Design method of semi-empirical model for vertical load output voltage of non-pneumatic tire based on pvdf sensor

Abstract

The application is based on a semi-empirical model of the vertical load output voltage of a non-pneumatic tire PVDF sensor, belongs to the field of tire intelligent monitoring, and aims at the special structure of the non-pneumatic tire, establishes a semi-empirical model of the output voltage of the PVDF sensor and the vertical load based on the relationship between the vertical load and the strain, takes the vertical load and the speed signal as the input quantity, obtains the output voltage through the hub center subsidence amount-spoke radial displacement-peak curvature-curvature conforming to the actual waveform-PVDF sensor surface charge, establishes the connection between the output voltage waveform of the PVDF sensor and the tire vertical load, provides guidance for further vertical load estimation of the spoke non-pneumatic tire based on the PVDF sensor, avoids the hardware computing power burden caused by the multi-sensor fusion, and can efficiently obtain the tire vertical load by using only a single PVDF sensor.

Description

Technical Field

[0001] This invention relates to the field of intelligent tire monitoring, and in particular to a semi-empirical model of the vertical load output voltage of a non-pneumatic tire based on a PVDF sensor. Background Technology

[0002] Since the early 21st century, Michelin first introduced the concept of spoked non-pneumatic tires (NPT), which completely avoid tire blowouts by replacing the pneumatic tire carcass with flexible spokes. While NPTs offer run-flat protection and maintenance-free operation, the contact area between the spokes and the rim is bonded with adhesive, which can lead to delamination and cracking under overload conditions, severely impacting vehicle safety. Besides static load, load transfer during vehicle operation is also a contributing factor to NPT failure. Real-time monitoring of the vertical load on the NPT can effectively reduce or avoid these risks. Furthermore, real-time monitoring of the vertical load data can provide essential tire information for vehicle rollover warning systems and electronic stability control systems.

[0003] Current sensor-based methods for estimating tire vertical force are diverse. Patent CN202011254568.8 proposes a system combining an accelerometer, wheel speed sensor, and tire pressure sensor. This system acquires acceleration signals during tire rolling by embedding an accelerometer inside the inflatable tire and indirectly estimates the vertical force based on the tire's contact angle interval and a tire model. This type of method requires numerous sensor signals, placing a significant computational burden on the hardware, and its estimation accuracy depends on the accuracy of the tire model. Patent CN202410664310.7 discloses a data-driven tire load estimation method. It obtains tire strain data through finite element simulation and uses a neural network model for training to establish a load-strain mapping relationship. However, this method has not been experimentally verified, and strain sensors suffer from fatigue failure after long-term use. Existing technology proposes a vertical load estimation method for agricultural machinery tires. This method acquires tire deformation signals using piezoelectric film sensors placed on the inner sidewall of the tire, combines tire rotation angle and speed signals, and establishes a vertical load correspondence using a BP neural network optimized by a genetic algorithm based on the signal characteristics. This method requires high computing power and is difficult to control in terms of cost.

[0004] The vertical load estimation systems proposed in the above patents all focus on pneumatic tires. When a vehicle is in motion, the interior of a pneumatic tire experiences high temperatures, high pressures, and low-frequency vibrations, placing high demands on tire sealing and sensors. When installing sensors inside a pneumatic tire, whether accelerometers, strain gauges, or piezoelectric sensors, the requirement for accurate data sampling necessitates opening holes in the rim to arrange wires, which severely impacts the tire's airtightness. Spoke-type non-pneumatic tires offer advantages in sensor integration due to their open structure. Tire pressure monitoring is unnecessary; tire force signals can be directly obtained through sensors embedded in the tire body or surface-mounted on the spokes, facilitating maintenance and reducing installation and equipment costs. However, due to the significant structural differences between spoke-type non-pneumatic tires and pneumatic tires, existing vertical load estimation systems for pneumatic tires are not applicable to spoke-type non-pneumatic tires. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a design method for a semi-empirical model of the output voltage of a non-pneumatic tire under vertical load based on a PVDF sensor. The technical solution adopted is as follows:

[0006] A semi-empirical model for the vertical load output voltage of a non-pneumatic tire based on a PVDF sensor includes a vehicle speed signal conversion module, a vertical load-sag mapping model, a radial displacement regression model, a peak curvature module, a curvature generation model that conforms to the actual waveform, a PVDF sensor charge calculation model, and an amplifier output voltage calculation model.

[0007] This semi-empirical model uses vertical load and vehicle speed signals as inputs. The vehicle speed signal conversion module converts the vehicle speed signal into the tire circumferential angle. The vertical load-sag mapping model converts the vertical load into the wheel hub center sag. The radial displacement regression model converts the wheel hub center sag and the tire circumferential angle into the spoke radial displacement. The peak curvature module converts the spoke radial displacement into peak curvature based on the mapping relationship between spoke radial displacement and peak curvature. The curvature generation model that conforms to the actual waveform generates curvature that conforms to the actual waveform using the peak curvature and the tire circumferential angle. The PVDF sensor charge calculation model calculates the PVDF sensor surface charge using the curvature that conforms to the actual waveform. Finally, the amplifier output voltage calculation model obtains the output voltage from the PVDF sensor surface charge.

