Inductance gradient-current matching method based on external winding and Fourier series fitting

Abstract

The invention discloses an inductance gradient-current matching method based on an external winding and Fourier series fitting. The inductance gradient-current matching method specifically comprises the steps that a reconnection type electromagnetic propulsion model is built in a Maxwell eddy current field; measuring inductance data of the system model when the armature plate is located at different positions by adopting an external winding method; fourier series fitting is adopted, and an optimal fitting formula is obtained according to the goodness of fit; deriving the inductance gradient formula obtained by fitting to obtain corresponding data, and drawing an inductance gradient image; performing inductance gradient and corresponding current waveform matching to obtain a relationship between system efficiency and armature thickness; and the efficiency of the whole reconnection type electromagnetic propulsion system is improved by changing the thickness of the armature plate. According to the method, more accurate acquisition of the inductance gradient of the reconnection type electromagnetic propulsion system model and analysis of the matching degree of the inductance gradient of the system model and the current are realized, and the influence of the thickness change of the armature plate on the efficiency of the reconnection type electromagnetic propulsion system is intuitively reflected.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic propulsion, and particularly relates to an inductance gradient-current matching method based on external winding and Fourier series fitting. Background Technology

[0002] In the field of electromagnetic propulsion, launch efficiency is the most important performance indicator. The launch performance of a reconnected electromagnetic launch system mainly depends on two core parameters: the inductance gradient of the device model and the magnitude of the current in the discharge circuit. The inductance gradient reflects the rate at which the equivalent inductance of the device model changes with armature displacement; a larger gradient indicates stronger electromagnetic coupling between the drive coil and the armature plate at that point, resulting in a greater driving force on the armature plate. The inductance gradient is primarily affected by the armature plate structure and the current frequency of the discharge circuit. Properly adjusting the armature plate structure and setting the pulse power supply system parameters can improve the waveform matching between these two parameters, thereby enhancing the launch performance of the reconnected electromagnetic propulsion system. Summary of the Invention

[0003] To address the efficiency problem of electromagnetic propulsion systems, this invention provides an inductor gradient-current matching method based on external windings and Fourier series fitting.

[0004] The present invention provides an inductor gradient-current matching method based on an external winding and Fourier series fitting, comprising the following steps:

[0005] Step 1: Construct a reconnected electromagnetic propulsion model in the Maxwell vortex field.

[0006] The transmitting circuit of the reconnected electromagnetic propulsion model consists of a pulse capacitor C1, an IGBT switch Q1, a diode D1, a drive coil, and an armature plate.

[0007] According to Kirchhoff's voltage law, the voltage equation for the drive coil circuit is:

[0008] (1)

[0009] The armature plate circuit voltage equation is:

[0010] (2)

[0011] in, , L1 and L2 are the self-inductances of the upper and lower drive coils, respectively, M 12 For the mutual inductance between the upper and lower drive coils, L a M is the self-inductance of the armature plate. 1a M 2a These are the mutual inductances between the armature plate and the upper and lower drive coils, i d i is the pulse current flowing through the drive coil.a R1 is the induced current in the armature circuit, C is the equivalent resistance of the circuit, and U is the capacitance of the pulse capacitor. c1 The charging voltage for the pulse capacitor.

[0012] Step 2: Using the external winding method, measure the inductance data of the system model when the armature plate is in different positions.

[0013] A cube is cut out in the middle of the armature plate, and the armature plate is equivalent to an aluminum coil with 1 turn. While setting it as a solid winding, the skin effect is considered, so that it is equivalent to a coil loop. On this basis, the model inductance data corresponding to different positions are obtained during the process of the armature plate moving from the front end of the coil to the rear end of the coil.

[0014] According to the principle of conservation of magnetic flux: By simultaneously solving equations (1) and (2), we obtain:

[0015] (3)

[0016] Therefore, , These are the equivalent inductance L and equivalent resistance R of the electromagnetic transmitter, respectively.

[0017] The total inductance of the transmitter at each displacement is calculated using equation (3).

[0018] Step 3: Use Fourier series fitting to derive the best fitting formula based on the goodness of fit.

