三級(jí)齒輪減速器殼體的應(yīng)力分析與優(yōu)化設(shè)計(jì)外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯

三級(jí)齒輪減速器殼體的應(yīng)力分析與優(yōu)化設(shè)計(jì)外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯,三級(jí),齒輪,減速器,殼體,應(yīng)力,分析,優(yōu)化,設(shè)計(jì),外文,文獻(xiàn),翻譯,中英文 英文原文 Applied Mechanics and Materials Vol.658(2014)pp 183-188 Submitted: 29.04.2014 (2014) Trans Tech Publications, Switzerland Revised : 22.05.2014 Doi:10.4028/www.scientific.net/AMM.658.183 Accepted: 27.05.2014 Stress Analysis and Optimal Design of the Housing of a Three-Stage Gear Reducer COJOCARU Vasile 1,a*, KORKA Zoltan-losif 1,b And MICLOSINA Calin-Octavian 1,c 1”Eftimie Murgu” University of Resita, Faculty of Engineering and Management, Department of Mechanics and Materials Engineering, Traian Vuia Square, No.1~4, 320085 Resita, Romania a*v.cojocaru@uem.ro, bz.korka@uem.ro, cc.miclosina@uem.ro Keywords: gear reducer; housing stress; displacement; finite element analysis Abstract. The design of the housings of the gear reducers is made, usually, using empirical equations based on the center distance (the distance between shafts). These equations can lead to inappropriate stresses distribution and inadequate material consumption at the final product. In the manufacturing of large series and in the manufacturing of the gear reducers/ gearboxes with large dimensions it is necessary an optimization of the housing dimensions. The use of the finite element analysis in this process, combined with experimental researches, can generate significant improvements. The paper is focused on the analysis of stresses distribution and displacements on the housing of a two-stage helical gear reducer with parametric dimensions and loads. The housing is subjected to a static finite element study. The optimization process aimed to minimize the total weight of the housing. The next features were submitted to dimensional changes: the thickness of the housing walls and the thickness of the ribs. The results presented as diagrams of stresses and displacements distributions show real opportunities to reduce the total weight of the housing and the material consumption. Introduction One of the major trends of the mechanical engineering is the design of compact equipment with lower mass and lower material consumption. On the gear reducers/ gear boxes this goal can be reach by an optimal design of the gearing [1,2] and of gear supporting elements (shafts, housing). The design process of the helical gears reducers involves the calculations of the main parameters that influence the dimensions of the housing of the gear reducer: the center distance, the diameter of the bearings, the outside diameters of the gearwheels, the shafts lengths. The other dimensions of the housing are defined by empirical equations. In the scientific literature of the gear engineering are listed various equations for the calculus of the thickness of the housing walls, δ [mm]. These equations are based usually on the overall length (l) of the housing [3]: δ=(0.004...0.0005)?l+4，or on the total center distance (a) of the reducers[4]: