WO2020151683A1 - 一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法 - Google Patents

一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法 Download PDF

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WO2020151683A1
WO2020151683A1 PCT/CN2020/073343 CN2020073343W WO2020151683A1 WO 2020151683 A1 WO2020151683 A1 WO 2020151683A1 CN 2020073343 W CN2020073343 W CN 2020073343W WO 2020151683 A1 WO2020151683 A1 WO 2020151683A1
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Prior art keywords
tool
tooth
involute
tooth surface
formula
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PCT/CN2020/073343
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English (en)
French (fr)
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郭二廓
任乃飞
周长禄
王杰
张新洲
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江苏大学
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Priority to GB2009212.8A priority Critical patent/GB2585982B/en
Publication of WO2020151683A1 publication Critical patent/WO2020151683A1/zh

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
    • B23F5/20—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by milling
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F19/00—Finishing gear teeth by other tools than those used for manufacturing gear teeth
    • B23F19/002—Modifying the theoretical tooth flank form, e.g. crowning
    • B23F19/005—Modifying the theoretical tooth flank form, e.g. crowning using a face-mill-type tool, e.g. a milling or a grinding tool
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/182—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by the machine tool function, e.g. thread cutting, cam making, tool direction control
    • G05B19/186—Generation of screw- or gearlike surfaces
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45214—Gear cutting