[0008] The vehicle speed signal conversion module converts the vehicle speed signal (km / h) into the tire rolling angular velocity (deg / s), as shown in the following formula:

[0009] (1)

[0010] In equation (1), v is the longitudinal velocity of the vehicle, and d is the diameter of the non-pneumatic tire;

[0011] Then, based on the tire's rolling angular velocity, the mod command is used to make it cycle between 0 and 360 degrees to simulate the actual tire rotation.

[0012] The vertical load-sinking mapping model is shown below:

[0013] (2)

[0014] In equation (2), S is the center depression of the wheel hub, and F z t0 represents the vertical load on the tire, and t0, t1, t2, and t3 are the fitting parameters.

[0015] The radial displacement regression model is as follows:

[0016] (3)

[0017] In equation (3), S r Let θ be the radial displacement of the spokes, θ be the circumferential angle of the tire, w be the constant to be identified, and a0, a1, a2, a3, a4, a5, b1, b2, b3, b4, and b5 be the parameters to be identified related to the wheel hub center sinking S.

[0018] (4)

[0019] In equation (4), z1, z2, z3, z4, z5, z6, z7, z8, z9, z 10 z 11 z 12 z 13 z 14 z 15 z 16 z 17 z 18 z 19 z 20 z 21 z 22 z 23 z 24 z 25 z 26 and z 27 All of these are fitting parameters.

[0020] The peak curvature module uses a three-point circumcircle curvature solution model to calculate the curvature of any three adjacent nodes on the spokes with different hub center depressions. Based on the solution results, the peak curvature ρ is established. max The mapping relationship between the radial displacement of the spokes and the solution formula used is:

[0021] (5)

[0022] In equation (5), any three adjacent nodes A on the spokes s B s C s Forming triangle A s B s C s a s For B s C s Side length, b s For A s C s Side length, c s For A s B s Side length.

[0023] The curvature generation model that conforms to the actual waveform generates curvature based on the peak curvature and the tire circumferential angle, as shown in the following formula:

[0024] (6)

[0025] In equation (6), ρ1 is the curvature that conforms to the true waveform, θ is the tire circumferential angle, θ1 is the tire circumferential angle corresponding to the extreme point of radial displacement of the spoke stretching section, θ2 is the tire circumferential angle corresponding to the extreme point of radial displacement of the spoke stretching section, line1 is the charge waveform of the spoke recovery section, and line2 is the charge waveform of the spoke compression section, expressed as:

[0026] (7).

[0027] The formula for calculating the surface charge of a PVDF sensor is as follows:

[0028] (8)

[0029] In equation (8), Q is the surface charge of the PVDF sensor, and d 31 denoted as PVDF along the film thickness direction, A is the area of ​​the piezoelectric film, Y is the Young's modulus of PVDF, and h is the spoke thickness.

[0030] The amplifier output voltage calculation model is expressed by the following formula:

[0031] (9)

[0032] In equation (9), V out For the output voltage, A cq This represents the sensitivity of the charge amplifier.

[0033] The semi-empirical model of the vertical load output voltage of a non-pneumatic tire based on a PVDF sensor is used to infer the waveform and peak voltage of the PVDF sensor output voltage, as well as the installation position of the PVDF sensor. Then, a vertical load estimation system for spoke-type non-pneumatic tires based on a PVDF sensor is further constructed.

[0034] The beneficial effects of this invention are:

[0035] 1. This invention combines data-driven approaches with physical modeling. The semi-empirical model established is based on finite element simulation results and physical principles, and each process signal acquired has physical meaning. By establishing a semi-empirical model, the vertical characteristics of non-pneumatic tires equipped with PVDF sensors can be characterized. Simulation of the model can guide hardware selection and reduce testing costs.

[0036] 2. This invention establishes a relationship between the output voltage waveform of the PVDF sensor and the vertical load of the tire, providing guidance for further estimation of the vertical load of spoke-type non-pneumatic tires based on PVDF sensors. It avoids the hardware computing burden caused by multi-sensor fusion, and only requires a single PVDF sensor to efficiently obtain the vertical load of the tire. Attached Figure Description

[0037] Figure 1 Main structure and load-bearing principle of X3 type non-pneumatic tire

[0038] Figure 2 PVDF sensor structural dimensions

[0039] Figure 3 Spoke micro-element strain model

[0040] Figure 4 Single spoke finite element model

[0041] Figure 5 Discrete point curvature solution principle

[0042] Figure 6 Hardware assembly diagram

[0043] Figure 7 Example of voltage acquisition in drum test bench

[0044] Figure 8 technical route

[0045] Figure 9 Relationship between settlement and vertical load

[0046] Figure 10 Nodal curvature calculation results

[0047] Figure 11 Variable load radial displacement regression results

[0048] Figure 12 Model output voltage

[0049] Figure 13 Hardware integration diagram Detailed Implementation

[0050] The technical solution of the present invention will be further explained and described below with reference to specific embodiments.

