螺旋锥齿轮断面加工外文翻译

面滚齿螺旋锥齿轮加工机床优化设置 在这项研究中，提出一种优化方法来系统地确定刀具几何和机床的最佳设置，同时减少驱动齿轮的齿面接触压力和位移误差（传输错误），和减少对错额面滚齿螺旋锥齿轮的灵敏度。提出的优化过程，在很大程度上依赖于轮齿加载接触 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 预测的接触压力分布和传输错误在齿轮副的固有误差的影响。本研究采用的是由本文作者开发的负载分布和传输误差的计算方法。此外，目标函数和约束条件都是不可分析的，但它们是可计算的，即，他们的存在数值是通过加载接触分析。由于这些原因，选择一个可导的方法来解决这个优化问题。这是所提出的非线性 规划 污水管网监理规划下载职业规划大学生职业规划个人职业规划职业规划论文 程序的核心算法是基于直接搜索法的原因。Hooke和Jeeves模式搜索方法的应用。这种优化结果是一个面滚齿螺旋锥齿轮的论证。得到在最大接触时急剧减少压力（62%）及传动误差（70%）。 1 引言 1.1 文献综述。在过去几十年里，许多学者进行了许多对螺旋锥齿轮和准双曲面齿轮的端面铣削方法进行了陈述和 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 。极少的分析用于被称为面滚齿机的齿轮连续切削过程。本文的研究课题，相关参考资料如下。 利特[ 1 ]描述了面滚齿切削过程的共性，并将其应用于螺旋锥齿轮。利特等人[ 2 ]提出了一种用面滚齿齿准双曲面齿轮的均匀深度的节锥角和螺旋角之间的关系的直接测定方法。制造大型螺旋锥齿轮的一个齿克林贝格系统采用多轴控制和多任务机床是由川崎提出的[ 3 ]。在原有基础上施塔特菲尔德[ 4 ]提出了一种新的加工方法，一种由外部和内部刀片相结合的切割系统，每个刀片之间都是等距的。范[ 5 ]提出了格里森面滚齿过程理论，提出了一个通用的齿面生成模型采用自由曲面数控加工（数控）齿轮发电机[ 6 ]的螺旋锥齿轮和准双曲面齿轮的端面铣削面铣刀。逊等人[ 7 ]提出了一个通用的准双曲面齿轮发生器的数学模型，它可以模拟所有主要的面滚齿面弧齿锥齿轮的铣削过程。槐马卡迪 [ 8 ]提出了一种能够代表一个复杂的齿轮传动的齿面数学模型：减少准双曲面齿轮的端面滚齿的方法。 参考文献对在面铣螺旋锥齿轮和准双曲面齿轮的载荷和应力分布的计算方法进行了描述[9-15]。比贝尔等人[9]应用有限元法（FEM）采用间隙单元建立了螺旋锥齿轮齿面接触模型。通过应用影响矩阵来分析预测螺旋锥齿轮组加载的吃面接触的运动误差是由戈塞尔林等人[10]提出的。方等人[11]认为接触边缘加载在轮齿接触分析。沃德亚尼等人[ 12 ]提出了一种数值模拟加载的螺旋齿轮和一个真正的直升机齿轮箱进行了实验测试网格工具。在文献[ 13-15 ]，给出了一种在失配的螺旋锥齿轮和准双曲面齿轮载荷分布的计算机模拟的新方法。 只有少数的文献可以查询到在面滚齿螺旋锥齿轮和准双曲面齿轮的载荷和应力分布计算。加载的齿面接触模式和传输错误的双面研磨和面滚齿螺旋锥齿轮和准双曲面齿轮在卡利万德和卡勒曼发表的文献[ 16 ]齿轮啮合的兼容性和均衡条件下执行计算。同一作者[17]提出了一种基于易断变形的具有全局和局部偏差的面铣和面滚齿准双面齿轮加载面接触分析方法。川崎和迁政信[ 18 ]研究了大型摆线齿锥齿轮的齿面接触分析和实验模式。 齿面修形相关资料如下。施和方[ 19 ]提出了一种螺旋锥齿轮和准双曲面齿轮滚齿齿面修正方法，以减轻齿轮传动的形变。一个侧面校正方法直接来自于六轴直角型数控铣齿机是在参考文献[ 20 ]提出的。文献[ 21 ]提出了为了获得在面滚齿的情况和相应的原型齿轮切割机施工齿面修形机床设置校正值。范[ 22 ]应用数控机床的的多项式表示机床的运动设置以纠正齿面的误差。 在文献[ 23 ]和[ 24 ]研究了轮齿接触失调的影响。川崎等人[23]提出的设计方法，齿面接触分析，并研究了装配误差对接触轨迹和传动误差的克林贝格摆线锥齿轮副小螺旋角的情况下的影响。霍推特等人[24]从实验和理论上研究了错位设置对准双曲面齿轮的齿根应力的影响。 最近的文章针对螺旋锥齿轮的优化如下：安敦尼等人[25]提出了一个完全自动化的过程来优化加载的齿面接触的模式。参考文献[26]提出了一个自动程序，以优化在位规定的范围内变化的面铣准双曲面齿轮的轮齿加载接触图案错。通过制定一个适当的非线性优化问题，参考文献[27]提出了一种新的方法系统地确定最佳的形变，同时最大限度地减少承载传动误差和齿面接触压力，同时将对齿面加载接触模式约束在规定的允许范围内以避免边缘接触或角接触。安敦尼等人[28]提出了一个算法框架准确地解决减轻螺旋锥齿轮多目标优化问题。 由于在加工过程中不可避免的缺陷所设计的功能特性，安敦尼等人[ 29 ]提出了一种新的方法来恢复准双曲面齿轮组的齿偏离其理论模型。 1.2优化的目标。为了使螺旋锥齿轮组达到最大寿命，适当的轴承位置必须同时满足低接触压力和较低的振动水平。承载传动误差是振动与噪声的主要来源。最大限度地减少承载传动误差会引起振动激励的减少（所谓噪声）。传动误差之间的差定义为从动齿轮的实际角位置和角位置将占据如果小齿轮和齿轮是完全刚性的共轭。啮合条件，其最大接触压力和传动误差，基本取决于齿的几何形状。在理论上，真正的共轭面滚齿螺旋锥齿轮是线接触。为了降低齿面接触压力和传输错误，并降低了齿轮副在齿面误差的敏感性和配合部件的相对位置，一组精心挑选的修改的齿通常适用于一个或两个配对齿轮。由于这些修改，齿轮副变为“不匹配”，并且接触点取代了理论线接触。在实践中，这些修改是通过将适当的机床设置小齿轮的制造和齿轮通常引入/或通过使用一个磁头刀片具有优化的切割边缘轮廓。 本研究的主要目的是系统地确定最佳的刀具几何形状和机床设置，同时减少从动齿轮通过齿轮副固有的失调影响齿面接触压力和位移误差。提出的优化程序依赖于一个轮齿加载接触分析预测的接触压力分布和传输误差。在这项研究中所采用的负载分配和传输误差计算方法是由本文作者开发[13-15]。 最后，数值结果将同时在最小化最大接触压力和传动误差齿面滚齿螺旋锥齿轮证明了这种方法的有效性。 2 配方的优化问题 2.1头刀具几何和机床设置。在面滚齿螺旋锥齿轮，齿面修正了以下的变化在头的刀具结构和机床设置：（一）头刀片轮廓组成的两个圆弧( 和 )，（二）对接触齿面齿轮制造和齿轮刀具半径的差异（ ），（三）倾斜（ ）和旋转（ ）相对于托架旋转轴刀具主轴角度（图1），(四)倾斜距离（ ，图1），（五）变化的径向机床设置（ ，图1），和（六）在小齿轮齿面生成的滚比变化（ ）。 图1 头铣刀在冠齿轮的相对位置 图2 小齿轮和齿轮的相对位置 一个假想的产生冠齿轮的概念是用来解释生成切割工艺的面滚齿螺旋锥齿轮和齿轮齿[ 30 ]。这是一个虚拟的假想齿齿轮的齿是由头部的刀片切削刃形成的痕迹，虽然它的齿数不一定是一个整数。它可被视为一个锥齿轮的一种特殊情况90°俯仰角。获得齿轮/齿轮齿面形成过程中，工作齿轮滚与假想齿轮。互补发电冠齿轮的概念是当产生的啮合齿面齿轮和齿轮完全共轭。共轭是指小齿轮和齿轮在每个角位置线接触。运动传递发生在具有精确且恒定比例的每个扎辊的位置。接触面积，是一对齿轮所有接触线的总和，分布在整个有效齿面的边缘。正如前面所指出的，为防止齿面误差，在荷载作用下的挠度，齿轮和齿轮之间的齿面误差引起的齿边应力集中，当修改应用；齿轮副的变为“不匹配”。在这种情况下，产生的冠齿轮的小齿轮和齿轮不互补。齿面的小齿轮和齿轮是由以下方程定义： （1a） (1b) 啮合基本方程（1b）说每一点躺在包络齿面，单位向量 对于生成的整个冠齿表面应垂直于所产生相对速度的齿轮/齿轮的产形轮齿， 。 该矩阵用于执行坐标转换,叶片轮廓点的矢径, ,和活性载体 和 ，在文献[30]提到。 2.2小齿轮和齿轮的相对位置。根据图2，啮合的小齿轮和齿轮的相对位置由以下方程定义： （2） 在矩阵 定义了静止坐标系 和 的关系，其中的小齿轮和齿轮通过旋转啮合。这个矩阵包含可能未配合齿轮的偏移（ ），齿轮和齿轮轴的调整误差（ ），在小齿轮轴的水平（ ）和垂直（ ）平面的角误差。矩阵 是在参考文献[ 30 ]定义。 Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition,the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained. [DOI: 10.1115/1.4027635] 1 Introduction 1.1 Literature Review. Over the past few decades, numerous authors have carried out many studies on the representation and design of spiral bevel and hypoid gears cut by the face-milling method. Many fewer analyses have been performed for gears cut by the continuous indexing process that is often referred to as face-hobbing. To the topic of this study, the relevant references are as follows. Litvin [1] described the generality of the face-hobbing cutting process and applied it to spiral bevel gears. Litvin et al. [2] proposed a method for the direct determination of relations between the pitch cone angles and spiral angles in hypoid gears with face-hobbed teeth of uniform depth. The manufacturing of large-sized spiral bevel gears in a Klingelnberg cyclo-palloid system using multi-axis control and a multitasking machine-tool is presented by Kawasaki [3]. The basis of the new face-hobbing method, presented by Stadtfeld [4], is a cutter system that uses an outside and an inside blade per blade group only and has equal spacing between all blades. Fan [5] presented the theory of the Gleason face-hobbing process, who later presented a generic model of tooth-surface generation for spiral bevel and hypoid gears produced by face-milling and face-hobbing processes using freeform computer numerical control (CNC) hypoid gear generators [6]. A mathematical model for the universal hypoid generator that can simulate all primary face-hobbing and face-milling processes for spiral bevel and hypoid gears was proposed by Shih et al. [7]. Vimercati [8] presented a mathematical model able to represent the tooth surfaces of a complex gear drive: hypoid gears cut by the face-hobbing method. Methods for load and stress distribution calculations in face-milled spiral bevel and hypoid gears were presented in Refs. [9–15]. Bibel et al. [9] applied the finite element method (FEM) to establish the model of tooth contact of spiral bevel gears by using gap elements. The loaded tooth contact analysis predicting the motion error of spiral bevel gear sets, by applying influ-ence matrices, is presented by Gosselin et al. [10]. Fang et al. [11]considered the edge contact in loaded tooth contact analysis. De Vaujany et al. [12] presented a numerical tool that simulates the loaded meshing of spiral gears and experimental tests carried out on a real helicopter gear box. In Refs. [13–15], a new approach for the computerized simulation of load distribution in mismatched spiral bevel and hypoid gears was presented. Only a few numbers of references can be found on load and stress distribution calculations in face-hobbed spiral bevel and hypoid gears. The loaded tooth contact patterns and transmission error of both face-milled and face-hobbed spiral bevel and hypoid gears were computed by enforcing the compatibility and equilibrium conditions of the gear mesh in Ref. [16] published by Kolivand and Kahraman. The same authors [17] proposed a practical methodology based on easy-off topography for loaded tooth contact analysis of face-milled and face-hobbed hypoid gears having both local and global deviations. Kawasaki and Tsuji[18] investigated the tooth contact patterns of large-sized Cyclo Palloid spiral bevel gears both analytically and experimentally. Tooth flank modification related references are as follows. Shih and Fong [19] proposed a flank modification methodology for face-hobbing of spiral bevel and hypoid gears, based on the ease-off topography of the gear drive. A flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator is proposed in Ref. [20]. Procedure to obtain the correction values of machine-tool settings