A review of research on tire burst and vehicle stability control

Abstract

Tire burst is an accidental occurrence that poses a serious threat to the driving stability and road safety of vehicles. Therefore, it is of great practical significance to investigate early warning systems for tire burst and develop stability and safety control measures after burst incidents. The development of an accurate model that can effectively represent the impact of tire burst on vehicle dynamics is crucial for the design of control systems and the development of stability control strategies. Most of the existing research on tire burst models is based on static tire tests, the effectiveness of these models still needs to be further verified. The main approach to studying the impact of burst tires on vehicle performance is to embed a burst tire model into a vehicle dynamics model. Understanding the impact of tire burst on vehicle performance is essential for identifying burst incidents and developing stability control strategies. The research on burst identification primarily focuses on early warning systems and estimating vehicle state parameters after burst incidents, while the current research on stability control strategies focuses on enabling vehicles to continue running safely after burst incidents through braking, active steering, and collaborative control. Currently, there is no comprehensive review of research on vehicle tire burst stability control. Therefore, this paper primarily reviews five aspects: (a) the causes and prevention of tire burst, (b) the impact of tire burst on vehicle performance, (c) burst identification, (d) stability control strategies for burst incidents, and (e) future prospects for tire burst research.

Introduction

In the past decade, there has been a significant increase in automobile production and sales. Alongside improvements in vehicle performance and road conditions, the speed of vehicles has also risen. These factors have indirectly contributed to increased road traffic and a higher likelihood of traffic accidents. As the only part of the vehicle in contact with the ground, a tire plays a fundamental role in providing support. The tire–ground friction enables a vehicle to perform essential functions such as driving, steering, and braking. Additionally, a tire acts as a damping component, absorbing and reducing the impact from the road during driving. Therefore, the normal functioning of tires is directly linked to the safety, comfort, and stability of vehicles. The sudden change in mechanical characteristics after a tire burst can cause a vehicle to roll, yaw, or even lose control, posing a significant risk to driving safety. ¹ According to a report from the US Highway Safety Administration, prior to the installation of tire pressure monitoring systems (TPMSs) in vehicles, tire bursts resulted in 414 fatalities and 10,275 injuries annually. In 78,392 tire-related accidents, the fatality rate caused by tire bursts was nearly 100% when a vehicle was traveling at speeds above 120 km/h. It is evident that abnormal tire failure or bursts during high-speed driving pose a significant challenge to vehicle stability and road safety.^2,3

Given the significant harm caused by tire bursts, scholars have conducted extensive research and discussions on this topic. Orengo et al. developed a finite-element model of a tire to predict and verify the final shape of a burst tire under various working conditions, such as crashing onto the road shoulder or driving on bumpy roads. ⁴ Wang conducted tire tests and found that the vertical, longitudinal, and lateral stiffness of a tire significantly decrease after a burst, while the roll resistance coefficient increases significantly. ⁵ Sassi et al.⁶ studied the dynamic characteristics of a vehicle after a tire burst using a nine-degree-of-freedom (DOF) vehicle model. They discovered that changes in the vehicle's center of gravity, operating conditions, and the interaction between the tire and the road can alter the lateral acceleration, leading to loss of stability and deviation from the original trajectory. ⁶ Liu et al. ⁷ designed a fuzzy synovial control algorithm and braking force distribution strategy to control vehicle yaw torque. Simulation results showed that the controller effectively controlled the driving trajectory of a vehicle with a flat tire and improved its stability. ⁷ Quran et al.⁸ proposed a design and evaluation method for an automatic deviation correction safety controller based on brake/traction drive, which effectively enhanced the stability of vehicles after a tire burst. Overall, extensive research has been conducted to address the challenges brought by tire bursts. Scholars have explored various aspects, including the mechanical characteristics of burst tires, dynamic effects on vehicle stability, and control strategies to mitigate the risks associated with tire bursts. These studies contribute to the understanding and improvement of automotive safety and stability control systems.

Although there have been numerous studies on tire burst and stability control, there is currently no comprehensive literature review on the research specifically focused on tire burst during vehicle operation. This paper aims to address this gap by discussing the causes of tire burst, preventive measures, changes in tire and vehicle dynamics after burst, estimation of vehicle state parameters, identification of tire burst, and vehicle stability control strategies. Tire burst during vehicle operation can be attributed to various factors, such as insufficient load capacity, excessive internal stress, and high tire temperature. In response to these causes, tire companies and scholars have proposed corresponding countermeasures, including non-inflatable tires, ⁹ safety tires, ¹⁰ Tyrone Automobile burst safety device, ¹¹ tire burst emergency safety device (TESD), nano-burst warning agent, and leak-proof tire repair agent introduced by tire manufacturers.^12,13 Research on the changes in tire characteristics after burst primarily employs simulation and testing methods. However, conducting transient characteristic tests for tire burst is costly and risky, so most research focuses on the static characteristics of blown tires. This includes selecting the blown tire model, ¹⁴ establishing and validating the blown tire model,^4,15 simulating the burst process,^16,17 and analyzing the changes in tire characteristics after burst.^18,19

The impact of tire burst on vehicle driving conditions is another area of research focus. This includes constructing multi-DOF tire burst models, studying the differential effects of tire burst on vehicle movement on different road surfaces, analyzing changes in vehicle state considering driver intervention after burst, and investigating the dynamic response of the vehicle under various driving conditions. Research on tire pressure monitoring and vehicle state parameter estimation involves improving direct and indirect tire pressure monitoring mechanisms,^20,21 developing vehicle state estimation models based on different algorithms,^22,23 and designing vehicle state parameter observers.^24,25 Lastly, research on vehicle stability control strategies after tire burst encompasses differential braking,^26–28 active steering,^29,30 active suspension,^31,32 cooperative control of differential braking and active steering,^33,34 and emergency inflation and deflation of blown tires.^35–37 Overall, this paper provides a comprehensive overview of the current research on tire burst and stability control, covering various aspects such as causes, preventive measures, changes in tire and vehicle dynamics, estimation of vehicle state parameters, identification of tire burst, and vehicle stability control strategies.

Research status of tire burst

Causes of tire burst

With the increasing frequency of tire burst accidents, it has become imperative to analyze the underlying causes of such incidents. Tire burst refers to the sudden bursting of a tire within a very short period of time (typically less than 0.1 seconds), resulting in a rapid drop in tire pressure to 0 kPa. This occurrence represents a process of rapid pressure loss, with the tire's working conditions tending to stabilize within approximately 0.5 seconds.^13,16

There are numerous factors that contribute to vehicle tire bursts, which can be broadly categorized into three main groups: insufficient normal load capacity, excessive internal stress, and elevated tire temperature. Each of these categories encompasses various specific reasons, as illustrated in Figure 1. In order to comprehensively address the issue of tire bursts, it is essential to analyze and evaluate each individual cause in detail.

Figure 1.

Summary of causes for tire burst.

