本文選題：轉(zhuǎn)子動(dòng)力學(xué) + 有限元　； 參考：《浙江大學(xué)》2013年博士論文

【摘要】：轉(zhuǎn)子軸承系統(tǒng)的動(dòng)力學(xué)行為預(yù)測(cè)中,除理論分析與實(shí)驗(yàn)研究外,常借助于傳遞矩陣法和有限單元法這兩種數(shù)學(xué)建模方法。國(guó)內(nèi)傳遞矩陣法的研究水平與應(yīng)用現(xiàn)狀已接近國(guó)際領(lǐng)先,但有限單元法在轉(zhuǎn)子動(dòng)力學(xué)中的運(yùn)用尚顯得相對(duì)薄弱,需要提升與發(fā)展。一方面,引入有限單元法對(duì)轉(zhuǎn)子軸承系統(tǒng)建模具有大量?jī)?yōu)勢(shì)：可以考慮陀螺力矩、轉(zhuǎn)動(dòng)慣量、橫向剪切變形、重力項(xiàng)等因素的影響；其運(yùn)動(dòng)微分方程表達(dá)清晰規(guī)范,物理意義明確；可以方便地耦合周邊環(huán)境中的結(jié)構(gòu)和作用力,特別適用于復(fù)雜轉(zhuǎn)子耦合系統(tǒng),而這一點(diǎn)正是傳遞矩陣法的不足之處。盡管有限單元法建模往往編程困難、矩陣維數(shù)大且計(jì)算耗時(shí),但現(xiàn)代計(jì)算機(jī)的軟件與硬件能力減小了此不利因素。另一方面,相對(duì)簡(jiǎn)單轉(zhuǎn)子系統(tǒng),目前線性范圍內(nèi)的數(shù)值計(jì)算已較為成熟,國(guó)內(nèi)外研究者相當(dāng)?shù)墓ぷ髁哭D(zhuǎn)移到考察各種非線性因素的影響,其動(dòng)力學(xué)方程多基于Jeffcott轉(zhuǎn)子模型；而針對(duì)復(fù)雜轉(zhuǎn)子耦合系統(tǒng),即使線性分析計(jì)算也不夠成熟,建模方法上仍有發(fā)展空間且值得探索。 齒輪傳動(dòng)在機(jī)械領(lǐng)域廣泛應(yīng)用,多平行軸齒輪嚙合轉(zhuǎn)子系統(tǒng)是轉(zhuǎn)子系統(tǒng)中重要且特殊的一類,齒輪副的存在使其動(dòng)力學(xué)研究十分復(fù)雜。各平行軸轉(zhuǎn)子相互耦合,系統(tǒng)動(dòng)力學(xué)特性與非耦合的單軸轉(zhuǎn)子不同,因此對(duì)各平行軸轉(zhuǎn)子單獨(dú)設(shè)計(jì)計(jì)算已無法滿足高精度計(jì)算的要求。雙轉(zhuǎn)子系統(tǒng)在航空發(fā)動(dòng)機(jī)中已有應(yīng)用,內(nèi)外轉(zhuǎn)子反向旋轉(zhuǎn)時(shí),可抵消部分陀螺力矩,提高飛機(jī)機(jī)動(dòng)性能。其轉(zhuǎn)子系統(tǒng)由高壓轉(zhuǎn)子和低壓轉(zhuǎn)子兩個(gè)子系統(tǒng)組成,相對(duì)單轉(zhuǎn)子發(fā)動(dòng)機(jī),其結(jié)構(gòu)復(fù)雜,振動(dòng)特性的分析計(jì)算也更為困難。為研制先進(jìn)航空發(fā)動(dòng)機(jī)以提升戰(zhàn)機(jī)的振動(dòng)性能和確�？煽窟\(yùn)行,進(jìn)行雙轉(zhuǎn)子系統(tǒng)動(dòng)力學(xué)研究具有重大戰(zhàn)略意義,而在這方面國(guó)外公開的資料很少。以往國(guó)內(nèi)學(xué)者常采用傳遞矩陣法研究雙轉(zhuǎn)子結(jié)構(gòu),但此方法很難計(jì)入飛行中空間運(yùn)動(dòng)的影響,而采用有限單元法建�？梢钥朔@一困難。鑒于以上原因,本文以有限單元法為理論基礎(chǔ),重點(diǎn)研究多平行軸齒輪嚙合轉(zhuǎn)子系統(tǒng)和雙轉(zhuǎn)子系統(tǒng)的建模方法,通過數(shù)值計(jì)算分析了兩類系統(tǒng)的動(dòng)力特性,具體開展了以下工作： 1)針對(duì)常見的單轉(zhuǎn)子軸承系統(tǒng),應(yīng)用有限單元法并結(jié)合Rayleigh梁理論和Timoshenko梁理論,詳細(xì)地推導(dǎo)出了其系統(tǒng)運(yùn)動(dòng)微分方程：在此基礎(chǔ)上理論分析了系統(tǒng)特征值問題、不平衡響應(yīng)和瞬態(tài)響應(yīng)的求解方法；基于MATLAB平臺(tái)編寫程序?qū)崿F(xiàn)轉(zhuǎn)子系統(tǒng)的臨界轉(zhuǎn)速、不平衡響應(yīng)和瞬態(tài)計(jì)算。 2)參與了浙江省某企業(yè)某款徑流式汽輪機(jī)在設(shè)計(jì)階段的轉(zhuǎn)子動(dòng)力學(xué)分析,分別應(yīng)用商業(yè)軟件ANSYS和本文開發(fā)的程序?qū)ζ溥M(jìn)行靜撓度、臨界轉(zhuǎn)速、振型及不平衡響應(yīng)計(jì)算,兩種途徑得到的結(jié)果一致,驗(yàn)證了本文開發(fā)程序的正確與有效。同時(shí),分析結(jié)果為徑流式汽輪機(jī)轉(zhuǎn)子結(jié)構(gòu)的確定和軸承參數(shù)的選取提出了指導(dǎo)意見。 