for tooth-surface modification in the case of face-hobbing and the construction of the corresponding prototype gear cutting machine were presented in Ref. [21]. Fan [22] applied the polynomial representation of the universal motions of machine-tool settings on CNC machines to correct tooth-surface errors. The influence of misalignments on tooth contact was studied in Refs. [23] and [24]. Kawasaki et al. [23] presented the design method, tooth contact analysis, and investigated the influence of assembly errors on the path of contact and transmission errors in the case of a Klingelnberg spiral bevel gear pair with small spiral angle. Hotait et al. [24] investigated experimentally and theoretically the impact of misalignments on root stresses of hypoid gear sets. Recent papers addressing the optimization of spiral bevel and hypoid gears are as follows: Artoni et al. [25] proposed a fully automatic procedure to optimize the loaded tooth contact pattern.Reference [26] presented an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. Through the formulation of an appropriate nonlinear optimization problem, Ref. [27]proposed a novel methodology to systematically define optimal ease-off topography to simultaneously minimize the loaded transmission error and tooth contact pressures, while concurrently confining the loaded contact patterns within a prescribed allowable region on the tooth surface to avoid any edge-contact or corner- contact conditions. An algorithmic framework was proposed by Artoni et al. [28] to accurately solve the problem of multi-objective ease-off optimization for spiral bevel and hypoid gears.Artoni et al. [29] presented a novel methodology to restore the designed functional properties of hypoid gear sets whose teeth deviate from their theoretical models due to inevitable imperfections in the machining process. 1.2 The Goal of the Optimization. In order to achieve maximum life in a spiral bevel gear set, an appropriate bearing pattern location with low tooth contact pressure and low vibration levels must coexist. Loaded transmission error is the primary source of noise and vibration. Minimizing the loaded transmission error would certainly entail a reduction in vibratory excitation (hence noise). The transmission error is defined as the difference between the actual angular position of the driven gear and the angular position it would occupy if the pinion and the gear were perfectly rigid and conjugate. The conditions of meshing, characterized by maximum tooth contact pressure and transmission error, depend substantially on tooth geometry. In theory, truly conjugated face-hobbed spiral bevel gears have line contacts. In order to reduce the tooth contact pressure and the transmission errors, and to decrease the sensitivity of the gear pair to errors in tooth surfaces and to the relative positions of the mating members, a set of carefully chosen modifications is usually applied to the teeth of one or both mating gears. As a result of these modifications, the gear pair becomes “mismatched,” and a point contact replaces the theoretical line contact. In practice, these modifications are usually introduced by applying the appropriate machine-tool setting for the manufacture of the pinion and the gear and/or by using a head-cutter with an optimized cutting edge profile. The main goal of this study is to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear influenced by the misalignments inherent in the gear pair. The proposed optimization procedure relies heavily on a loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper [13–15]. At the end, numerical results will be presented to demonstrate the effectiveness of this methodology in simultaneously minimizing the maximum tooth contact pressure and transmission errors in face-hobbed spiral bevel gears. 