Tire wear and corrosion

With the improvement of tire reliability, vehicle users often neglect the regular replacement of tires. Instead, they only replace the tire when it starts to affect the normal operation of the vehicle. As a result, many tires experience excessive wear. Prolonged wear leads to tire aging, causing the tire pattern to wear down, the tire wall to become thinner, and even the exposure of the tire curtain layer. At this stage, the tire's load capacity and compressive strength are no longer able to support the weight of the vehicle, making the tire prone to bursting. Automobile tires primarily consist of rubber material, which is an organic substance. This organic matter is soluble in gasoline, oil, and other organic solvents. When the tire is corroded by these solvents, it can crack, further reducing its load capacity and making it susceptible to bursting, especially when driving at high speeds.

Abnormal tire pressure

Abnormal tire pressure is the main cause of tire bursts. Each tire has a specified pressure load corresponding table, and it is crucial to maintain the air pressure within this range to ensure the tire's optimal performance. Deviations from the recommended tire pressure can lead to various issues, including local tire wear, reduced vehicle handling stability and comfort, and increased fuel consumption. When the tire pressure is too low, the contact area between the tire and the ground increases, resulting in higher friction resistance during driving. This, in turn, causes the tire temperature to rise, leading to increased tire temperature. The elevated temperature causes the tire to expand and weakens its pressure resistance, ultimately resulting in tire fatigue and bursts. On the other hand, when the tire pressure is too high, it accelerates wear on the crown part of the tire, subjecting the tire to prolonged overload conditions and reducing its service life. High tire pressure also increases the internal stress on all parts of the tire and the tension of the tire body cord. This accelerates the tire fatigue process, causing the tire to be in a highly stretched state with reduced wear resistance and an increased likelihood of bursting. Refer to Figure 2 for the impact of both high and low tire pressure on tire performance, and to Figure 3 for the influence of tire pressure on tire lifespan. The performance loss in the longitudinal coordinate in Figure 2 does not refer to the performance of a single dimension as shown in Figure 2, when the tire underpressure is 20%, the performance loss in the longitudinal coordinate can be characterized as the vehicle's power performance loss of about 18%. The reason for the loss is that the insufficient tire inflation pressure will increase the rolling resistance and damage the car's power performance. The right half of Figure 2 can represent the loss of a certain tire performance with the increase of tire pressure, which can be specifically characterized as the impact of tire pressure on vehicle ride comfort. Specifically, according to Figure 2, when the tire pressure is 20% higher than the standard tire pressure, the vehicle ride performance will lose about 23%. Figure 3 can be specifically described as: when the tire pressure is 40% of the standard tire pressure, the tire durability life will be reduced to 20% of the normal life, when the tire pressure is 1.2 times the standard tire pressure, the tire durability life will be reduced by 10%.

Figure 2.

Influence of tire pressure on tire performance.

Figure 3.

Influence of tire pressure on tire life.

Poor road condition

The influence of road conditions on car tires is significant. When a vehicle encounters stones, nails, or broken glass on the road, the tire can get scratched, leading to tire leakage or even a direct burst. Additionally, if the tire collides directly with a large stone or the road shoulder, or if it traverses a pothole road at high speed, the tire will experience a strong external impact. This can cause the tire to burst due to the concentration of internal stress in the impacted area of the tire.

Vehicle overload

The bearing capacity of a tire is determined by its structure, inflation pressure, and driving speed. When a vehicle is overloaded, the internal pressure of the tire increases. If the internal pressure exceeds the sealing pressure of the valve, the tire will burst. Normally, when the load on the wheel is at its maximum allowable value, the internal pressure of a high-pressure tire is around 5–7 atmospheric pressure. However, if the actual load of the vehicle exceeds the maximum allowable load of the wheel, the internal pressure of the tire can increase to 10 atmospheric pressure. ³⁶ If a tire leak is not recognized in time, it can result in excessive tire load on the other side, leading to tire burst.

Climate factors

In high temperature weather, the internal gas of automobile tires heats up and expands, causing the tire pressure to rise significantly. If the tire pressure becomes too high, it can result in a tire burst. Tires in a static state are not commonly affected by high temperatures, but vehicles driving in hot weather have a greater chance of experiencing tire bursts due to the elevated tire temperature. When driving, the tire is subjected to thermal expansion and contraction, making it prone to deformation. This leads to a decrease in tensile force and the continuous production of heat during the driving process. As a result, heat dissipation is relatively slow, causing the air pressure to increase. This can result in the tire body becoming too thin and ultimately leading to a tire burst.

Vehicle speeding

Tire bursts frequently occur in small buses due to high speeds. When a car maintains a high speed or engages in speeding for an extended period, the frequency of contact between the tire and the ground increases. This, in turn, generates a larger centrifugal force from the tread, causing the tread to undergo reverse deformation. The tread experiences alternating positive and negative forces, leading to fluctuations.

When the speed reaches a certain critical value, the wave velocity of the tread aligns with the speed of the tire, resulting in static deformation of the crown surface of the tire. This phenomenon is known as the “standing wave” phenomenon, as illustrated in Figure 4. The point of contact between the tire and the ground (P point) becomes compressed and deformed. At higher speeds, the P point remains compressed and deformed before it can fully restore to its original state, causing the tread to appear “stagnant.” Once the “standing wave” phenomenon occurs, the tire undergoes severe distortion, experiences a rapid increase in rolling resistance, and the temperature rises sharply. This ultimately leads to the rupture of the entire tire.

Figure 4.

Generation of tire stationary wave phenomenon.

Tire burst prevention and explosion-proof measures

Non-pneumatic tire

Based on the analysis of tire burst causes discussed in the previous chapter, preventive measures for tire burst can be proposed. To address issues related to tire wear and corrosion, it is essential to regularly inspect the tread pattern for signs of wear and aging caused by corrosion. To prevent excessive internal stress, tires should be inflated according to standard guidelines, and tire pressure should be regularly checked. Additionally, it is important to ensure that the vehicle is not overloaded to avoid sudden braking situations. To prevent tire overheating, drivers should adhere to speed limits and take regular breaks during long-distance drives to allow the wheels to cool down. In order to prevent punctures caused by external factors, tire maintenance should be prioritized, including regular tire rotation, and the use of refurbished tires should be avoided. In addition to the aforementioned measures to control tire operating conditions, tire manufacturers have introduced non-pneumatic tires (NPT) as a means to mitigate the risk of bursts. Notable examples include Michelin's Tweel, Bridgestone's AirFree, Hankook's iFLEX, and Dunlop's GYROBLADE, ⁹ as shown in Figure 5.

Figure 5.

Non-pneumatic tires from different manufactures ⁹ : (a) Tweel, (b) AireFree, (c) iFLEX, and (d) GYROBLADE.

