on a plane.

[0117] The correspondence between the translational system and the transmission system has been explained in Embodiment 3, so it will not be repeated here. According to the correspondence in Table 1, in this embodiment, for the translational system, the current is used as an analogy for thrust, the voltage as an analogy for velocity, the conductance as an analogy for damping, the capacitance as an analogy for mass, the inductance as an analogy for stiffness, the controlled current source as an analogy for thrust control, and Kirchhoff's current law as an analogy for thrust synthesis, thereby converting the translational system into an equivalent circuit.

[0118] In this embodiment, the further analysis and simulation experimental methods are the same as in Embodiment 1, so they will not be described again.

[0119] Functions and effects of the embodiments

[0120] According to the circuit analogy-based mechanical system analysis and experimental method provided in this embodiment, variables in the circuit are analogous to variables in the mechanical system, thereby converting the mechanical system into an equivalent circuit. Then, circuit analysis methods are used to analyze the equivalent circuit, and the analysis results can be directly mapped to the analysis results of the mechanical system. In terms of analysis and calculation, the method of this invention has the following advantages: First, circuit calculation methods are mature; therefore, the steady-state condition of the circuit can be easily obtained using existing methods such as loop current method and nodal voltage method. Second, circuit theorems are complete, and the equivalent transformation principle is clear; therefore, the circuit can be simplified, thereby simplifying the calculation. Third, the time-domain dynamic analysis and complex frequency domain analysis methods for circuits are very mature; methods such as network functions can be used to analyze the dynamic characteristics of small signals. Fourth, the circuit elements have no rotating parts, the direction of circuit variables is easy to understand, and it is easy to represent them on a plane, thus facilitating analysis. In summary, the method of this embodiment has the advantages of intuitive and simple analysis.

[0121] Furthermore, the actual circuit can be built based on the converted circuit diagram for simulation experiments of the corresponding transmission system. In terms of experiments, the method of this embodiment has the following advantages: First, the types of circuit components are abundant, and relatively easy to obtain and low in cost; second, the parameters of the circuit components are easy to measure, and components with the required parameters can be easily constructed by series or parallel connection; third, compared to the structurally complex transmission system, the circuit is easier and faster to build and deploy. Therefore, the method of this embodiment also has the advantage of simpler experimental simulation.

[0122] In Examples 1 and 2, two different circuit analogy conversion methods were used to convert the transmission system into a corresponding equivalent circuit. In Examples 3 and 4, two different circuit analogy conversion methods were used to convert the translational system into a corresponding equivalent circuit, and further analysis and experiments were conducted using circuit analysis and experimental methods. It is evident that the methods of these embodiments can be applied to transmission systems and translational systems in mechanical systems.

[0123] The above embodiments are only used to illustrate specific implementations of the present invention, and the present invention is not limited to the scope of the description of the above embodiments.

[0124] In the above embodiments, the mechanical system analysis and experimental method based on circuit analogy is applied to a two-mass shaft system model. In fact, any transmission system model of arbitrarily complex composition composed of the above three basic components can be transformed into an equivalent circuit and analyzed and experimented on using the above method. Similarly, in the above embodiments, the mechanical system analysis and experimental method based on circuit analogy is applied to a spring oscillator model on a plane. In fact, any translational system model of arbitrarily complex composition can be transformed into an equivalent circuit and analyzed and experimented on using the above method.

