A method of pvdf sensor arrangement for non-pneumatic tire vertical force monitoring

Abstract

The application discloses a PVDF sensor arrangement method for non-pneumatic tire vertical force monitoring. Firstly, a PVDF (polyvinylidene fluoride) piezoelectric charge model is established, and the physical principle of piezoelectric material deformation-electric signal conversion is analyzed; then, a spoke-PVDF sensor strain transmission model is established, and the strain transmission efficiency between the sensor and the spoke is quantified; then, the potential displacement distribution of the PVDF sensor arrangement area is calculated, and the sliding window discrete integral method is used to determine the radial optimal arrangement position of the sensor; the maximum charge gradient under different compression amounts is taken as an evaluation index to determine the optimal installation surface; finally, a complete mathematical model from the tire vertical load to the output voltage of the charge amplifier is established. The application provides a theoretical basis for the PVDF sensor arrangement, realizes quantitative determination of the radial optimal arrangement position of the sensor, and effectively improves the sensitivity and consistency of the vertical force monitoring signal.

Description

Technical Field

[0001] This invention relates to the field of intelligent tire monitoring technology, and in particular to a method for arranging PVDF (polyvinylidene fluoride) sensors for monitoring the vertical force of non-pneumatic tires. Background Technology

[0002] Pneumatic tires, due to their unique structural advantages, have broad application prospects in military vehicles, construction machinery, and other fields. Real-time monitoring of the vertical force on pneumatic tires is of great significance for ensuring vehicle driving safety and extending tire life. PVDF sensors, due to their flexibility, wide frequency response, and high sensitivity, have become a research hotspot for force monitoring in pneumatic tires.

[0003] However, existing technologies have the following shortcomings:

[0004] (1) Existing research has not fully considered the physical principle of deformation-electric signal conversion and strain transmission process of piezoelectric materials, and the correspondence between sensor output and stress state lacks theoretical support;

[0005] (2) The sensor location determination lacks theoretical basis and usually relies on experience or trial and error. The calibration process has low repeatability and it is difficult to ensure the consistency of the monitoring signal.

[0006] (3) Existing methods only establish the relationship between tire force and PVDF sensor output voltage or charge from the perspective of results. Signal feature extraction is difficult. The influence of the adhesive layer on strain transfer between the sensor and the spokes is not considered. Furthermore, the method of using the gradient of output voltage characteristic value as an evaluation index is limited to the fixed load application frequency. Summary of the Invention

[0007] The technical problem to be solved by this invention is: how to establish a strain transfer model that includes the influence of the adhesive layer based on the physical principles of piezoelectric materials, so as to quantitatively determine the optimal radial arrangement position of PVDF sensors and provide a theoretical basis for monitoring the vertical force of non-pneumatic tires.

[0008] To address the aforementioned technical problems, this invention provides a method for arranging PVDF sensors for monitoring the vertical force of non-pneumatic tires, the method comprising the following steps:

[0009] Step 1: Establish the piezoelectric charge model of the PVDF sensor

[0010] A PVDF sensor model was established in the multiphysics simulation software Comsol, simplifying the sensor into a five-layer rectangular thin-plate structure, including a PVDF piezoelectric layer, two PET (polyethylene terephthalate) protective layers, and two silver-ink electrode layers. A surface charge model of the PVDF sensor was established based on the electrostatic Gaussian theorem.

[0011] (1)

[0012] In equation (1): D is the electrical displacement of the PVDF sensor, d 31 Let d be the piezoelectric constant along the length of the PVDF. 32 d is the piezoelectric constant in the width direction of the PVDF. 33 T is the piezoelectric constant in the thickness direction of PVDF. xx For the stress along the length of the PVDF piezoelectric layer, T yy For the width direction stress of the PVDF piezoelectric layer, T zz Let be the stress in the thickness direction of the PVDF piezoelectric layer, Q be the surface charge of the PVDF sensor, n be the outward normal vector of the dielectric and conductor, A be the area of ​​the PVDF piezoelectric layer, and P be the polarization direction of the PVDF. When the polarization direction is upward, P=1, and when the polarization direction is downward, P=-1.

[0013] Step 2: Establish a strain transfer model between the spokes and the PVDF sensor, and obtain the strain distribution functions of the PVDF sensor and the spokes along the axial direction:

[0014] (2)

[0015] In formula (2): Let be the strain distribution function along the axial direction of the PVDF sensor. Let be the strain distribution function of the spokes along the axial direction. The stiffness ratio of polyurethane to PVDF, rate ε Let L be the strain transmissivity, L be the half-length of the PVDF sensor, and ε be the strain transmissivity. u E represents the axial strain experienced at both ends of the spoke. ft E represents the Young's modulus of the spokes. pvdf h is the Young's modulus of PVDF. ft h is the spoke thickness. pvdf The thickness of the PVDF piezoelectric layer;

[0016] Step 3: Establish the relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes;

[0017] (3)