NPTs offer a fundamental solution to the problem of tire bursts. However, compared to regular tires, these tires experience an increase in rolling resistance of approximately 5%. ⁹ Consequently, this leads to reduced fuel efficiency. Additionally, NPTs generate strong vibrations, produce significant noise, and generate excessive heat at high speeds. As a result, they are not suitable for high-speed usage. In response to these challenges, major tire manufacturers have developed safety tires, which can be categorized into four types: self-supported tires, auxiliary support tires, multi-cavity tires, and self-sealing tires (as depicted in Figure 6(a)–(d)). While these tires do not completely eliminate the safety risks associated with tire bursts, they do offer some preventive measures. However, the increased thickness and hardness of the tire wall may compromise driving and riding comfort. To address the stability issues that arise after a tire burst, Tyrone Automobile has developed a tire burst safety device. This device is designed to mitigate the effects of vehicle direction and brake control failure following a tire burst. By ensuring that the tire remains attached to the rim without falling out and causing the rim to touch the ground as shown in Figure 6(e). The device effectively maintains the stability of the vehicle. Similarly, Tesford Company has designed and developed the TESD as depicted in Figure 6(f). This device operates on a similar principle to the TYRON automobile tire burst emergency safety device developed by Tyrone Company in Britain. It involves installing a safety device on the wheel hub, which creates a rubber cushion by increasing the thickness and toughness of the tire in the event of a burst. This cushion prevents the rim from making contact with the ground. As a result, the device effectively maintains the direction and braking stability of the vehicle with a flat tire within a certain mileage range.

Figure 6.

Run-flat tire^10,11: (a) self-supporting type, (b) auxiliary-supported type, (c) multi-cavity type, (d) self-sealing type, (e) TYRON emergency safety device, and (f) tire burst emergency safety device (TESD) emergency safety device.

Nano-tire warning agent

A nano-tire warning agent is a tire indicator made of nanomaterials. It is designed to provide an early warning system for tire bursts by sending an alarm 60–180 seconds before tire bursts. ¹⁰ This alarm serves to remind the driver to slow down and stop for inspection, thus preventing tire bursts. The working principle of this system is as follows: when the tire's local pressure becomes too high and the temperature reaches a critical point, indicating an imminent tire burst, the tire burst indicator collects data and transmits it to an electronic coding transceiver system. Upon receiving this information, the system sends an alarm. This technology, combined with the TPMS system, allows for real-time monitoring of tire conditions and the issuance of early warning signals during actual driving. However, it is important to note that this system cannot fully guarantee driving safety in cases of tire bursts caused by exceptional circumstances.

Anti-leakage tire repair agent

An anti-leakage tire repair agent is designed to prevent slow air leakage from the wheel. It can effectively seal punctures in the tire and prevent the tire temperature from rising. While this product serves as a preventive measure against tire bursts, its effectiveness in preventing damage caused by tire bursts is limited. Additionally, it should be noted that this product is reactive in nature, meaning it cannot respond to a burst tire in a very timely manner. Currently, the main sources of tire explosion-proof repair agents include the tire lifetime leak-proof and explosion-proof repair agent imported from the USA and the one invented by China East Asia Technology Development Company.^12,13

Research status of vehicle dynamics with tire burst

Research status of tire burst

The study of tire burst is crucial for understanding the movement characteristics and response of a vehicle when a tire bursts. Researchers mainly employ test and simulation analysis methods to investigate the characteristics of a burst tire. Due to the high cost and risk associated with real vehicle tire burst tests, computer simulation has become the mainstream research method for studying burst tires. The accuracy of simulation analysis results depends on the precise modeling of the burst tire and the vehicle. Currently, there are several existing tire models, including theoretical models, empirical–semi-empirical models, and finite-element models. ¹⁴ When modeling a vehicle tire burst, it is important to select a model that can effectively describe the transient response of the burst tire. The commonly used tire burst models in research include UniTire, ³⁶ Dugoff, ²⁸ MF, ³² and Pac models. ³⁰ For example, Bolarinwa used ABAQUS to establish a tire model for P195/65 R15 H91, simulated tire burst by increasing the load borne by the material, and analyzed the ultimate tire pressure and load that this type of tire could bear. ³⁸ Redia established a high tire pressure tire model using LS-DYNA, simulated tire burst under different road conditions, and obtained the tire force response. ¹⁵ Orengo used LS-DYNA to establish a tire burst model for situations where the tire bursts after hitting the shoulder or pavement bump. Through simulation analysis, Orengo explained the final state of the tire under different forms of tire burst and carried out the corresponding tests to verify the established tire burst model. ⁴ Blythe et al. established a simple tire burst model, where tire roll stiffness, lateral stiffness, and vertical stiffness decreased linearly while rolling resistance coefficient increased linearly during the tire burst process. ³⁹ As shown in Figure 7, Guo Konghui conducted low-speed tests on tires under different vertical loads, standard tire pressure, and zero tire pressure, and the results showed that the rolling resistance coefficient of the tire increased 10–30 times after tire burst, while the lateral stiffness and longitudinal sliding stiffness decreased to 10% of the normal tire, ¹ which is consistent with the literature. ³⁹ Based on this, the performance of burst tires is further quantified. Cai et al. proposed a test and simulation method for the tire burst process. They realized static tire burst through a burst trigger and established the corresponding finite-element model of the burst tire. Through analysis, it was found that the proposed method effectively simulated the process of tire burst. Using sensor-measured data, the changing characteristics of the tire during the tire burst process were described as follows: stiffness increases at the beginning stage, sharply decreases after tire burst, and then stabilizes.^16,17 Cai then focused on the analysis of a 215/60 R16 tire, examining the changes in vertical stiffness and lateral stiffness of the burst tire. The change in vertical stiffness and lateral stiffness before and after tire burst was summarized, and a three-dimensional finite-element model of the burst tire was established based on these findings. The analysis revealed the characteristics of the burst tire in the X and Z axes: there was a significant difference in the reduction of vertical stiffness of the tire with different tire pressure, while the difference in lateral stiffness was small, and the reduction was about 30%.^18,19

Figure 7.

Parameters variation of flat tire.

