碳纤维波纹管弯曲刚度的测量及有限元分析
|
摘要
飞轮存储动能正比于其转动惯量和角速度平方,使用碳纤维复合材料可有效提高转子线速度,而通过波纹管连接圆筒的多节式飞轮转子设计,不仅便于增大转动惯量,而且考虑到波纹管弯曲刚度对转子固有频率的影响,可实现在较低转速下过临界,增大工作转速范围。该文针对渐变铺层的碳纤维波纹管,通过轴向施力法测量其静态弯曲刚度,建立对应的有限元模型,计算不同载荷下线性和考虑几何非线性的弯曲刚度,并模拟不同下铺层的弯曲刚度。研究结果表明:波纹管弯曲刚度与载荷是非线性关系,载荷较大时测量值与理论值数量级一致,弯曲刚度随铺层数增多、轴向铺层比增加而增大,且受铺层次序影响。
The kinetic energy stored in a flywheel depends on its rotational inertia and linear velocity. The use of carbon fiber composite materials can effectively improve the rotor speed and increasing the rotor length can increase its rotational inertia.Furthermore,multi-section flywheel rotors formed by connecting tubes through bellows enables the rotor to pass through critical frequencies at low speeds,which increases the working speed range.This paper studies the bending stiffnesses of variable thickness carbon fiber bellows with the static bending stiffness measured by the axial force method.A finite element model was then used to predict the linear and geometric nonlinear bending stiffness for various loads and various laminates.The research indicates that bending stiffness variation is nonlinear with the load,with the measured stiffness being of the same order of magnitude as the theoretical values for large load.The simulations also show how the thickness,angle and stacking sequence of the laminate affect the bending stiffness.
The kinetic energy stored in a flywheel depends on its rotational inertia and linear velocity. The use of carbon fiber composite materials can effectively improve the rotor speed and increasing the rotor length can increase its rotational inertia.Furthermore,multi-section flywheel rotors formed by connecting tubes through bellows enables the rotor to pass through critical frequencies at low speeds,which increases the working speed range.This paper studies the bending stiffnesses of variable thickness carbon fiber bellows with the static bending stiffness measured by the axial force method.A finite element model was then used to predict the linear and geometric nonlinear bending stiffness for various loads and various laminates.The research indicates that bending stiffness variation is nonlinear with the load,with the measured stiffness being of the same order of magnitude as the theoretical values for large load.The simulations also show how the thickness,angle and stacking sequence of the laminate affect the bending stiffness.
引文
[1]李永生,李建国.波形膨胀节实用技术[M].北京:化学工业出版社,2000.LI Y S,LI J G.Practical technology for bellows expansion joints[M].Beijing:Chemical Industry Press,2000.(in Chinese)
[2]IL’IN L A,LOBKOVA N A,LOS A O,et al.Approximate method of calculations for a helically corrugated tube[J].Soviet Applied Mechanics,1983,19(9):764-767.
[3]BOLUND B,BERNHOFF H,LEIJON M.Flywheel energy and power storage systems[J].Renewable&Sustainable Energy Reviews,2007,11(2):235-258.
[4]戴兴建,邓占峰,刘刚,等.大容量先进飞轮储能电源技术发展状况[J].电工技术学报,2011,26(7):133-140.DAI X J,DENG Z F,LIU G,et al.Review on advanced flywheel energy storage system with large scale[J].Transactions of China Electrotechnical Society,2011,26(7):133-140.(in Chinese)
[5]MOUSAVI G S M,FARAJI F,MAJAZI A,et al.Acomprehensive review of flywheel energy storage system technology[J].Renewable&Sustainable Energy Reviews,2017,67:477-490.
[6]汤双清.飞轮储能技术及应用[M].武汉:华中科技大学出版社,2007.TANG S Q.Flywheel energy storage technology and its application[M].Wuhan:Huazhong University of Science and Technology Press,2007.(in Chinese)
[7]PEREZ-APARICIO J L,RIPOLL L.Exact,integrated and complete solutions for composite flywheels[J].Composite Structures,2011,93(5):1404-1415.
[8]HA S K,KIM S J,NASIR S U,et al.Design optimization and fabrication of a hybrid composite flywheel rotor[J].Composite Structures,2012,94(11):3290-3299.
[9]戴兴建,张小章,姜新建,等.清华大学飞轮储能技术研究概况[J].储能科学与技术,2012,1(1):64-68.DAI X J,ZHANG X Z,JIANG X J,et al.Flywheel energy storage technology in Tsinghua University[J].Energy Storage Science and Technology,2012,1(1):64-68.(in Chinese)
[10]唐长亮,戴兴建,汪勇.多层混杂复合材料飞轮力学设计与旋转试验[J].清华大学学报(自然科学版),2015,55(3):361-367.TANG C L,DAI X J,WANG Y.Mechanical design and spin test of a multi-layer commingled composite flywheel[J].Journal of Tsinghua University(Science and Technology),2015,55(3):361-367.(in Chinese)
[11]杨启述.气体离心机技术基础[M].北京:原子能出版社,1991.YANG Q S.Technical foundation of gas centrifuge[M].Beijing:Atomic Energy Press,1991.(in Chinese)
[12]REICH J,CARDELLA A,CAPRICCIOLI A,et al.Experimental verification of the axial and lateral stiffness of large W7-X rectangular bellows[J].Fusion Engineering&Design,2007,82(15-24):1924-1928.
