Abstract: In order to effectively build the propeller mathematical model and the turboprop engine mathematical model, and to lay the foundation for the turboprop engine control laws design, by referring to the scaling method of the component characteristics of the compressor, the revised scaling equation of the component characteristics suitable for the propeller was proposed. The modeling optimization algorithm of the propeller under the static thrust state was proposed based on the static characteristics of the propeller. Two different propeller modeling algorithms were proposed respectively based on the operating characteristics of the propeller in the low-speed forward state and high-speed forward state so that the propeller mathematical model built based on the proposed algorithms can be simulated under any flight conditions in the full flight envelope. Compared with the simulation data of GSP software, the results show that the maximum relative errors of the output thrust, power and efficiency of propeller mathematical model built based on the proposed algorithms do not exceed 3×10^-6, 3×10^-6 and 6×10^-5 respectively, and they also verify the effectiveness and versatility of the proposed algorithms.

Key words: Scaling equations;Static thrust state;Low-speed forward state;Propeller mathematical model;General algorithm

摘要： 为了有效地建立螺旋桨数学模型和涡桨发动机数学模型，以及为涡桨发动机控制规律设计奠定基础，借鉴压气机部件特性缩比方法，提出了一种适用于螺旋桨部件特性的修正缩比方程；基于螺旋桨静态特性，提出了静拉力状态下的螺旋桨建模优化算法；针对螺旋桨低速前进状态下和高速前进状态下的不同工作特点，提出了两种不同的螺旋桨建模算法，以实现全飞行包线内的螺旋桨数学建模。通过与GSP(Gas turbine Simulation Program)软件仿真数据对比验证，其结果表明，基于所提出的算法建立的螺旋桨数学模型输出拉力、功率和效率的最大相对误差分别不超过3×10^-6，3×10^-6和6×10^-5，同时，验证了算法有效性和通用性。

关键词: 缩比方程;静拉力状态;低速前进状态;螺旋桨数学模型;通用算法