提高复合滚刀工作的准确性外文文献翻译、中英文翻译

附录一：外文翻译提高复合滚刀工作的准确性摘要本文介绍了具有可更换烧结碳化物切割板的复合炉盘的几何分析。 切割板通常布置在滚刀刀片的前刀面上，垂直于滚刀螺纹线或平行于滚刀轴线。 切割板通常是平坦的，具有直线的切割边缘轮廓，并且左右切割轮廓角度相等。 可以通过对切削刃轮廓角进行校正并使用切削刃的圆形轮廓来提高滚刀精度。关键词：复合滚刀; 轮廓角误差; 直线性误差 替代资料1 介绍模块化滚刀用于在 0.25 至 25mm 的整个模块范围内切割正齿轮和斜齿轮1,2,3 4。这些工具的设计的开发主要涉及使用具有增加的直径的炉盘，或者滚刀周边上的刀片数量增加（挡板切割器）。 使用长度增加的多螺纹滚刀; 而且还使用了复合滚刀3,5,6。此外，在加工过程中，所谓的移动被应用，由此滚刀平行于旋转轴线移动，这提高了其耐久性（通过在整个刀具长度上提供滚刀的均匀磨损）。复合式滚刀具有可更换的单齿（板），高速钢制成的分段或机架，或可替换的烧结碳化物板（图 1a）5,7或固定在叶片侧面的可更换的烧结碳化物板（图 1b） 3,8,9。还使用了由单个圆形切片制成的滚刀以及单个复合圆盘滚刀的设计9。在小模块的情况下，切割板被钎焊或粘合到由工具钢制成的炉体上。工具与可替换板的特点是生产率非常高7,10，主要用于数控机床（CNC）。这些工具的设计开发与齿轮技术的发展有关11,12,13。圆柱齿轮不仅可以在滚齿机上切割，而且可以在通用多轴多功能数控机床上切割6。图 （a）具有可更换硬质合金刀片的现代滚刀5; （b）Coro Mill 176 具有可更换烧结碳化物板的复合滚刀14,15。复合工具的缺点是与传统的模块式固体炉盘相比具有较低的精度。这是由于复合工具设计本身 - 切割板在工具体中制成的座椅中正确定位的问题。定义滚刀精度的主要参数之一是作用表面的轮廓16,18，其由叶片切削刃轮廓围绕滚刀轴的螺旋运动所描述，这意味着它是几何轨迹刀刃。渐开线齿轮滚动条件意味着滚刀动作表面是在与圆柱相切的平面中具有直线轮廓的渐开线螺旋4。渐开线螺旋体在轴向部分或与滚刀线螺纹正交的部分的轮廓为曲线。因此，平板轮廓也应该是曲线的。用于精加工的滚刀在精度等级 AA 或甚至 AAA 中执行，并且非常昂贵。对质量的要求越来越高，要求在设计阶段理论上进行研究5,6,12,16,18。对其几何的描述的简化越来越多地被拒绝，而努力的目的是建立一个可能准确的数学模型的炉盘与其真正的技术。该文件详细介绍了如何改变复合式滚刀中使用的切割板轮廓和轮廓角度，以提高滚刀精度。2 复合滚刀的几何分析2.1 滚刀动作表面轮廓对称和平坦的板的切削刃轮廓可以用下面的等式（图 2）来描述。其中：u-板切削刃轮廓参数，lw-顶端间隙，s - 切割板在板尖处的半宽（对应于形成加工齿轮齿廓的主动渐开线原点的高度） ， - 切削刃轮廓角度，分别为 - 左侧和右侧切割板边缘。对于不同于零的滚刀前角，从下面的关系确定顶端间隙和活动板轮廓高度x (ab)cosJ (acosJ)2 b(2ab)(sinJ)2（2）图 2， 切割轮廓其中采用以下指定：其中：mn - 正常滚刀模块，rp - 滚刀节距半径，h - 活动板高度。图 3 需要设计几何元素：1 - 作用面; 2 - 前刀面（切割板）; 3 侧侧面; 4 - 外侧面; 5 - 切边通过考虑到板的定位并给予其相对的螺旋运动，可以用如下方程描述滚刀作用表面（图 3）其中：v - 滚刀动作面参数， - 齿参考圆柱上的滚刀导程角，尖端边缘与滚刀轴的距离，滚刀螺旋作用面参数，- 手和左手螺纹滚刀，x - 下标标识坐标系。当从已知的（旧的）坐标系转换到新的坐标系时，接受在右旋螺纹规则之后的任何轴上指定 x 的旋转方向，并用箭头标记坐标系变换的方向而不是身体在图纸中的旋转。在大多数关于切削刀具和齿轮理论的研究中，复合运动被分解成坐标系轴线周围的平移和旋转。使用基本旋转矩阵（即坐标系周围的旋转）简化了分析关系的描述，用于描述齿切割过程中甚至复杂的相对工具和车轮运动（或齿分析过程中齿轮元件的运动），以及也使得他们的验证更容易。为了制定所提供的关系，使用了一个球面坐标系变换矩阵（6），即通过坐标系原点的轴的旋转矩阵13,4：其中采用以下名称：其中：n，n1，n2，n3 - 已知坐标系中旋转轴线及其部件的指定;* - 旋转角度。对于基本旋转（即坐标系轴线周围的旋转），旋转轴由其数量（X / Y / Z 轴分别为 1/2/3）确定，该分量等于 1， 而其他组件每个等于 1。对于复合滚刀的渐开线螺旋作用表面和铣刀的螺旋前刀面，铣刀的切削刃在相对的轴线侧与基座圆筒相切。为了确定滚刀的精度，需要确定与底座相切的平面中的作用面。 为此，从条件：其中：rz - 螺旋渐开线滚刀动作面的基础圆的半径，分别为左侧和右侧滚刀动作曲面侧的 - x - 右侧上标标识坐标，为该组 在切割板边缘轮廓上的点定位参数的连续值，可以确定滚刀动作表面参数 v 的值，而从等式 （5），与基座相切的平面中的滚刀动作表面轮廓的点的坐标。 在这样做时，有必要考虑到对于不同于零的前角，切割板的高度改变（图 3 中的（2）。2.2 替代资料与基座相切的平面中的滚刀动作表面轮廓对于左侧和右侧是曲线的并且是不同的。因此，轮廓误差已被分成轮廓角误差和直线性误差。 轮廓角误差定义为穿过极限轮廓点的直线的角度的误差当直线性误差是从该直线定义轮廓点的距离时42其中：n - 轮廓点数，i - 连续轮廓点数，* - 轮廓点识别索引， - 与基座相切的平面中的滚刀动作表面轮廓角， - 与直线的偏差。从将圆圈定义为三点（起点和终点以及剖面中高点）的条件，根据与圆柱体相切的平面中的滚刀作用面轮廓确定替代圆的半径其中：nr - 连接接中点指数。应对左侧和右侧剖面进行计算。 将确定的轮廓角度和替代半径作为切割板切割刃的轮廓角度和轮廓半径。如果垂直于板切割刃的平面中的板间隙角度假定为不同于零，并且板侧面形成为圆柱形表面的扇形，则该表面的半径可以是根据关系（10）代入其中：f-板侧面间隙角。在这种情况下，切削刃轮廓将是椭圆的扇形。2.3 一个计算实例滚刀和切割板的数据：mn = 5 mm，= 20 ，= -15 ，螺纹数 z = 1， 滚刀外径 dz = 20 mm 手线滚刀对于初始数据，与基座圆筒相切的平面中的滚刀动作表面轮廓分别具有分别为 21 2234“和 201823”的左侧和右侧轮廓，以及 获得了分别为-0,009 mm和-0.002 mm的左侧和右侧轮廓的最大偏差（图 4图 4.从直线与基座相切的平面中的滚刀动作表面轮廓的偏差。左侧和右侧切削刃的替代圆半径分别为 6718 mm和 2859 mm。为了校正轮廓误差，必须使用凹形滚刀动作表面轮廓来给板边缘提供凸形轮廓。类似地，对于小于标称值的滚刀动作表面轮廓角度值，必须通过这些误差的值来增加板轮廓角度。在所考虑的情况下，左侧和右侧切割角度的平板轮廓角分别等于：183726and 194137”。对于板的这种形状，在与底座相切的平面中的滚刀作用的表面轮廓分别具有左侧和右侧轮廓角，分别为 195742”和 195930”并且获得了分别为-0,006 mm和-0,001 mm 的左侧和右侧轮廓的直线的最大偏差（图 5）。实现了相当小的滚刀作表面轮廓误差。图 5.与直线相切的底座圆柱面上的滚刀作用面轮廓的偏差发生的小轮廓误差是由于切割板轮廓高度与在基底圆柱切向的平面中的滚刀作用表面轮廓的高度之间的差异。 这些错误仍然可以减少。 如果在所讨论的情况下，左侧和右侧板的轮廓角分别增加了 215”和 28”，则平面中的滚刀作用表面轮廓的角度 与基本圆柱体相切的将等于 2000”。通过前角显示对滚刀轮廓精度的非常大的影响。对于相同的输入数据，但是对于前角分别等于-6和 6，获得与-0.002 mm直线相同的轮廓偏差和 202436”的轮廓角，获得了左侧和右侧滚刀轮廓侧面。轮廓对称。在这种情况下，两个板边缘的替代圆形轮廓的半径为 22937 mm。对于 22937 mm的板轮廓半径和 194524”的轮廓角， 获得与基座圆相切的平面中的滚刀轮廓角等于 195949”（与直线的轮廓偏差线保持在-0.002 mm）。