螺杆泵容积效率特性分析与螺杆齿面精确成型方法研究
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摘要
课题来源于国家自然科学基金面上项目“高效三螺杆泵转子型线设计新方法及关键技术研究”（项目编号：50875268）和“多级变速螺杆泵基础理论与关键技术研究”（项目编号：51175522）。
螺杆泵因具有优越的工程适应性和经济实用性在海洋钻井平台、舰船、精密机床、石油化工等领域应用日趋广泛。《中共中央关于制定国民经济和社会发展第十二个五年规划的建议》明确指出，高端装备制造业处于七大战略性新兴产业的核心地位，将在重点领域集中力量加快推进。螺及杆泵作为重点发展的高端装备部件，将为我国高端装备制造业的发展增加动力，成为战略性新兴产业发展的重要支撑。同时，“十二五”期间我国将投入3000亿重点发展海洋工程装备，包括海洋钻井平台、各种海洋工程船舶及潜艇等。因此，螺杆泵作为重要的高端装备基础部件，需求量巨大，具有广阔的发展前景。然而，螺杆泵属于高精度机械产品，其对设计和制造的精度很敏感。由于我国生产企业对螺杆泵工作机理认识不清晰，设计及加工方面的技术不够完善，使得生产出的产品存在容积效率低、流量特性不稳定、齿面磨损严重、功耗大等技术瓶颈，长期以来高端螺杆泵产品基本上依赖进口。为此，为提高我国高端装备制造业的国际化水平，减小我国在螺杆泵等高端装备部件对国外的依赖，开展螺杆泵系统创新设计理论与方法研究，突破螺杆泵设计制造关键技术难题，对提高我国机械装备配套自主创新能力具有十分重要的社会经济意义和工程实用价值。
本文以螺杆泵关键核心部件螺杆副为研究对象，利用流体动力学、泄漏理论、接触理论、空间包络理论等，深入分析泵腔内流场运动学、动力学特性，研究探讨螺杆构型原理及其结构与螺杆泵容积效率特性参数匹配的设计理论和方法，建立考虑啮合间隙的螺杆齿形设计模型，形成螺杆齿面成型刀具精确齿形设计方法。论文主要工作如下：
①在定义容积式机械吸入能力的基础上，建立螺杆泵吸入能力计算数学模型，详细分析螺杆泵转速、螺杆螺旋升角、输送介质等对螺杆泵吸入能力的影响；研究螺杆泵吸入能力对容积效率特性的影响，得到螺杆泵关键设计参数与螺杆泵吸入能力的匹配关系，提出提高螺杆泵吸入能力的设计方法。
②基于流体力学边界层分离理论，在深入分析螺杆泵吸入能力的基础上，结合圆柱绕流现象，对圆柱绕流迹线及其分离点进行计算，建立圆柱绕流边界层分离优化模型，运用图形和解析的方法求解优化方程，结合螺杆转子端面几何特性，获得优化流线型体三维模型，通过理论分析的方法验证优化模型的合理性。
③内泄漏是泵泄漏的主要因素。针对螺杆泵桶壁间隙、啮合间隙等决定螺杆泵性能的关键间隙的设计问题，在研究螺杆各项间隙构成原理的基础上，运用流体力学间隙泄漏理论和小孔泄漏理论，分别建立泵腔间隙泄漏压差流和剪切流模型，分析螺杆泵桶壁间隙和啮合间隙的泄漏量，得到螺杆泵不同间隙泄漏的数学模型；以主动螺杆2头、从动螺杆3头的双螺杆泵为例，理论计算与试验对比分析螺杆转速、压差对泵泄漏的作用机理，揭示螺杆转速、泵进出口压差对螺杆泵流量特性及容积效率特性的影响规律。
④针对螺杆泵关键部件螺杆转子设计过程复杂、加工难度高导致啮合间隙不均匀的问题，在分析螺杆啮合间隙形成机理基础上，运用空间解析几何基础理论，提出基于啮合间隙的螺杆齿形优化设计新方法，建立螺杆加工过程进刀轨迹-螺杆齿形-啮合间隙转换方程，深入分析轴向、径向、法向等不同进刀方式对螺杆啮合间隙、螺杆齿形偏差的影响规律；结合微分几何等距曲面构型原理，得到预定加工间隙的螺杆端面齿形。
⑤针对由离散点组成的任意端截面螺杆齿形，基于齿轮啮合原理，运用三次样条插值方法求得螺杆成型刀具齿形；研究螺杆与刀具在加工过程中的空间包络特性与几何特性，结合机床、螺杆、刀具的协同运动所生成的接触线的形状和空间位置参数，创新性地提出一种基于离散点齿形的螺杆加工成型刀具设计方法--形位几何法，与齿轮啮合原理的方法进行对比表明：形位几何法简化刀具-工件包络求解模型，克服传统啮合理论设计刀具时无法精确计算齿形曲线尖点的关键技术难点，提高螺杆成型刀具齿形设计精度，并通过试验验证形位几何法的可行性及精确性。
The research subject of the dissertation stems from the National Natural ScienceFunds (NNSF)"Research on key technical and new design method of rotor profile forhigh efficiency three screw pump (50875268)" and "Research on key technical andbasic theory of multistage variable speed screw pump (51175522)".