Claims

1. A mechanical system analysis and experimental method based on circuit analogy, characterized in that, include: Step S1: Convert the mechanical system analogy into the corresponding equivalent circuit according to the predetermined analogy rules; Step S2: Simplify the equivalent circuit using circuit equivalence transformations and / or circuit theorems; Step S3: Perform circuit analysis on the equivalent circuit to obtain the circuit analysis results; Step S4: Map the circuit analysis results to the transmission system analysis results according to the analogy rule. The mechanical system is a transmission system consisting of several mechanical rotors and several flexible transmission shafts connected together. Its basic components include three types: The mechanical rotor has the parameter of moment of inertia; The mechanical rotor is self-damped, and its parameters are the friction torque coefficient; and The flexible drive shaft has the following parameters: drive shaft stiffness and drive shaft mutual damping. In step S1, the analogy rules are as follows: voltage is used to analogize the torque of the mechanical rotor; current is used to analogize the rotational speed of the mechanical rotor; resistance is used to analogize the self-damping of the mechanical rotor and the mutual damping of the transmission shaft; inductance is used to analogize the moment of inertia; capacitance is used to analogize the stiffness of the transmission shaft; a controlled voltage source is used to analogize the control of the torque; and Kirchhoff's voltage law is used to analogize the torque synthesis on the mechanical rotor. The equation of motion for any one of the mechanical rotors is analogous to: In the formula, J is the moment of inertia of the mechanical rotor, ω is the rotational speed of the mechanical rotor, ΔT is the resultant torque acting on the mechanical rotor, L is the inductance used to analogize the moment of inertia of the mechanical rotor, and i L For the inductance used to analogize the rotational speed of the mechanical rotor, u L The voltage across the inductor is The frictional torque coefficient generated by the self-damping of any one of the mechanical rotors is analogous to: In the formula, D is the self-damping of the mechanical rotor, and R D For analogy to the self-damping resistance of the mechanical rotor, ω is the rotational speed of the mechanical rotor, i is the current for analogy to the rotational speed of the mechanical rotor, and T D u is the frictional torque generated by the self-damping of the mechanical rotor. D The voltage used to analogize the frictional torque, The torque analogy on any of the aforementioned flexible drive shafts is as follows: In the formula, ω1 and ω2 are the rotational speeds of the two mechanical rotors connected to the two ends of the flexible transmission shaft, respectively, and K s D is the stiffness of the drive shaft. s C is the mutual damping of the drive shaft, and C is the capacitance used to analogize the stiffness of the drive shaft, the value of which is equal to 1 / K. s R s The resistor is used as an analogy to the mutual damping of the drive shaft. Step S3 includes dynamic analysis of the equivalent circuit, comprising the following sub-steps: Step S3-1: Use Laplace transform to obtain the operational circuit of the equivalent circuit; Step S3-2: Decompose the operational circuit into a steady-state sub-circuit and a small-signal dynamic sub-circuit; Step S3-3: For the small-signal dynamic sub-circuit, obtain the network function of interest, i.e., the transfer function, for dynamic response analysis.

2. The mechanical system analysis and experimental method based on circuit analogy according to claim 1, characterized in that: in, The mechanical system is a translational system, possessing thrust, velocity, damping, mass, and stiffness. In step S1, the analogy rules are as follows: voltage is used to analogize the thrust, current is used to analogize the velocity, resistance is used to analogize the damping, inductance is used to analogize the mass, capacitance is used to analogize the stiffness, a controlled voltage source is used to analogize the control of the thrust, and Kirchhoff's voltage law is used to analogize the synthesis of the thrust.

3. The mechanical system analysis and experimental method based on circuit analogy according to claim 1, characterized in that: in, The mechanical system is a translational system, possessing thrust, velocity, damping, mass, and stiffness. In step S1, the analogy rules are as follows: the thrust is analogized to current, the velocity to voltage, the damping to conductance, the mass to capacitance, the stiffness to inductance, the control of the thrust to a controlled current source, and the synthesis of the thrust to Kirchhoff's current law.

4. The mechanical system analysis and experimental method based on circuit analogy according to claim 1, characterized in that: in, In step S3-3, Thevenin's theorem is applied to simplify the small-signal dynamic sub-circuit during the process of obtaining the network function.

5. The mechanical system analysis and experimental method based on circuit analogy according to claim 4, characterized in that: in, Step S3 also includes: Step S3-4: Perform steady-state analysis on the steady-state sub-circuit using the loop current method or the nodal voltage method.

6. The mechanical system analysis and experimental method based on circuit analogy according to claim 5, characterized in that, Also includes: Step S5: Construct an actual circuit based on the equivalent circuit, the steady-state sub-circuit, or the small-signal dynamic circuit for conducting simulation experiments of the mechanical system.

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