这种解决方案对于在叶片侧面具有两个切割板的炉盘是可能的，在这种情况下可能具有不同的前角。由于与直线偏差小的误差，与现有的情况相比，限制自己改变切割板轮廓角度就足够了。对于开始时的输入数据，但是对于 0的前角，获得了与基座圆切割的平面中的滚刀作用表面对称的轮廓，轮廓角为 20457”，最大偏差 从直线为-0.001 mm的轮廓。对于 19553”的板轮廓角度和 103648 mm的替代半径，获得 1”的轮廓角误差和距离直线为 0,000 mm的轮廓偏差。3. 结 论固定在滚刀刀面表面上的切割板垂直于滚刀螺旋线或平行于滚刀轴线布置。 对于这两种设计类型，配置文件错误都是类似的。 切割板垂直于滚刀螺纹的设计更好，因为左侧和右侧板边缘的工作前角相同。 滚刀动作表面轮廓的误差由轮廓角误差和切削刃非直线性误差组成。 刀刃轮廓角误差通常大于切削刃非直线性误差，在技术上更容易消除。 这是由于板切割刃替代圆半径为数米左右，这在技术上难以执行。对于 0的前角，滚刀动作表面轮廓对称，因此切割板也具有对称轮廓。 随着前角和滚刀螺纹数的增加，轮廓误差大大增加，滚刀动作面轮廓变得不对称。 如果使用固定在刀片侧面上的两个板，则可以使用左右切割板的不同前角，从而减少滚刀动作表面轮廓的误差。 在大型模块（25-40mm）的情况下，可以使用这种滚刀设计，这可能是炉盘设计（具有变化的前角）的新方向。附录二：外文原文Available online at ScienceDirectProcedia Engineering 177 ( 2017 ) 155 161XXI International Polish-Slovak Conference “Machine Modeling and Simulations 2016”Enhancing the accuracy of composite hobsTadeusz Nieszporek, Andrzej Piotrowski*Czestochowa University of Technology, ul. Dabrowskiego 69, Czestochowa, PolandAbstractThe paper presents a geometrical analysis of composite hobs with replaceable sintered carbide cutting plates. The cutting plates are normally arranged on the rake surface of hob blades either perpendicularly to the hob thread helical line or in parallel to the hob axis. The cutting plates are generally flat, have a rectilinear cutting edge profile, and the left- and right-hand cutting edge profile angles are equal. The hob accuracy can be enhanced by making a correction to the cutting edge profile angles and using circular profiles of the cutting edges. 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2017 The Authors.Published by Elsevier Ltd.(Peer/licenses/by-nc-nd/4.0/-review under responsibility of the organizing committee of MMS 2016).Peer-review under responsibility of the organizing committee of MMS 2016Keywords: composite hob; profile angle error; rectilinearity error; substitute profile;1. IntroductionModular hobs are used for cutting spur gears and helical gears 1,2,3 within the whole range of modules from 0.25 to 25 mm 4. The development of the design of these tools involves mainly the use of hobs with an increased diameter, or an increased number of blades on the hob perimeter (flap cutters); the use of multi-thread hobs with an increased length; but also the use of composite hobs 3,5,6. Moreover, so called shifting is applied during machining, whereby the hob is shifted in parallel to the axis of rotation, which enhances its durability (by providing a uniform wear of the hob blades over the entire tool length).Composite hobs have replaceable single teeth (plates), segments or racks made of high-speed steel, or replaceable sintered carbide plates (Fig. 1a) 5,7, or replaceable sintered carbide plates fixed on the blade flanks (Figure 1b) 3,8,9. Designs of a hob made of single rounded segments, as well as single composite disc hobs are also used 9. In the case of small modules, cutting plates are brazed or glued to the hob body made of tool steel. Tools with* Corresponding author. Tel.: +48 34 3250509; fax: +48 34 3250509. E-mail address: itmitm.pcz.pl1877-7058 2017 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (/licenses/by-nc-nd/4.0/).replaceable plates are characterized by very high productivity 7,10 and are used mainly on numerically controlled machine tools (CNC). The development of the design of these tools is associated also with the development of gear wheel technology 11,12,13. Cylindrical