δ=0.025?a+5. The value calculated for δ, is used in the calculus of the dimensions of the housing ribs and flanges [3]. This design algorithm can generate the oversizing of housing, increasing the mass of the reducer and the manufacturing costs. These conclusions lead to the necessity of optimization of the design process of the housing. The complexity of the housing geometry makes difficult to accomplish the determination of the strains and stresses by analytical relations. Evaluation of the strains and stresses by experimental methods is expensive and it is difficult to extrapolate the results of the measurements. The use of the finite element simulations, validated through experimental researches, can generate solutions for a proper stress distributions and an optimal design of the gear housing [5,6]. The use of parametric models in the finite element analysis allows the rapid changes of the dimensions and the loads applied to the part. Thereby the analysis can be run for a wide range of typo-dimensions, decreasing the time needed to release a new product. The current research aims to highlight the possibilities of improvement of the housing of a two-stage helical gear reducer using finite element simulations. Conclusions The results of the FEM simulations performed on the housing of a two-stage gear reducer submitted to static loads show that the geometry and dimensions obtained from empirical equations can be optimized. This optimization can be made based on the FEM simulations validated by experimental measurements. The maximum values of the Von Misses stresses obtained for the geometries analyzed are far below the allowable limit of the steel used in simulations. The maximum values of displacements are within acceptable limits, however shall be deemed that these displacements can accentuate the housing vibrations in the dynamic loads conditions. This observation leads to the conclusion that the criterion of rigidity should be a priority in the designing process of the housing. The charts of stresses and displacements distributions allow the identification of the weak areas. The geometrical changes of the housing made in these areas generate adequate solutions with the best ratio between the mass decrease and the stress/displacement increase. Acknowledgment The work has been funded by the Sectoral Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132395. References [1] L. Tudose et al., Optimal design of two-stage speed reducer using two-phase evolutionary algorithm, International Journal of Mechanics, Issue 3, Volume 2, 2008, pp.55-66. [2] O. Buiga, C.O. Popa, Optimal Mass Design of a Single-Stage Helical Gear Unit with Genetic Algorithms, Proceedings of the Romanian Academy, Series A. Vol. 13, No.3/2012,pp.243-250. [3]D. Muhs,H. Wittcl,D. Jannasch, Roloff/Matck - Machinc Elements, in Romanian, Vol. II, Matrix Rom, ISBN 978-973-755-412-3, Bucuresti, 2008. [4] I. Palade et al.,Gear reducers, in Romanian,Dunarea de Jos University,Galati,2008, available online at http://www.om.ugal.ro/om/biblioteca. [5] M. Davis et al., Designing