[0051] This invention first constructs a semi-empirical model of the vertical load output voltage of a non-pneumatic tire based on a polyvinylidene fluoride (PVDF) sensor, simulates the output voltage of the PVDF sensor on a non-pneumatic tire (NPT), and infers the waveform, peak voltage, and installation position of the PVDF sensor output voltage. Then, it further constructs a spoke-type non-pneumatic tire vertical load estimation system based on the PVDF sensor.

[0052] The following section provides a more detailed explanation of the process of constructing a semi-empirical model for the vertical load output voltage of a non-pneumatic tire based on a polyvinylidene fluoride (PVDF) sensor.

[0053] The main structure and load-bearing principle of the spoked non-pneumatic tire (NPT) are as follows: Figure 1 As shown. In Figure 1 In this system, the NPT (Near-Tire Plate) consists of a tread, shear band, reinforcing layer, spokes (spokes, outer spoke ring, inner spoke ring), and hub. Its load-bearing mechanism is top-load, meaning that when a vertical load is applied to the center of the hub, the vertical force is transmitted to the tread through the spokes. At this time, the spokes within the contact patch are under compression, while the spokes outside the contact patch are under tension. When the vertical load changes, the deformation of the spokes within the contact patch is significant; therefore, it is hypothesized that there is a corresponding relationship between the load-bearing capacity of the NPT and the spoke deformation.

[0054] To explore this correspondence, this invention focuses on a polyvinylidene fluoride (PVDF) sensor. A PVDF sensor is a sensor that utilizes the piezoelectric effect to convert surface pressure into an electrical charge signal, and its structure is as follows: Figure 2 As shown, it consists of two electrode layers, a piezoelectric film, and two pins. Under external force, a charge shift occurs on the surface of the PVDF sensor. After being amplified by a charge amplifier, a voltage signal is generated. The simplified formula for calculating the surface charge of the PVDF sensor is as follows:

[0055] (1)

[0056] In formula (1): d 31 Let A be the piezoelectric coefficient of PVDF along the film thickness direction, A be the area of ​​the piezoelectric film, Y be the Young's modulus of PVDF, and ε be the piezoelectric coefficient of PVDF along the film thickness direction. PVDFThe strain on the PVDF sensor surface; in this invention, the PVDF sensor is attached to the spoke surface, therefore the PVDF surface strain ε is... PVDF It can be approximated as equal to the spoke surface strain ε;

[0057] The NPT spoke micro-element strain model established in this invention is as follows: Figure 3 As shown. During quasi-static loading, considering only the bending deformation of the spokes, it is assumed that a neutral layer of constant length exists inside the spokes, dividing the spoke surface into a tensile zone and a compression zone. Before bending deformation, the neutral layer is a straight beam, and after deformation, it becomes a circular arc. Based on the principle of curved beam strain calculation, this invention obtains the following surface strain calculation equations for the compression and tensile zones:

[0058] (2)

[0059] In equation (2), ds is the length of the infinitesimal element before deformation of the neutral layer, dS is the length of the infinitesimal element after deformation of the neutral layer, dθ is the central angle after deformation of the neutral layer, R is the radius of curvature after deformation of the neutral layer, ρ is the curvature of the arc (i.e., the curvature of the node on which the PVDF sensor is installed on the spoke), h is the thickness of the spoke, and ε s ε is the surface strain of the tensile zone. c The surface strain of the compression zone.

[0060] The surface strain of the PVDF sensor at this time can be expressed as follows:

[0061] (3)

[0062] Substituting formula (3) into formula (1), the formula for calculating the surface charge of PVDF can be transformed into:

[0063] (4)

[0064] Based on formula (4), a PVDF sensor charge calculation model is established in Simulink. This model requires obtaining the curvature of NPT spokes under different load conditions to calculate the surface charge of the PVDF sensor.

[0065] To further obtain the curvature of NPT spokes under different load conditions, this invention establishes an NPT finite element model based on the X3 non-pneumatic tire produced by Feynman Technology (Qingdao) Co., Ltd., and performs static loading simulation.

[0066] First, the simulated vertical load-settlement relationship is fitted using a polynomial, and the fitting formula is as follows:

[0067] (5)

[0068] In equation (5), S is the center depression of the wheel hub, and F zThe vertical load is t0, t1, t2, and t3, which are all fitting parameters.

[0069] A vertical load-sag mapping model is established in Simulink based on formula (5), in which the tire vertical load F is used as the basis. z The input quantity is the wheel hub center depression S, and the output quantity is the wheel hub center depression S.