gears can be cut not only on hobbing machines, but also on universal multi-axial multi-purpose CNC machine tools 6.Fig. 1. (a) A modern hob with replaceable carbide inserts 5; (b) A Coro Mill 176 composite hob with replaceable sintered carbide plates 14,15.2. Geometric analysis of the composite hob2.1. The hob action surface profileThe cutting edge profile of a plate, symmetric and flat, can be described with the following equation (Fig.2).where: u - plate cutting edge profile parameter, lw - tip clearance, s - half-width of the cutting plate at the plate tip (at the height corresponding to the forming of the origin of the active involute of the machined gear tooth profile), - cutting edge profile angle, - respectively, for the left-hand and right-hand cutting plate edge.For a hob rake angle different from zero, the tip clearance and the active plate profile height are determined from the relationship below(acosJ)2 b(2ab)(sinJ)2x (ab)cosJ(2)Fig. 2. Cutting plate profile.where the following designation is takenwhere: mn - normal hob module, rp - hob pitch radius, h - active plate height.Fig. 3. Elements of hob geometry: 1 action surface; 2 rake surface (cutting plate); 3 side flank face; 4 outer flank face; 5 cutting edge.By taking into account the positioning of the plate and giving it relative helical motion, the hob action surface can be described with the equation as follows (Fig. 3)where: v - hob action surface parameter, - hob thread lead angle on the tooth reference cylinder, ro - distance of the tip plate edge from the hob axis, p - hob helical action surface parameter, # - respectively, for the right-hand and left-hand thread hob, x - the subscript identifies the coordinate system.When making transition from the known (old) coordinate system to a new one it is accepted to designate the x direction of rotation around any axis following the right-handed screw rule, and to mark with the arrow the direction of coordinate system transformation rather than the rotation of the body in drawings. In the majority of studies on cutting tools and the theory of toothing, a composite motion is broken down into translations and rotations around the axes of the coordinate systems. Using matrices of elementary rotations (i.e. the rotations around the coordinate systems) simplifies the formulation of analytical relationships for the description of evencomplex relative tool and wheel motion in the toothing cutting process (or the motion of gear elements in the toothing analysis process) and also makes their verification easier. For formulating the relationships provided, a spherical coordinate system transformation matrix (6) was used, that is the matrix of rotation around the axis passing through the origin of the coordinate system 13,4:where the following designations are adopted:where: n, n1, n2 , n3 - designation of the rotation axis versor and its components in the known coordinate system; * - angle of rotation.For the elementary rotations (i.e. rotations around the coordinate system axes), the axis of rotation is identified by its number (1/2/3 respectively, for the X/Y/Z axes), and this component is equal to 1, while the other components are equal to 1, each.For the involute helical action surface of the composite hob and the helical rake surface of the mill, the cutting edges of the mill blade are tangential to the base cylinder on the opposite axis sides.In