[0018] In equation (3): rate εxx The strain transmissivity along the length of the PVDF piezoelectric layer is denoted as rate. εyy ε is the strain transmissivity in the width direction of the PVDF piezoelectric layer. xxPVDF For the strain along the length of the PVDF sensor, ε yyPVDF For the strain in the width direction of the PVDF sensor, ε zzPVDF ε represents the strain in the thickness direction of the PVDF sensor. xxft ε is the axial strain of the spokes.yyft For the radial strain of the spokes, ε zzft For the circumferential strain of the spokes;

[0019] Step 4: Calculate the electric displacement distribution in the PVDF sensor deployment area;

[0020] The correspondence between the tire coordinate system and the sensor coordinate system is determined. Based on the PVDF piezoelectric charge model, the spoke-PVDF sensor strain transfer model, and the relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes, the electric displacement distribution in the sensor arrangement area is calculated. The electric displacement corresponding to the PVDF sensor arrangement area is expressed as follows:

[0021] (4)

[0022] In equation (4), T yyft T zzft T xxft These are the radial, circumferential, and axial components of the spoke stress tensor, respectively. ε1 Spoke front strain transmissivity, rate ε2 Strain transmissivity of the spoke front;

[0023] Step 5: Calculate the charge per unit length using discrete integration with a sliding window; the charge per unit length of the PVDF piezoelectric layer at all discrete locations within the spoke length range is:

[0024] (5)

[0025] In equation (5): N pvdf x1 represents the charge per unit length in the sensor arrangement area, x2 represents the position corresponding to the tail of the PVDF piezoelectric layer of the sensor, and x2 represents the position corresponding to the head of the PVDF piezoelectric layer of the sensor.

[0026] Step 6: Determine the optimal radial placement position of the sensor

[0027] The differential operation is performed on the charge per unit length under different compression amounts to find the position corresponding to the maximum gradient of charge per unit length, and the optimal radial arrangement position of the sensor is determined.

[0028] Step 7: Determine the optimal mounting surface for the sensor

[0029] Calculate the charge amount of different mounting surfaces under various radial displacements, compare the linearity of charge amount and radial displacement, select the mounting surface with higher linearity as the optimal mounting surface, and perform function fitting on the charge amount in all states.

[0030] Preferably, the method for calculating the charge per unit length using the sliding window discrete integral in step 5 is as follows:

[0031] Import the electric displacement data into the Matlab workspace, use timesseries to convert the electric displacement data into time series data, with a sampling frequency of 10Hz, and input the workspace data into the Buffer module through the From Workspace module; the sampling time in Simulink is 0.1s, the output buffer size of the Buffer module is set to the corresponding PVDF piezoelectric layer length, and the buffer overlap is the PVDF piezoelectric layer length - 1, that is, the sliding window moves to the right by 0.1 for each simulation step. The output of the Buffer module is accumulated using the SUM module and multiplied by the sampling time to achieve discrete integration of the region. As the sliding window moves to the right, the regional charge per unit length at all discrete positions of the PVDF piezoelectric layer within the spoke length range can be obtained.

[0032] Preferably, the method for determining the optimal radial arrangement position of the sensor in step 6 is as follows:

[0033] For the linear variation range of the spoke electric displacement gradient, the charge per unit length at the compression length x1 is... Subtract the charge per unit length when the compression length is x2 The calculation formula is as follows:

[0034] (6)

[0035] In formula (6): The maximum gradient of charge per unit length, and the position x corresponding to the peak of the maximum gradient of charge per unit length. final This is the optimal position for the sensor's end.

[0036] Preferably, the method for determining the optimal mounting surface of the sensor in step 7 is as follows:

[0037] After calculating the charge per unit length corresponding to each radial displacement at the two optimal positions of the mounting surface under spoke tension and compression, multiplying it by the sensor width, the final charge calculation formula is as follows:

[0038] (7)

[0039] In equation (7): Q1 is the surface charge when the sensor is placed on the front side of the spoke, Q2 is the surface charge when the sensor is placed on the back side of the spoke, B is the width of the PVDF piezoelectric layer of the sensor, and N pvdf-1 N represents the charge per unit length when the sensor is positioned on the front of the spoke. pvdf-2 This represents the charge per unit length when the sensor is positioned on the reverse side of the spokes.

[0040] The charge quantities under the two optimal compression states are fitted using a polynomial, and the fitting formula is as follows:

[0041] (8)

[0042] In equation (8): Q 1press Let Q be the charge quantity in the compressed state at position 1. 2press S represents the charge quantity in the compressed state at position 2. r p1, p2, p3, p4, p5, and p6 are the radial displacement of the spokes, and p1, p2, p3, p4, p5, and p6 are the fitting parameters.

[0043] Based on the linear correlation between the charge amount under compression and the radial displacement of the spokes, a higher position is selected as the optimal arrangement position.

