数学建模在应用型人才培养中的作用分析

数学建模可以提升学生综合素质，培养其创新及实践能力，因此，提高高校大学生的数学建模能力，对于培养应用型人才具有十分重要的意义。针对数学建模在应用型人才培养中的作用进行了分析，并提出了若干建议，以提升高校大学生的数学建模能力。     

A fast and automatic full-potential finite volume solver on Cartesian grids for unconventional configurations

To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design,a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper.Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algo rithms.The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES) algorithm.During computation,solution-based mesh adaptation is also applied so as to capture flow features more accurately.An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead.According to the characteristics of the Cartesian grids,the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces,which can significantly improve the solution con verging speed.The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing,a DLR-F4 wing-body,and an unconventional figuration of a blended wing body (BWB).The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation,and the results suggest its capacity in application for aircraft conceptual design.     

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell(RUC)is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element(DFE)method,and merely applying Periodic Displacement Boundary Conditions(PDBCs)to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions(PTBCs,also known as traction continuity conditions)are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element(FE)analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional(UD)fiber-reinforced composites.     

高速铣削铝合金7055铣削力和铣削温度的仿真研究

采用有限元分析软件AdvantEdge模拟了航空铝合金7055高速铣削过程,获得了单个刀齿高速加工中铣削力变化曲线,预测了不同切削时间下工件及刀具上的温度分布,获得了刀具前刀面和后刀面的温度分布曲线;建立了高速铣削参数对铝合金7055铣削力和铣削温度的影响曲线,可辅助优化切削加工参数,有助于减小切削过程中刀具的磨损,改善刀具切削状态,提高刀具使用寿命.     

铣削加工工艺力学机理研究

结构件数控铣削加工技术广泛应用于航空航天工业中。铣削加工中,不合理工艺参数下的切削力会引起较大刀具-工件变形及加工颤振,极大影响着加工精度和质量。深入研究工艺过程的力学机理,进而采用建模仿真技术来优选工艺参数,对高效高精度加工技术的实现具有重要意义。本研究围绕切削力建模、动力学建模与颤振稳定性分析以及变形误差预测与控制技术等相关工作进行介绍。     

基于不同前角的航空铝合金切削过程分析

为合理选用刀具前角,研究前角变化对航空铝合金7050-T7451切削过程的影响.对前角影响进行理论分析,并借助有限元软件ABAQUS/Explict建立热力耦合的平面应变正交切削模型,采用Johnson-Cook材料本构关系及失效准则模拟不同刀具前角时切屑的形成过程,对比分析了前角变化对切屑形态、切削力和切削温度的影响.仿真结果表明,大前角的刀具有利于改善切削过程,但为避免产生带状切屑,合理的前角范围应为8°～l6°.通过对两种方法的分析结果对比,验证了有限元模型的准确性,对实际加工具有一定的指导意义.     

基于虚拟正交试验的压气机叶轮轴-毂径向微动特性研究

用Pro/E建立压气机叶轮轴-毂三维模型,利用ANSYS软件采用子结构结合网格随移技术的分析方法,建立其有限元模型。采用虚拟正交试验方法对压气机叶轮轴-毂进行仿真,得出过盈量、摩擦系数、转速对最大单位摩擦功和平均摩擦功影响显著性次序及影响规律,得到最优组合。结果表明,模拟及正交试验优化结果准确、可靠,有效地降低了摩擦磨损程度,对实际装配过程具有一定的指导作用。     

智能机床的误差补偿技术

误差补偿技术是智能机床精度提高与保持的关键技术之一.分析了国内外机床误差补偿技术研究现状,提出智能机床误差补偿技术总框架;总结了智能机床误差源、误差元素、几何与热误差的误差元素模型及建模方法,以及典型的误差补偿方法;研究了力误差补偿技术、基于零件在线测量的误差综合补偿技术;最后,对未来智能机床误差补偿技术的发展重点进行展望.     

鼠笼式弹性支承结构参数分步优化设计方法

为进一步提高鼠笼式弹性支承结构支承刚度设计的准确性,同时最大限度地减小鼠笼受到的最大应力,在相关研究的基础上,基于参数化建模思想,并结合有限元优化技术提出分步优化设计方法.采用鼠笼式弹性支承的刚度和应力计算公式并结合加工装配条件初定1组满足设计要求的结构参数值;建立鼠笼式弹性支承的有限元优化模型,并将初定的结构参数值代入到有限元优化模型作为优化的初始迭代值,同时以鼠笼笼条的长度和厚度为优化参数,经过迭代计算得到满足工程需求的结构参数.该方法可提高设计精度,节省设计时间.最后,结合具体算例验证了优化设计方法的有效性和实用性.     

测试三轴转台误差分析及建模

以用于测斜仪的三轴转台为研究背景,通过分析其运动规律,探讨了三轴转台不正交度误差源对三轴转台精度的影响,并用MATLAB对它进行了误差建模,仿真计算得出了系统装配不正交时三个坐标的误差率;最后,引入实际测试过程中角度传感器的测量误差,在三轴不正交的前提下又对三坐标测量误差进行了数学建模,通过仿真分析,研究探讨了角度传感器带来的误差规律,在实际应用中为测斜仪标定测试和误差补偿提供了理论依据.