[0019] Regarding Fourier series:

[0020] (4)

[0021] The parameters are calculated as follows:

[0022] (5)

[0023] (6)

[0024] (7)

[0025] Where f(t) is the periodic function corresponding to the fitted data, a0 is the DC component, and a n b is the amplitude of the cosine component. n Let f(t) be the amplitude of the sinusoidal component, and T be the period of the function f(t). ω is the angular frequency, n=1,2,3…, representing the harmonic number.

[0026] Fit evaluation index, goodness of fit:

[0027] (8)

[0028] in, This represents the i-th data value of the actual measured inductance data. To fit the predicted i-th data value using Fourier series, The average value of the actual measured inductance data is given by N, where N is the number of data points for the actual measured inductance.

[0029] Step 4: Differentiate the fitted inductance gradient formula to obtain the corresponding data and plot the inductance gradient image.

[0030] Step 5: Match the inductance gradient and the corresponding current waveform to obtain the relationship between system efficiency and armature thickness; change the thickness of the armature plate to improve the efficiency of the entire reconnected electromagnetic propulsion system.

[0031] Furthermore, the parameters of the reconnected electromagnetic propulsion model are set as follows: the inner diameter of the drive coil cross-section is 40mm. An 80mm rectangle with an outer diameter of 40mm. The model is 80mm in diameter, with a coil height of 60mm and 20 turns. The armature plate is 60mm long and 100mm wide. To measure the inductance data of the model under different armature plate thicknesses, the armature plate thickness and the distance between the center of the armature plate and the upper and lower coils are increased in 1mm increments within the (2,7)mm range to keep the distance between the upper and lower edges of the armature plate and the upper and lower coils constant at 2mm.

[0032] Furthermore, in step 2, a parametric scan is performed in the range of (-60, 60) mm with a step size of 0.5 mm to measure the inductance data of the drive coil and the armature plate.

[0033] The beneficial technical effects of this invention compared to the prior art are as follows:

[0034] This invention discloses an inductance gradient matching method based on external windings and Fourier analysis. By analyzing the waveform matching degree between the inductance gradient and the current in the model, the efficiency of the entire reconnected electromagnetic propulsion system can be improved by changing the thickness of the armature plate. An external winding method is proposed to obtain the inductance data of the system model when the armature is in different positions. The inductance data of the system model is obtained more accurately in an eddy current field. For obtaining the inductance gradient data of the system model when the armature is in different positions, a Fourier series fitting is used to obtain a fitting formula for the inductance changing with the armature position, and then the derivative is used to obtain the formula and graph of the inductance gradient. This invention achieves more accurate acquisition of the inductance gradient of the reconnected electromagnetic propulsion system model and analysis of the matching degree between the system model inductance gradient and the current, intuitively reflecting the impact of changes in armature plate thickness on the efficiency of the reconnected electromagnetic propulsion system. Attached Figure Description

[0035] Figure 1 This is a flowchart of the inductor gradient-current matching method based on external winding and Fourier series fitting of the present invention.

[0036] Figure 2 This is an example of a reconnected electromagnetic propulsion model.

[0037] Figure 3 This is a schematic diagram of the parameters of a reconnected electromagnetic propulsion model (left is a top view, right is a side view).

[0038] Figure 4 This is a comparison between the hollow armature structure using the external winding method and the normal armature structure.

[0039] Figure 5 This is a schematic diagram of the armature plate inductance measurement process in an eddy current field.

[0040] Figure 6 This is the equivalent circuit for reconnected electromagnetic propulsion.

[0041] Figure 7 The image shows the fitting result of the 5th Fourier series.

[0042] Figure 8 This is the inductance gradient image of the model.

[0043] Figures 9-14 To match the inductance gradient and current waveform of the model under different armature plate thicknesses (2-7mm). Detailed Implementation

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0045] The flowchart of an inductor gradient-current matching method based on external winding and Fourier series fitting according to the present invention is as follows: Figure 1 As shown, the feature is that it specifically includes the following steps:

[0046] Step 1: Construct a reconnected electromagnetic propulsion model in the Maxwell eddy current field. The structure of the reconnected electromagnetic propulsion model is as follows: Figure 2 As shown, the parameters of the reconnected electromagnetic propulsion model are as follows: Figure 3 As shown, the perforated armature structure using the external winding method is as follows: Figure 4 As shown, the thickness of the armature plate is set to vary between 2 and 7 mm.