[13]任宁,欧开良,王长路,等.Ω形波纹管的轴向刚度研究[J].机械强度,2011,33(5):719-723.REN N,OU K L,WANG C L,et al.Research on the axial stiffness ofΩ-shaped bellows[J].Journal of Mechanical Strength,2011,33(5):719-723.(in Chinese)
[14]徐志翘,刘燕,杨嘉实,等.变厚度U型波纹壳大挠度问题的摄动解[J].清华大学学报(自然科学版),1985(1):39-51.XU Z Q,LIU Y,YANG J S,et al.Large deflection of a U-shaped bellows with varying thickness[J].Journal of Tsinghua University(Science and Technology),1985(1):39-51.(in Chinese)
[15]修筑,王纪民,马建敏.厚度变化对U型波纹管轴向刚度的影响[J].噪声与振动控制,2012,32(5):189-192.XIU Z,WANG J M,MA J M.The effects of thickness variation on axial stiffness of U-shaped bellows[J].Noise and Vibration Control,2012,32(5):189-192.(in Chinese)
[16]BECHT C.Predicting bellows response by numerical and theoretical methods[J].Journal of Pressure Vessel Technology,1986,108(3):334-341.
[17]SHEN Z P.Approximate calculation of U-shaped bellows[J].Tsinghua Science and Technology,1996,1(3):305-309.
[18]王永岗,戴诗亮,吕英民.波纹管在任意载荷作用下的几何非线性分析[J].清华大学学报(自然科学版),2002,42(2):220-223.WANG Y G,DAI S L,LY M.Geometrically nonlinear analysis for arbitrarily loaded bellows[J].Journal of Tsinghua University(Science and Technology),2002,42(2):220-223.(in Chinese)
[19]STEINBRINK S E,AGGARWAL M C,SHEPHERD K IM.Linear and nonlinear finite element analysis of an exhaust manifold with included bellows[C]//ASME 2007 Pressure Vessels and Piping Conference.New York:American Society of Mechanical Engineers,2007:89-94.
[20]张承宗.复合材料板壳力学解析理论[M].北京:国防工业出版社,2009.ZHANG C Z.Mechanics analysis theory of composite plate and shell[M].Beijing:National Defense Industry Press,2009.(in Chinese)
[21]MEYER-PIENING H R,FARSHAD M,GEIER B,et al.Buckling loads of CFRP composite cylinders under combined axial and torsion loading experiments and computations[J].Composite Structures,2001,53(4):427-435.
[22]PARK J S,HONG C S,KIM C G,et al.Analysis of filament wound composite structures considering the change of winding angles through the thickness direction[J].Composite Structures,2002,55(1):63-71.
[23]舒朝霞,杨福江.波纹管弯曲刚度测试方法研究[C]//中国核科学技术进展报告(第四卷)---中国核学会2015年学术年会论文集第4册(同位素分离分卷).北京:中国核学会,2015:196-200.SHU Z X,YANG F J.Research on measuring method of bending stiffness of bellows[C]//China Nuclear Science and Technology Progress Report(Volume IV)-Proceedings of2015Annual Meeting of Chinese Nuclear Society,Volume 4(Isotope Separation Sub-volume).Beijing:Chinese Nuclear Society,2015:196-200.(in Chinese)
[2]IL’IN L A,LOBKOVA N A,LOS A O,et al.Approximate method of calculations for a helically corrugated tube[J].Soviet Applied Mechanics,1983,19(9):764-767.
[3]BOLUND B,BERNHOFF H,LEIJON M.Flywheel energy and power storage systems[J].Renewable&Sustainable Energy Reviews,2007,11(2):235-258.
[4]戴兴建,邓占峰,刘刚,等.大容量先进飞轮储能电源技术发展状况[J].电工技术学报,2011,26(7):133-140.DAI X J,DENG Z F,LIU G,et al.Review on advanced flywheel energy storage system with large scale[J].Transactions of China Electrotechnical Society,2011,26(7):133-140.(in Chinese)
[5]MOUSAVI G S M,FARAJI F,MAJAZI A,et al.Acomprehensive review of flywheel energy storage system technology[J].Renewable&Sustainable Energy Reviews,2017,67:477-490.