Research status of vehicle dynamics with tire burst

After a tire burst occurs, the vehicle experiences significant changes in force and dynamic response, which are reflected in longitudinal, transverse, and vertical responses. These changes can lead to extreme conditions such as roll, yaw, and even tail spinning. The main research method for studying the impact of early tire burst on vehicle performance is through real car tests of tire bursts. Blythe et al. validated the accuracy of the built-in tire burst model in EDVSM by using tire burst test data from different steering and braking scenarios. They increased the rolling resistance to 30 times the original state and modified the built-in tire burst model accordingly to establish a vehicle dynamics model after tire burst. Through simulation analysis of this model, they found that improper driver operation after tire burst was the main cause of escalated accidents. ³⁹ Building upon the research in literature, ³⁹ a zero tire pressure test was conducted to study the changes in radial stiffness of tires before and after tire burst. The tire radial stiffness in literature was modified based on the test data, and the dynamic response of different tires to tire burst on dry and slippery road surfaces under straight running and steady steering was analyzed using a modified two-axle vehicle model. The influence of deflating time on vehicle movement was also analyzed, although the tire burst model was not explained in detail. The results showed that the dynamic response of tire burst on the road surface with different degree of wetness was very different. The main reason for this phenomenon is the difference of road surface characteristics. The difference of tire surface contact surface causes the discrepancy of tire dynamic characteristics, so the road surface factor should be considered in the establishment of tire burst dynamic mechanics model. It can be seen from the tire burst test and simulation results carried out on the pavement with different road adhesion coefficients that not all tire bursts will inevitably lead to runaway, and the runaway phenomenon will occur only when additional factors act at the same time, among which the road adhesion coefficient is a very important influencing factor, and the road with low adhesion coefficient is easier to reach the runaway boundary. At the same time, the position of the tire with a blown tire also has a great impact on the dynamic response of the vehicle, in which the front tire with a blown tire usually presents a trend of under-steering, and the rear wheel usually presents an over-steering, because the side stiffness of the tire after the tire with a blown tire will show a trend of reduction, and the front wheel as a steering wheel will directly affect the size of the steering force, and then affect its steering state. After the vehicle has a flat tire, the driver's operation is also crucial to the vehicle's movement characteristics after the flat tire, and if the wrong operation may aggravate the vehicle's loss of control. ³⁹ Patwardhan et al.⁴⁰ studied the vehicle state parameters before and after tire burst and found that the rolling radius and side stiffness of the tire decreased. The vehicle suspension force was redistributed, causing interference in vehicle roll and pitch. Additionally, the vehicle roll resistance and the moment arm rotating around the kingpin increased. ⁴⁰ Richard J. Fay ⁴¹ and Ric D. Robinette^42,43 conducted a series of real vehicle tests on vehicles with burst tires from 1997 to 2000. The maximum speed of the test vehicle in reference was 45 miles/h, and the longitudinal and lateral movements of the vehicle under low and zero tire pressure were analyzed. ⁴¹ The test vehicles included six models, ranging from 0.75 ton pickup trucks to minibuses, and because the maximum speed used in the test was 45 miles/h, the results were no longer applicable for speeds higher than 45 miles/h. It can be seen that the vehicle type/speed and other conditions have an impact on the dynamic response characteristics of the vehicle after the tire burst. Reference ⁴² analyzed the longitudinal and lateral motion of the vehicle after the tread separated from the rim at a test speed of 50–75 miles/h. The experimental conditions in reference ⁴³ were consistent with those in Ref., ⁴¹ and the longitudinal and transverse responses of vehicles equipped with air leakage protection tires after tire burst were analyzed. These tests provided a method to study the motion of a vehicle with a burst tire. However, this series of tests focused on the performance of vehicle movement from a macro perspective and did not analyze the motion state of the car with a burst tire from a dynamic point of view, nor did they consider the impact of driver intervention. After a tire burst occurs, drivers typically hold the steering wheel and apply the brakes simultaneously to control the vehicle's direction. Blythe et al. conducted a study that combined simulation and testing to examine the impact of this intervention on vehicle dynamics. ³⁹ Lozia developed a 15-DOF model to characterize various aspects of tire burst in vehicles. Using this model, they analyzed changes in vehicle load transfer, yaw velocity deviation, vehicle lateral deviation, and steering wheel torque during a tire burst event. ³ Foei et al. designed a responsive tire burst control method based on a low-DOF model. However, this model did not consider vertical motion and load transfer, limiting its ability to fully capture the dynamic response of the vehicle after a tire burst. ⁴⁴ Hen et al.⁴⁵ established a seven-DOF tire burst model for vehicles based on the Dugoff tire model. They conducted simulation and test studies under straight and turning conditions. The results showed that swerving was more severe during a tire burst while turning, and the stability index exhibited more dramatic changes. ⁴⁵ Liu et al.⁴⁶ used the principles of multiple regression and data analysis to establish a regression equation involving tire pressure, speed, and yaw. The research findings indicated that under turning conditions, the inside tire experienced more severe yaw, making it more prone to skidding and side scaling compared to the outside wheel during a tire burst event. ⁴⁶

Key technical problems of TPMS and vehicle condition parameter estimation after tire burst

Tire pressure monitoring system

TPMS is the abbreviation for “automobile tire pressure monitoring system”; the main function is to monitor, display, and confirm the working status of the tire, and timely alarm the abnormal condition of the tire (such as overpressure, underpressure, overtemperature, pressure mutation, etc.), when the tire pressure is not monitored within the set threshold range, the current situation is displayed through sound and light, digitally. Make the driver know the car condition at any time, which can further reduce the probability of traffic accidents caused by abnormal tire pressure, and extend the service life of the tire and suspension system.

TPMS consists of two types: direct type and indirect type. The system is capable of real-time monitoring of tire pressure. When the air pressure deviates from normal, the system will issue a warning to alert the driver and ensure driving safety (Figure 8).

Figure 8.

Types of tire pressure monitoring system (TPMS).

Direct tire pressure monitoring system

The direct TPMS consists of a main engine and an auxiliary unit. The main engine serves as the display module, while the auxiliary unit is the monitoring module composed of a sensor, a microcontroller, and a wireless transmitter. When the tire pressure is abnormal, the monitoring module transmits a signal to the main engine, which then analyzes the signal and issues an audible and visual alarm. However, the auxiliary power supply of the direct monitoring system requires further study.

Indirect tire pressure monitoring system

The indirect TPMS obtains the relationship between tire pressure and measurable variables through the vehicle's sensor, enabling real-time monitoring of tire pressure. Persson et al.⁴⁷ studied a sensorless TPMS based on the analysis of the relationship between vibration and wheel radius. The working principle of this system was to optimize vehicle driving performance by monitoring pressure loss and robustness under different driving conditions. ⁴⁷ There exists a functional relationship between tire pressure, tire load, and tire side stiffness. Sierra et al.⁴⁸ conducted algorithm analysis of effective side stiffness using the two-DOF vehicle model, employing time-domain and frequency-domain methods. The feasibility of the algorithm was verified by comparing it with simulation data from Carsim software. ⁴⁸ Sienel estimated the lateral stiffness of vehicle tires through vehicle dynamic parameters, such as lateral acceleration and yaw velocity. It was necessary to consider whether the vehicle dynamic parameters reached the tire saturation zone. However, this method was limited by the equality of the lateral stiffness of coaxial wheels. ⁴⁹ Miller et al.⁵⁰ provided a detailed method for obtaining longitudinal slip rate using GPS, and obtained the effective rolling radius and longitudinal stiffness of the wheel through the least squared method combined with specific vehicle speed measurement. Based on these tire characteristic parameters, indirect real-time monitoring of tire pressure can be achieved. ⁵⁰