[0044] Compared with the prior art, the beneficial effects of the present invention are:

[0045] (1) Starting from the PVDF piezoelectric constitutive model, a strain transfer model including the influence of the adhesive layer was established, providing a theoretical basis for sensor placement;

[0046] (2) The strain transfer efficiency between the sensor and the spokes was quantified, avoiding the error caused by the default 100% transfer rate;

[0047] (3) The optimal radial arrangement position of the sensor was quantitatively determined by calculating the electric displacement distribution and using the sliding window discrete integration method;

[0048] (4) The evaluation index is the maximization of the charge gradient under different compression amounts, and is not limited to a fixed load frequency;

[0049] (5) Select the mounting surface by comparing the linearity of the positive and negative charge outputs to make the sensor output highly linear with the radial displacement;

[0050] (6) A complete mathematical model from the vertical load of the tire to the output voltage of the charge amplifier was established, which is beneficial to simplify the subsequent signal processing and calibration process;

[0051] (7) Effectively improves the sensitivity and consistency of vertical force monitoring signals. Attached Figure Description

[0052] Figure 1 This is a flowchart of the method provided in an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of the main structure of the PVDF sensor provided in an embodiment of the present invention;

[0054] Figure 3 The following are the simulation results of steady-state piezoelectric PVDF provided in the embodiments of the present invention: (a) XX component of strain tensor, (b) ZZ component of strain tensor, (c) YY component of strain tensor, (d) electrode potential.

[0055] Figure 4This is a circuit diagram of a charge amplifier provided in an embodiment of the present invention;

[0056] Figure 5 This is a graph of PVDF sensor test data provided in an embodiment of the present invention;

[0057] Figure 6 This is a schematic diagram illustrating the strain transfer principle between the PVDF sensor and the spoke substrate provided in this embodiment of the invention.

[0058] Figure 7 These are strain distribution diagrams of the sensor provided in the embodiments of the present invention; (a) strain distribution over the length range of the PVDF piezoelectric layer, (b) strain distribution over the width range of the PVDF piezoelectric layer;

[0059] Figure 8 These are finite element model diagrams of non-pneumatic tires provided in embodiments of the present invention; (a) NPT whole tire model, (b) front node of spokes, (c) back node of spokes;

[0060] Figure 9 This is a stress distribution diagram of spoke compression provided in an embodiment of the present invention; (a) YY component of the stress tensor on the front side of the spoke, (b) YY component of the stress tensor on the back side of the spoke, (c) ZZ component of the stress tensor on the front side of the spoke, (d) ZZ component of the stress tensor on the back side of the spoke, (e) XX component of the stress tensor on the front side of the spoke, (f) XX component of the stress tensor on the back side of the spoke.

[0061] Figure 10 This is a stress distribution diagram of spokes under tension provided in an embodiment of the present invention; (a) YY component of the stress tensor on the front side of the spoke, (b) YY component of the stress tensor on the back side of the spoke, (c) ZZ component of the stress tensor on the front side of the spoke, (d) ZZ component of the stress tensor on the back side of the spoke, (e) XX component of the stress tensor on the front side of the spoke, (f) XX component of the stress tensor on the back side of the spoke.

[0062] Figure 11 The following is a diagram showing the electrical displacement distribution of the front and back sides of the spokes provided in an embodiment of the present invention: (a) electrical displacement of the front side of the spokes under compression, (b) electrical displacement of the back side of the spokes under compression, (c) electrical displacement of the front side of the spokes under tension, and (d) electrical displacement of the back side of the spokes under tension.

[0063] Figure 12 These are the discrete integration results of the sliding window provided in the embodiments of the present invention; (a) maximum gradient of charge per unit length on the front side, (b) maximum gradient of charge per unit length on the back side;

[0064] Figure 13 This is a charge distribution diagram of the sensor area provided in an embodiment of the present invention;

[0065] Figure 14 The output voltage diagram of the charge amplifier provided in this embodiment of the invention is shown in (a) the model simulation voltage and (b) the experimentally acquired voltage. Detailed Implementation

[0066] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] This invention provides a method for arranging PVDF sensors for monitoring the vertical force of non-pneumatic tires, such as... Figure 1 As shown, the specific steps are as follows:

[0068] Step 1: Establish the piezoelectric charge model of the PVDF sensor

[0069] A model of the LDT0-028K PVDF sensor was created in the multiphysics simulation software (Comsol). The PVDF sensor model can be simplified to a five-layer rectangular thin plate of 15mm × 9mm × 168μm, as shown below. Figure 2 As shown in the figure. The PVDF piezoelectric layer is 28 μm thick, the polyethylene terephthalate (PET) protective layer is 60 μm thick, and the silver electrode layer is 10 μm thick. A rotating coordinate system is established in the component definition, rotating the Z-axis of the coordinate system by π radians. The coordinate system is then applied to piezoelectric materials in solid mechanics to achieve downward polarization. The upper electrode is grounded, the lower electrode is at a floating potential, one end of the sensor is fixed, and a uniformly distributed load of 0.1 N is applied from top to bottom. The steady-state piezoelectric simulation results are as follows. Figure 3 As shown.

[0070] Figure 3 In the figure, the average value of the XX component of the strain tensor is 6.6115 × 10⁻⁶. -9 The average value of the Z-components of the strain tensor is -3.1492 × 10⁻⁶. -7 The average value of the YY component of the strain tensor is 1.6805 × 10⁻⁶. -8 The lower electrode potential is 3.6 mV, and the surface charge of the lower electrode is 7.3398 × 10⁻⁶. -5 pC. The piezoelectric constants of PVDF are d 31 =13.5pC / N, d 32 =1.47pC / N, d 33 =-33.8pC / N. When the sensor is subjected to bending force, the ZZ component of the strain tensor dominates, and the piezoelectric coefficient d in the thickness direction is... 33 Since the value is negative, the electric displacement of the sensor surface is positive according to the PVDF constitutive equation.

