涡旋压缩腔几何模型与涡旋齿强度研究
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摘要
研究涡旋压缩机的工作特性,基于通用型线理论确定涡旋齿基本参数,建立了涡旋压缩腔几何模型,并用模型分析、模拟了圆渐开线涡旋压缩腔。通过理论研究与有限元模拟分析了涡旋齿的作用载荷、应力和变形的基本规律。基于涡旋齿载荷、应力、变形和工程实践分析了涡旋齿的失效形式,并结合试验和样机研制研究涡旋齿的强度,建立了涡旋齿强度模型,确定了涡旋齿的基本设计准则和强度计算的一般流程。涡旋压缩腔几何模型与涡旋齿强度研究为涡旋机械的几何学、运动学、动力学、热力学、强度及可靠性等研究及设计提供了理论基础,提出了获得高性能样机的基本思路,对涡旋机械的研究与应用具有重要意义。
涡旋机械的基本组成有涡旋盘、防自转机构、轴向和径向随变机构、密封和润滑机构等。定义动涡旋齿外型线和静涡旋齿内型线对应的节线为a类节线,动涡旋齿内型线和静涡旋齿外型线对应的节线为b类节线。定义与涡旋齿中线法向角对应的涡旋齿外、内型线法向分量之差为涡旋齿法向齿厚,对应的涡旋齿外、内型线上两点之间的距离为全齿厚。基于涡旋型线及涡旋机械的特点,确定涡旋齿公转半径、型线最大切向分量、齿厚系数和涡旋齿高为涡旋齿的四个基本参数;
依据节线类型把压缩腔分为a类压缩腔和b类压缩腔。建立了由型线、压缩腔形状变化、生命周期和压缩腔数综合构成的涡旋压缩腔几何模型。利用该几何模型可对压缩腔的特性进行全面分析。圆渐开线涡旋压缩腔用压缩腔长度和容积可作为压缩腔的基本特性,分析和模拟表明圆渐开线压缩腔变形稳定且效率高,工程中适宜采用以圆渐开线为基础的型线,如PMP型线;
建立了综合内压作用和稳态温度场作用的涡旋齿载荷模型。涡旋齿工作中相当于受到间隔为π的π展角区域内压作用,载荷大小为涡旋齿内外壁面的压力差。涡旋齿内压载荷变化不连续,当动涡旋齿转角为开始排气角时不但载荷最大,而且作用区域离涡旋齿中央区域最远。对于小参数涡旋齿,涡旋齿的稳态温度可由其中面温度代替,靠近涡旋齿中央区域的部分涡旋齿温度为排气温度,而其余部分温度随法向角增大而近似于线性下降,涡旋齿末端的温度为吸气温度;
涡旋齿应力分析适宜分析等效应力,变形以分析涡旋齿的径向和轴向变形为主。不同内压作用、稳态温度场作用、π展角区域内压作用、多π展角区域内压作用及其耦合作用下的应力与变形有限元分析表明:不同参数的涡旋齿模型模拟得到的涡旋齿等效应力和变形基本规律相同;涡旋齿等效应力和变形主要由内压载荷和稳态温度场作用引起,内压作用的等效应力和变形以涡旋齿公转周期而变化,稳态温度场作用的等效应力和变形基本保持不变;整个涡旋齿上齿根处等效应力最大,涡旋齿的径向变形比轴向变形量大,但轴向变形对压缩机的性能影响更大;内压作用的等效应力和轴向变形比稳态温度场作用的小,尽管内压和稳态温度场对涡旋齿变形与应力的作用效应相反,但都不能简单叠加,应力与变形基本受稳态温度场控制;内压作用对等效应力和变形有明显的削弱作用,而且使等效应力和变形的变化更加平稳。受均匀内压作用、π展角区域内压作用时涡旋齿根等效应力以及稳态温度场作用时的涡旋齿高变形都可进行简化计算,计算实例证明简化计算与有限元模拟结果的偏差较小,可满足工程实践要求;
常见的涡旋齿失效形式有涡旋齿折断失效、表面损伤失效和过大变形三种基本类型,其中涡旋齿根弯曲疲劳折断、涡旋齿面点蚀、涡旋齿轴向磨损、胶合和涡旋齿过大变形是其主要的失效形式。所建立的涡旋齿强度模型由涡旋齿根强度(静强度和齿根弯曲强度)和涡旋齿轴向刚度组成。确定了涡旋齿根强度为涡旋齿的基本设计准则,并校核轴向刚度。以多π展角区域内压作用的应力作为应力幅,以稳态温度场和内压耦合作用的应力作为平均应力,可通过计算齿根安全系数计算齿根弯曲疲劳强度,钢制的涡旋齿强度计算中可简化计算涡旋齿根应力集中综合影响系数。涡旋齿强度计算或基于涡旋齿强度进行参数设计都可按基本相同的流程进行,为提高涡旋齿轴向的密封性能和磨损强度,可基于稳态温度场的涡旋齿变形规律对涡旋齿高尺寸公差进行修正;
通过理论与工程实践相结合,得到了获得高性能涡旋机械的基本思路:
1)利用压缩腔几何模型选择并优化型线,获得变形效率、稳定性良好的涡旋压缩腔;
2)通过强度模型选择合理的涡旋齿材料和参数,预测涡旋机械的强度和基本性能;
3)采用合理的轴系结构、防自转机构、随变机构的同时,采用齿顶密封条结构,并基于稳态温度场对涡旋齿高公差进行修正。
Working characteristics of scroll compressor are investigated. The scroll wrap's essential parameteres are determined and scroll chamber's geometrical model is established based on general profile theory. Using the model, the scroll compressor chamber that in form of aircle involute is analysised and simulated. The distribution of loadinging, stress and deformation of scroll wrap are analysised by theoretical studying and finite element method. Based on loadinging, stress and deformation, failure types of scroll wrap are investigated. Scroll wrap's strength is investigated and strength model is established by synthesizing failure types, the prototype scroll machines and their testing. At the same time, the basic design criterions are ditermined and a current approaches for strength calculation is propsed. Modeling of scroll compressor chambers and investigation on strength of scroll wrap could provied the foundations in theory for scroll machine researches on geometry, kinematics, dynamics, thermodynamics, strength, reliability and parameterized design. It could also provide a direction for obtaining outstanding performances scroll machine and has important significance to the scroll machine's stdudy and application.