order to determine the accuracy of the hob, its action surface in the plane tangential to the base cylinder needs to be determined. To that end, from the condition:where: rz - radius of the base cylinder of the helical involute hob action surface, - respectively, for theleft-hand and right-hand hob action surface profile side, x - the right-hand superscript identifies the coordinate, for the set consecutive values of the parameter of point positioning on the cutting plate edge profile, it is possible to determine the values of the hob action surface parameter v , while from Eq. (5), the coordinates of the pointsof the hob action surface profile in the plane tangential to the base cylinder. In doing this, it is necessary to takeinto account the fact that for a rake angle different from zero, the height of the cutting plate changes (2) in Fig. 3).2.2. The substitute profileThe hob action surface profile in the plane tangential to the base cylinder is curvilinear and different for the lefthand and right-hand side. For this reason, the profile error has been divided into the profile angle error and the rectilinearity error. The profile angle error is defined as the error of the angle of the straight line passing through the extreme profile pointsy the while the rectilinearity error is defined bdistance of the profile points from this straight linewhere: n - number of profile points, i - successive profile point number, * - profile point identification index, - hob action surface profile angle in the plane tangential to the base cylinder, - deviations from the straight line.From the condition, which defines a circle by three points (the starting and end points and the profile mid-height point), the radius of the substitute circle was determined for the hob action surface profile in the planetangential to the base cylinderwhere: nr - profile midpoint index.Calculation should be carried out for the left-hand and right-hand profile sides. The determined profile angles and substitute radii are taken as the profile angles and profile radii of the cutting plate cutting edges.If the plate clearance angle in the plane perpendicular to the plate cutting edge is assumed to be different from zero, and the plate flank is formed as a sector of the cylindrical surface, then the radius of this surface can becalculated from relationship (10) by substituting in itnr nrcosDf(11)where: f - plate flank clearance angle.In that case, the cutting edge profiles will be sectors of an ellipse.2.3. A calculation exampleData for the hob and the cutting plate: mn=5mm, =20, =-15, number of threads z=1 , hob outer diameter dz=20mm, right-hand thread hob.For the initial data, an hob action surface profile in the plane tangential to the base cylinder with a left-hand and a right-hand profile of, respectively, 212234 and 201823, and the maximum deviations from the left-hand and the right-hand profile of, respectively, -0,009mm and -0,002mm were obtained (Fig. 4).Fig. 4. Deviations of the hob action surface profile in the plane tangential to the base cylinder from the straight line.The substitute circle radii for the left-hand and the right-hand cutting edge were, respectively, 6718 mm and 2859 mm. In order to correct the profile errors, it is necessary, with a concave hob action surface profile, to give a convex profile to the plate edges. Similarly, for hob action surface profile angle