[0070] Then, the radial displacement data of each spoke is extracted from the finite element simulation results. Under different sinking conditions, the radial displacement data of the tire in one rotation is used with respect to the tire circumferential angle, and a 6th order Fourier function is used for global identification to obtain the regression equation, which is expressed as follows:

[0071] (6)

[0072] In equation (6), S r θ represents the radial displacement of the spokes, θ represents the circumferential angle of the tire, a0, a1, a2, a3, a4, a5, b1, b2, b3, b4 and b5 are all parameters to be identified related to the sinking amount, and w is a constant to be identified.

[0073] From formula (6), we can see that when the subsidence S=0, the radial displacement S r =a0+a1+a2+a3+a4+a5, therefore, zero-point constraints need to be established, that is, when S=0, a0+a1+a2+a3+a4+a5=0.

[0074] After identification, the relationship between the above-mentioned parameters to be identified and the subsidence amount is as follows:

[0075] (7)

[0076] In equation (7): z1, z2, z3, z4, z5, z6, z7, z8, z9, z 10 z 11 z 12 z 13 z 14 z 15 z 16 z 17 z 18 z 19 z 20 z 21 z 22 z 23 z 24 z 25 z 26 and z 27 All of these are fitting parameters.

[0077] A radial displacement regression model is established in Simulink based on formulas (6) and (7). In this model, the hub center sinking S and the tire circumferential angle θ output from the vertical load-sinking mapping model are used as inputs, and the spoke radial displacement S is used as the input. r For output quantity;

[0078] To further establish the spoke radial displacement S r Based on the mapping relationship with the spoke node curvature, this invention extracts the spoke node positions from the simulation results of an NPT finite element model (selecting a single-spoke model portion of the model) with a certain amount of subsidence, such as... Figure 4 As shown. Select any three adjacent node positions A. s B s and C s The curvature of discrete spoke nodes is solved using the three-point circumcircle method, such as... Figure 5 As shown.

[0079] Let triangle A be an example. s B s C s The three sides are a s b s and c s Draw the perpendicular bisectors of the lines connecting any two adjacent points; their intersection point forms triangle A. s B s C s Circumcenter O, connected to C s O and extend it to intersect the circumference at D. s Point, at this time circle O is also quadrilateral A. s B s C s D s The curvature of the circumcircle of a quadrilateral can be expressed as follows, based on the property that opposite angles of a quadrilateral are supplementary:

[0080] (8)

[0081] In equation (8), ρ is the circumcircle curvature, i.e., the spoke node curvature, and R is the circumcircle radius. s b s c s The lengths of the three sides can be obtained from the coordinates of the nodes, and ∠B can be solved using the Law of Cosines. s :

[0082] (9)

[0083] In equation (9), a s b s c s They are triangles A and B respectively. s B s Cs B s C s A s C s A s B s Side length.

[0084] According to ∠B s The size of the circumcircle, combined with formulas (8) and (9), gives the formula for calculating the curvature of the circumcircle as follows:

[0085] (10)

[0086] Based on this method, the curvature of any three adjacent nodes in spokes with different subsidence amounts is solved, and the curvature solution results are as follows: Figure 10 As shown, according to Figure 10 The peak value of the waveform in the middle data can be used to obtain the maximum deformation zone in the middle section of the spoke, as well as the peak curvature ρ of that node during compression. max The maximum deformation zone obtained determines the installation position of the subsequent PVDF sensor. Based on the correlation between the sinking and the radial displacement of the spokes, the relationship between the radial displacement of the spokes and the peak curvature ρ at the spoke nodes can be obtained. max Based on the mapping relationship, a peak curvature module is established. This module takes the radial displacement of the spokes as input and outputs the peak curvature ρ of the spoke nodes. max .

[0087] The above modeling assumes that the PVDF sensor outputs a charge signal throughout the entire process, but this is inconsistent with reality. The charge generation of the PVDF sensor is related to the strain and strain rate of the piezoelectric film, where the strain affects the signal amplitude, and the strain rate affects the signal amplitude and waveform.

[0088] Within the grounding region, the spokes are in a compression zone, undergoing two processes: a compression phase, where the spoke moves from the zero point of radial displacement to the negative peak of radial displacement; and a recovery phase, where the spoke moves from the negative peak of relative displacement back to the zero point. Outside the grounding region, the area is a tension zone. In actual PVDF sensors, the charge waveform between the tension zone and the compression phase, and between the recovery phase and the tension zone, generates a peak and a trough. The modeling method described above divides the spoke micro-element into a compression layer, a neutral layer, and a tension layer. When the spoke is attached to the surface of the tension layer, it is in a compressed state and generates a positive charge; in the recovery state, it generates a negative charge. The signal waveform of the spoke compression zone is now described using a sine function based on the signal period. Line 1 represents the charge waveform of the spoke recovery phase, and line 2 represents the charge waveform of the spoke compression phase. The waveforms are shown below:

[0089] (11)

[0090] In equation (11), θ is the tire circumferential angle, θ1 is the tire circumferential angle corresponding to the extreme point of radial displacement of the spoke stretching section, and θ2 is the tire circumferential angle corresponding to the extreme point of radial displacement of the spoke stretching section.