for Static and Dynamic Loading of a Gear Reducer Housing with FEA. Power Transmission Engineering Magazine, February 2010, available at www.powertransmission.com,pp.32-37. [6] S.M. Patil, S.M, Pise, Modal and Stress Analysis of Differential Gearbox Casing with Optimization, Int. Journal of Engineering Research and Applications, ISSN: 2248-9622, Vol.3,Issue 6, Nov-Dec 2013. pp.188-193. [7] V. Cojocaru, Z. Korka, C. Miclosina, Influence of the Mesh Parameters on Stresses and Strains in FEM Analysis of a Gear Housing, Analele Universitatii Eftimie Murgu, Fascicula I, anul XX, no.2, 2013, ISSN 1453 - 7397,pp.47-52. [8] S.Radzevich,Dudley’s Handbook of Practical Gear Design and Manufacture, CRC Press, NewYork,2012, ISBN: 978-1-4398-6602-3. [9] E.J.Hearn, Mechanics of Materials, Third Edition, Blutterworth Heinemann, Oxford, 2000. [10]G.X. Zhang, E. Rigaud, J.C. Pascal, J. Sabot, Gearboxes: Indirect Identification of Dynamic Forces Transmitted to Housing Through Bearings, 4th World Congress on Gearing and Power Transmission,Paris, France, 1999. 中文譯文 三級(jí)齒輪減速器殼體的應(yīng)力分析與優(yōu)化設(shè)計(jì) 發(fā)表于應(yīng)用力學(xué)與材料學(xué)報(bào)658期，由Vasile, Zoltan Losif和Calin Octavian編寫，由瑞士Trans Tech出版物出版 關(guān)鍵詞:減速器，殼體，應(yīng)力，位移，有限元分析。 摘要：齒輪減速器箱體的設(shè)計(jì)，通常采用基于中心距(軸間距離)的經(jīng)驗(yàn)公式。這些方程會(huì)導(dǎo)致在最終產(chǎn)品有著不適當(dāng)?shù)膽?yīng)力分布和不充分的材料消耗。在大批量生產(chǎn)和大尺寸齒輪減速器/變速箱的生產(chǎn)中，必須對(duì)箱體尺寸進(jìn)行優(yōu)化。在這個(gè)過(guò)程中使用有限元分析，結(jié)合實(shí)驗(yàn)研究，可以產(chǎn)生顯著的改進(jìn)。本文對(duì)具有參數(shù)尺寸和載荷的兩級(jí)斜齒輪減速器殼體的應(yīng)力分布和位移進(jìn)行了分析。該殼體進(jìn)行了靜力有限元研究。優(yōu)化過(guò)程的目標(biāo)是使外殼的總重量最小。下一個(gè)特征描述了尺寸的變化:減速器箱體的厚度和肋的厚度。應(yīng)力和位移分布的圖表結(jié)果，顯示了減少箱體的總重量和材料消耗的真實(shí)情況。 介紹： 機(jī)械工程的主要趨勢(shì)之一是設(shè)計(jì)出質(zhì)量更小、材料消耗更低的緊密型設(shè)備。在齒輪減速器/齒輪箱上，這一目標(biāo)可以通過(guò)齒輪[1,2]和齒輪支撐元件(軸，外殼)的優(yōu)化設(shè)計(jì)來(lái)實(shí)現(xiàn)。 斜齒輪減速器的設(shè)計(jì)過(guò)程中涉及到影響減速器殼體尺寸的主要參數(shù)的計(jì)算：中心距離，軸承的直徑，齒輪外徑，軸的長(zhǎng)度。箱體的其他維度是由經(jīng)驗(yàn)方程定義的。 在齒輪工程的科學(xué)文獻(xiàn)中列出了計(jì)算殼體壁厚度的各種公式，δ [mm]. 這些方程式通常以殼體的總長(zhǎng)度(l)為基礎(chǔ)[3]: δ=(0.004...0.0005)?l+4，或在減速器的總中心距離(a)上[4]: δ=0.025?a+5。計(jì)算δ值，用于計(jì)算箱體肋和法蘭盤[3]的尺寸。該設(shè)計(jì)算法可能產(chǎn)生箱體過(guò)大，增大減速器的質(zhì)量和制造成本的問(wèn)題。這些結(jié)論引出了對(duì)箱體設(shè)計(jì)過(guò)程進(jìn)行優(yōu)化的必要性。 由于殼體幾何形狀的復(fù)雜性，很難通過(guò)解析關(guān)系來(lái)確定應(yīng)力和應(yīng)變。用實(shí)驗(yàn)方法評(píng)估應(yīng)變和應(yīng)力是昂貴的，而且很難推斷測(cè)量結(jié)果。使用有限元模擬，通過(guò)實(shí)驗(yàn)研究驗(yàn)證，可以產(chǎn)生適當(dāng)?shù)膽?yīng)力分布和齒輪殼的優(yōu)化設(shè)計(jì)的解決方案[5,6]。在有限元分析中參數(shù)化模型的使用允許快速變化的尺寸和載荷應(yīng)用到零件。因此，該分析過(guò)程可以針對(duì)較為廣泛的尺寸進(jìn)行，從而減少發(fā)布新產(chǎn)品所需的時(shí)間。目前的研究旨在強(qiáng)調(diào)利用有限元模擬改進(jìn)兩級(jí)斜齒輪減速器外殼的可能性。 總結(jié)： 對(duì)靜載荷作用下的兩級(jí)減速器殼體進(jìn)行了有限元仿真，結(jié)果表明，根據(jù)經(jīng)驗(yàn)方程得到的殼體幾何尺寸是可以優(yōu)化的。這種優(yōu)化可以在有限元模擬和實(shí)驗(yàn)測(cè)量的基礎(chǔ)上進(jìn)行。所分析的幾何形狀的最大應(yīng)力值遠(yuǎn)低于模擬中使用的鋼的允許極限。最大位移值在可接受的范圍內(nèi)，但應(yīng)認(rèn)為這些位移在動(dòng)荷載條件下會(huì)加重殼體振動(dòng)。這一觀察得出的結(jié)論是，剛度標(biāo)準(zhǔn)應(yīng)優(yōu)先考慮箱體的設(shè)計(jì)過(guò)程中。應(yīng)力和位移分布圖允許識(shí)別薄弱區(qū)域。在這些區(qū)域中箱體的幾何變化產(chǎn)生了適當(dāng)?shù)慕鉀Q方案，質(zhì)量下降和應(yīng)力/位移增加之間的最佳比例。