本文選題：非Fourier效應(yīng) + 溫度場(chǎng)　； 參考：《北京理工大學(xué)》2015年碩士論文

【摘要】：電磁感應(yīng)淬火是曲軸廣泛采用的表面強(qiáng)化技術(shù)之一。本文在深入理解電磁感應(yīng)淬火原理和實(shí)際淬火工藝的基礎(chǔ)上，開(kāi)展了電磁感應(yīng)淬火非Fourier效應(yīng)溫度場(chǎng)的理論及數(shù)值分析。主要內(nèi)容包括： 根據(jù)電磁感應(yīng)淬火過(guò)程這一工程背景，在分析電磁感應(yīng)加熱過(guò)程分布內(nèi)熱源的基礎(chǔ)上，推導(dǎo)得到了直角坐標(biāo)系下一維含內(nèi)熱源非Fourier效應(yīng)溫度場(chǎng)的數(shù)學(xué)模型。采用格林函數(shù)，拉氏變換及其逆變換得到了直角坐標(biāo)系下含矩形分布內(nèi)熱源和線性分布內(nèi)熱源的非Fourier溫度場(chǎng)解析解。由此分析對(duì)比了Fourier效應(yīng)溫度場(chǎng)與非Fourier效應(yīng)溫度場(chǎng)，結(jié)果表明，考慮熱傳播非Fourier效應(yīng)時(shí)，由于熱傳播速度有限，在溫度穩(wěn)定之前，溫度變化有明顯的震蕩，需要經(jīng)過(guò)相對(duì)于Fourier導(dǎo)熱更長(zhǎng)的時(shí)間，才能達(dá)到穩(wěn)定溫度。同時(shí)，分析了內(nèi)熱源脈沖寬度對(duì)非Fourier效應(yīng)的影響，結(jié)果表明，非Fourier效應(yīng)與加熱脈沖寬度有關(guān)，寬度越大，非Fourier效應(yīng)越不明顯。同時(shí)，對(duì)比分析了線性分布內(nèi)熱源與矩形分布內(nèi)熱源對(duì)應(yīng)的溫度場(chǎng)，結(jié)果表明，這兩種內(nèi)熱源形式對(duì)應(yīng)的溫度場(chǎng)基本一致，，因此，在研究線性分布內(nèi)熱源時(shí)，可以簡(jiǎn)化為對(duì)應(yīng)的矩形分布內(nèi)熱源問(wèn)題以簡(jiǎn)化計(jì)算。 針對(duì)柱坐標(biāo)系及球坐標(biāo)系下的一維含內(nèi)熱源非Fourier強(qiáng)瞬態(tài)導(dǎo)熱問(wèn)題，根據(jù)轉(zhuǎn)軸公式，由直角坐標(biāo)系分別推導(dǎo)出柱坐標(biāo)系及球坐標(biāo)系下的溫度場(chǎng)控制方程。運(yùn)用格林函數(shù)法對(duì)其進(jìn)行求解，采用無(wú)量綱法和離散化積分法，獲得了柱坐標(biāo)系及球坐標(biāo)系下一維含內(nèi)熱源的非Fourier效應(yīng)溫度場(chǎng)。結(jié)果表明，由于其形狀的特點(diǎn)，柱坐標(biāo)系及球坐標(biāo)系下的熱量傳播與直角坐標(biāo)系下不同，不再是以矩形方波的形式傳播，而是出現(xiàn)尖峰，因此，其震蕩會(huì)相對(duì)于直角坐標(biāo)時(shí)更劇烈。由此可以預(yù)測(cè)，在同樣的熱擾動(dòng)下，柱坐標(biāo)系及球坐標(biāo)系下溫度波動(dòng)性更明顯，出現(xiàn)的最大溫度更高，由此導(dǎo)致的工程問(wèn)題會(huì)更顯著。 采用數(shù)值差分方法，針對(duì)二維非Fourier效應(yīng)的導(dǎo)熱溫度場(chǎng)進(jìn)行了研究，得到了其顯式差分格式，分析了其穩(wěn)定性。結(jié)果表明，二維非Fourier效應(yīng)溫度場(chǎng)的顯式差分格式不符合穩(wěn)定性要求。
[Abstract]:Electromagnetic induction quenching is one of the widely used surface strengthening techniques for crankshaft. Based on the deep understanding of the principle of electromagnetic induction quenching and the actual quenching process, the theory and numerical analysis of the temperature field of non- effect of electromagnetic induction quenching have been carried out in this paper. The main elements include: According to the engineering background of electromagnetic induction quenching process, based on the analysis of the distribution of internal heat source in electromagnetic induction heating process, the mathematical model of non- effect temperature field of one-dimensional internal heat source in right-angle coordinate system is derived. By using Green's function, Laplace transform and inverse transformation, the analytical solutions of non- temperature field with rectangular and linear internal heat sources are obtained in rectangular coordinate system. The temperature field of Fourier effect and that of non- effect are analyzed and compared. The results show that, considering the non- effect of heat propagation, the temperature change has obvious oscillation before the temperature is stabilized because of the limited heat propagation velocity. It takes longer than the Fourier heat conduction to achieve a stable temperature. At the same time, the influence of the pulse width of the internal heat source on the non- effect is analyzed. The results show that the non- effect is related to the width of the heating pulse, and the larger the width, the less obvious the non- effect is. At the same time, the temperature field corresponding to the internal heat source in the linear distribution is compared with that in the rectangular distribution. The results show that the temperature field corresponding to the two internal heat sources is basically the same. Therefore, in the study of the internal heat source in the linear distribution, It can be simplified to the corresponding internal heat source problem of rectangular distribution to simplify the calculation. In view of the non- strong transient heat conduction problem in cylindrical and spherical coordinates, the governing equations of temperature field in cylindrical coordinate system and spherical coordinate system are derived according to the formula of rotation axis. The Green's function method is used to solve the problem and the dimensionless method and discrete integral method are used to obtain the non- effect temperature field in the cylindrical coordinate system and the spherical coordinate system. The results show that the heat propagation in cylindrical coordinate system and spherical coordinate system is different from that in rectangular coordinate system because of its shape characteristics. The shock will be more intense than the rectangular coordinates. It can be predicted that under the same thermal disturbance, the temperature fluctuation in cylindrical coordinate system and spherical coordinate system is more obvious, the maximum temperature is higher, and the engineering problem will be more obvious. The numerical difference method is used to study the thermal conduction temperature field of two-dimensional non- effect. The explicit difference scheme is obtained and its stability is analyzed. The results show that the explicit difference scheme of two-dimensional non- effect temperature field does not meet the requirements of stability.
【學(xué)位授予單位】：北京理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TG156.3

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