Definitions

  • the invention relates to the technical field of mechanical processing, in particular to an envelope milling processing method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface.
  • Gears are the key basic parts of machinery-related applications.
  • the traditional gear hobbing, gear shaping, gear shaving and other gear processing methods have problems such as the long processing cycle of single-piece, small-batch, large-modulus gear parts, and the high cost of special gear making equipment and special gear tools.
  • a method for flexible envelope milling of cylindrical gears with universal tools on a universal multi-axis machining center is proposed, which can provide a low-cost, high-efficiency, and short-cycle for the processing of single-piece, small-batch and large-modulus gears for enterprises And fast response flexible tooth manufacturing method.
  • this advanced multi-axis turning-milling combined processing technology still has the problem of low processing efficiency in the processing of cylindrical gears.
  • the reason is that the principle of turning-milling compound envelope milling is to fit the tooth surface into a free-form surface before planning the tool path, without considering the differential geometric characteristics of the tooth surface.
  • the radius of curvature of each micro-segment on the tooth profile is different, which has a certain particularity.
  • this free-form surface-based tool path planning method does not consider the requirement of meshing accuracy at the pitch circle of the tooth surface.
  • the main meshing area is the tooth surface near the pitch circle, and the machining accuracy of this area should be given priority during the machining process.
  • the milling form they adopt is to process the tooth surfaces as free-form surfaces, which leads to contradictions between machining efficiency and machining accuracy.
  • the present invention provides an envelop milling method for involute cylindrical gears considering the characteristics of tooth surface accuracy, which is used to improve the processing of milling involute cylindrical gears with general tools on a general machining center. Efficiency and tooth surface meshing performance.
  • the present invention achieves the above technical objects through the following technical means.
  • An envelope milling method for involute cylindrical gears considering the accuracy characteristics of the tooth surface including:
  • S01 Select the tool according to the parameters of the gear workpiece to be processed, and determine the tool diameter and the length of the cutting edge of the tool;
  • S04 Plan the tool path according to the tool location point.
  • an end mill or a rod milling cutter is selected for the medium and small modulus involute cylindrical gears, and a conical disc milling cutter or a rod milling cutter is selected for the large modulus involute cylindrical gears.
  • the tool diameter D t ⁇ 10 mm, and the blade length L t ⁇ 20 mm are the same.
  • the calculation formula of the eccentricity e i is:
  • r b is the gear base circle radius
  • ⁇ 0 is the base circle tooth groove half angle
  • u i is the involute expansion angle corresponding to each tool position on the tooth surface
  • D t is the tool diameter.
  • the step S03 is specifically:
  • S03.1 divides the tool position points of the tool along the gear tooth profile direction into n equal parts, and each tool position point on the tooth surface is distributed according to the parabolic equation.
  • Set the maximum distance of the cutting step along the tooth profile direction as ⁇ l max and the minimum distance It is ⁇ l min ⁇ l max /5, the distance between adjacent steps of two tool positions is ⁇ l i , and the step length of the tool along the tooth profile direction satisfies the following formula:
  • r f is the radius of the root circle
  • r b is the radius of the base circle
  • ⁇ 0 is the half angle of the base circle tooth groove
  • point C Is the maximum residual height difference between adjacent tool location points, assuming that the coordinates of point C are (x C ,y C ), assuming that the slopes of two adjacent tool location points A and B on the involute line are k A and k respectively B , from the geometric relationship of A, B, and C, the following formula can be obtained:
  • the slopes k A and k B of two adjacent tool positions A and B on the involute line are respectively:
  • u A and u B are the involute expansion angles of two adjacent tool positions A and B respectively;
  • the residual height difference ⁇ t i between adjacent tool positions can be obtained in turn. From the known involute tooth profile expansion angle ⁇ u i , the involute tooth profile expansion angle ⁇ u i and The curve equation between tooth surface residual height difference ⁇ t i is:
  • the specific method for determining the machining tool position point in step S03.6 is to make the tool path trajectory from the pitch circle of the tooth surface to the tooth profile of the upper and lower ends present a dense to sparse distribution, even if it is close to the pitch circle.
  • the main engaging flank region residues minimum elevation ⁇ t i, ⁇ t i elevation residues flank pitch distance farther secondary engagement region is gradually increased, and the non-engagement region close to the tooth root and the tooth tip portion of the tooth surface height difference [Delta] t residues i is the largest.
  • the step S04 is specifically:
  • the tool starts from one end face of the tooth tip, and first moves the first tool along the tooth direction to complete the milling of the entire tooth width b;
  • the present invention comprehensively considers the differential geometric characteristics of the involute tooth surface on the premise of ensuring the accuracy of the involute cylindrical gear tooth surface processing, and calculates The tool location point is exited and the tool path is planned, so that the tool path is allocated on demand, reducing the redundant path of the tooth root and tooth tip, thereby improving the processing efficiency of envelope milling.
  • the present invention considers the accuracy characteristics of the involute tooth surface, so that the tool path from the pitch circle of the tooth surface to the tooth profile at both ends shows a dense to sparse Distribution to meet the machining requirements of high precision in the middle of the tooth surface and low precision at both ends, thereby improving the meshing performance of the tooth surface.
