本文關(guān)鍵詞： 對數(shù)螺旋錐齒輪 三維參數(shù)化建模 Boolean求差建模 均值-極差控制圖 Lanczos數(shù)值計算法 罰函數(shù)法求解接觸問題 銑削參數(shù)優(yōu)化　出處：《華僑大學》2017年博士論文　論文類型：學位論文

【摘要】：常規(guī)螺旋錐齒輪齒向線上的螺旋角,隨著齒向線位置的不同而變化,為了確保嚙合點的螺旋角相等,在加工過程中需要調(diào)整機床若干參數(shù),給制造帶來了困難。對數(shù)螺旋錐齒輪是以圓錐對數(shù)螺旋曲線為齒向線,以漸開線為齒廓曲線的新型螺旋錐齒輪,圓錐對數(shù)螺旋曲線上任一一點沿著圓錐對數(shù)螺旋曲線的切線方向與圓錐母線的夾角為定值,即螺旋角為定值,具有更好的傳動特性。本文擬以對數(shù)螺旋錐齒輪為研究對象,重點圍繞三維參數(shù)化建模、嚙合角速度及切向接觸力仿真、自由模態(tài)分析、齒面接觸數(shù)值分析及五軸聯(lián)動數(shù)控加工實驗等進行系統(tǒng)的研究,論文的主要研究內(nèi)容概括如下:(1)基于Boolean求差運算的對數(shù)螺旋錐齒輪三維參數(shù)化建模的研究。提出基于Boolean求差運算的建模方法,并以主要參數(shù):齒數(shù)為9:37,大端模數(shù)為5.4 mm,壓力角為20°,螺旋角為35°的一對對數(shù)螺旋錐齒輪為例,對其進行精確建模。以UG/OPEN GRIP為二次開發(fā)工具,設(shè)計出參數(shù)化建模的界面,實現(xiàn)對數(shù)螺旋錐齒輪的三維參數(shù)化建模。(2)基于Hertz接觸理論的對數(shù)螺旋錐齒輪的嚙合角速度及切向接觸力的仿真研究。構(gòu)建適用于嚙合角速度與切向接觸力仿真的計算公式,模擬對數(shù)螺旋錐齒輪嚙合和常規(guī)螺旋錐齒輪嚙合的角速度和切向接觸力的工作狀態(tài)和性能,仿真結(jié)果表明對數(shù)螺旋錐齒輪傳動的平穩(wěn)性優(yōu)越于常規(guī)螺旋錐齒輪。(3)基于Lanczos法的螺旋錐齒輪的自由模態(tài)分析與Poly Max法實驗驗證�；贚anczos數(shù)值計算方法進行迭代計算求解,就對數(shù)螺旋錐齒輪的小齒輪、大齒輪、裝配體和常規(guī)螺旋錐齒輪大齒輪做有限元自由模態(tài)分析。借助LMS模態(tài)分析模塊,搭建螺旋錐齒輪自由模態(tài)分析的實驗平臺,采用最小二乘復頻域Poly Max方法提取出模態(tài)參數(shù),實驗?zāi)B(tài)測試結(jié)果與有限元分析結(jié)果有較好的一致性。(4)基于罰函數(shù)法的對數(shù)螺旋錐齒輪齒面接觸分析研究。根據(jù)罰函數(shù)法將附加約束條件引入泛函求極值,建立罰函數(shù)法求解接觸問題的有限元求解方程。分別對常規(guī)螺旋錐齒輪和對數(shù)螺旋錐齒輪進行齒面接觸應(yīng)力和齒根彎曲應(yīng)力的數(shù)值分析,并與ISO10300-2001解析計算進行對比。嚙合接觸印痕的數(shù)值分析結(jié)果與實驗結(jié)果基本吻合。(5)對數(shù)螺旋錐齒輪實物的五軸聯(lián)動數(shù)控加工工藝與銑削參數(shù)優(yōu)化研究。在普通臥式車床C6140A1上加工出齒坯,根據(jù)球頭銑刀與對數(shù)螺旋錐齒輪齒面的關(guān)系,生成刀具軌跡,確定走刀行距,編制出對數(shù)螺旋錐齒輪數(shù)控加工的刀具路徑。在德瑪吉DMU 40 mono BLOCK五軸聯(lián)動立式加工中心上加工出收縮齒對數(shù)螺旋錐齒輪大、小齒輪實物。
[Abstract]:The spiral angle on the tooth line of the conventional spiral bevel gear varies with the position of the tooth direction. In order to ensure the equal helical angle of the meshing point, some parameters of the machine tool need to be adjusted in the process of machining. The logarithmic spiral bevel gear is a new type of spiral bevel gear which takes the cone logarithmic spiral curve as the tooth direction and the involute as the tooth profile curve. The angle between the tangent direction of the cone logarithmic spiral curve and the cone busbar is a definite value, that is, the spiral angle is a definite value, which has better transmission characteristics. In this paper, the logarithmic spiral bevel gear is taken as the research object. Focusing on 3D parametric modeling, meshing angular velocity and tangential contact force simulation, free mode analysis, tooth surface contact numerical analysis and five-axis linkage NC machining experiment, etc. The main research contents of this paper are summarized as follows: (1) 3D parametric modeling of logarithmic spiral bevel gears based on Boolean difference operation. Taking a pair of logarithmic spiral bevel gears with tooth number of 9: 37, large end modulus of 5.4 mm, pressure angle of 20 擄and spiral angle of 35 擄as an example, a pair of logarithmic spiral bevel gears with a