[0091] Therefore, the curvature of a single-cycle spoke can be rewritten as follows:

[0092] (12)

[0093] In equation (12): ρ1 is the curvature related to the charge waveform, ρ max The peak curvature of the spokes in the compression section.

[0094] Combining formulas (11) and (12), there are a total of 4 characteristic points in the single-cycle charge waveform of the PVDF sensor, namely the upper and lower peak points of the sine curve and (θ1, 0) and (θ2, 0).

[0095] Based on formulas (11) and (12), a curvature generation model conforming to the actual waveform is established in Simulink. In this model, the tire circumferential angle θ and the peak curvature ρ of the spoke nodes output by the peak curvature module are used. max As the input, the output is the curvature ρ1 related to the charge waveform (i.e., the curvature that conforms to the actual waveform). By inputting this curvature into the PVDF sensor charge calculation model, the surface charge of the PVDF sensor can be simulated.

[0096] To simulate real-world working conditions, the curvature generation model, which conforms to the actual waveform, uses the tire circumferential angle after the vehicle speed signal is transformed as input. The tire rolling angular velocity (deg / s) is calculated from the vehicle speed signal (km / h) using the following formula:

[0097] (13)

[0098] In equation (13): v is the longitudinal speed of the vehicle, and d is the diameter of the non-pneumatic tire.

[0099] Set the tire roll angle ramp input with a slope of 1. Multiply the tire roll angle by the roll angular velocity and use the mod command to make it cycle between 0 and 360 degrees to simulate the actual tire rotation.

[0100] Because the charge output by the PVDF sensor is relatively small and difficult to measure directly, it needs to be connected to a charge amplifier. After amplification by the charge amplifier, the final output voltage expression can be obtained:

[0101] (14)

[0102] In equation (14), V out For the output voltage, A cqThe sensitivity of the charge amplifier is given. Based on formula (14), an amplifier output voltage calculation model is established in Simulink. In this model, the PVDF sensor surface charge Q, output from the PVDF sensor charge calculation model, is used as the input, and the output voltage V is used as the input. out This is the output quantity.

[0103] Thus, a semi-empirical model for the output voltage of a PVDF sensor, consisting of a vehicle speed signal conversion module, a vertical load-sinking mapping model, a radial displacement regression model, a peak curvature module, a curvature generation model conforming to the actual waveform, a PVDF sensor charge calculation model, and an amplifier output voltage calculation model, has been established. This model establishes a complete estimation model for the output voltage, which takes vertical load and vehicle speed signal as inputs, and processes hub center sinking, spoke radial displacement, spoke curvature, spoke curvature conforming to the actual PVDF charge waveform, and PVDF surface charge. This model can be used to characterize the vertical load of NPT systems equipped with PVDF sensors, and the output signal of this model can provide guidance for the selection of hardware parameters for physical systems.

[0104] Guided by the aforementioned semi-empirical model, this invention constructs a vertical load estimation system for spoke-type non-pneumatic tires based on PVDF sensors, such as... Figure 6 As shown, the system consists of a remote processing end and a non-pneumatic tire acquisition end; the non-pneumatic tire acquisition end includes: a PVDF sensor, an RF cable, a charge amplifier, a voltage acquisition module, a Bluetooth module, a 9V power supply, and a single power supply to positive and negative 5V power supply module; the remote processing end includes: an Arduino UNO R4 microcontroller and a PC host computer;

[0105] When a non-pneumatic tire rolls under load, the PVDF sensor generates a charge signal during spoke deformation. This signal is transmitted to a charge amplifier via an RF line. After amplification by the charge amplifier, a voltage signal is output and acquired by a voltage acquisition module. The acquired data is then wirelessly transmitted to a remote processing terminal via a Bluetooth module for data analysis by a PC or online processing by a microcontroller. The charge amplifier and voltage acquisition module are powered by a 9V power supply through a single power supply to positive and negative 5V power module pins.

[0106] Regarding the sensor mounting area, due to the small size of the PVDF sensor, it needs to be attached to the area of ​​maximum deformation within the NPT spokes. This invention determines the spoke curvature for this area using the semi-empirical model established above. The effective deformation area length of the PVDF sensor is 15mm, and the sensor is radially attached to the center of the maximum deformation area along the NPT spokes.