In general, scroll machine mainly constructed with scroll wrap plane, anti-rotation mechanism, axial and radial compliance mechanism, sealing and lubrication mechanism. The scroll wrap's pitch lines are defined as a-type and b-type. A-type pitch line forms orbitting scroll's outer-line and fixed scroll's inner-line. B-type pitch line forms orbitting scroll's inner-line and fixed scroll's outer-line. Corresponding to scroll wrap middle line's normal angle, the normal wrap thickness is defined as the normal component diffence between outer-line and inner-line and the all wrap thickness is defined as the distence between two point that one point on outer-line and other on inner-line. Considering the characteristics of scroll profile and scroll machine, the orbitting radious, the maximum tangent component of general profile, the wrap thickness coefficient, and the scroll wrap height can be regarded as the essential parameters of scroll wrap.
The scroll compressor chambers are classified as a-type and b-type by its types of pitch line. The geometrical model that synthesized the profile, form, deformation, lifecycle and the living numbers of scroll compressor chambers is established. Using established geometrical model, all of geometric characteristics of scroll compressor chambers can be overall analyzed. For scroll compressor chamber that in form of aircle involute, its length and volume can serve as the basic geometric characteristics and it is found that its deformation characteristics are more steady and deformation efficiency is higher. Consequently, the profile which based on aircle involute profile is well adopted in practice, such as PMP profile.
The loadinging model that synthesized the inner-pressure loadinging and stable conditions temperature fluid is established. The scroll's inner-pressure loading is correspond to 71-involute angle region inner- pressure loadinging which have an interval ofπangle, the value of inner-pressure loadinging is the pressure difference between inner-side and outer-side of scroll wrap. The inner-pressure loadinging is discontinuous. When the crank angle equal to discharge angle, the inner pressure's value is not only maximal but also the acting region of the maximum inner pressure loading is farthest off the center part of scroll. For small parameter scroll wrap, the scroll wrap's temperature can be substituted by its middle area's temperature .In the centre partion of scoll wrap, scroll wrap's temprature equal to discharge temperature, the other's temperature decrease Vs. normal-angle nearly linearly and equal suction temperature at the end of scroll wrap.