2 Formulation of the Optimization Problem  Fig. 1 Relative position of the head-cutter to the imaginary generating crown gear Fig. 2 Relative position of the pinion and the gear in mesh 2.1 Head-Cutter Geometry and Machine-Tool Settings. In face-hobbed spiral bevel gears, the tooth-surface modifications are introduced by the following variations in head-cutter geometry and machine-tool settings: (a) head-cutter blade profile consisting of two circular arcs ( and ), (b) difference in head-cutter radii for the manufacture of the contacting tooth flanks of the pinion and the gear ( ), (c) tilt ( ) and swivel ( ) angles of the cutter spindle with respect to the cradle rotation axis (Fig. 1), (d)tilt distance ( , Fig. 1), (e) variation in the radial machine-tool setting ( , Fig. 1), and (f) variation in the ratio of roll in the generation of the pinion tooth-surface (Di g1 ). he concept of an imaginary generating crown gear is used to explain the generating cutting process of the face-hobbed spiral bevel pinion and gear teeth [30]. This imaginary generating gear is a virtual gear whose teeth are formed by the traces of the cutting edges of the head-cutter blades, although its tooth number is not necessarily an integer. It can be considered as a special case of a bevel gear with 90 deg pitch angle. To obtain the pinion/gear tooth surface in the generating process, the work gears are rolled with the imaginary gear. The concept of complementary generating crown gear is considered when the generated mating tooth surfaces of the pinion and the gear are fully conjugated. Conjugate means that the pinion and the gear have a line contact in each angular position. The motion transmission happens in each roll position precisely with the same constant ratio. The contact area, the summation of all contact lines during the complete roll of one pair of teeth, is spread out over the entire active flank. As pointed out earlier, to prevent stress concentrations on the tooth edges, caused by tooth errors,deflections under load, and misalignments between pinion and gear, tooth-surface modifications are applied; the gear pair becomes “mismatched.” In this case, the generating crown gears for the pinion and the gear are not being complementarily identical. The tooth surfaces of the pinion and of the gear are defined by the following system of equations: （1a） (1b) The fundamental equation of meshing (1b) states that for each point to lie on the envelope tooth surface, the unit normal vector to the family of the generating crown gear surfaces should be perpendicular to the relative velocity of the generated pinion/gear to the generating crown gear, . The matrices for performing the coordinate transformations, the radius vector of the blade profile points, , and the expressions for vectors and are presented in Ref. [30]. 2.2 Relative Position of the Pinion and the Gear in Mesh.According to Fig. 2, the relative position of the pinion and gear in mesh is defined by the following equation: (2) where matrix defines the relation between the stationary coordinate systems and , in which the pinion and the gear are rotating through mesh. This matrix contains the possible misalignments of the mating members in the form of the pinion offset ( ), the pinion and gear axial adjustment error ( ), and the angular misalignments of the pinion axis in the horizontal ( ) and vertical ( ) planes. Matrix is defined in Ref. [30].