Estimation of vehicle state parameters

In the development of stability control strategies for vehicles experiencing tire bursts, it is crucial to obtain real-time vehicle state information. This serves as the foundation for ensuring stability control under extreme conditions. As there is no suitable sensor capable of directly acquiring the target state, parameters can only be obtained through state estimation. The real-time, reliable, and accurate acquisition of vehicle state under tire burst conditions holds significant theoretical and practical engineering importance for the design and verification of tire burst control strategies. Currently, vehicle motion state estimation methods can be broadly categorized into two groups: those based on kinematic models and those based on dynamic models. The kinematic-based estimation method involves an open-loop estimation of the motion state. In the open-loop estimation of the motion state, the open loop refers to that there is only a forward effect and no reverse connection with the controlled object, that is, there is no signal feedback effect in the estimation of the motion state of the vehicle. Although the vehicle sensor's sampling frequency is relatively high, the cumulative error caused by noise gradually increases due to the long-term integration of measured acceleration and other signals. Consequently, a substantial error may arise between the estimated value and the actual value. On the other hand, the estimation methods based on dynamic models can be further divided into two subcategories: the Kalman filter-based estimation method and the observer-based estimation method. Kalman filter is an autoregressive filter which is widely used in state estimation of dynamic multi-variable systems. It can be used to estimate uncertain information and give the situation of the state quantity at the next moment. Even in the case of noise interference, it can better predict the situation of the next state, and find the unobtrusive correlation between the variables. Therefore, Kalman filters can adapt to the constantly changing system, and the memory consumption is low, the reasoning speed is fast, and it is more suitable for resource-limited scenes.

Hac et al.²² investigated the lateral velocity of vehicles using a vehicle kinematics estimation model based on the Kalman filter. However, the accuracy of this method was found to be low for nonlinear systems. ²² Baffet et al. ²³ and Kobayashi et al. ⁵¹ employed extended Kalman filter and adaptive Kalman filter algorithms, respectively, to estimate the vehicle state. Although these methods were suitable for nonlinear systems and improved estimation accuracy, calculating the Jacobian matrix and covariance matrix for nonlinear systems with higher DOF proved to be complex. Shraim et al. designed a sliding mode observer to estimate vehicle state parameters and tire forces, but the observer gain required a large number of experiments to obtain. ²⁴ Brien et al.²⁵observed the vehicle state using an observer based on the H∞ robust control theory and proposed principles for selecting observer parameters. H∞ robust control is a kind of research method for uncertain systems. Robust control theory is based on norm theory and structural singular value, and provides a relatively complete theoretical system to describe model errors and uncertainties. For example, the influence of white noise interference and bounded interference on system performance can be characterized by H∞ of system output, while the structural singular value can be used to represent the influence of parameter uncertainty on system stability and dynamic performance. However, further verification of the estimation effect was necessary. Katriniok et al. ⁵² proposed an adaptive Kalman filter observer combined with an established vehicle model to estimate the yaw velocity and side deflection angle of the vehicle's center of mass. They also introduced two additional adaptive states to capture the uncertainty of the tire–road contact, which were used to independently measure the longitudinal force and lateral force on the wheel. However, this study did not consider the impact of uncertainty in other variables on the estimation results. ⁵² Liu et al. developed a general five-input and three-output state estimation system based on a multiplicator extended Kalman filter, using the minimum model error criterion. This system accounted for arbitrary nonlinear model errors and Gaussian white measurement noise. The five inputs referred to the speed of the four wheels and the steering wheel angle, while the three outputs referred to the longitudinal speed, lateral speed, and yaw angle speed of the vehicle. However, due to the high DOF of the vehicle, calculating the Jacobian matrix and covariance matrix for a high DOF was complex, resulting in long observation times and insufficient real-time observation. ⁵³ Wielitzka developed a seven-DOF model for the vehicle. They utilized an unscented Kalman filter to estimate the yaw velocity and side deflection angle of the vehicle's center of mass. Unlike the linearized nonlinear system with the extended Kalman filter algorithm, this approach allowed for the filtering of a nonlinear system. However, the parameters of the unscented Kalman filter needed to be pre-set for different systems, making it difficult to adapt this algorithm. ⁵⁴ Jin et al. employed a volumetric Kalman filter algorithm to estimate the side deflection angle of the center of mass of electric vehicles based on the DOF vehicle model. The volumetric Kalman filter algorithm required the calculation of the state covariance matrix, and if the operation conditions were not met, the filtering process would be interrupted, affecting the stability of the algorithm and the accuracy of the estimation results. ⁵⁵ Paiano et al. proposed a model-based vehicle state estimation method, but it was designed based on the linear two-DOF vehicle model. ⁵⁶ The Kalman filter algorithm used in the estimation process was not well-suited for the nonlinear system of vehicles, thus requiring improvement in estimation accuracy. Among the various methods for vehicle state parameter estimation, the Kalman filter and its improved algorithms are the most commonly used. However, these algorithms rely on accurate knowledge of the vehicle system's model and noise statistical characteristics. In practice, errors in the model and uncertainty in noise characteristics limit the optimal estimation results achievable with the Kalman filter method. While the Kalman filter method can handle nonlinear factors and provide more accurate estimations, the linearization of the nonlinear vehicle dynamics model introduces model errors. As a result, the method is more suitable for weakly nonlinear systems and often exhibits poor estimation accuracy in strongly nonlinear cases. In addition to the aforementioned methods, current research also includes fusion estimation algorithms,^53,57 neural network estimation algorithms,^58,59 and other related estimation algorithms.^60,61

The key technical problem of stability control of automobile after tire burst

Currently, the most widely accepted methods for dealing with tire burst are controlling the tire and the vehicle. Measures for tire control mainly include the use of burst protection devices, active blasting of different side tires, and the emergency inflation and degeneration system based on tire pressure monitoring. The vehicle control strategies after tire burst can be categorized into five main categories: differential braking and drive control, active steering control, active suspension control, differential braking and active steering of the synergistic stability control and active inflation and active tire burst. Li et al. proposed a novel automatic tire burst control design using the Liyaspuno stability theory of impulse differential systems. The proposed controller not only generates continuous lateral force and yaw moment but also generates impact yaw moment to overcome the disturbance caused by tire burst. However, no specific implementation was mentioned. ⁶² Some scholars focus on the design of control methods rather than specific implementation strategies. These include commonly used sliding mode control, linear quadratic regulator (LQR) optimization control, and feedback control to compensate for the error between the expected and actual states.^29,63 Li et al. conducted a comprehensive study on the stability control of vehicles during tire bursts at high speeds. They focused on the interference aspect and proposed a dangerous escape strategy that consists of three main stages: lane keeping, lane change, and emergency braking. To implement this strategy, they developed a vehicle stability controller based on model predictive control (MPC) and evaluated its effectiveness using the Simulink/Carsim platform. The results confirmed the efficacy of both the escape strategy and the controller. ⁶⁴