3)以浙江省重大科技專項(xiàng)《大功率船用齒輪箱關(guān)鍵技術(shù)的研究與應(yīng)用》(項(xiàng)目代號(hào)：2009C11062)為依托,對(duì)某款三平行軸的船用齒輪箱嚙合轉(zhuǎn)子傳動(dòng)系統(tǒng)進(jìn)行固有特征分析,考察工作轉(zhuǎn)速工況下的各傳動(dòng)級(jí)嚙合頻率與系統(tǒng)固有頻率,并通過考察各階固有頻率隨齒輪嚙合剛度的變化來區(qū)分彎曲振動(dòng)與扭轉(zhuǎn)振動(dòng)。在多平行軸齒輪嚙合轉(zhuǎn)子系統(tǒng)建模方法的研究上,首先推導(dǎo)了在壓力線坐標(biāo)系下齒輪嚙合單元的運(yùn)動(dòng)微分方程,通過坐標(biāo)變換得到在全局坐標(biāo)下的運(yùn)動(dòng)微分方程,然后給出了齒輪嚙合單元?jiǎng)偠染仃嚰傻秸w轉(zhuǎn)子剛度矩陣的方法以最終形成嚙合轉(zhuǎn)子系統(tǒng)運(yùn)動(dòng)方程。 4)在雙轉(zhuǎn)子系統(tǒng)建模方法的研究上,推導(dǎo)了中介軸承的力傳遞和內(nèi)外轉(zhuǎn)子的耦合過程,給出了雙轉(zhuǎn)子系統(tǒng)的動(dòng)力學(xué)模型,并發(fā)展了針對(duì)雙轉(zhuǎn)子結(jié)構(gòu)的傳遞矩陣法。結(jié)合數(shù)值案例,應(yīng)用基于有限單元法的動(dòng)力學(xué)模型和傳遞矩陣法模型計(jì)算雙轉(zhuǎn)子結(jié)構(gòu)正反向旋轉(zhuǎn)下的臨界轉(zhuǎn)速,兩種方法得到的結(jié)果一致�？疾炝藘�(nèi)外轉(zhuǎn)子間的中介軸承剛度、轉(zhuǎn)速比對(duì)系統(tǒng)振動(dòng)特性的影響；結(jié)合直接積分法,對(duì)系統(tǒng)啟動(dòng)與停機(jī)的瞬態(tài)響應(yīng)進(jìn)行數(shù)值模擬。本文建立的模型為雙轉(zhuǎn)子系統(tǒng)動(dòng)力學(xué)行為的預(yù)測(cè)研究提供了較為完整的基礎(chǔ),研究結(jié)果對(duì)于提高航空發(fā)動(dòng)機(jī)轉(zhuǎn)子系統(tǒng)的動(dòng)力學(xué)性能,指導(dǎo)雙轉(zhuǎn)子系統(tǒng)的設(shè)計(jì)和使用具有重要的理論意義和工程應(yīng)用價(jià)值。
[Abstract]:In the prediction of dynamic behavior of rotor bearing system , in addition to the theoretical analysis and experimental study , the research level and application situation of the domestic transfer matrix method are close to the international leading , but the application of the finite element method in the rotor dynamics is relatively weak , which needs to be promoted and developed . On the one hand , the introduction of finite element method has a great advantage in modeling the rotor bearing system .
The differential equation of motion differential equation is clear and normative , and the physical meaning is clear ;
Although the finite element method modeling tends to be difficult , the matrix dimension is large and the calculation is time consuming , the software and hardware capability of the modern computer is reduced . On the other hand , relative simple rotor system , the numerical calculation in the current linear range is mature , and the workload of the researchers at home and abroad is shifted to the influence of various nonlinear factors , and the dynamic equation is based on the Jeffcott rotor model .
For complex rotor coupling systems , even if the linear analysis is not mature enough , the modeling method still has the development space and is worth exploring .