[0047] The equivalent circuit of the reconnected electromagnetic propulsion model is as follows: Figure 6 As shown. A typical reconnection type electromagnetic transmitter circuit consists of a pulse capacitor C1, an IGBT switch Q1, a diode D1, a drive coil, and an armature board. Figure 6In the diagram, L1 and L2 are the self-inductances of the upper and lower drive coils, respectively, and M... 12 For the mutual inductance between the upper and lower drive coils, L a M is the self-inductance of the armature plate. 1a M 2a These are the mutual inductances between the armature plate and the upper and lower drive coils, i d i is the pulse current flowing through the drive coil. a This is the induced current in the armature circuit.

[0048] According to Kirchhoff's voltage law, the voltage equation for the drive coil circuit is:

[0049] (1)

[0050] The armature plate circuit voltage equation is:

[0051] (2)

[0052] in, , .

[0053] Step 2: Using the external winding method, measure the inductance data of the system model when the armature plate is in different positions.

[0054] In Maxwell's eddy current field model, previous studies on obtaining inductance data for reconnected electromagnetic propulsion models generally neglected the self-inductance of the armature plate and its mutual inductance with the upper and lower drive coils. To address this, this invention cuts a cube through the center of the armature plate, effectively forming a coil loop. Based on this, the model inductance data is obtained at different positions as the armature plate moves from the front end to the rear end of the coil. For example... Figure 5 As shown, parametric scanning was performed in the range of (-60, 60) mm with a step size of 0.5 mm to measure the inductance data of the drive coil and the armature plate.

[0055] According to the principle of conservation of magnetic flux: By simultaneously solving equations (1) and (2), we obtain:

[0056] (3)

[0057] Therefore, , These are the equivalent inductance L and equivalent resistance R of the electromagnetic transmitter, respectively.

[0058] The total inductance of the transmitter at each displacement is calculated using equation (3).

[0059] Step 3: Use Fourier series fitting to derive the best fitting formula based on the goodness of fit.

[0060] Regarding Fourier series:

[0061] (4)

[0062] The parameters are calculated as follows:

[0063] (5)

[0064] (6)

[0065] (7)

[0066] Fit evaluation index, goodness of fit:

[0067] (8)

[0068] For an armature plate thickness of 2mm, Fourier series fitting was performed. Based on the comparison of goodness of fit, a 5th order Fourier series fitting was selected, where the goodness of fit R² of equation (8) was 0.999. In equation (4), a0 = 3.4591e-05, a1 = -4.7355e-06, b1 = -3.2791e-08, a2 = -1.8832e-06, b2 = -2.8517e-08, a3 = -7.6261e-07, b3 = -1.0053e-08, a4 = -2.2392e-07, b4 = 9.1803e-09, a5 = -2.2850e-07, b5 = 0. =52.3599. The fitting result of the 5th Fourier series is as follows: Figure 7 As shown, the X-axis represents displacement (m) and the Y-axis represents inductance (H).

[0069] Step 4: Differentiate the fitted inductance gradient formula to obtain the corresponding data, and plot the inductance gradient image. An example inductance gradient image is shown below. Figure 8 As shown.

[0070] Step 5: Match the inductance gradient and the corresponding current waveform to obtain the relationship between system efficiency and armature thickness; change the thickness of the armature plate to improve the efficiency of the entire reconnected electromagnetic propulsion system.

[0071] Figure 9-14The waveform matching relationship between current and inductance gradient is shown for armature plate thicknesses of 2mm, 3mm, 4mm, 5mm, 6mm, and 7mm, respectively. Based on the characteristics shown, the waveform matching process can be divided into two characteristic regions: Region A1 represents the mismatch stage between the inductance gradient and current waveforms, specifically, after the armature plate leaves the driving coil's operating range, the residual current in the coil is not yet zero, directly leading to energy dissipation; Region A2 represents the coupling state between the peak inductance gradient and the peak current. Previous literature indicates a positive correlation between the driving force and the product of the inductance gradient and the driving current amplitude; the larger the product, the greater the driving force on the armature plate. Therefore, the morphological characteristics of this region directly affect the system's energy conversion efficiency.

