Development Of Variable Cross-section Beam And Its Application In Lightweight Of Bus Frame

Chinese buses sales reached 537,700 in 2016,ranking first in the world for 16 consecutive years.A large number of buses will cause great pressure on environment and fuel consumption,and bus is much heavier than car,so bus light-weighting will improve fuel economy effectively and reduce exhaust emissions.As the main bearing structure and the largest weight proportion of bus,the bus body should also ensure the stiffness to meet the requirements.The paper presents a kind of beam with variable cross-section to achieve the lightweight of bus frame.Based on a thin-walled box girder,it is formed with one or more of the four walls of the girder tilted to produce the beam with variable cross-section.In development of the bus,the existing FE software has complicated process of building model by using the shell element.When the beam element is developed,for thin-walled beam with variable cross-section(span-height ratio is equal to or greater than 5:1),the stiffness matrix of the two-node and three-node element under axial force,torsion and bending are derived based on the theory of Euler-Bernoulli Beam.For short-heavy beam(span-height ratio is less than 5:1),the stiffness matrix of the three-node element under bending is derived based on the theory of Timoshenko Beam.Next,stiffness matrix of various working conditions is assembled to obtain the three-dimensional spatial stiffness matrix.Then,stiffness matrix of the beam element in the local coordinate system is transformed into the overall coordinate system of the bus frame.Solving of stiffness matrix needs to be programmed by MATLAB software.Then,it will be proved that the stiffness matrix is correct.The three kinds of working conditions of the stiffness matrix are verified.For axial and torsional conditions,the result will be got after modeling in CATIA,pre-processing in Hyper Works and solving in Optistruct,the simulation results are compared with results calculated MATLAB program.In the bending case,for thin-walled beam,bending test of beam will be performed,and test result will be compared with simulation result and program result.For short-heavy beam,the bending deflection of simulation in Hyper Works is compared with results of Euler-Bernoulli Beam and Timoshenko Beam calculated by program.Next,the bus frame is optimized by using variable cross-section beam.The paper establishes the model of bus frame and analyzes its static stiffness.According to the variation of the bending rigidity and torsional rigidity of the frame,the initial beams are replaced by beams with variable cross-section in order to get a frame with balance between rigidity and lightweight.Then the paper establishes a bus body skeleton model,and analyses bending stiffness and torsion stiffness sensitivity of different modules.According to the sensitivity information,the initial beams will be replaced by beams of variable cross-section to achieve the body skeleton optimization.Finally,the variable cross-section beam is used to optimize bus body frame.A model of bus body frame is established,which is divided into 11 modules.The sensitivity of each module to the bending stiffness and torsional stiffness are calculated respectively.And according to the sensitivity information,the variable cross-section beams are used in the bus frame.The body frame not only improves the static stiffness,but also realizes lightweight.The results show that the variable cross-section beam element has good effect on the lightweight of passenger cars.