[0071] The constitutive equation for PVDF piezoelectric materials is shown below:

[0072] (1)

[0073] In the formula: D is the PVDF electric displacement matrix, d is the piezoelectric stress constant matrix, and T is the PVDF stress matrix. Let be the transpose of the dielectric constant matrix, and E be the electric field strength matrix.

[0074] In actual PVDF applications, no external electric field is applied, and the above equation becomes

[0075] (2)

[0076] Since the PVDF sensor is arranged radially on the spoke surface, neglecting shear force, the stress is along the length, width, and thickness directions, with charge accumulating in the thickness plane. Its electric displacement can be simplified as:

[0077] (3)

[0078] In the formula: d 31 Let d be the piezoelectric constant along the length of the PVDF. 32 d is the piezoelectric constant in the width direction of the PVDF. 33 T is the piezoelectric constant in the thickness direction of PVDF. xx For the stress along the length of the PVDF, T yy For the stress in the width direction of the PVDF, T zz This represents the stress in the thickness direction of the PVDF.

[0079] Because the upper electrode of the sensor is grounded and the lower electrode is at a floating potential, when charge flows from the dielectric to the conductor, the outward normal vector n between the dielectric and the conductor is negative, the PVDF polarization direction is downward, and the final surface charge Q is positive. If the lower electrode of the sensor is grounded, the resulting charge sign is reversed. Based on the above sign characteristics, the charge model can be established as follows:

[0080] (4)

[0081] In the formula: Q is the surface charge of the PVDF sensor, n is the outward normal vector of the medium and conductor, A is the area of ​​the PVDF piezoelectric layer, and P is the polarization direction of PVDF. When the polarization direction is upward, P=1, and when the polarization direction is downward, P=-1.

[0082] Step 2: Establish the charge amplifier transfer function

[0083] When using a PVDF sensor, the sensor output needs to be connected to a charge amplifier. The charge amplifier circuit is as follows: Figure 4 As shown. Ideally, the PVDF sensor can be considered as a charge source, and the input charge of the charge amplifier can be expressed as:

[0084] (5)

[0085] In the formula: U is the output voltage of the charge amplifier, C f For feedback capacitor, C pvdfFor the PVDF sensor capacitor, C d For the capacitance of the wire, C i C is the input capacitor of the charge amplifier. in R is the total input capacitance. f For bleed resistor, This is the voltage at the negative input terminal of the operational amplifier.

[0086] Differentiating the above equation yields the transfer function of the output voltage with respect to the input charge:

[0087] (6)

[0088] In equation (6): s is the differential operator and I is the PVDF current.

[0089] (7)

[0090] In equation (7): f low This is the low-frequency cutoff frequency.

[0091] When the charge input frequency exceeds the low-frequency cutoff frequency f low When the input frequency of the charge is less than the low-frequency cutoff frequency, the output voltage waveform can be approximated as the waveform of the charge derivative. When the charge amplifier sensitivity is selected as 10... 9 At V / C, the corresponding low-frequency cutoff frequency is 15Hz. The rotational frequency of a non-pneumatic tire at 0-50km / h is approximately 0-9Hz, therefore the actual voltage waveform is closer to the waveform of the charge derivative.

[0092] This invention uses a physical PVDF sensor to verify the sign characteristics of the above charge model. The sensor's front end is pressed with a finger, bending it 90°, held for 3 seconds, and then quickly released. The output voltage waveform is as follows: Figure 5 As shown. Figure 5 During the bending test, the charge amplifier outputs a negative voltage (i.e., the sensor outputs a positive charge) at the instant the sensor is bent. Because the charge amplifier has a bleed resistor, the rate of change of charge on the PVDF surface is zero when the sensor is held in the pressed state; therefore, the output voltage returns from its lower peak value to zero. When the sensor is released after 4 seconds, it returns to its initial position due to its own elasticity. During the rebound, the charge amplifier outputs a reverse voltage, subsequently returning to zero. The simulation results and experimental phenomena are consistent with the charge sign characteristics described in this invention, verifying the effectiveness of the charge model.

[0093] Step 3: Establish a strain transfer model for the spoke-PVDF sensor

[0094] When used for vertical load monitoring in non-pneumatic tires, PVDF sensors are placed on the spoke surface, with the sensor connected to the spoke via an adhesive layer. It is typically assumed that the axial strain transfer efficiency between the sensor and the substrate is 100%. However, the actual strain transfer efficiency is affected by the shear modulus of the adhesive layer, the adhesive layer thickness, the Young's modulus of the substrate, and the Young's modulus of the sensor material. The strain transfer principle between the PVDF sensor and the spoke substrate is as follows: Figure 6 As shown. Assume that the polyurethane material of the non-pneumatic tire spokes, the acrylic resin and PVDF of the adhesive layer are all linear elastic materials, and there is no relative slippage between the connecting surfaces. When the spoke micro-element is subjected to tensile stress along the axial direction, the shear stress of the spoke is transferred to the PVDF through the adhesive layer, thus causing the bottom surface of the PVDF to experience the same shear stress as the top surface of the spoke.

