Theory And Application Of Mulit-point Chord Reference System For Track Geometry

Track geometry irregularity,the main excitation source of vehicle-track system,will lead to vehicle vibration,wheel-rail impact and noise.To measure the track geometry efficiently and precisely is of essential importance to ensure the safety of rail system.The straight chord with fixed length is widely used as a reference to describe the track geometry irregularity,and all this kind measurement system is named as Chord Reference System(CR-system).As the CR-system is widely used,it is found that there is an inevitable inherent vice of CR-system since the chord reference is always changing along with the rail.A lot of researchers had proposed methods to fix this inherent vice,but the problem is never solved fundamentally,and the measurement principle for Chord Reference System(MCR-system)is always a blank.To deal with this problem,this paper proposed theoretical and practical tools to realize and analyze different MCR-systems under a unified framework.The main points of this paper are summarized as the following points.(1)Beginning from the mid-point chord offset system(MCO-system),the linear system modeling method is applied to establish the measurement model and restoration model.Using statistics approaches and Fourier Transform,the error accumulation property is analyzed in detail.The performance of MCO-system can be enhanced by increasing the sampling frequency.The correctness of the model proposed in this paper is verified by comparing with the result from the inverse-filtering method.(2)A unified framework is proposed to describe the measurement model and restoration model of MCR-system.A series of definitions are given,such as the order,standard sampling frequency,configuration and minimum measurable wavelength(MMW)of MCR-system.Two propositions regarding the MMW and boundary conditions of MCR-system are proposed and proven.(3)Based on the MCR-system framework,the error property and stability of MCRsystem are analyzed using statistic tools.The Error Amplification Factor(EAF)is proposed to describe the error accumulation property.Four propositions,with each regarding the MMW with sparse configurations,regular stability,single point system stability and the EAF,are proposed and proven,respectively.(4)Based on the MCR-system framework,the error property in wavelength domain is analyzed in detail.The error distribution with respect to different wavelength component is analyzed and evaluated using numerical simulations.Furthermore,the Critical Wavelength(CW)is defined to evaluate the performance of a MCR-system in wavelength domain.(5)Based on the MCR-system framework,a combination optimization model is established using the EAF and configurations as the optimization target and variables,respectively.Solving the optimization model,the optimized configurations of mono-point,bipoint,tri-point and multi-point MCR-systems are obtained.The optimization rate of the optimized multi-point MCR-systems and the non-optimized are compared.At last,the Ultimate Precision Formula(UPF)of MCR-system is proposed by induction and function fitting.(6)Finally,to prove the feasibility and correctness of the MCR-system proposed in this paper,a rail corrugation measurement trolley is designed and manufactured to measure track geometry irregularity with short wavelengths.According to a series of field tests,the repeatability precision is about 10 um,and the minimum measured wavelength is 10 mm.At last,possible error sources are analyzed and countermeasures are discussed considering the manufacture accuracy,installation procedure,sensor property.