It is more reasonable to select equivalent stress analysis in alaysising stress of scroll wrap. The axial deformation and radial deformation can be mainly object in deformation analsys. To the scroll wrap acted various inner-pressure,π-involute angle region inner pressure, stable temperature fluid, and thieir coupling loading, the results simulated by finite element method shows that distribution of the equivalent stress of scroll wrap with various parameter is same basically, distribution of the deformation is also. The stress and deformatiom mainly result from the inner-pressure loading and stable tempreature fluid. The stress and deformation result from the inner-pressure loading change periodicity with duty cycle but the stress and deformation result from stable tempreature fluid have nearly no changes. In all scroll wrap, the maxmum equivalent stress occurs on root of scroll wrap at the same point of involute angle.The value of axidial deformation of scroll wrap is samller than the axidial deformation,but it influence on compressor's performance more gravely. The satble tempreature fluid results in stress and deformation quantity is much than inner-pressure's. Although the satble tempreature fluid and the inner-pressure's inflowence on stress and deformation is reverse, their value of stress and deformation could not add up simply. The stress and deformation scroll wrap acted coupling loading are controled by the satble tempreature fluid. The inner-pressure can obviously weaken the stress and deformation of acroll wrap and make changes of stress and deformation more steadily. The equivalent stress at root of scroll wrap with various inner-pressure or 71-involute angle region inner pressure, the deformation of scroll height with stable temperature fluid loading cab be calculatated by simplified formula. All of the calculated examples prove that the calculated results are well agree with the simulated results using finite element method, simplified calxulation can meet requirement of practices.
In general, the breakage failure, surface failure and excessive deformation failure are the basic type of scroll wrap failure. The bending fatigue failure,surface pitting,axial wear-out failure, Scuffing and excessive deformation failure are critical failures. The strength model is constructed from the strength of scroll root (including static strength and bending fatigue strength) and axial rigidity. The bending fatigue strength criterion for scroll root is ascertained as basic design criterion and the axial rigidity have to be examined. The stress resulted from inner-pressure loadinging as stress amplitude and stress resulted from coupling loading as mean stress ,the bending fatigue strength for scroll root could be calculated using safety factor. If the scroll wrap is machined by steel, the concentration coefficient of synthetic stress for scroll wrap root could be simplfied calculation must be considered.The scroll wrap's stength calculation and design based on its strength could be carried out by same approaches. To enhance axial sealing performanc and wear-out strength,the scroll height's dimensional tolerance must be modified base on the deformation of scroll wrap height based on stable temperature field.
Synthesizing theoretical research and experiences in engineering, an important direction for obtaining outstanding performances scroll machine cab be proposed as follow:
(1) Using geometrical model of compressor chamber to select optimized profile and better stability chamber;
(2) Using strength model to select scroll wrap's material and reasonable parameters and forecast the scroll machine's basic performances;
(3) Adoptting not only reasonable rotor-bearing system, anti-rotation mechanism, axial and radial compliance mechanism, Sealing and Lubrication mechanism, bu also carrying out modification to the scroll height's dimensional tolerance based on the deformation of scroll wrap height based on stable temperature field.