[0095] exist Figure 6 In this context, the shear stress on the PVDF and the spoke matrix can be expressed as:

[0096] (8)

[0097] In equation (8): τ pvdf For the shear stress of PVDF, τ ft For the spoke matrix shear stress, G pvdf G is the shear modulus of PVDF. ft For polyurethane shear modulus, γ pvdf For PVDF shear strain, γ ft For the spoke shear strain, u pvdf u represents the axial displacement of the PVDF. ft z1 represents the axial displacement of the spokes, z2 represents the position in the thickness direction of the PVDF, and z3 represents the position in the thickness direction of the spokes.

[0098] Integrating the above shear stress expression over z1 and z2, we can express the axial displacement of the PVDF and the spokes.

[0099] (9)

[0100] Substitute boundary conditions , postscript , Rewritten as:

[0101] (10)

[0102] The average displacement of the PVDF and spokes can be obtained by dividing the formula by the thickness after performing definite integrals over the thickness range.

[0103] (11)

[0104] From formula (11), the average displacement difference between the spokes and the PVDF can be obtained as:

[0105] (12)

[0106] Where: h J G represents the thickness of the adhesive layer. J τ is the shear modulus of the adhesive layer. J This represents the shear stress of the adhesive layer.

[0107] The axial force balance equation between the PVDF sensor and the spoke matrix element is as follows:

[0108] (13)

[0109] In equation (13): σ pvdf For the axial stress of PVDF, σ ft This refers to the axial stress of the spokes.

[0110] According to Hooke's Law, stress is expressed in terms of strain.

[0111] (14)

[0112] In equation (14): E pvdf For PVDF Young's modulus, ε pvdf E represents the axial strain of the PVDF. ft ε is the Young's modulus of polyurethane. ft This represents the axial strain of the spokes.

[0113] The following relationships exist between strain and displacement:

[0114] (15)

[0115] Substituting formula (13) into formula (12), and then combining formulas (14) and (15) for differentiation, we can obtain:

[0116] (16)

[0117] In equation (16): k is the shear hysteresis coefficient.

[0118] Solve formula (16) by substituting the boundary conditions as follows:

[0119] (17)

[0120] In equation (17): ε u Let L be the axial strain at both ends of the spoke, and L be the half-length of the PVDF sensor.

[0121] The strain distribution function along the axial direction of the PVDF sensor and spokes can be obtained as follows:

[0122] (18)

[0123] In formula (18): Let be the strain distribution function along the axial direction of the PVDF sensor. Let be the strain distribution function of the spokes along the axial direction. The stiffness ratio of polyurethane to PVDF, rate ε Let L be the strain transmissivity, L be the half-length of the PVDF sensor, and ε be the strain transmissivity. u E represents the axial strain experienced at both ends of the spoke. ft E represents the Young's modulus of the spokes. pvdf h is the Young's modulus of PVDF. ft h is the spoke thickness. pvdf The thickness is PVDF.

[0124] A strain transfer model is established in Simulink simulation software. Based on the actual material, the variable parameter in the model is determined as: E pvdf =3000MPa, E ft =105MPa, h pvdf =0.168mm, h ft =5mm, h J =0.12mm, G pvdf =1111MPa, G ft =35MPa, G J =346MPa. Set ε u The value is 0.01. A Ramp module with slopes of 0.45 and 0.75 and an initial output of -L is used as the input to the position interface x. The simulation duration is 20 seconds. The strain distribution of the model when L is 7.5 mm and 4.5 mm (corresponding to the length and width of the PVDF piezoelectric layer) is as follows: Figure 7 As shown. For Figure 7 The strain transfer efficiency of the PVDF piezoelectric layer is 5.77% in the length direction and 2.19% in the width direction after definite integration and division of the stress.

[0125] Step 4: Establish the relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes

[0126] After obtaining the strain transfer efficiency between the spokes and the PVDF sensor, the relationship between the triaxial strain of the PVDF and the triaxial strain of the spokes is as follows:

[0127] (19)

[0128] In equation (19): rate εxx The strain transmissivity along the length of the PVDF piezoelectric layer is denoted as rate. εyyε is the strain transmissivity in the width direction of the PVDF piezoelectric layer. xxPVDF For the strain along the length of the PVDF sensor, ε yyPVDF For the strain in the width direction of the PVDF sensor, ε zzPVDF ε represents the strain in the thickness direction of the PVDF sensor. xxft ε is the axial strain of the spokes. yyft For the radial strain of the spokes, ε zzft For the circumferential strain of the spokes.