  • FIG. 1 is a plan view of the cutting step length and the cutting path of the involute tooth surface considering the accuracy characteristics of the tooth surface according to an embodiment of the present invention.
  • Figure 2 is a schematic diagram of each movement axis of a typical four-axis machining center.
  • Figure 3 is a schematic diagram of enveloping and milling involute gears with a flat end mill on a four-axis machining center.
  • Fig. 4 is a curve of the relationship between the expansion angle ⁇ u i of the involute tooth profile and the residual height difference ⁇ t i of the tooth surface according to an embodiment of the present invention.
  • Figure 5 shows the tool envelope tool location points of the involute tooth surface according to the embodiment of the present invention, where (a) corresponds to the finishing method considering the accuracy characteristics of the tooth surface, and (b) corresponds to the traditional based on equal residual height difference Method of finishing.
  • Fig. 6 shows the relationship between the radial length of the involute tooth surface and the residual height difference according to an embodiment of the present invention, where (a) corresponds to a finishing method considering the accuracy characteristics of the tooth surface, and (b) corresponds to a traditional Finishing method of equal residual height difference method.
  • the present invention takes an involute cylindrical gear used in a certain transmission mechanism as an example to illustrate in detail an envelope milling method of an involute cylindrical gear in consideration of the accuracy characteristics of the tooth surface.
  • the machining accuracy is ISO 6
  • the total tooth profile deviation is 27.42 ⁇ m
  • when the machining accuracy is ISO 3 the total tooth profile deviation is 9.69 ⁇ m.
  • the existing processing equipment is a four-axis turning-milling composite machining center.
  • the three linear axes are X-axis, Y-axis, and Z-axis
  • one rotary axis is C-axis
  • the workpiece is installed on the C-axis to work.
  • the tool is installed on the spindle SP, and the Z-axis and C-axis can realize two-axis linkage.
  • an envelope milling method for an involute cylindrical gear considering the characteristics of tooth surface accuracy specifically includes the following steps:
  • a flat end mill 2 For the milling of involute cylindrical gears, a flat end mill 2 should be used.
  • the tool parameters are as follows:
  • the tool diameter D t of the flat end mill 2 According to the parameters of the gear workpiece 1, the smallest tooth groove width is calculated to be 21.9mm. In order to ensure that the tool has sufficient linear speed when cutting, the tool diameter D t is selected as ⁇ 18mm;
  • the cutting edge length L t of the flat end mill 2 According to the parameters of the gear workpiece 1, the cutting edge length L t is selected as 38mm;
  • r b is the gear base circle radius
  • ⁇ 0 is the base circle tooth groove half angle
  • u i is the involute expansion angle
  • D t is the diameter of the end mill 2.
  • the S03 step is specifically:
  • the slopes k A and k B of two adjacent tool position points A and B on the involute are respectively:
  • u A and u B are the involute expansion angles of two adjacent tool positions A and B respectively, which can be obtained by formula (4).
  • the residual height difference ⁇ t i between adjacent tool positions can be obtained sequentially, and the involute tooth profile expansion angle ⁇ u i is known , as shown in Figure 4, the involute tooth is constructed
  • the curve equation between the profile expansion angle ⁇ u i and the tooth surface residual height difference ⁇ t i is:
  • the tool path path from the pitch circle of the tooth surface to the upper and lower ends of the tooth profile presents a dense to sparse distribution, that is, the residual height difference ⁇ t of the tooth surface near the main meshing area near the pitch circle is realized.
  • minimum i residues flank height difference ⁇ t i pitch distance farther secondary engagement region gradually increases, and close to the addendum and dedendum portions of the non-engaging region residues flank the maximum height difference ⁇ t i.
  • the tool starts from one end face of the tooth tip, and first moves along the tooth direction to complete the milling of the entire tooth width b;
  • the processing step and the tooth surface accuracy are controlled according to a specific algorithm to achieve high-precision and high-efficiency envelope milling processing of involute cylindrical gears.
  • FIG. 5 it is the involute tooth enveloping tool position point simulated by the CAM software when the tool envelope cutter position points of the involute tooth surface are the same.
  • Fig. 5(a) is a finishing method considering the accuracy characteristics of the tooth surface according to the present invention, and the tool position points of the tooth surface are mainly concentrated near the pitch circle with higher accuracy requirements.
  • Figure 5(b) is a traditional finishing method based on the equal residual height method, and the tooth surface tool position points along the tooth root to the tooth tip show a trend from dense to sparse.
  • Figure 6 it is the relationship between the radial length of the involute tooth surface and the residual height difference.
  • Figure 6 (a) is the use of the present invention to consider the precision characteristics of the tooth surface, the residual height difference of the tooth surface obtained along the pitch circle to the tooth tip and tooth root ends respectively show an increasing trend, near the pitch circle (435mm ⁇ r v ⁇ 445mm) the residual height difference ⁇ t ⁇ 2.5 ⁇ m.
  • the involute tooth surface finishing based on the equal residual height difference method The method resulted in a large number of redundant passes in the tooth root and tooth tip, which not only reduced the machining efficiency, but also failed to consider the accuracy requirements of the meshing area at the pitch circle. Therefore, the envelope milling processing method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface proposed by the present invention can not only improve the envelope milling processing efficiency of the gear, but also make the tooth surface have better meshing performance.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Human Computer Interaction (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Gears, Cams (AREA)
  • Gear Processing (AREA)

