摘要
研究了平面曲线固有弧微分方程理论,利用切向角和曲率半径的固有弧微分方程形式和广义泛函理论,推导出了弧微分方程和笛卡尔坐标之间的变换方法,提出了涡旋型线的渐开特性条件。根据Taylor级数对等思想,建立了涡旋型线的广义泛函集成型线的统一形式,发展并完善了现有涡旋型线通用方程理论,并具体分析推导了4种典型的涡旋型线。突破了涡旋型线数学模型固有特性的限制,提出的表征涡旋型线本质特征的根本因素——涡旋型线的形函数统一形式,为涡旋压缩机型线的设计理论与方法研究拓宽了思路。
Study of scroll profiles theory at present mainly is aiming at the single profile and its ameliorate or parameter optimization, not aiming at the nature characteristic of the profiles-equation of scroll profiles itself. For this condition, the intrinsic differential equation bearing on arc length and tangent direction angle was studied. Using the inherent differential equation and general functional theory, the transform method between intrinsic differential equation and Cartesian coordinate was researched, and the condition of involutes characteristic was presented. Based on the method of Taylor series, the unified formalism of general functional integration molded lines was established, which perfected general theory of scroll profiles increasingly. The detail analysis of four typical scroll profiles was given. The inherent characteristics of scroll profiles model are broken through and the design method of scroll profiles is widen.
出处
《华东理工大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2007年第1期137-140,共4页
Journal of East China University of Science and Technology
基金
国家自然科学基金(50475063)
教育部高等学校博士学科点专项科研基金(20030611002)
重庆大学研究生科技创新基金资助项目(200609Y1A0030162)
关键词
涡旋压缩机
涡旋型线
平面曲线
固有方程
泛函集成
scroll compressor
scroll profiles
planar curve
inherent equation
functional integration