tooth number of 9: 37, a pair of logarithmic spiral bevel gears with a helical angle of 35 擄are modeled accurately. The interface of parameterized modeling is designed with UG/OPEN GRIP as a secondary development tool. The 3D parametric modeling of logarithmic spiral bevel gear is realized. (2) based on Hertz contact theory, the simulation study of the meshing angular velocity and tangential contact force of logarithmic spiral bevel gear is carried out, and the calculation formula suitable for the simulation of meshing angular velocity and tangential contact force is constructed. Simulating the working state and performance of logarithmic spiral bevel gear meshing and conventional spiral bevel gear meshing angular velocity and tangential contact force, The simulation results show that the smoothness of logarithmic spiral bevel gear transmission is superior to that of conventional spiral bevel gear. The free mode analysis of spiral bevel gear based on Lanczos method is verified by Poly Max method, and the iterative calculation is carried out based on Lanczos numerical method. The finite element free modal analysis of small gear, big gear, assembly body and conventional spiral bevel gear of logarithmic spiral bevel gear is done. With the help of LMS modal analysis module, the experimental platform of free modal analysis of spiral bevel gear is built. The modal parameters are extracted by the least square complex frequency domain Poly Max method. The experimental modal test results are in good agreement with the results of finite element analysis. (4) the contact analysis of logarithmic spiral bevel gears based on penalty function method is studied. According to the penalty function method, the additional constraint conditions are introduced into the functional to find the extreme value. The finite element equation for solving contact problem with penalty function method is established. The contact stress on tooth surface and bending stress on tooth root of conventional spiral bevel gear and logarithmic spiral bevel gear are numerically analyzed respectively. The numerical analysis results of meshing contact marks are in good agreement with the experimental results. (5) the five-axis linkage NC machining technology and milling parameter optimization of logarithmic spiral bevel gears are studied in this paper. On the lathe C6140A1, the tooth billet is processed, According to the relationship between the ball end milling cutter and the tooth surface of logarithmic spiral bevel gear, the tool path is generated and the line distance of the cutter is determined. The tool path for NC machining of logarithmic spiral bevel gears is worked out. The logarithmic spiral bevel gears with large shrinkage teeth and small gears are manufactured on the vertical machining center of DMU 40 mono BLOCK.
【學位授予單位】：華僑大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TG61

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