[0107] The integrated hardware assembly was installed on the inner wall of a non-pneumatic tire hub, and a drum test bench was used for data acquisition and testing, performing a full-condition test with characteristic vehicle speed × characteristic load cycles. During the test, the acquired data was transmitted to a PC via Bluetooth serial port for collection and analysis. The acquired voltage data signals were... Figure 7 For example,

[0108] Figure 7 (a) This represents the actual voltage data collected at a characteristic vehicle speed of 10 km / h and a characteristic load of 2000 N. When the non-pneumatic tire rotates, the spokes are compressed and deformed in the ground contact area, and the PVDF output signal collected by the acquisition terminal exhibits periodic changes. The voltage characteristics within a single cycle are analyzed as follows: Figure 7 As shown in (b). By Figure 7 (b) It can be seen that during tire rolling, the PVDF voltage signal is in the tensile zone for more than half the time, at which point the voltage amplitude is approximately 0. After entering the compression zone, the signal is symmetrically distributed around the center and produces two distinct peaks. Peak A corresponds to the point of maximum deformation rate in the spoke compression section, and similarly, peak B corresponds to the point of maximum deformation rate in the spoke recovery section. The voltage values ​​corresponding to points A and B are directly related to the tire load and tire speed. Therefore, the mapping relationship between the measured voltage value and the tire load and tire speed can be established through multiple experiments. Under the premise of ensuring the accuracy of the drum test bench, the estimation error of this method can be less than 5%.

[0109] Finally, the invention is programmed into a microcontroller, using a sliding window peak search algorithm to extract the peak value of the test signal online, thereby outputting the signal peak value. The corresponding load can then be obtained by looking up the mapping table based on the signal peak value. Thus, the vertical load estimation system for spoke-type non-pneumatic tires based on a PVDF sensor described in this invention has been completed.

[0110] like Figure 8 As shown, the present invention provides a method for estimating the vertical load of a spoke-type non-pneumatic tire based on a PVDF sensor, the steps of which are as follows:

[0111] Step 1: Finite element simulation of NPT vertical characteristics;

[0112] (1) Construction of the relationship between NPT vertical load and settlement

[0113] A finite element model of a non-pneumatic tire was established. In this embodiment, the X3 type non-pneumatic tire produced by Feynman Technology (Qingdao) Co., Ltd. was used as the prototype. A static load simulation of 4500N was performed on the NPT in Abaqus software. The data of the NPT hub center sinking and the applied vertical load were obtained according to the simulation results. The data were fitted according to the form of formula (5). The results are as follows. Figure 9 As shown.

[0114] (2) Construction of the relationship between radial displacement of spokes, circumferential angle and sinking

[0115] From the simulation results of step 001, according to the tire circumferential angle, the radial displacement data of the spokes under different sinking amounts are extracted, and the data are fitted and the parameters are identified according to the formulas (6) and (7).

[0116] (3) Simulation of displacement-deformation of a single spoke

[0117] A finite element model of a single spoke was established, and deformation simulations were performed under different radial displacements. The coordinates of the spoke nodes under each radial displacement were then extracted.

[0118] Step 2: Semi-empirical modeling of PVDF

[0119] (1) Based on the simulation results in step one, establish the vertical load-sag mapping model in Simulink according to formula (5), establish the radial displacement regression model according to formula (6) and formula (7), and input the vertical load-sag mapping model after the tire circumferential angle after the vehicle speed signal is transformed.

[0120] (2) Method of finding curvature using the three-point circumcircle method

[0121] For any three adjacent nodes in spokes with different subsidence amounts, the three-point circumcircle method is used to calculate the node curvature according to formula (8). The node coordinates and curvature calculation results are as follows: Figure 10 As shown in (a) and (b), the maximum deformation region can be determined based on the calculated curvature, and the radial displacement of the tire and the peak curvature ρ can be obtained. max The mapping relationship between tire radial displacement and peak curvature ρ; max The mapping relationship is used to establish the peak curvature module; according to formulas (11) and (12), the peak curvature ρ of the peak curvature module is used. max Using the tire circumferential angle as input, a curvature generation model that conforms to the actual waveform is built in Simulink;

[0122] (3) Solving surface strain using the curved beam method

[0123] Formula (4) is obtained by solving the surface strain using the curved beam method.

[0124] (4) PVDF strain-voltage model

[0125] In Simulink, a PVDF sensor charge calculation model is established based on the curvature output of the curvature generation model that conforms to the actual waveform as the input quantity according to formula (4). An amplifier output voltage calculation model is established based on the PVDF surface charge output by the PVDF charge calculation model as the input quantity according to formula (14).

[0126] This completes the construction of various calculation models in a method for estimating the vertical load of spoke-type non-pneumatic tires based on PVDF sensors, with vertical load and vehicle speed signals as inputs and PVDF voltage as output.

[0127] (5) Model validation

[0128] The solver was set to a fixed step size of 0.0001, and the simulation was run in Simulink. The vertical load ramp input was set to a slope of 45°, and the vehicle speed was 9.8 km / h. The radial displacement regression model was then validated, and the validation results are as follows: Figure 11 As shown.