Differential braking and driving

Chen et al. conducted a study on the additional yaw moment generated after a tire burst. They converted the yaw moment into the wheel cylinder pressurization time of differential braking, taking into account the braking characteristics. A verification test was performed on a real car. The results showed a significant decrease in the yaw speed of the vehicle after differential braking was applied. However, this study did not include closed-loop control, which means that a method to restore the vehicle to its original lane after deviating from the track was not proposed. ²⁶ Liu conducted tire mechanics tests under three different tire pressures to address the yaw and instability of vehicles with tire burst. They modified the UniTire tire burst model accordingly and further analyzed the motion characteristics of vehicles with tire burst. They proposed a driver model with state compensation and a differential braking control method. ²⁷ Qi developed a braking system based on the response of a vehicle with a flat tire. He achieved differential braking control of the vehicle with a flat tire by using brake pressure control, resulting in better stability control. ⁶⁵ Chen et al. proposed an emergency automatic braking system for tire burst. The principle is to calculate the additional yaw moment caused by tire burst through a fuzzy control method and distribute the yaw moment of the vehicle tire burst through electronic hydraulic braking to realize deviation correction and stability control. ⁶⁶ Geely Automobile Company in China developed a tire burst monitoring and safety control system. ⁶⁷ The system operates as follows: a sensor monitors the tire pressure and quickly applies the brakes. After the tire burst, the control unit sends instructions to activate the brake system, combining the ABS function to prevent the vehicle from slipping. However, the issue of yaw in vehicles with a flat tire has not been effectively resolved, resulting in noticeable yaw after a tire burst. Zhou et al. ⁶⁸ designed a fuzzy PI controller with yaw speed as the main input and considered the influence of the side deflection angle of the center of mass to achieve stability control in vehicles with flat tires through differential braking. ⁶⁸ The results showed that the controller can better ensure vehicle stability and effectively reduce braking distance and time. Huang studied the control effect of the electronic stability program (ESP) controller on vehicles after a tire burst and found that the existing ESP and control strategies had little effect on improving the handling stability of vehicles with tire burst. Based on the control idea of ESP direct yaw moment, he further proposed a differential braking control strategy for vehicles with tire burst. ⁶⁹ Mi analyzed the motion characteristics of a car with a flat tire, the influence of steering and braking operations on the motion performance and control stability of the car, and proposed the method of joint braking of the unexploded wheel to achieve emergency control of the car's motion track and speed, reducing the difficulty of the driver's control after a tire burst. The possibility of early control of a vehicle with a flat tire was discussed based on the principle of efficiency load radius variation and efficiency side deflection angle. ⁷⁰ Liu et al.⁷ designed a fuzzy synovial control algorithm and braking force distribution strategy to control vehicle yaw torque. According to the simulation results, the controller had a good control effect on the driving trajectory of the vehicle with a flat tire and could improve its stability. ⁷ X. Wang et al. established a nonlinear tire model of tire burst with Simulink based on the steady-state mechanical characteristics of tires. They imported the established tire burst model into the Carsim vehicle model to build a co-simulation platform and conducted simulations of front and rear tire bursts under straight driving conditions. Based on the simulation results, they proposed a differential braking control strategy and further simulated the effectiveness of the control strategy. The results showed that the control strategy of differential braking could effectively improve stability after a tire burst. ⁷¹ Yang et al. proposed a load stability control strategy for electric vehicles with a tire burst that explicitly considered vertical load redistribution, multiple constraints, uncertainty, and redundancy. The strategy included a longitudinal speed controller controlled by a synoptic film to maintain the original longitudinal speed of vehicles after a tire burst and reduce the occurrence of rear-end accidents. Additionally, a reconfigurable torque distributor based on the constraint weighted least squared method was designed to track the synthetic signals of virtual yaw torque and tire longitudinal force generated by the controller. ⁷² Liu et al.⁷³ proposed a differential braking control strategy based on the optimal control algorithm according to the location of the tire burst and the established two-DOF vehicle model to avoid vehicle rollover. However, the uncertainty of the driver's operation after a tire burst challenges the robustness of the control strategy. ⁷³ Li et al.⁷⁴ proposed a vehicle controller with a flat tire based on fractional order to ensure control stability and robustness after a tire burst. The stability control simulation of the vehicle with a flat tire was realized through the established seven-DOF model and fractional order proportional–integral–derivative (PID) controller, guaranteeing lateral stability and vehicle safety. ⁷⁴ In the development and application of the tire burst stability control strategies mentioned above, there are few studies on driver intervention after a tire burst. Aki used a driving simulator to simulate the driver's reaction to the vehicle after a tire burst, ⁷⁵ and the driver model was embedded into the bicycle model to achieve closed-loop control.^76,77

Active steering control

In his study, Guo utilized a rolling optimization approach to implement active steering control for maintaining the vehicle on the desired trajectory and bringing it to a stop in a timely manner. This was achieved through steering control and leveraging the natural resistance of the vehicle. However, the vehicle model used in this study was a relatively simple “bicycle” model, which did not accurately represent the dynamics of the vehicle after a tire burst. Additionally, this control strategy did not incorporate braking, which could result in the vehicle traveling a longer distance after a tire burst and increasing the associated risk. ⁷⁸ Zhang et al. achieved ideal vehicle yaw speed control by designing an active steering fuzzy controller. However, their modeling process only considered the longitudinal and yaw movements of the vehicle, making it difficult to control the lateral displacement of the vehicle and correct deviations from the intended track. ⁷⁹ Patwardhan et al. designed a steering controller for a vehicle with a flat tire based on a study of the dynamic equation of the vehicle after a tire burst. By solving differential equations or optimization problems, they calculated the necessary steering angle to maintain the vehicle on its intended path. ⁴⁰ The controller was then validated through closed-loop testing on an AMC-Concord vehicle. It is worth noting that the closed-loop test was conducted at a relatively low speed of 15 miles/h, and the effectiveness of the controller at higher speeds remains unknown. ²⁹ Mokhiamar et al.³⁰ employed simulation technology to investigate the effectiveness of adapting weighting coefficients in the simultaneous optimal configuration of transverse and longitudinal forces. This approach aimed to enhance vehicle handling and stability. Based on the simulation results, it was observed that the comprehensive control of yaw torque and active front wheel steering yielded the best combination for steering control and direct yaw torque, allowing for the full utilization of tire performance. ³⁰ Zheng et al. designed an LQR based on a two-DOF model to determine the necessary yaw moment for stabilizing a vehicle with a flat tire. This approach enabled the correction of the motion state of the vehicle with a flat tire. ⁸⁰ Building upon this foundation, Zheng et al. introduced a compensatory current to the electric power steering system, mitigating the steering wheel's reaction to a tire burst and thus facilitating easier driver control. ⁸¹ Liu et al.⁸² employed a self-tuning PID algorithm to achieve stability control for vehicles experiencing a tire deflation. Upon detecting a tire burst, the system autonomously initiated control, employing rolling resistance to decelerate and harnessing the steering system to maintain yaw stability. The findings indicated that the system could promptly realign the vehicle to its initial trajectory and reduce speed following lateral displacement caused by the tire burst, demonstrating robust resistance to disturbances. ⁸² Yu et al.⁸³ delved into the effects of tire bursts on vehicle yaw motion at varying speeds, scrutinizing the dynamic responses and implementing variable gain adjustments to the PID parameters for online, real-time stability control and trajectory tracking. ⁸³ Liu et al.⁸⁴ developed a steering angle strategy post-tire burst that may prove challenging for actual drivers to execute, underscoring the need to integrate steering control into the overarching stability control strategy. ⁸⁴ Hu et al.⁸⁵ proposed a continuous-time domain adaptive predictive control approach for steering unmanned vehicles post-tire burst, balancing the demands for real-time and control performance. This method not only reduced computational time but also narrowed the constraint range for control input saturation, enabling control with minimal deviation despite nonlinear vehicular motion inaccuracies during linearization. ⁸⁵ Li et al. suggested an enhanced linear time-varying MPC methodology, grounded in the Pacejka tire model, to administer post-burst vehicle stability control through active steering, ensuring the vehicle remained within the stability region. ⁸⁶ Erlien et al. noted in their investigation of flat tire stability control that the imposed stability constraints might interfere with the desired collision avoidance trajectory. They proposed that stability controllers should permit deviations from stability constraints to fulfill safe collision avoidance objectives. ⁸⁷ Lu designed an adaptive fuzzy PID controller, which utilized the deviation and rate of change between the target and actual trajectory as system inputs, to govern the speed and trajectory stability of a vehicle with a deflated tire. ⁷⁷