Gear drive is widely used in machinery field . Multi - parallel shaft gear mesh rotor system is an important and special kind of rotor system . The existence of gear pair makes the dynamics research very complicated . The rotor system is composed of two sub - systems of high - pressure rotor and low - pressure rotor .

1 ) According to the common single - rotor bearing system , the differential equation of motion of the system is deduced in detail by using finite element method and combining Rayleigh beam theory and the theory of the beam theory of the Rayleigh beam , and the solution method of the system characteristic value problem , the unbalance response and the transient response is analyzed theoretically .
The critical speed , unbalance response and transient calculation of rotor system are realized based on MATLAB platform .

2 ) The analysis of rotor dynamics of a radial steam turbine in a certain enterprise in Zhejiang Province in the design stage is carried out . The results are consistent with the results obtained by the commercial software ANSYS and the program developed in this paper . The results are consistent with the results obtained by the two methods . At the same time , the analysis results provide guidance for the determination of the rotor structure of the radial steam turbine and the selection of the bearing parameters .

3 ) Based on the research and application of the key technology of high - power marine gearbox in Zhejiang Province , this paper analyzes the natural characteristics of gear - gear meshing rotor transmission system of a three - parallel shaft .

4 ) In the research of the modeling method of the double - rotor system , the force transmission of the intermediate bearing and the coupling process of the inner and outer rotors are derived , the dynamic model of the double - rotor system is given , and the transmission matrix method for the double - rotor structure is developed .
Combined with the direct integral method , the transient response of system start - up and shutdown is simulated numerically . The model established in this paper provides a more complete foundation for predicting the dynamic behavior of the double - rotor system . The research results are of great theoretical significance and engineering application value to improve the dynamic performance of the aero - engine rotor system and guide the design and use of the double - rotor system .
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：TH133

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