[0129] Step 3: Hardware Selection and Manufacturing

[0130] (1) Selection of hardware size and electrical parameters

[0131] To simulate the test conditions of the drum test bench, the load was set to the maximum load that the test tire could withstand, 4500N, and the vehicle speed was 10km / h. The model output voltage was as follows: Figure 12 As shown, according to Figure 12 The peak voltage value determines the amplification factor of the charge amplifier and the approximate acquisition range of the voltage acquisition module. Hardware size and power supply range are considered. The parameters of the PVDF sensor, RF line, charge amplifier, voltage acquisition module, and single-supply to positive / negative power supply module are determined as follows:

[0132] The PVDF sensor used is the TE Connectivity LDT0-28K PVDF sensor, with a piezoelectric film thickness of 28 μm and a thickness-direction piezoelectric coefficient d. 31 =33pC / N, dimensions 13mm×25mm×0.1mm.

[0133] The RF cable is an SMA RF cable with an SMA (male) connector and a length of 20cm.

[0134] The charge amplifier uses an OPA128 charge amplifier, powered by ±5~±18V, with a sensitivity (amplification factor) of 3×10⁻⁶. 9 V / C, connector type SMA (female), size 50 mm × 34 mm × 15 mm.

[0135] The voltage acquisition module uses the ES23C voltage acquisition module, which is powered by 5V, has an acquisition range of ±10V, an acquisition frequency of 500Hz, and dimensions of 30 mm × 50 mm × 15 mm.

[0136] Single power supply to positive / negative power supply module: Input voltage range 6.5~35V, output voltage ±5V, output voltage ripple <10mV, output current 500mA (MAX), dimensions 55mm×45mm×20mm. Powered by 9V power supply.

[0137] Waterproof protective case, with dimensions of 75mm×75mm×50mm.

[0138] (2) Sensor connection and installation process

[0139] Connect the pins of the PVDF sensor to the SMA connector RF cable. Note that the center wire of the RF cable should be connected to pin 2, and the shielding layer should be connected to pin 1. Connect the single-supply to positive / negative power supply module, voltage acquisition module, and charge amplifier to their respective interfaces using wires. After securing them, install them into the waterproof protective case to assemble the hardware assembly. After installation, as shown... Figure 13 As shown. Cut a 25mm x 9mm groove on the side of the waterproof protective shell to ensure the SMA connector will not loosen after it is inserted. Install the hardware assembly to the non-pneumatic tire rim and secure it with bolts or straps. Clean the spokes of the non-pneumatic tire with gasoline or alcohol to remove surface dust. Apply a layer of 3M super adhesive to the back of the sensor, with a thickness of 0.12mm, and attach the PVDF sensor to the center of the determined area of ​​maximum spoke deformation.

[0140] (3) Data acquisition test

[0141] To test the hardware's acquisition capability, gently move the PVDF film after powering on and observe whether the signal acquisition is normal.

[0142] Step 4: Bench Test Calibration

[0143] (1) Speed-load rolling condition test

[0144] Non-pneumatic tires are installed on a rotary drum test bench for testing under fixed speed and fixed characteristic load conditions. Test data is transmitted via Bluetooth serial port, saved and analyzed on a PC host computer, and a three-dimensional mapping relationship between output voltage peak value, vertical load and vehicle speed is established based on the characteristics of periodic data.

[0145] (2) Online data acquisition test

[0146] In the Arduino UNO R4 microcontroller, a sliding window peak search algorithm is written. This algorithm completes the acquisition of voltage peaks through the following steps:

[0147] Define the number of data items the window array can hold, and define the window array and its state. In the main function, set the serial port baud rate to 9600, and use the pinMode function to set the LED_BUILTIN pin as an output to determine the operating status. Set up a loop function to read the analog value from port A0 and store it in brightness. Define the PWM size as brightness / 1023, then define a newValue array, store the new value, and update the index. Use an if function to check if the window is full, and calculate the maximum value by traversal when the window is full.

[0148] Burn the program into the microcontroller and test it using the following method. Prepare an electronic ruler displacement sensor or a sliding rheostat. Connect the positive terminal of the displacement sensor to the microcontroller's 5V interface and the negative terminal to GND. Connect the signal interface to port A0 of the microcontroller's analog input interface, and connect the analog voltage acquisition module to output the signal. After the test is complete, press the displacement sensor contact. The signal peak tracking status can be seen in the serial port plotter of the Arduino IDE software, enabling peak search functionality.

[0149] At this point, all the functions described in this invention have been implemented.