values smaller than the nominal values, the plate profile angles have to be increased by the values of these errors. The plate profile angles for the left-hand and the right-hand cutting angle in the case under consideration are equal to, respectively: 183726and 194137. For such shape of a plate a hob acting surface profile in the plane tangential to the base cylinder with a left-hand and a right-hand profile angle of, respectively, 195742 and 195930 and the maximum deviation from the straight line for the left-hand and the right-hand profile of, respectively, -0,006 mm and -0,001 mm were obtained (Figure 5). Considerably smaller hob action surface profile errors were achieved.Fig. 5. Deviations of the hob action surface profile in the plane tangential to the base cylinder from the straight line.The occurring small profile errors are due to the difference between the cutting plate profile height and the height of the hob action surface profile in the plane tangential to the base cylinder. These errors can still be reduced. If, in the case under discussion, the profile angle of the left-hand and the right-hand plate is increased by, respectively, 215 and 28 , then the angles of the hob action surface profile in the plane tangential to the base cylinder will be equal to 2000.A very great effect on the hob profile accuracy is shown by the rake angle. For the identical input data, but for rake angles being equal to, respectively, -6 and 6 , identical profile deviations from the straight line of -0,002 mm and profile angles of 202436 were obtained for the left-hand and right-hand hob profile sides. The profile is symmetrical. The radius of the substitute circular profile is in this case 22937 mm for both plate edges. For plate profile radii of 22937 mm and profile angles of 194524, hob profile angles in the plane tangential to the base cylinder equal to 195949 were obtained (the profile deviations from the straight line have remained unchanged at -0,002 mm). Such a solution is possible for hobs with two cutting plates on the blade flanks, which may have in that case different rake angles. With small errors of deviations from the straight line, as in the case at hand, it is sufficient to limit oneself to changing the cutting plate profile angles.For the input data as at the beginning, but for a rake angle of 0, a profile symmetrical to the hob action surface in the plane tangential to the base cylinder was obtained with profile angles of 20457 and maximum deviations from the straight line for the profile of -0,001 mm. For a plate profile angle of 19553 and a substitute radius of 103648 mm, a profile angle error of 1 and profile deviations from the straight line of 0,000 mm were obtained.3. ConclusionsCutting plates fixed on the hob blade face surface are arranged either perpendicularly to the hob thread helix or in parallel to the hob axis. For both design types, the profile errors are similar. The design, in which the cutting plates are perpendicular to the hob thread helix, is better, because the working rake angles for the left-hand and the righthand plate edge are identical. The error of the hob action surface profile is composed of the profile angle error and the cutting edge non-rectilinearity error. The cutting edge profile angle error is generally larger that the cutting edge non-rectilinearity error and is technologically easier to eliminate. This