Screw pumps have been widely used in the offshore drilling platforms, ships,precision machine tools, petrochemical industry and other fields due to its superioradaptability and economic practicability."The Central Committee of CPC onformulating the12th five-year plan for economic and social development suggestions"clearly pointed out that the high-end equipment manufacturing is the core position ofseven strategic emerging industries and will be highly supported by the government inthe important fields. As a key component of the high-end equipments, the developmentof screw pumps will power the high-end equipment manufacturing industry, and supportthe strategic emerging industry. Meanwhile, during the12th five-year, the governmentwill invest300billion in marine equipment, including offshore drilling platforms,offshore vessels and submarines, etc. Therefore, screw pump as an importantfundamental part of the high-end equipment have huge demands and broad prospects.However, screw pump, which is a high precision mechanical product, is sensitive to theprecision of the design and manufacturing. The products that are manufactured in ourcountry usually have various defects, including low volumetric efficiency, unstable flowcharacteristic, serious tooth surface wear, large power consumption, because of the lackof the understanding of the working mechanism and the lack of the comprehensivetechnique in design and machining. As a result, the high-end screw pumps basically relyon imports for a long time. In order to improve the internationalization level of high-endequipment manufacturing industry in our country and reduce the dependence on foreignhigh-end equipment parts such as screw pump, we need to carry out the innovationstudy in design principles and methods of screw pump system and solve the keytechnical problems of the design and manufacture of screw pump. Such breakthroughwill be socially and economically crucial to the independent innovation of machineryequipment in our country and have great practical value in engineering.
In this paper, screw rotors that are the core parts of the screw pump are the researchobjects. Fluid dynamics, leak theory, contact theory, spatial envelope theory, etc., have been used as tools to analyze the flow kinematics and dynamics of the pump chamber,to study the structure of screw motors and the design principles and methods onparam-pattern between the volumetric efficiency of screw pump and the configurationprinciples, to establish the screw tooth profile model basing on the meshing clearance,and to form the precision profile of forming cutter of the screw tooth surface. The maincontents of this dissertation are shown as follows:
①Based on the definition of suction capacity of positive displacement machine,the screw pump suction capacity calculation model has been set up. The impacts ofscrew speed, screw helix angle, the transmission medium, etc., on the screw pumpssuction capacity have been analyzed in detail. In addition, the matching relationshipbetween the key design parameters and the suction capacity of screw pump have beenobtained by studying the volumetric efficiency characteristics influence on its suctioncapacity. Furthermore, the improving method for the capability of screw pump's suctionhas been proposed.
②Based on theory of hydrodynamic boundary layer separation, the path line andthe separated points have been calculated by in-depth analyzing the capacity of screwpump's suction and the flow around a cylinder. Then, the optimization model of theboundary layer separation flow around cylinder has been established and solved byusing graphics and analytical methods. Moreover, the optimized3D model of thestreamline body has been obtained through the cross section geometry of the screw rotor.Finally, the feasibility of the optimization model has been validated by the theoreticalanalysis method.