Differential braking and active steering coordination control

Wang et al. proposed a collaborative control method for vehicles with flat tires driving at high speeds, which achieved stability control and trajectory correction through the inner ring controller of rear wheel differential braking and the outer ring controller of front wheel active steering. The results showed significant improvements in trajectory correction and stability control compared to single control methods, ensuring the vehicle stays on the desired path with minimal lateral displacement. ⁸⁸ To further address uncertain interference factors after a tire burst, Wang et al.³³ designed a new active front wheel steering system and differential braking system based on simulation analysis. Through robust control, the coupling of the two control systems was reduced, enhancing the system's ability to resist interference caused by a tire burst. ³³ However, the coupling problem between multiple systems involved in tire stability control still needs to be addressed. Wang et al. proposed a non-affine system based on second-order multi-input multi-output. Using a linear decoupling method, they achieved stability control of a vehicle with a flat tire under small lateral displacement by utilizing active steering and differential braking control methods. ³⁴ However, this control method may cause the vehicle to stop quickly in the longitudinal direction, increasing the risk of rear-end collisions. Based on a tire burst model, Mi developed a joint simulation platform to study vehicle dynamic response under different wheel conditions, speeds, and loads. They proposed a joint control strategy using a sliding mode fuzzy control algorithm and fuzzy PID control algorithm to achieve outer ring trajectory control and inner ring differential braking control. Simulation results demonstrated that the control strategy effectively controlled the trajectory and stability of the vehicle with a flat tire. ⁷⁰ Chen et al. proposed a fuzzy controller based on the adhesion ellipse theory to solve the tire burst problem in autonomous vehicles. By applying braking and fine-tuning the front wheel steering angle, the proposed fuzzy control-based method effectively controlled tire burst and improved vehicle safety and stability. ⁸⁹ Choi et al.⁹⁰ introduced a control architecture that utilized active front wheel steering and differential braking to achieve lateral stability while minimizing longitudinal disturbance. They used the matrix inverse method of an affine model MPC problem to solve the target state tracking problem and maintained lateral stability on various road surfaces. ⁹⁰ Wang et al. proposed a nonlinear coordinated motion controller for road vehicles after a tire burst, addressing path tracking and safety problems. They developed a control strategy to coordinate steering and braking simultaneously, improving control performance and solving constraint problems. To compensate for model uncertainties, an improved robust design method was proposed within the input-state stability theory framework. ⁹¹

Additionally, the proposed coordination controller and the separate steering and braking controller are evaluated, and the evaluation results demonstrate the effectiveness and advantages of the proposed method. Jing proposed a robust control method to maintain vehicle directionality and driving stability after a tire burst. This controller utilizes front wheel steering angle and yaw control moment as inputs, and an optimal control distribution method is proposed to implement differential braking on the other three tires to control the yaw moment. The veDYNA high-fidelity software program and a hardware-in-the-loop test system with a real automotive hydraulic brake system were employed to verify the controller. The verification results confirm the effectiveness of the proposed coordination controller in improving vehicle directional stability and robustness against interference caused by a burst tire. ⁹² Dai et al. put forward a vehicle stability control strategy based on an active steering and differential braking system, which is divided into two layers. The first layer is the yaw torque control layer, and the second layer involves additional steering ratio and tire force distribution controlled by LQR. Simulation experiments were conducted on different road surface adhesion coefficients to verify the superiority of the proposed control strategy in terms of driving performance, tire burst protection, and handling stability. ⁹³

Active suspension control

Shi ³¹ and Chen et al. ⁹⁴ conducted studies on the effect of vertical load distribution on vehicle handling stability after a tire burst and proposed achieving the goal of vehicle stability control through the control of an active suspension system. Simulations of the controlled vehicle were performed, and a method of adjusting the vertical load of each wheel using PID control was provided in conjunction with the vehicle's seven-DOF model. The simulation results demonstrated that this method effectively improved the stability performance of the vehicle with a flat tire. However, it should be noted that serious consequences could still occur due to driver misoperation. Building upon this research, the impact of driver reaction after the front wheel burst on the stability of straight-line driving was analyzed based on the transient response of the steering system and vertical load. Additionally, the force characteristics of kingpin deflection of the tire under the influence of longitudinal force were investigated. The kingpin deflection refers to the lateral distance from the intersection of the steering shaft and the ground to the center plane of the wheel is the offset on the ground. An equation for the vertical load response was established considering the sudden change in the tire center's vertical direction. Moreover, it was found that after a tire burst, the braking deceleration would be subject to the instantaneous reversal torque of the steering system. ³² Yang et al. proposed a directional stability control method for electric vehicles with tire burst accidents on curved expressways. This method considered exogenous interferences such as lateral wind and changes in road surfaces. The control method involved a vehicle dynamic simulation platform, a robust MPC controller, and a pseudo-inverse switch control distributor based on tire vertical force redistribution. ⁹⁵ Sathishkumar et al. proposed an independent and roll-connected active suspension scheme for a four-axle truck. This scheme aimed to reduce the lateral speed and displacement of the vehicle within the suspension limit by generating main power within the suspension actuator, without compromising the steering characteristics. The effectiveness of the control strategy was demonstrated. ⁹⁶

Emergency inflating and deflating of tire burst

Ma et al. designed a tire burst emergency inflation system based on tire pressure monitoring. When a tire burst occurs, the real-time tire pressure signal monitored by the sensor is sent to the controller. The controller then sends instructions to the gas generator to produce a large amount of gas, which inflates the blown tire and enables the vehicle to continue driving. ³⁵ Zhang proposed a tire burst emergency technology based on the principle of reinflation after a burst. When a burst is detected, the spare airbag inside the tire is quickly activated for instant inflation. The airbag helps alleviate the body inclination caused by the sudden burst, provides the driver with more reaction time, and improves driving safety to a certain extent. ³⁶ Xue adopted a programmed air release control method to achieve stability control after a tire burst. Once a burst is detected, the control system releases the air from the other three tires to maintain the balance of force on all four wheels. This improves the driving stability of the vehicle after a burst and enables quick stopping. ³⁷ It should be noted that as vehicle systems become more complex, the tire system alone may not effectively solve the problem of stability control after a burst because inflating and deflating the tire takes a certain amount of time. Since a burst occurs almost instantaneously, there have been few studies on this method.