[0072] from Figures 9-14 It can be seen that as the armature plate thickness increases, in the range of 2mm-4mm, region A1 continuously decreases, indicating a reduction in the area where the inductance gradient and current waveform are mismatched. Region A2 becomes increasingly narrower; its reduced lateral length reflects a decrease in the phase difference between the peak inductance gradient and the peak current, with the peak current and inductance gradient increasingly approaching each other, while its longitudinal length also increases synchronously. In the range of 5mm-7mm, region A2, after becoming narrower, increases in the opposite direction; this reverse increase in lateral length reflects a continuous increase in the phase difference between the peak inductance gradient and the peak current, while the mismatched area A3 between current and inductance gradients shows an increasing trend. Finally, comparison reveals that the waveform matching is optimal when the armature plate thickness is 4mm.

[0073] The exit velocities of armature plates with different thicknesses under this condition were obtained in the Maxwell transient field, and their corresponding launch efficiencies were calculated as shown in Table 1.

[0074] Table 1. Comparison of efficiency for armature plates of different thicknesses

[0075]

[0076] Table 1 shows that the emission efficiency first increases and then decreases with increasing thickness under these conditions, and the emission efficiency is highest when the armature plate thickness is 4mm. This corresponds to the optimal matching degree between the current and inductance gradient waveforms when the armature plate thickness is 4mm.

Claims

1. An inductor gradient-current matching method based on external winding and Fourier series fitting, characterized in that, Includes the following steps: Step 1: Construct a reconnected electromagnetic propulsion model in a Maxwell vortex field; The transmitting circuit of the reconnected electromagnetic propulsion model consists of a pulse capacitor C1, an IGBT switch Q1, a diode D1, a drive coil, and an armature plate. According to Kirchhoff's voltage law, the voltage equation for the drive coil circuit is: （1） The armature plate circuit voltage equation is: （2） in, , L1 and L2 are the self-inductances of the upper and lower drive coils, respectively, M 12 For the mutual inductance between the upper and lower drive coils, L a M is the self-inductance of the armature plate. 1a M 2a These are the mutual inductances between the armature plate and the upper and lower drive coils, i d i is the pulse current flowing through the drive coil. a R1 is the induced current in the armature circuit; C is the equivalent resistance of the circuit; and U is the capacitance of the pulse capacitor. c1 The charging voltage for the pulse capacitor; Step 2: Using the external winding method, measure the inductance data of the system model when the armature plate is in different positions; A cube is cut out in the middle of the armature plate so that the armature plate is equivalent to a coil loop; based on this, the model inductance data corresponding to different positions are obtained as the armature plate moves from the front end of the coil to the rear end of the coil. According to the principle of conservation of magnetic flux: By simultaneously solving equations (1) and (2), we obtain: （3） Therefore, , These are the equivalent inductance L and equivalent resistance R of the electromagnetic transmitter, respectively. The total inductance of the transmitter at each displacement is calculated using equation (3); Step 3: Use Fourier series fitting to derive the best fitting formula based on the goodness of fit. Regarding Fourier series: （4） The parameters are calculated as follows: （5） （6） （7） Where f(t) is the periodic function corresponding to the fitted data, a0 is the DC component, and a n b is the amplitude of the cosine component. n Let f(t) be the amplitude of the sinusoidal component, and T be the period of the function f(t). Angular frequency, n=1,2,3…, representing the harmonic number; Fit evaluation index, goodness of fit: （8） in, This represents the i-th data value of the actual measured inductance data. To fit the predicted i-th data value using Fourier series, The average value of the actual measured inductance data is given by N, where N is the number of data points for the actual measured inductance. Step 4: Differentiate the fitted inductance gradient formula to obtain the corresponding data and plot the inductance gradient image; Step 5: Match the inductance gradient and the corresponding current waveform to obtain the relationship between system efficiency and armature thickness; change the thickness of the armature plate to improve the efficiency of the entire reconnected electromagnetic propulsion system.

2. The inductor gradient-current matching method based on external winding and Fourier series fitting according to claim 1, characterized in that, The parameters of the reconnection-type electromagnetic propulsion model are set as follows: the inner diameter of the drive coil cross-section is 40mm. An 80mm rectangle with an outer diameter of 40mm. The coil is 80mm in diameter, with a coil height of 60mm and 20 coil turns; the armature plate is 60mm long and 100mm wide.

3. The inductor gradient-current matching method based on external winding and Fourier series fitting according to claim 1, characterized in that, In step 2, a parametric scan is performed in the range of (-60, 60) mm with a step size of 0.5 mm to measure the inductance data of the drive coil and the armature plate.

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