Abstract

一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，包括以下步骤：S01：选择铣削刀具，确定刀具直径、刀具切削刃长度；S02：确定刀具轴线相对于齿轮轴线的动态偏心量e i；S03：构建齿廓方向走刀步长公式，构建渐开线齿廓展开角度与齿面残高差之间的曲线方程，计算刀位点；S04：规划走刀路径。该方法在保证渐开线圆柱齿轮齿面加工精度的前提下，综合考虑渐开线齿面的微分几何特性，计算出刀位点，规划刀具路径，使刀具走刀轨迹按需分配，减小齿根和齿顶的冗余走刀，从而提高包络铣齿的加工效率以及齿面的啮合性能。

Description

一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法 技术领域
本发明涉及机械加工技术领域，尤其涉及一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法。
背景技术
齿轮是机械相关应用行业的关键基础零件。近年来，针对传统的滚齿、插齿、剃齿等齿轮加工方法存在的单件小批量、大模数齿轮类零件的加工周期长、专用制齿装备和专用齿轮刀具成本高的问题，出现了一种在通用多轴加工中心上采用通用刀具对圆柱齿轮进行柔性包络铣削加工的方法，可为企业的单件小批量和大模数齿轮加工提供一种低成本、高效率、短周期和快响应的柔性制齿方法。
然而，这种先进的多轴车铣复合加工技术在圆柱齿轮的加工上仍存在着加工效率不高的问题。究其原因，一是车铣复合包络铣削原理是将齿面拟合成自由曲面后再进行刀具路径规划，并未考虑到齿面的微分几何特性。尤其是针对渐开线圆柱齿轮，其齿形上每一微段的曲率半径均不相同，具有一定的特殊性。二是这种基于自由曲面的走刀路径规划方法也未考虑齿面节圆处啮合精度的需求。在渐开线圆柱齿轮副啮合过程中，主要参与啮合的区域是靠近节圆附近的齿面，在加工过程中要优先保证该区域的加工精度。现有技术中虽然有五轴车铣复合加工中心能实现对圆柱齿轮的铣削加工，但是它们所采用的铣削形式是将齿面按自由曲面处理，导致加工效率和加工精度之间相互矛盾。
因此，如果不能综合考虑到齿面的微分几何特性和齿面的精度特征要求，仅将齿面上各处的加工精度按照相同的残高差处理，必然会造成大量的冗余走刀，导致加工效率低下，或是齿面啮合区域精度不高。
发明内容
针对现有技术中存在不足，本发明提供了一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，用于提高在通用加工中心上采用通用刀具铣削渐开线圆柱齿轮的加工效率和齿面啮合性能。
本发明是通过以下技术手段实现上述技术目的的。
一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，包括：
S01：根据待加工齿轮工件参数，选择刀具，确定刀具直径和刀具切削刃长度；
S02：采用偏心铣削方式进行加工，确定刀具轴线相对于齿轮轴线的动态偏心量e i；
S03：根据齿轮的齿面主要啮合区域的精度要求，通过构建齿廓方向走刀步长公式，求解走刀步长沿齿廓方向的最大间距Δl max、两个刀位点的相邻步长间距Δl i以及齿面上各刀位点对应的渐开线展开角度u i，构建渐开线齿廓展开角度与齿面残高差之间的曲线方程Δt i＝f(Δu i)，最终确定加工刀位点；
S04：根据刀位点规划走刀路径。
优选地，所述步骤S01中，对于中小模数渐开线圆柱齿轮选用立铣刀或棒铣刀，对于大模数渐开线圆柱齿轮选用圆锥盘形铣刀或棒铣刀。
优选地，所述步骤S01中，刀具直径D t≥φ10mm，刀刃长度L t≥20mm。
优选地，所述偏心量e i的计算公式为：
Figure PCTCN2020073343-appb-000001
式中，r b为齿轮基圆半径；σ 0为基圆齿槽半角；u i为齿面上各刀位点对应的渐开线展开角度；
Figure PCTCN2020073343-appb-000002
为与齿轮固连的回转工作台转动角度，且
Figure PCTCN2020073343-appb-000003
D t为刀具直径。
优选地，所述S03步骤具体为：
S03.1将刀具沿齿轮齿廓方向的刀位点等分成n等份，齿面上各刀位点按照抛物线方程分布，设走刀步长沿齿廓方向的最大间距为Δl max，最小间距为Δl min＝Δl max/5，两个刀位点的相邻步长间距为Δl i，刀具沿齿廓方向的走刀步长满足下式：