涡旋机械的基本组成有涡旋盘、防自转机构、轴向和径向随变机构、密封和润滑机构等。定义动涡旋齿外型线和静涡旋齿内型线对应的节线为a类节线,动涡旋齿内型线和静涡旋齿外型线对应的节线为b类节线。定义与涡旋齿中线法向角对应的涡旋齿外、内型线法向分量之差为涡旋齿法向齿厚,对应的涡旋齿外、内型线上两点之间的距离为全齿厚。基于涡旋型线及涡旋机械的特点,确定涡旋齿公转半径、型线最大切向分量、齿厚系数和涡旋齿高为涡旋齿的四个基本参数;
依据节线类型把压缩腔分为a类压缩腔和b类压缩腔。建立了由型线、压缩腔形状变化、生命周期和压缩腔数综合构成的涡旋压缩腔几何模型。利用该几何模型可对压缩腔的特性进行全面分析。圆渐开线涡旋压缩腔用压缩腔长度和容积可作为压缩腔的基本特性,分析和模拟表明圆渐开线压缩腔变形稳定且效率高,工程中适宜采用以圆渐开线为基础的型线,如PMP型线;
建立了综合内压作用和稳态温度场作用的涡旋齿载荷模型。涡旋齿工作中相当于受到间隔为π的π展角区域内压作用,载荷大小为涡旋齿内外壁面的压力差。涡旋齿内压载荷变化不连续,当动涡旋齿转角为开始排气角时不但载荷最大,而且作用区域离涡旋齿中央区域最远。对于小参数涡旋齿,涡旋齿的稳态温度可由其中面温度代替,靠近涡旋齿中央区域的部分涡旋齿温度为排气温度,而其余部分温度随法向角增大而近似于线性下降,涡旋齿末端的温度为吸气温度;
涡旋齿应力分析适宜分析等效应力,变形以分析涡旋齿的径向和轴向变形为主。不同内压作用、稳态温度场作用、π展角区域内压作用、多π展角区域内压作用及其耦合作用下的应力与变形有限元分析表明:不同参数的涡旋齿模型模拟得到的涡旋齿等效应力和变形基本规律相同;涡旋齿等效应力和变形主要由内压载荷和稳态温度场作用引起,内压作用的等效应力和变形以涡旋齿公转周期而变化,稳态温度场作用的等效应力和变形基本保持不变;整个涡旋齿上齿根处等效应力最大,涡旋齿的径向变形比轴向变形量大,但轴向变形对压缩机的性能影响更大;内压作用的等效应力和轴向变形比稳态温度场作用的小,尽管内压和稳态温度场对涡旋齿变形与应力的作用效应相反,但都不能简单叠加,应力与变形基本受稳态温度场控制;内压作用对等效应力和变形有明显的削弱作用,而且使等效应力和变形的变化更加平稳。受均匀内压作用、π展角区域内压作用时涡旋齿根等效应力以及稳态温度场作用时的涡旋齿高变形都可进行简化计算,计算实例证明简化计算与有限元模拟结果的偏差较小,可满足工程实践要求;
常见的涡旋齿失效形式有涡旋齿折断失效、表面损伤失效和过大变形三种基本类型,其中涡旋齿根弯曲疲劳折断、涡旋齿面点蚀、涡旋齿轴向磨损、胶合和涡旋齿过大变形是其主要的失效形式。所建立的涡旋齿强度模型由涡旋齿根强度(静强度和齿根弯曲强度)和涡旋齿轴向刚度组成。确定了涡旋齿根强度为涡旋齿的基本设计准则,并校核轴向刚度。以多π展角区域内压作用的应力作为应力幅,以稳态温度场和内压耦合作用的应力作为平均应力,可通过计算齿根安全系数计算齿根弯曲疲劳强度,钢制的涡旋齿强度计算中可简化计算涡旋齿根应力集中综合影响系数。涡旋齿强度计算或基于涡旋齿强度进行参数设计都可按基本相同的流程进行,为提高涡旋齿轴向的密封性能和磨损强度,可基于稳态温度场的涡旋齿变形规律对涡旋齿高尺寸公差进行修正;
通过理论与工程实践相结合,得到了获得高性能涡旋机械的基本思路:
1)利用压缩腔几何模型选择并优化型线,获得变形效率、稳定性良好的涡旋压缩腔;
2)通过强度模型选择合理的涡旋齿材料和参数,预测涡旋机械的强度和基本性能;
3)采用合理的轴系结构、防自转机构、随变机构的同时,采用齿顶密封条结构,并基于稳态温度场对涡旋齿高公差进行修正。
Working characteristics of scroll compressor are investigated. The scroll wrap's essential parameteres are determined and scroll chamber's geometrical model is established based on general profile theory. Using the model, the scroll compressor chamber that in form of aircle involute is analysised and simulated. The distribution of loadinging, stress and deformation of scroll wrap are analysised by theoretical studying and finite element method. Based on loadinging, stress and deformation, failure types of scroll wrap are investigated. Scroll wrap's strength is investigated and strength model is established by synthesizing failure types, the prototype scroll machines and their testing. At the same time, the basic design criterions are ditermined and a current approaches for strength calculation is propsed. Modeling of scroll compressor chambers and investigation on strength of scroll wrap could provied the foundations in theory for scroll machine researches on geometry, kinematics, dynamics, thermodynamics, strength, reliability and parameterized design. It could also provide a direction for obtaining outstanding performances scroll machine and has important significance to the scroll machine's stdudy and application.
In general, scroll machine mainly constructed with scroll wrap plane, anti-rotation mechanism, axial and radial compliance mechanism, sealing and lubrication mechanism. The scroll wrap's pitch lines are defined as a-type and b-type. A-type pitch line forms orbitting scroll's outer-line and fixed scroll's inner-line. B-type pitch line forms orbitting scroll's inner-line and fixed scroll's outer-line. Corresponding to scroll wrap middle line's normal angle, the normal wrap thickness is defined as the normal component diffence between outer-line and inner-line and the all wrap thickness is defined as the distence between two point that one point on outer-line and other on inner-line. Considering the characteristics of scroll profile and scroll machine, the orbitting radious, the maximum tangent component of general profile, the wrap thickness coefficient, and the scroll wrap height can be regarded as the essential parameters of scroll wrap.