Conclusions

Focusing on the topic of vehicle active safety, the phenomenon of vehicle tire burst, the causes of tire burst, the existing prevention and response measures, the identification of vehicle state and the stability control after tire burst were comprehensively reviewed.

This paper introduced the specific causes and countermeasures of tire burst. The causes can be attributed to three categories: tire has no normal load capacity, tire internal stress is too large, and tire temperature is too high. According to the causes of tire burst, NPT, safety tire, tire burst device, nano-tire warning agent, and anti-leakage tire repair agent were put forward. As the characteristics of a blown tire are the premise and basis for analyzing the movement characteristics and response of a blown tire to the vehicle, a review was carried out to find that the research in this part focused on the change of the characteristics of a blown tire and its impact on the movement characteristics of the vehicle. Most of the tire blown test studies were static test studies, and their effectiveness needed to be further verified. In order to carry out stability research on vehicles after a tire burst, the identification and prediction of vehicle state are the premise of the proposed control strategy. Therefore, this paper summarizes the research on the key issues of TPMSs and vehicle state parameter estimation after a tire burst. It can be seen from the review that there are two types of TPMS currently used, direct and indirect. However, due to the lack of slow response speed, Kalman filter and its improved algorithm are used in most studies of vehicle state estimation, and the effect of state estimation is currently at an acceptable level with large optimization space. We further carried out a review on the stability control strategies of the vehicle with a flat tire in the existing studies. Through the review of the existing studies, we found that the vehicle control strategies after flat tire can be mainly divided into five categories as follows: differential braking control, active suspension control, active steering control, cooperative stability control of differential braking and active steering, and emergency inflation and deaeration of tire burst. Differential braking control is usually based on the side deflection angle deviation of the center of mass and the yaw angle velocity deviation as the input of the controller, and the effective control of vehicle yaw and yaw is realized through the control algorithm. Meanwhile, the tire with larger braking efficiency should be selected as the control wheel of differential braking. Differential braking control can effectively control yaw, but the speed will decrease significantly, which is easy to cause rear-end accident when driving at high speeds. Active steering control usually takes the difference and change rate of the vehicle's normal target trajectory and the vehicle's yaw after a flat tire as the input of the selected control algorithm, and finally outputs the steering wheel angle through the controller to achieve effective yaw control. However, the control effect is lower than that of differential braking, and there is a situation of left and right yaw of the vehicle in the early and middle stages of control. But it can reduce the probability of rear-end accident. The limitation of a single tire burst stability control also makes many scholars carry out research on the cooperative control of differential braking and active steering, that is, the trajectory control of the inner ring is differential control and the outer ring is active steering. The cooperative control can effectively avoid the deficiency of single control and make the vehicle with a tire burst drive stably according to the predetermined trajectory, but the cooperative control strategy is more complicated. Basically stay in the simulation level, the real car is more difficult to achieve. The control principle of the tire burst stability control based on active suspension is to control the vertical load of the tire after the tire burst through the active control force provided by each suspension, and adopt the controller to adjust the dynamic response characteristics, accurately and quickly adjust the steady vertical load of each tire after the tire burst to the required size, so as to achieve the purpose of improving the stability of the vehicle with a tire burst. However, the stability control method based on active suspension cannot directly control the yaw distance, but can only provide gain effect for the stability control of the tire by indirectly improving the mechanical properties of the tire after the tire burst. Although there are many control strategies at present, the verification of control strategies is mostly in the simulation stage, and the working conditions of vehicles before tire burst are relatively simple, so the robustness of existing control strategies needs to be further improved. Finally, based on the shortcomings and gaps of existing research, the future research direction in the field of vehicle tire burst stability was prospected.

Future developments

In the field of stability control for vehicles with a flat tire, most current research focuses on single control methods. However, single steering control alone cannot eliminate the impact torque caused by a flat tire, and single differential braking cannot solve the yaw problem of vehicles with a flat tire. To achieve effective stability control for vehicles with a burst tire, it is necessary to adopt more coordinated control methods. Current studies mainly focus on straight-line and curve driving, without considering stability control during acceleration, deceleration, and lane changes. In the future, there is a need to develop stability control strategies for vehicle tire bursts under multiple operating conditions. Currently, yaw speed is commonly used as the reference parameter for stability control after a tire burst. However, vehicle offset, body roll angle, and centroid side deflection angle also change after a burst. Therefore, future research should explore stability control after a tire burst using multiple parameters.

Optimization of ESP strategy considering blowout conditions

Conventional electronic stability control does not consider burst prevention, which may increase the probability of tire bursts. Additionally, the load transfer after a burst is not adequately considered, and the yaw torque generated during braking is low, affecting the control effect. Therefore, the control strategy needs further optimization.

The improvement of tire burst sensing speed and vehicle state estimation accuracy

The use of tire pressure sensors for burst detection is limited to a single dimension and longer identification times, making it challenging for accident prevention. The current algorithms for vehicle state estimation are relatively simple, but the overall effect is acceptable. Further research is needed to improve the speed and accuracy of vehicle state and tire burst perception, providing faster and more accurate signals for stability control after a tire burst.

Integration of tire burst control strategy into the electronic stability control system

Currently, the electronic stability control system is designed for vehicles without a flat tire, and there are some limitations in the stability control of vehicles with a flat tire. The electronic stability control system can be extended to include different control strategies for tire bursts, while still maintaining the conventional stability control function when the tire is not blown out. This integration improves the universality of the electronic stability control system without significantly increasing costs.

Research on multi-strategy cooperative stability control for tire bursts under complex driving conditions

Existing studies on tire burst stability control mainly focus on simple driving conditions, and the universality of the control strategies is limited. The verification of these control strategies is mostly concentrated in simulation verification, and a single control strategy may not be sufficient to handle the stability control of complex systems with distributed drive and multiple inputs and outputs. Future studies should explore stability control strategies based on multiple scenarios. Various stability control strategies should be effectively integrated to enhance their robustness, and the verification methods should gradually transition to real vehicle testing.