Research On The Method And Evaluation Of Linear Three-Dimensional Kinematics Analysis Of Expressway

The quality of highway route design not only directly affects the safety and comfort of vehicle driving,but also relates to the quality of highway construction project and the cost of investment.In the past,limited to the complexity of highway3 D lines and the development of computer technology,designers usually divided the highway centerline into plane and longitudinal profile alignments for design,and then combined them to obtain a three-dimensional alignment.Most of the constraints and evaluation methods for route design are based on this separation design method,which are not substantially detached from the two-dimensional category.However,the two-dimensional design method cuts off the internal connection of the three-dimensional route and ignores the effect of coupling when combining horizontal and vertical alignments.Similarly,the route evaluation method based on the two-dimensional design cannot fully and accurately reflect the quality of the three-dimensional route.This paper starts with the essence that the highway route is a three-dimensional curve.On the basis of previous studies,the differential geometry principle is used to express the actual route with a regular parameter curve.The arc length is used as the design parameter,and the curvature and deflection are used as the design indicators to describe the geometric characteristics of the three-dimensional curve,and the expression model of the three-dimensional highway route is established.At the same time,the relationship between the two-dimensional design index and the three-dimensional index is established to facilitate the analysis of the current highway design.Based on the above research,this paper establishes a car motion model in three-dimensional space,analyzes the motion state of the car driving on the three-dimensional curve to study the relationship between the three-dimensional design index and the car motion state.Under the constraints of comfort,the dynamics evaluation and analysis of the actual project-Yakang Expressway is carried on.The main work and results are as follows:(1)An expression equation of a three-dimensional highway route with arc length as parameters and curvature and torsion as design indexes is established.At the same time,through derivation,the conversion formula between the traditional two-dimensional flat and vertical design indicators(planar curvature,plane curvature change rate,longitudinal slope and longitudinal slope change rate)and the three-dimensional design indicators(curvature and deflection)is established.(2)Based on the Frenet frame,a motion model with three-dimensional design indicators(curvature,deflection)and vehicle driving speed as basic parameters is established to promote two-dimensional motion analysis to three-dimensional motion analysis.The study shows that factors that affect the vehicle’s motion state include driving speed,curvature,deflection,curvature change rate,and the roll of Frenet frame.Among them,curvature and speed are the main factors that affect the acceleration of the car,curvature change rate and deflection are the main factors that affect the jerkiness of the car,the roll angle of the Frenet frame determines the distribution ratio of acceleration and jerk to the horizontal and vertical of the car.(3)This paper refers to the previous design experience,takes comfort as the constraint condition,and calculates the three-dimensional design index threshold at each constant speed of 80km/h to 120km/h,and combines with the actual project Yaye Expressway C8 contract section for analysis.The study shows that in addition to lateral acceleration,axial jerk also affects driving comfort in curved sections.Lateral acceleration has a greater influence on high-speed and large-radius sections,while axial jerk has a greater influence on low-speed and small-radius sections.At the same time,the road section after the combination of horizontal and vertical lines will easily cause continuous attenuation at the position where the two-dimensional design index changes,thereby affecting driving comfort.(4)With the help of Carsim software,models of cars,roads and drivers are established to simulate the state of variable-speed movement during actual driving,which is compared with the state of constant-speed movement.The study shows that the speed change state will slightly aggravate the jerkiness of the car while driving,especially when the speed change occurs at a position of continuous attenuation.Therefore,the speed limit sign can be set in front of the continuous attenuation position,so that the driver has at least 3s preview time to adjust the vehicle speed.