缸套-活塞系统中DAE与PDE联合求解方法

A COMBINED SOLUTION FOR DAE AND PDE OF CYLINDER-PISTON SYSTEM

针对内燃机缸套-活塞系统中DAE(Differential-Algebraic Equation)和PDE(Partial Differential Equation)难以用专业软件进行求解的问题,提出一种联合求解该系统中DAE与PDE的新方法。首先,在Dymola平台上建立该系统的DAE模块,同时在Matlab平台上构建它的PDE部分,然后通过建立DAE和PDE模块之间连接通信接口实现联合求解。这里,以某型号汽油机为实例,在考虑其活塞二阶运动、缸套-活塞之间油膜厚度变化、摩擦力及摩擦功耗等因素的条件下,建立了缸套-活塞系统模型,并对该模型进行了数值分析求解。通过对求解结果的分析,验证了这种求解方法的可行性。结果表明,采用上述方法求解,大大减少了缸套-活塞系统建模工作量,避免了活塞动力学方程变量代换,减少建模中方程编辑出错,同时也保证求解过程中算法的稳定性和求解结果的正确性。

Since it is difficult to solve the DAE and PDE of cylinder-piston system in internal combustion engine with professional software,we proposed a new approach for combined solution of DAE and PDE in the system. First,we established DAE module of the system on Dymola platform,and constructed its PDE section on Matlab platform. Then,we realised the combined solution by establishing the connection communication interface between DAE and PDE modules. Here,taking a particular model of gasoline engine as an example,we built its cylinder-piston system model by taking into account its second-order motion of piston,oil film thickness variation between the cylinder and the piston,as well as friction and friction power loss,etc.,and conducted the numerical analysis solution on the model. Through analysing the solution results,we verified the feasibility of this solving method. Results showed that by using the above solution,the workload of cylinderpiston system modelling was significantly reduced,the transformation of piston dynamics equations was avoided,and the equation editing errors in modelling was eliminated as well,meanwhile the method also ensured the algorithm stability and the correctness of the results in solving process.