[6]汤双清.飞轮储能技术及应用[M].武汉:华中科技大学出版社,2007.TANG S Q.Flywheel energy storage technology and its application[M].Wuhan:Huazhong University of Science and Technology Press,2007.(in Chinese)
[7]PEREZ-APARICIO J L,RIPOLL L.Exact,integrated and complete solutions for composite flywheels[J].Composite Structures,2011,93(5):1404-1415.
[8]HA S K,KIM S J,NASIR S U,et al.Design optimization and fabrication of a hybrid composite flywheel rotor[J].Composite Structures,2012,94(11):3290-3299.
[9]戴兴建,张小章,姜新建,等.清华大学飞轮储能技术研究概况[J].储能科学与技术,2012,1(1):64-68.DAI X J,ZHANG X Z,JIANG X J,et al.Flywheel energy storage technology in Tsinghua University[J].Energy Storage Science and Technology,2012,1(1):64-68.(in Chinese)
[10]唐长亮,戴兴建,汪勇.多层混杂复合材料飞轮力学设计与旋转试验[J].清华大学学报(自然科学版),2015,55(3):361-367.TANG C L,DAI X J,WANG Y.Mechanical design and spin test of a multi-layer commingled composite flywheel[J].Journal of Tsinghua University(Science and Technology),2015,55(3):361-367.(in Chinese)
[11]杨启述.气体离心机技术基础[M].北京:原子能出版社,1991.YANG Q S.Technical foundation of gas centrifuge[M].Beijing:Atomic Energy Press,1991.(in Chinese)
[12]REICH J,CARDELLA A,CAPRICCIOLI A,et al.Experimental verification of the axial and lateral stiffness of large W7-X rectangular bellows[J].Fusion Engineering&Design,2007,82(15-24):1924-1928.
[13]任宁,欧开良,王长路,等.Ω形波纹管的轴向刚度研究[J].机械强度,2011,33(5):719-723.REN N,OU K L,WANG C L,et al.Research on the axial stiffness ofΩ-shaped bellows[J].Journal of Mechanical Strength,2011,33(5):719-723.(in Chinese)
[14]徐志翘,刘燕,杨嘉实,等.变厚度U型波纹壳大挠度问题的摄动解[J].清华大学学报(自然科学版),1985(1):39-51.XU Z Q,LIU Y,YANG J S,et al.Large deflection of a U-shaped bellows with varying thickness[J].Journal of Tsinghua University(Science and Technology),1985(1):39-51.(in Chinese)
[15]修筑,王纪民,马建敏.厚度变化对U型波纹管轴向刚度的影响[J].噪声与振动控制,2012,32(5):189-192.XIU Z,WANG J M,MA J M.The effects of thickness variation on axial stiffness of U-shaped bellows[J].Noise and Vibration Control,2012,32(5):189-192.(in Chinese)
[16]BECHT C.Predicting bellows response by numerical and theoretical methods[J].Journal of Pressure Vessel Technology,1986,108(3):334-341.
[17]SHEN Z P.Approximate calculation of U-shaped bellows[J].Tsinghua Science and Technology,1996,1(3):305-309.
[18]王永岗,戴诗亮,吕英民.波纹管在任意载荷作用下的几何非线性分析[J].清华大学学报(自然科学版),2002,42(2):220-223.WANG Y G,DAI S L,LY M.Geometrically nonlinear analysis for arbitrarily loaded bellows[J].Journal of Tsinghua University(Science and Technology),2002,42(2):220-223.(in Chinese)
[19]STEINBRINK S E,AGGARWAL M C,SHEPHERD K IM.Linear and nonlinear finite element analysis of an exhaust manifold with included bellows[C]//ASME 2007 Pressure Vessels and Piping Conference.New York:American Society of Mechanical Engineers,2007:89-94.
[20]张承宗.复合材料板壳力学解析理论[M].北京:国防工业出版社,2009.ZHANG C Z.Mechanics analysis theory of composite plate and shell[M].Beijing:National Defense Industry Press,2009.(in Chinese)
[21]MEYER-PIENING H R,FARSHAD M,GEIER B,et al.Buckling loads of CFRP composite cylinders under combined axial and torsion loading experiments and computations[J].Composite Structures,2001,53(4):427-435.
[22]PARK J S,HONG C S,KIM C G,et al.Analysis of filament wound composite structures considering the change of winding angles through the thickness direction[J].Composite Structures,2002,55(1):63-71.
[23]舒朝霞,杨福江.波纹管弯曲刚度测试方法研究[C]//中国核科学技术进展报告(第四卷)---中国核学会2015年学术年会论文集第4册(同位素分离分卷).北京:中国核学会,2015:196-200.SHU Z X,YANG F J.Research on measuring method of bending stiffness of bellows[C]//China Nuclear Science and Technology Progress Report(Volume IV)-Proceedings of2015Annual Meeting of Chinese Nuclear Society,Volume 4(Isotope Separation Sub-volume).Beijing:Chinese Nuclear Society,2015:196-200.(in Chinese)