Research On Design Theories And Performances Of Scroll Compressor Profiles Based On Frenet Frame

The scroll compressor is a kind of fluid machinery which can compress gas by means of volume change,it has been widely applied in many important fields,such as refrigeration,air-conditioning,medical instruments,electricity,chemical industry and so on,due to its advantages of compact structure,low vibration and noise,high reliability,high efficiency and energy saving.Under the special needs of high-end equipment manufacturing industry,such as medical oil-free lubrication compressor and new energy electric vehicle,scroll compressor has developed rapidly with its unique advantages over traditional compressor.However,as the core technical problem of scroll compressor,the research on scroll profile is confined to the traditional design patterns,which brings great challenges to the design of the new type of scroll tooth profiles with high efficiency and satisfying different performance requirements.In this dissertation,from a standpoint of innovative design of scroll tooth profiles,the design of scroll profiles with different tooth profiles are systematically studied by using Frenet moving frame in differential geometry,which provides theoretical guidance for the design and manufacture of the new high efficiency scroll compressor.The main research contents and achievements of this dissertation include the following aspects:(1)Meshing theories of conjugate scroll profiles based on differential geometry.Firstly,conditions for smooth continuous tangent contact of curves were defined,and the concept of conjugate scroll profiles was put forward.Subsequently,the basic meshing theories of conjugate scroll profiles were established,and its mathematical description were given,the quantitative transformation relationships between the coordinate systems of conjugate scroll profile were deduced.Moreover,the meshing characteristics of scroll profiles were thoroughly studied by using the envelope method of single parameter curve family.Finally,the necessary and sufficient conditions of conjugate scroll profiles meshing were demonstrated from the perspectives of the kinematics.(2)The normalized mathematical model of scroll tooth profiles based on Frenet moving frame.In the design of scroll tooth profiles,aiming at the issue of~2lacking of concise and effective unified mathematical model,a new method of constructing scroll tooth profiles by using Frenet moving frame was proposed.To begin with,according to the curves of the scroll tooth profiles,the profiles could be divided into three categories,equal wall thickness scroll tooth profile,tapered wall thickness scroll tooth profile and variable wall thickness scroll tooth profile.Secondly,a Frenet moving frame was attached to the curves constituting these three categories of scroll tooth profiles to replace the fixed Cartesian coordinate system.Lastly,using the curvature of the plane curve and Frenet moving frame to express the intrinsic characteristics of the scroll tooth profiles,a normalized mathematical model of scroll tooth profiles with curvature and Frenet moving frame as parameters was established.The results show that the established model not only includes the profiles of different tooth profiles,but also optimizes and reconstructs them according to the expected geometric performance,so as to design the scroll tooth profiles with the best performances,which greatly improves the design freedom.(3)Research on geometric performances and strategies of optimum selection for scroll tooth profiles with equal wall thickness and tapered wall thickness.In order to make the designed scroll tooth profiles meet the practical engineering requirements,the first two control coefficients of the equal wall thickness scroll tooth profile and the first three control coefficients of the tapered wall thickness scroll tooth profile in the normalized mathematical model of the scroll tooth profiles were studied respectively.the influences of various control coefficients change alone on the geometric performances of the scroll tooth profiles were analyzed.And then the strategies of optimum selection for control coefficients of the scroll tooth profiles with equal and tapered wall thickness were established,numerous equal wall thickness and tapered wall thickness scroll tooth profiles which have excellent comprehensive performances and satisfy the engineering requirements could be constructed with these strategies of optimum selection.The results show that the strategies of optimum selection can take the actual requirements and design tendentiousness of scroll compressors into consideration to construct the scroll tooth profiles with equal wall thickness and tapered wall thickness,and break through the restriction of only paying attention to compression ratio or area utilization coefficient in the design of scroll tooth profiles.(4)Construction method and geometric theories of variable wall thickness scroll tooth profiles based on Frenet frame.Aiming at the problem that it is difficult to achieve the optimum compression characteristics for the equal wall thickness and tapered wall thickness profiles,a method of constructing the variable wall thickness scroll profiles based on Frenet frame was proposed.First of all,three new types of variable wall thickness scroll tooth profiles,type I,type ? and type ?,were constructed by using the method,the basic geometrical theories of these three profiles were established and the working chamber volumes were also derived.Then,the influences of profile parameters on the geometric performances(displacement volume,compression ratio and area utilization coefficient)of these three types of scroll tooth profiles were analyzed,and the strategies of optimum selection for profile parameters were obtained.Furthermore,three types of variable wall thickness scroll tooth profiles were compared in terms of geometric performances and dynamic performances(axial gas force and tangential gas force).Eventually,high order curves in the type ? and type ? variable wall thickness scroll tooth profiles were coded by combination,and the influences of high order curves for different coding sequences on the performances of type ? and type ? variable wall thickness tooth profiles were analyzed.(5)Research on mathematical model and variation laws of tooth thickness for variable wall thickness scroll teeth.In order to quantitatively study the law governing the change in the thickness of the variable wall thickness scroll teeth,a mathematical model for calculating the thickness of variable wall thickness scroll teeth was established.The profile parameters that influence tooth thickness of type I,type ? and type ? variable wall thickness scroll teeth were analyzed systematically by solving the mathematical model,the relationship between the variations in profile parameters and in scroll tooth thickness was studied.Besides,the influences of the combined coded curve on the tooth thickness of type ? variable wall thickness scroll tooth were also analyzed.The results show that the proposed mathematical model can accurately describe the law governing the change in the thickness of these three variable wall thickness teeth.Moreover,scroll teeth can be flexibly designed given that tooth thickness and the initial tooth thickness can be quantitatively adjusted in accordance with design requirements,which makes it more accurate and flexible to design variable wall thickness scroll teeth with arbitrary tooth thickness,the mathematical model can also be applied to calculate tooth thickness in other combination curves.(6)An experimental research on performance of scroll compressor with variable wall thickness scroll tooth profile.Firstly,according to the above design theories and strategies of optimum selection,the type ? variable wall thickness scroll tooth profile with excellent comprehensive performance was selected as the research object,the interpolation operation was processed via using equal tangential angle and variable step double circular interpolation algorithm,and the interpolation error was analyzed.Secondly,the data from the interpolation were used to mill the type ? variable wall thickness scroll tooth.Lastly,the scroll tooth machined by milling were tested on the scroll compressor prototype,the variation laws of power,air displacement,volumetric efficiency and exhaust temperature for scroll compressor prototype at different spindle speeds were studied.The results show that the designed type ? variable wall thickness scroll profile has excellent comprehensive performances,the profile design theories of scroll compressor based on Frenet frame presented in this dissertation provide theoretical guidance for the design of scroll compressor with variable wall thickness.