③Clearance leakage is the main cause of pump leakage. For the design andcontrol of the key clearance which determines the performance of screw pump such asclearance of barrel wall and meshing area, the model of differential pressure flow andshear flow of clearance leakage in pump cavity has been established. Furthermore, themathematical expressions of leakage from different clearance are obtained by analyzingthe leakage for clearance of barrel wall and meshing area. Then, the influence of therotation speed and pressure difference between import and export on flowcharacteristics and volumetric efficiency characteristics of screw pump has beenrevealed by theoretical calculation and experimental analysis of twin-screw pump (2heads for main and3heads for follower, respectively).
④Aiming at the problem of the nonuniform meshing clearance that is caused bythe complicated design and the highly difficult process of the rotors which are the key components of screw pump, a new optimized design method of screw tooth profilebased on the given clearance is proposed by analyzing the formation mechanism ofscrew clearance and using the space analytic geometry theory. The transformationequations related to the feed path, screw tooth profile and the clearance in screwmanufacturing process are then established. Furthermore, the influence of feed directionsuch as axial, radial and normal on the meshing clearance and the tooth profile deviationof rotors has been analyzed in detail. Thus, in combination with the isometric surfaceconfiguration of differential geometry, the screw cross tooth profile with thepredetermined clearance is obtained.
⑤Let’s take the processing of screws for screw pumps as an example. Based uponthe principle of gearing mesh we can use the cubic spline interpolation method to obtainthe tooth profile of the screw forming cutter according to the tooth profile at any crosssection of screw composed of discrete points. Furthermore, a design method isinnovatively proposed for the screw forming cutter based on discrete points, namelyForm-Position Geometric Method (FPGM). This method is obtained by combining thespace enveloping and geometric characteristics between the screw and cutter during theprocessing and the shape of the contact line which is generated by the cooperativemothion of the machine tool, screw and cutter, as well as the spatial location parameters.After comparing the proposed method with the principle of gear meshing, it can beobserved that the cutter-workpiece enveloping solution model which is simplified by theFPGM can overcome the key technical difficulty. For example, it is difficult toaccurately calculate the cusp of the tooth curve using the cutter-workpiece model, butthe proposed cutter design method can improve the machining precision of the screwtooth profile. Finally, the feasibility and superiority of FPGM is verified byexperiments.
螺杆泵因具有优越的工程适应性和经济实用性在海洋钻井平台、舰船、精密机床、石油化工等领域应用日趋广泛。《中共中央关于制定国民经济和社会发展第十二个五年规划的建议》明确指出，高端装备制造业处于七大战略性新兴产业的核心地位，将在重点领域集中力量加快推进。螺及杆泵作为重点发展的高端装备部件，将为我国高端装备制造业的发展增加动力，成为战略性新兴产业发展的重要支撑。同时，“十二五”期间我国将投入3000亿重点发展海洋工程装备，包括海洋钻井平台、各种海洋工程船舶及潜艇等。因此，螺杆泵作为重要的高端装备基础部件，需求量巨大，具有广阔的发展前景。然而，螺杆泵属于高精度机械产品，其对设计和制造的精度很敏感。由于我国生产企业对螺杆泵工作机理认识不清晰，设计及加工方面的技术不够完善，使得生产出的产品存在容积效率低、流量特性不稳定、齿面磨损严重、功耗大等技术瓶颈，长期以来高端螺杆泵产品基本上依赖进口。为此，为提高我国高端装备制造业的国际化水平，减小我国在螺杆泵等高端装备部件对国外的依赖，开展螺杆泵系统创新设计理论与方法研究，突破螺杆泵设计制造关键技术难题，对提高我国机械装备配套自主创新能力具有十分重要的社会经济意义和工程实用价值。