[0129] In Abaqus finite element analysis software, a single spoke was subjected to radial tension of 15mm and compression of 25mm. The radial component T of the stress tensor at 17 nodes on both the front and back sides of the spoke was extracted. yyft Circumferential component T zzft Axial component T xxft The finite element model of a non-pneumatic tire and the positions of the nodes on the front and back sides of the spokes are as follows: Figure 8 As shown. The stress at the nodal points on the front and back sides of the spokes under compression is as follows. Figure 9 The horizontal axis represents the actual distance between each node. Under compression, the triaxial stress of the spokes exhibits significant gradient changes with different radial displacements at the center and root positions. Under tension, the stress distribution at the nodes on both the front and back sides is uniform, as shown in the figure. Figure 10 As shown.

[0130] Step 5: Calculate the electric displacement distribution in the PVDF sensor deployment area.

[0131] In the tire coordinate system, the circumferential direction of the spokes corresponds to the Z-axis of the sensor, the radial direction of the spokes corresponds to the X-axis of the sensor, and the axial direction of the spokes corresponds to the Y-axis of the sensor.

[0132] The electric displacement corresponding to the PVDF sensor arrangement area is expressed as follows: PVDF piezoelectric charge model [i.e., formula (4)], spoke-PVDF sensor strain transfer model [i.e., formula (18)], and relationship between PVDF sensor triaxial strain and spoke triaxial strain [i.e., formula (19)].

[0133] (20)

[0134] In equation (20), T yyft T zzft T xxft These are the radial, circumferential, and axial components of the spoke stress tensor, respectively. ε1 Spoke front strain transmissivity, rate ε2 Strain transfer rate on the front of the spokes.

[0135] Will Figure 9 , Figure 10Substituting the triaxial stress data into the above electric displacement formula, the electric displacement distributions of the spokes under tension and compression states can be obtained as follows: Figure 11 As shown. Figure 11 In the compression state, the distribution trend of electric displacement is basically consistent with the negative of the circumferential component of the spoke stress. In the tension state, the electric displacement gradient does not change significantly with the radial displacement, and the value is significantly reduced compared with the compression state.

[0136] Step 6: Calculate the charge per unit length using discrete integration with a sliding window.

[0137] To find the optimal location for the PVDF sensor, the obtained electric displacement distribution data was discretized and integrated using a sliding window in Simulink to obtain the charge per unit length of the region, as shown below:

[0138] (twenty one)

[0139] In equation (21): N pvdf x1 represents the charge per unit length in the sensor arrangement area, x2 represents the position corresponding to the tail of the PVDF piezoelectric layer of the sensor, and x2 represents the position corresponding to the head of the PVDF piezoelectric layer of the sensor.

[0140] The specific implementation involves importing the electric displacement data into the Matlab workspace, converting it into time-series data using timesseries, sampling at a frequency of 10Hz, and inputting the workspace data into the Buffer module via the From Workspace module. In Simulink, the sampling time is 0.1s, the output buffer size of the Buffer module is set to 150 (corresponding to a PVDF piezoelectric layer length of 15mm), and the buffer overlap is 149 (i.e., the sliding window moves 0.1 to the right for each simulation step). The output of the Buffer module is accumulated using the SUM module and multiplied by the sampling time to achieve discrete integration of the region. As the sliding window moves continuously to the right, the charge per unit length at all discrete locations within the spoke length range of the PVDF piezoelectric layer can be obtained. The effect of the discrete integration via the sliding window is shown below. Figure 12 As shown.

[0141] Step 7: Determine the optimal radial placement of the sensor

[0142] The strain in the axial direction of the spokes (corresponding to the width direction of the PVDF sensor) can be considered uniformly distributed. Since the change in electrical displacement of the spokes under compression is more significant and essentially linear than that under tension, this invention addresses the linear change range of the spoke electrical displacement gradient by subtracting the charge per unit length under 5mm compression from the charge per unit length under 25mm compression. The calculation formula is as follows:

[0143] (twenty two)

[0144] In equation (22): This represents the maximum gradient of charge per unit length. The peak position of the maximum gradient of charge per unit length is x. final This is the optimal position for the sensor's end. Figure 12 In the middle, the peak charge per unit length on the front of the spoke corresponds to a position of 52.1 mm (corresponding to position 1 at the end of the sensor), and the peak charge per unit length on the back of the spoke corresponds to a position of 38.1 mm (corresponding to position 2 at the end of the sensor).

[0145] Step 8: Determine the optimal mounting surface for the sensor

[0146] After calculating the charge per unit length corresponding to each radial displacement at positions 1 and 2 under spoke tension and compression, multiply it by the sensor width. The final charge calculation formula is as follows:

[0147] (twenty three)

[0148] In equation (23): Q1 is the surface charge when the sensor is placed on the front side of the spoke, Q2 is the surface charge when the sensor is placed on the back side of the spoke, B is the width of the PVDF piezoelectric layer of the sensor, and N is the surface charge of the sensor. pvdf-1 N represents the charge per unit length when the sensor is positioned on the front of the spoke. pvdf-2 This represents the charge per unit length when the sensor is positioned on the reverse side of the spoke.