Claims

1. A design method for a semi-empirical model of the vertical load output voltage of a non-pneumatic tire based on a PVDF sensor, characterized in that, The semi-empirical model comprises a vehicle speed signal conversion module, a vertical load-sinkage mapping model, a radial displacement regression model, a peak curvature module, a curvature generation model conforming to an actual waveform, a PVDF sensor charge calculation model, and an amplifier output voltage calculation model. The semi-empirical model takes the vertical load and the vehicle speed signal as input quantities, the vehicle speed signal conversion module is used to convert the vehicle speed signal into a tire circumferential angle, the vertical load-sinkage mapping model converts the vertical load into a hub center sinkage, the radial displacement regression model converts the hub center sinkage and the tire circumferential angle into a spoke radial displacement, the peak curvature module converts the spoke radial displacement into a peak curvature according to the mapping relationship between the spoke radial displacement and the peak curvature, the curvature generation model conforming to an actual waveform generates a curvature conforming to an actual waveform based on the peak curvature and the tire circumferential angle, the PVDF sensor charge calculation model calculates the PVDF sensor surface charge using the curvature conforming to an actual waveform, and finally the amplifier output voltage calculation model obtains the output voltage from the PVDF sensor surface charge.

2. The design method of the semi-empirical model of the non-pneumatic tire vertical load output voltage based on the PVDF sensor according to claim 1, characterized in that wherein The vehicle speed signal conversion module converts the vehicle speed signal into a tire rolling angular velocity, and the formula is as follows: （1） In formula (1), v is the vehicle longitudinal speed, km / h; d is the non-pneumatic tire diameter, m; is the tire rolling angular velocity, deg / s; then based on the tire rolling angular velocity, the mod instruction is used to make it circulate between 0 and 360 deg to simulate the actual tire rotation, and the tire circumferential angle is obtained.

3. The design method of a PVDF sensor based semi-empirical model for non-pneumatic tire vertical load output voltage of claim 2, wherein, The vertical load-sinkage mapping model is as follows: （2） In formula (2), S is the hub center drop amount, F z is the tire vertical load, t0, t1, t2, t3 are fitting parameters.

4. The design method of a semi-empirical model of the output voltage of a non-pneumatic tire vertical load based on a PVDF sensor according to claim 3, characterized in that, The radial displacement regression model is as follows: （3） In formula (3), S r is a spoke radial displacement amount, θ is a tire circumferential angle, w is a constant to be identified, a0, a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 are parameters to be identified related to the hub center sag amount S: （4） In formula (4), z1, z2, z3, z4, z5, z6, z7, z8, z9, z 10 , z 11 , z 12 , z 13 , z 14 , z 15 , z 16 , z 17 , z 18 , z 19 , z 20 , z 21 , z 22 , z 23 , z 24 , z 25 , z 26 and z 27 are fitting parameters.

5. The design method of a PVDF sensor based semi-empirical model for non-pneumatic tire vertical load output voltage of claim 4, wherein, The peak curvature module solves the curvature of any adjacent three nodes on the spoke under different hub center sunken amounts based on a three-point circumcircle method curvature solving model, and establishes a mapping relationship between the peak curvature p max and the spoke radial displacement amount; wherein the solving formula used is: （5） In equation (5), any three adjacent nodes A on the spokes s B s C s Forming triangle A s B s C s a s For B s C s Side length, b s For A s C s Side length, c s For A s B s Side length.

6. The design method of a PVDF sensor based semi-empirical model for non-pneumatic tire vertical load output voltage of claim 5, wherein, The curvature generation model conforming to an actual waveform generates a curvature conforming to an actual waveform based on the peak curvature and the tire circumferential angle, and the formula is as follows: （6） In formula (6), p1 is the curvature conforming to the actual waveform, theta is the tire circumferential angle, theta1 is the tire circumferential angle corresponding to the radial displacement extreme point of the spoke stretching section, theta2 is the tire circumferential angle corresponding to the radial displacement extreme point of the spoke stretching section, line1 is the spoke recovery section charge waveform, line2 is the spoke compression section charge waveform, and the formula is as follows: （7）。 7. The design method of a PVDF sensor based semi-empirical model for non-pneumatic tire vertical load output voltage of claim 6, wherein, The formula of the PVDF sensor surface charge calculation model is as follows: （8） In formula (8), Q is the surface charge of the PVDF sensor, d 31 is the piezoelectric coefficient of the PVDF along the thickness direction of the film, A is the area of the piezoelectric film, Y is the Young's modulus of the PVDF, and h is the spoke thickness.

8. The design method of a PVDF sensor based semi-empirical model for non-pneumatic tire vertical load output voltage of claim 7, wherein, The formula of the amplifier output voltage calculation model is as follows: （9） In formula (9), V out is an output voltage, A cq is a charge amplifier sensitivity.

9. Use of the method for designing a semi-empirical model of the output voltage of a non-pneumatic tire vertical load based on a PVDF sensor according to claim 1, characterized by the fact that, The model obtained by the method is used to deduce the waveform and voltage peak of the PVDF sensor output voltage, and the installation position of the PVDF sensor, and then a spoke non-pneumatic tire vertical load estimation system based on the PVDF sensor is further constructed.

Images