本文以螺杆泵关键核心部件螺杆副为研究对象，利用流体动力学、泄漏理论、接触理论、空间包络理论等，深入分析泵腔内流场运动学、动力学特性，研究探讨螺杆构型原理及其结构与螺杆泵容积效率特性参数匹配的设计理论和方法，建立考虑啮合间隙的螺杆齿形设计模型，形成螺杆齿面成型刀具精确齿形设计方法。论文主要工作如下：
①在定义容积式机械吸入能力的基础上，建立螺杆泵吸入能力计算数学模型，详细分析螺杆泵转速、螺杆螺旋升角、输送介质等对螺杆泵吸入能力的影响；研究螺杆泵吸入能力对容积效率特性的影响，得到螺杆泵关键设计参数与螺杆泵吸入能力的匹配关系，提出提高螺杆泵吸入能力的设计方法。
②基于流体力学边界层分离理论，在深入分析螺杆泵吸入能力的基础上，结合圆柱绕流现象，对圆柱绕流迹线及其分离点进行计算，建立圆柱绕流边界层分离优化模型，运用图形和解析的方法求解优化方程，结合螺杆转子端面几何特性，获得优化流线型体三维模型，通过理论分析的方法验证优化模型的合理性。
③内泄漏是泵泄漏的主要因素。针对螺杆泵桶壁间隙、啮合间隙等决定螺杆泵性能的关键间隙的设计问题，在研究螺杆各项间隙构成原理的基础上，运用流体力学间隙泄漏理论和小孔泄漏理论，分别建立泵腔间隙泄漏压差流和剪切流模型，分析螺杆泵桶壁间隙和啮合间隙的泄漏量，得到螺杆泵不同间隙泄漏的数学模型；以主动螺杆2头、从动螺杆3头的双螺杆泵为例，理论计算与试验对比分析螺杆转速、压差对泵泄漏的作用机理，揭示螺杆转速、泵进出口压差对螺杆泵流量特性及容积效率特性的影响规律。
④针对螺杆泵关键部件螺杆转子设计过程复杂、加工难度高导致啮合间隙不均匀的问题，在分析螺杆啮合间隙形成机理基础上，运用空间解析几何基础理论，提出基于啮合间隙的螺杆齿形优化设计新方法，建立螺杆加工过程进刀轨迹-螺杆齿形-啮合间隙转换方程，深入分析轴向、径向、法向等不同进刀方式对螺杆啮合间隙、螺杆齿形偏差的影响规律；结合微分几何等距曲面构型原理，得到预定加工间隙的螺杆端面齿形。
⑤针对由离散点组成的任意端截面螺杆齿形，基于齿轮啮合原理，运用三次样条插值方法求得螺杆成型刀具齿形；研究螺杆与刀具在加工过程中的空间包络特性与几何特性，结合机床、螺杆、刀具的协同运动所生成的接触线的形状和空间位置参数，创新性地提出一种基于离散点齿形的螺杆加工成型刀具设计方法--形位几何法，与齿轮啮合原理的方法进行对比表明：形位几何法简化刀具-工件包络求解模型，克服传统啮合理论设计刀具时无法精确计算齿形曲线尖点的关键技术难点，提高螺杆成型刀具齿形设计精度，并通过试验验证形位几何法的可行性及精确性。
The research subject of the dissertation stems from the National Natural ScienceFunds (NNSF)"Research on key technical and new design method of rotor profile forhigh efficiency three screw pump (50875268)" and "Research on key technical andbasic theory of multistage variable speed screw pump (51175522)".
Screw pumps have been widely used in the offshore drilling platforms, ships,precision machine tools, petrochemical industry and other fields due to its superioradaptability and economic practicability."The Central Committee of CPC onformulating the12th five-year plan for economic and social development suggestions"clearly pointed out that the high-end equipment manufacturing is the core position ofseven strategic emerging industries and will be highly supported by the government inthe important fields. As a key component of the high-end equipments, the developmentof screw pumps will power the high-end equipment manufacturing industry, and supportthe strategic emerging industry. Meanwhile, during the12th five-year, the governmentwill invest300billion in marine equipment, including offshore drilling platforms,offshore vessels and submarines, etc. Therefore, screw pump as an importantfundamental part of the high-end equipment have huge demands and broad prospects.However, screw pump, which is a high precision mechanical product, is sensitive to theprecision of the design and manufacturing. The products that are manufactured in ourcountry usually have various defects, including low volumetric efficiency, unstable flowcharacteristic, serious tooth surface wear, large power consumption, because of the lackof the understanding of the working mechanism and the lack of the comprehensivetechnique in design and machining. As a result, the high-end screw pumps basically relyon imports for a long time. In order to improve the internationalization level of high-endequipment manufacturing industry in our country and reduce the dependence on foreignhigh-end equipment parts such as screw pump, we need to carry out the innovationstudy in design principles and methods of screw pump system and solve the keytechnical problems of the design and manufacture of screw pump. Such breakthroughwill be socially and economically crucial to the independent innovation of machineryequipment in our country and have great practical value in engineering.