[0149] The charge corresponding to each radial displacement of the spokes at the two positions mentioned above is as follows: Figure 13 As shown. In Figure 13 In the model, a negative radial displacement of the spokes corresponds to a compression state, while a positive radial displacement corresponds to a tension state. The charge in the compressed state is essentially linearly related to the radial displacement, while the rate of change of charge in the tension state is almost zero. Since the radial displacement of the spokes is linearly related to the vertical load, the charge in the compressed state corresponds one-to-one with the vertical load on a non-pneumatic tire. The charge at sensor positions 1 and 2 under compression states is then fitted using a polynomial, with the following fitting formula:

[0150] (twenty four)

[0151] In equation (24): Q 1press Let Q be the charge quantity in the compressed state at position 1. 2press S represents the charge quantity in the compressed state at position 2. r p1, p2, p3, p4, p5, and p6 are the radial displacement of the spokes, and p1, p2, p3, p4, p5, and p6 are the fitting parameters.

[0152] The fitting results show that the charge quantity at sensor position 2 (on the reverse side of the spokes) under compression has a higher linear correlation with the radial displacement of the spokes. Therefore, position 2 is determined to be the optimal placement position for the PVDF sensor. After selecting the position, the total charge quantity at position 2 is fitted with respect to the radial displacement of the spokes using a third-order sine function:

[0153] (25)

[0154] In equation (25): a1, a2, a3, b1, b2, b3, c1, c2, c3 are fitting parameters.

[0155] Step 9: Establish a radial displacement model of spokes when a non-pneumatic tire is rolling.

[0156] When a non-pneumatic tire is subjected to a vertical load, the hub center experiences vertical displacement, resulting in varying degrees of radial displacement in each spoke. Based on the simulation data fitting results from Abaqus finite element analysis software, a numerical model of the radial displacement of a single spoke with respect to the circumferential angle during one revolution of a non-pneumatic tire is established as follows:

[0157] (26)

[0158] In equation (26): S r Let S be the radial displacement of the spokes, S be the tire sinking, θ be the tire circumferential angle, a0-a5 and b1-b5 be the parameters to be identified related to the sinking, and w be the constant to be identified.

[0159] The relationship between the vertical load and the deflection of a non-pneumatic tire is shown below:

[0160] (27)

[0161] In equation (27): d1, d2, and d3 are fitting parameters.

[0162] The tire roll angle is related to the vehicle speed:

[0163] (28)

[0164] In equation (28): v is the vehicle speed and d is the diameter of the non-pneumatic tire.

[0165] Step 10: Establish and validate a complete mathematical model for vertical force monitoring.

[0166] The above models were built in the Simulink system simulation software, including the tire rolling angle model, sinkage model, spoke radial displacement model, position 2 full-state charge model, and charge amplifier model. The feedback capacitor C in the charge amplifier model... f Choose 1000pF, bleed resistor R fA value of 10 MΩ corresponds to a sensitivity of 10. 9 V / C. The vehicle speed v was set to 10 km / h, the vertical load to 1500 N, and the model sampling rate to 500 Hz. A drum test bench was used to perform tests under the same operating conditions. The simulated voltage and test bench results are as follows: Figure 14 As shown.

[0167] Figure 14 The voltage waveform and amplitude in the test results are basically consistent with the experimental results, which verifies the effectiveness of the PVDF sensor arrangement method for monitoring the vertical force of non-pneumatic tires proposed in this invention.

Claims

1. A method for arranging PVDF sensors for monitoring the vertical force of non-pneumatic tires, characterized in that, The method includes the following steps: Step 1: Establish the piezoelectric charge model of the PVDF sensor A PVDF sensor model was established in the multiphysics simulation software Comsol, simplifying the sensor into a five-layer rectangular thin plate structure, including a PVDF piezoelectric layer, two PET protective layers, and two silver-ink electrode layers; a surface charge model of the PVDF sensor was established based on the electrostatic Gaussian theorem. Step 2: Establish a strain transfer model for the spoke-PVDF sensor and obtain the strain distribution function of the PVDF sensor and spokes along the axial direction; Step 3: Establish the relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes; Step 4: Calculate the electric displacement distribution in the PVDF sensor deployment area; The correspondence between the tire coordinate system and the sensor coordinate system is determined. Based on the PVDF piezoelectric charge model, the spoke-PVDF sensor strain transfer model, and the relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes, the electric displacement distribution in the sensor arrangement area is calculated. Step 5: Calculate the charge per unit length using discrete integration with a sliding window; Step 6: Determine the optimal radial placement of the sensor: The differential operation is performed on the charge per unit length under different compression amounts to find the position corresponding to the maximum gradient of charge per unit length, and the optimal radial arrangement position of the sensor is determined. Step 7: Determine the optimal mounting surface for the sensor Calculate the charge amount of different mounting surfaces under various radial displacements, compare the linearity of charge amount and radial displacement, select the mounting surface with higher linearity as the optimal mounting surface, and perform function fitting on the charge amount in all states. In step 2, the strain distribution function of the PVDF sensor and spokes along the axial direction is expressed as: （2） In formula (2): Let be the strain distribution function along the axial direction of the PVDF sensor. Let be the strain distribution function of the spokes along the axial direction. The stiffness ratio of polyurethane to PVDF, rate ε Let L be the strain transmissivity, L be the half-length of the PVDF sensor, and ε be the strain transmissivity. u E represents the axial strain experienced at both ends of the spoke. ft E represents the Young's modulus of the spokes. pvdf h is the Young's modulus of PVDF. ft h is the spoke thickness. pvdf PVDF thickness; The relationship between the triaxial strain of the PVDF sensor and the triaxial strain of the spokes in step 3 is expressed as follows: （3） In equation (3): rate εxx The strain transmissivity along the length of the PVDF piezoelectric layer is denoted as rate. εyy ε is the strain transmissivity in the width direction of the PVDF piezoelectric layer. xxPVDF For the strain along the length of the PVDF sensor, ε yyPVDF For the strain in the width direction of the PVDF sensor, ε zzPVDF ε represents the strain in the thickness direction of the PVDF sensor. xxft ε is the axial strain of the spokes. yyft For the radial strain of the spokes, ε zzft For the circumferential strain of the spokes.

2. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 1, characterized in that, The surface charge model of the PVDF sensor in step 1 is expressed as follows: （1） In equation (1): D is the electrical displacement of the PVDF sensor, d 31 Let d be the piezoelectric constant along the length of the PVDF. 32 d is the piezoelectric constant in the width direction of the PVDF. 33 T is the piezoelectric constant in the thickness direction of PVDF. xx For the stress along the length of the PVDF piezoelectric layer, T yy For the width direction stress of the PVDF piezoelectric layer, T zz Let denoted as PVDF piezoelectric layer thickness direction stress, Q as PVDF sensor surface charge, n as the outward normal vector of the dielectric and conductor, A as PVDF piezoelectric layer area, and P as PVDF polarization direction, where P=1 when polarization direction is upward and P=-1 when polarization direction is downward.

3. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 2, characterized in that, The electric displacement corresponding to the PVDF sensor arrangement area in step 4 It is expressed as follows: （4） In equation (4), T yyft T zzft T xxft These are the radial, circumferential, and axial components of the spoke stress tensor, respectively. ε1 Spoke front strain transmissivity, rate ε2 Strain transfer rate on the front of the spokes.

4. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 3, characterized in that, Step 5 calculates the charge per unit length at all discrete locations of the PVDF piezoelectric layer within the spoke length range as follows: （5） In equation (5): N pvdf x1 represents the charge per unit length in the sensor arrangement area, x2 represents the position corresponding to the tail of the PVDF piezoelectric layer of the sensor, and x2 represents the position corresponding to the head of the PVDF piezoelectric layer of the sensor.

5. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 4, characterized in that, The method for calculating the charge per unit length using the sliding window discrete integral in step 5 is as follows: Import the electric displacement data into the Matlab workspace, use timesseries to convert the electric displacement data into time series data, with a sampling frequency of 10Hz, and input the workspace data into the Buffer module through the From Workspace module; the sampling time in Simulink is 0.1s, the output buffer size of the Buffer module is set to the corresponding PVDF piezoelectric layer length, and the buffer overlap is the PVDF piezoelectric layer length - 1, that is, the sliding window moves to the right by 0.1 for each simulation step. The output of the Buffer module is accumulated using the SUM module and multiplied by the sampling time to achieve discrete integration of the region. As the sliding window moves to the right, the regional charge per unit length at all discrete positions of the PVDF piezoelectric layer within the spoke length range can be obtained.

6. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 5, characterized in that, The method for determining the optimal radial placement of the sensor in step 6 is as follows: For the linear variation range of the spoke electric displacement gradient, the charge per unit length at compression length x1 is subtracted from the charge per unit length at compression length x2, and the calculation formula is as follows: （6） In formula (6): The maximum gradient of charge per unit length, and the position x corresponding to the peak of the maximum gradient of charge per unit length. final This is the optimal position for the sensor's end.

7. The PVDF sensor arrangement method for monitoring vertical force in non-pneumatic tires according to claim 6, characterized in that, Step 7, determining the optimal mounting surface for the sensor, is as follows: After calculating the charge per unit length corresponding to each radial displacement at the two optimal positions of the mounting surface under spoke tension and compression, multiplying it by the sensor width, the final charge calculation formula is as follows: （7） In equation (7): Q1 is the surface charge when the sensor is placed on the front side of the spoke, Q2 is the surface charge when the sensor is placed on the back side of the spoke, B is the width of the PVDF piezoelectric layer of the sensor, and N pvdf-1 N represents the charge per unit length when the sensor is positioned on the front of the spoke. pvdf-2 This represents the charge per unit length when the sensor is positioned on the reverse side of the spokes. The charge quantities under the two optimal compression states are fitted using a polynomial, and the fitting formula is as follows: （8） In equation (8): Q 1press Let Q be the charge quantity in the compressed state at position 1. 2press S represents the charge quantity in the compressed state at position 2. r p1, p2, p3, p4, p5, and p6 are the radial displacement of the spokes, and p1, p2, p3, p4, p5, and p6 are the fitting parameters. Based on the linear correlation between the charge amount under compression and the radial displacement of the spokes, a higher position is selected as the optimal arrangement position.

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