The scroll compressor chambers are classified as a-type and b-type by its types of pitch line. The geometrical model that synthesized the profile, form, deformation, lifecycle and the living numbers of scroll compressor chambers is established. Using established geometrical model, all of geometric characteristics of scroll compressor chambers can be overall analyzed. For scroll compressor chamber that in form of aircle involute, its length and volume can serve as the basic geometric characteristics and it is found that its deformation characteristics are more steady and deformation efficiency is higher. Consequently, the profile which based on aircle involute profile is well adopted in practice, such as PMP profile.
The loadinging model that synthesized the inner-pressure loadinging and stable conditions temperature fluid is established. The scroll's inner-pressure loading is correspond to 71-involute angle region inner- pressure loadinging which have an interval ofπangle, the value of inner-pressure loadinging is the pressure difference between inner-side and outer-side of scroll wrap. The inner-pressure loadinging is discontinuous. When the crank angle equal to discharge angle, the inner pressure's value is not only maximal but also the acting region of the maximum inner pressure loading is farthest off the center part of scroll. For small parameter scroll wrap, the scroll wrap's temperature can be substituted by its middle area's temperature .In the centre partion of scoll wrap, scroll wrap's temprature equal to discharge temperature, the other's temperature decrease Vs. normal-angle nearly linearly and equal suction temperature at the end of scroll wrap.
It is more reasonable to select equivalent stress analysis in alaysising stress of scroll wrap. The axial deformation and radial deformation can be mainly object in deformation analsys. To the scroll wrap acted various inner-pressure,π-involute angle region inner pressure, stable temperature fluid, and thieir coupling loading, the results simulated by finite element method shows that distribution of the equivalent stress of scroll wrap with various parameter is same basically, distribution of the deformation is also. The stress and deformatiom mainly result from the inner-pressure loading and stable tempreature fluid. The stress and deformation result from the inner-pressure loading change periodicity with duty cycle but the stress and deformation result from stable tempreature fluid have nearly no changes. In all scroll wrap, the maxmum equivalent stress occurs on root of scroll wrap at the same point of involute angle.The value of axidial deformation of scroll wrap is samller than the axidial deformation,but it influence on compressor's performance more gravely. The satble tempreature fluid results in stress and deformation quantity is much than inner-pressure's. Although the satble tempreature fluid and the inner-pressure's inflowence on stress and deformation is reverse, their value of stress and deformation could not add up simply. The stress and deformation scroll wrap acted coupling loading are controled by the satble tempreature fluid. The inner-pressure can obviously weaken the stress and deformation of acroll wrap and make changes of stress and deformation more steadily. The equivalent stress at root of scroll wrap with various inner-pressure or 71-involute angle region inner pressure, the deformation of scroll height with stable temperature fluid loading cab be calculatated by simplified formula. All of the calculated examples prove that the calculated results are well agree with the simulated results using finite element method, simplified calxulation can meet requirement of practices.
In general, the breakage failure, surface failure and excessive deformation failure are the basic type of scroll wrap failure. The bending fatigue failure,surface pitting,axial wear-out failure, Scuffing and excessive deformation failure are critical failures. The strength model is constructed from the strength of scroll root (including static strength and bending fatigue strength) and axial rigidity. The bending fatigue strength criterion for scroll root is ascertained as basic design criterion and the axial rigidity have to be examined. The stress resulted from inner-pressure loadinging as stress amplitude and stress resulted from coupling loading as mean stress ,the bending fatigue strength for scroll root could be calculated using safety factor. If the scroll wrap is machined by steel, the concentration coefficient of synthetic stress for scroll wrap root could be simplfied calculation must be considered.The scroll wrap's stength calculation and design based on its strength could be carried out by same approaches. To enhance axial sealing performanc and wear-out strength,the scroll height's dimensional tolerance must be modified base on the deformation of scroll wrap height based on stable temperature field.
Synthesizing theoretical research and experiences in engineering, an important direction for obtaining outstanding performances scroll machine cab be proposed as follow:
(1) Using geometrical model of compressor chamber to select optimized profile and better stability chamber;
(2) Using strength model to select scroll wrap's material and reasonable parameters and forecast the scroll machine's basic performances;
(3) Adoptting not only reasonable rotor-bearing system, anti-rotation mechanism, axial and radial compliance mechanism, Sealing and Lubrication mechanism, bu also carrying out modification to the scroll height's dimensional tolerance based on the deformation of scroll wrap height based on stable temperature field.
引文
[1]Creux.Rotary Engine[P].U.S.Patent,801,182,1905.
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