In this paper, screw rotors that are the core parts of the screw pump are the researchobjects. Fluid dynamics, leak theory, contact theory, spatial envelope theory, etc., have been used as tools to analyze the flow kinematics and dynamics of the pump chamber,to study the structure of screw motors and the design principles and methods onparam-pattern between the volumetric efficiency of screw pump and the configurationprinciples, to establish the screw tooth profile model basing on the meshing clearance,and to form the precision profile of forming cutter of the screw tooth surface. The maincontents of this dissertation are shown as follows:
①Based on the definition of suction capacity of positive displacement machine,the screw pump suction capacity calculation model has been set up. The impacts ofscrew speed, screw helix angle, the transmission medium, etc., on the screw pumpssuction capacity have been analyzed in detail. In addition, the matching relationshipbetween the key design parameters and the suction capacity of screw pump have beenobtained by studying the volumetric efficiency characteristics influence on its suctioncapacity. Furthermore, the improving method for the capability of screw pump's suctionhas been proposed.
②Based on theory of hydrodynamic boundary layer separation, the path line andthe separated points have been calculated by in-depth analyzing the capacity of screwpump's suction and the flow around a cylinder. Then, the optimization model of theboundary layer separation flow around cylinder has been established and solved byusing graphics and analytical methods. Moreover, the optimized3D model of thestreamline body has been obtained through the cross section geometry of the screw rotor.Finally, the feasibility of the optimization model has been validated by the theoreticalanalysis method.
③Clearance leakage is the main cause of pump leakage. For the design andcontrol of the key clearance which determines the performance of screw pump such asclearance of barrel wall and meshing area, the model of differential pressure flow andshear flow of clearance leakage in pump cavity has been established. Furthermore, themathematical expressions of leakage from different clearance are obtained by analyzingthe leakage for clearance of barrel wall and meshing area. Then, the influence of therotation speed and pressure difference between import and export on flowcharacteristics and volumetric efficiency characteristics of screw pump has beenrevealed by theoretical calculation and experimental analysis of twin-screw pump (2heads for main and3heads for follower, respectively).
④Aiming at the problem of the nonuniform meshing clearance that is caused bythe complicated design and the highly difficult process of the rotors which are the key components of screw pump, a new optimized design method of screw tooth profilebased on the given clearance is proposed by analyzing the formation mechanism ofscrew clearance and using the space analytic geometry theory. The transformationequations related to the feed path, screw tooth profile and the clearance in screwmanufacturing process are then established. Furthermore, the influence of feed directionsuch as axial, radial and normal on the meshing clearance and the tooth profile deviationof rotors has been analyzed in detail. Thus, in combination with the isometric surfaceconfiguration of differential geometry, the screw cross tooth profile with thepredetermined clearance is obtained.
⑤Let’s take the processing of screws for screw pumps as an example. Based uponthe principle of gearing mesh we can use the cubic spline interpolation method to obtainthe tooth profile of the screw forming cutter according to the tooth profile at any crosssection of screw composed of discrete points. Furthermore, a design method isinnovatively proposed for the screw forming cutter based on discrete points, namelyForm-Position Geometric Method (FPGM). This method is obtained by combining thespace enveloping and geometric characteristics between the screw and cutter during theprocessing and the shape of the contact line which is generated by the cooperativemothion of the machine tool, screw and cutter, as well as the spatial location parameters.After comparing the proposed method with the principle of gear meshing, it can beobserved that the cutter-workpiece enveloping solution model which is simplified by theFPGM can overcome the key technical difficulty. For example, it is difficult toaccurately calculate the cusp of the tooth curve using the cutter-workpiece model, butthe proposed cutter design method can improve the machining precision of the screwtooth profile. Finally, the feasibility and superiority of FPGM is verified byexperiments.
引文
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