CHEN Qing-zhang(陳慶樟)，GUO Li-shu(郭立書(shū))，YANG Xiong(楊雄)

(1.Changshu Institute of Technology，Changshu 215500，Jiangsu，China;2.Zhejiang Asia-Pacific Mechanical and Electronic Co.，Ltd.，Hangzhou 313012，Zhejiang，China)

Introduction

The tire blowout or severe leakage weakens the tire’s mechanical strength seriously and results in an emergency fault.It is generally difficult to get the information on the tire blowout or severe leakage in time，because of driving in focus，sound insulation，and noise of vehicle itself.The best time to carry out braking and stability controlling could be lost［1－2］.Some works show that the controllability of the vehicle changes a little in 2 to 3 seconds after the tire blowout，and this is the best time to lower speed and keep vehicle stable，and the speed can be reduced to safe range under proper operation.So that，to realize the real-time monitoring of tire blowout or severe leakage is an essential prerequisite to solve the safe problem of vehicle after tire blowout or severe leakage［3］.

An indirect real-time monitoring method to fuse analyses of tire vibration and effective radius is proposed.After tire blowout or severe leakage，it can find out the situation in time according to multiple criteria，then drive an emergency automatic braking system and inform the driver，so that the safety in sudden tire blowout or severe leakage can be improved greatly.

1 Principle

As shown in Fig.1，according to the wheel speed signal，the tire’s resonance frequency and effective radius are determined by spectrum analysis and calculation.On the basis of empirical formula and experiment，the thresholds and criterion of tire blowout or severe leakage are determined.If the characteristic of the tire frequency or radius is in the range of criterion，then a weighted judge is carried out to determine the tire’s status and drive an emergency automatic braking system if necessary.

Fig.1 Sketch of system

2 Vibration Analysis

Each wheel speed signal is sent to electronic con-trolling unit(ECU)，where the vibration analysis is carried out.

Firstly，the threshold of resonance frequency for tire blowout or severe leakage is calculated，according to empirical formula related natural frequency to the elastic torsion stiffness［4］.

where fresonaceis the tire’s resonance frequency，k the elastic torsion stiffness，Δk the variation of k，Nithe normal force applied on the tire，and the subscript i=FL，F(xiàn)R，RL，RR means front left，front right，rear left or rear right wheel respectively.In the simplified tire model，the change of k is proportional to the pressure.We can define the tire blowout or severe leakage as the decrease of tire pressure by 50%，then，the resonance frequency can be expressed as［5］

where fresonace-minis the threshold of tire natural frequency，k0the elastic torsion stiffness obtained from static measurement under normal tire pressure，G the vehicle’s weight.

The wheel speed signal in time domain can be transformed into frequency domain one with fast Fourier transform(FFT)to get the corresponding real-time resonance frequency fresonance-real.

Discrete Fourier transform(DFT)can be got from FFT，defining a sequence x with length N.

If the sampling period of wheel speed signal x(k)is Ts，then the corresponding frequency of X(n)is f(n)=n/NTs.The resonance frequency can be calculated as follows

In expression(4)，n^ is the estimated speed rate.if fresonance-real≤fresonance-minfor a tire，then the real-time resonance frequency can be corrected by weight，according to vehicle turning，acceleration and deceleration conditions.The weight value tiis related to the steering direction，turning radius，severity of braking，and acceleration.To simplify the algorithm，the weight value can be defined as ti=1 if the vertical load increase of the detected abnormal wheel due to steering，braking and acceleration is less than 0.25G，and ti=0.8，if the load increase is greater than 0.25G.If ti·fresonance-real≤fresonance-min，then one of the necessary condition of tire blowout or severe leakage is fulfilled，and further judge can be carried out according to the effective radius.

3 Effective Radius Analysis

Due to either tire’s blowing out or severe leakage resulting in large deformation of tire，the effective wheel radius will decrease fast.According to relevant technical literature，we can suppose that，if the deformation of tire is more than half of tire height htirewithin 200 ms，then blowout or severe leakage happens.If the change rate of wheel speed ω'jin this time is larger than its threshold ω'j－max，then the other criterion for judging tire blowout or severe is fulfilled.

where r is the wheel radius under normal pressure，j means the tire judged to be blowout or severe leakage.If the pressure in each tire is normal，the ratio η of the product of two radii of diagonal wheel pair to another one equals to 1 approximately.If one of the tires is blowout or severe leakage，the effective radius change leads to η variation，and then the criterion can be expressed as

If the above two criteria derived from the effective radius analysis are fulfilled，then the tire is judged as blowout or severe leakage.

If the criteria from the tire vibration and effective radius analysis are all fulfilled，then the tire blowout or severe leakage is confirmed.

4 Software and Calibration

The software flow chart is shown in Fig.2.

Fig.2 Software flow chart

Designed the system hardware and software，the matching and calibrating test should be carried out for a vehicle.The test equipment is shown in Fig.3.There are 8 exhausting holes drilled on the wheel rim.The holes connect with an exhausting control valve by soft-pipes to achieve the leakage control，and different leakage intensities can be simulated by using different number of exhausting holes.The changes of tire natural frequency and effective radius at different leakage intensities are measured，and fresonace-min，ω'j-max，ηmaxcan be determined under different wheel loads.If the number of combining exhausting holes is greater than 4，this situation can be defined as tire blowout，otherwise，severe leakage.

The calibration results show that the tire blowout can be detected effectively in the vehicle speed range

Fig.3 Test equipmentfrom 30 to 70 km/h，and the severe leakage can only be detected if the vehicle speed is more than 30 km/h.

5 Conclusions

The judge criterions for the tire blowout or severe leakage monitoring system are rationally simplified.When the situation happens，it can be accurately detected in time，then，an emergency automatic braking system can be driven，so that the security of the vehicle can be improved with lower detecting cost.But，for the high speed vehicle，the sampling rate of wheel speed signal is not increased，the efficiency of the monitoring system will be bad，so the algorithm should be developed further.

［1］Patwardhan S，Tomizuka M.Theory and experiments of tire blow-out effects and hazard reduction control for automated vehicle lateral control system［C］∥Proceedings of the American Control Conference，Baltimore Maryland，1994.

［2］Patwardhan S，Tan S H.Experimental results of a tireburst controller for AHS control［J］.Eng Practice，1997，5(11):34－39.

［3］Ipser J，Renfroe A D，Roberts A H.Solid axle tramp response near the natural frequency and its effect on vehicle longitudinal stability［C］∥SAE Conference Paper 2008-01-0583，2008.

［4］Kurashinge T.Low tire pressure warning device［R］.SAE Technical Paper 820458，1982.

［5］Braun F.Method and apparatus for monitoring the tire pressureofmotorvehiclewheels［R］. European:EP0938987，1999.