Figure PCTCN2020073343-appb-000004
S03.2根据给定的齿轮工件，得到齿面渐开线沿径向高度为H，由公式(3)可以求解出走刀步长沿齿廓方向的最大间距Δl max：
Figure PCTCN2020073343-appb-000005
S03.3将S03.2步骤中求解得到Δl max代入公式(2)中，遍历走刀数目i∈[0,n]，依次得到齿面上各刀位点对应的的步长间距为Δl i；
S03.4已知Δl max和当前走刀数目i，由公式(4)，得到抛物线方程上每一个刀位点(x p，y p)对应的齿面上渐开线展开角度u i：
Figure PCTCN2020073343-appb-000006
式中，r f为齿根圆半径；r b为基圆半径；σ 0为基圆齿槽半角；
S03.5假设渐开线上两个相邻的刀位点A和B的坐标分别为(x A,y A)和(x B,y B)，A和B相交于C点，则C点为相邻刀位点之间的最大残高差，假设C点坐标为(x C,y C)，假设渐开线上两个相邻的刀位点A和B的斜率分别为k A和k B，由A、B、C三点的几何关系可得到下式：
Figure PCTCN2020073343-appb-000007
由渐开渐的特性可知，渐开线上两个相邻的刀位点A和B的斜率k A和k B分别为：
Figure PCTCN2020073343-appb-000008
式中，u A和u B分别为两个相邻的刀位点A和B的渐开线展开角度；
且两个相邻的刀位点A和B的渐开线方程分别为：
Figure PCTCN2020073343-appb-000009
Figure PCTCN2020073343-appb-000010
将公式(6)(7)(8)代入公式(5)中可以得到C点坐标(x C,y C)，
计算C点的残高差：
Figure PCTCN2020073343-appb-000011
根据公式(9)，可以依次得到相邻刀位点之间的齿面残高差Δt i，由已知的渐开线齿廓展开角度Δu i，构建出渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程为：
Δt i＝f(Δu i)     式(10)
S03.6根据渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程，确定加工刀 位点。
优选地，所述步骤S03.6中确定加工刀位点的具体方法为：使刀路轨迹从齿面节圆至上下两端齿廓分别呈现由密到疏的分布，即使靠近节圆附近的主要啮合区域的齿面残高差Δt i最小，距离节圆较远的次要啮合区域的齿面残高差Δt i逐渐增大，且靠近齿根和齿顶部分的非啮合区域齿面残高差Δt i最大。
优选地，所述S04步骤具体为：
刀具从齿顶部分的一侧端面开始，首先沿着齿向方向走第一刀，完成对整个齿宽b的铣削；
沿着渐开线齿廓向齿槽方向进给Δu i的长度；
再沿着齿向方向走第2刀；
依此类推，直至完成对齿个齿面的包络铣削。
本发明的有益效果：
1)当采用通用刀具在多轴加工中心上加工渐开线圆柱齿轮时，本发明在保证渐开线圆柱齿轮齿面加工精度的前提下，综合考虑渐开线齿面的微分几何特性，计算出刀位点，并规划刀具路径，使刀具走刀轨迹按需分配，减小齿根和齿顶的冗余走刀，从而提高包络铣齿的加工效率。
2)本发明在保证渐开线圆柱齿轮齿面加工效率的前提下，考虑渐开线齿面的精度特性，使刀路轨迹从齿面节圆至两端齿廓分别呈现由密到疏的分布，满足齿面中间精度高、两端精度低的加工需求，从而提高齿面的啮合性能。
附图说明
图1为根据本发明实施例考虑齿面精度特性的渐开线齿面走刀步长及走刀路径规划图。
图2为典型四轴加工中心的各运动轴示意图。
图3为在四轴加工中心上采用平头立铣刀包络铣削渐开线齿轮示意图。
图4为根据本发明实施例渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的关系曲线。
图5为根据本发明实施例渐开线齿面的刀具包络刀位点，其中(a)图对应为考虑齿面精度特性的精加工方法，(b)图对应为传统的基于等残高差法的精加工方法。
图6为根据本发明实施例渐开线齿面的径向长度与残高差之间关系，其中(a)图对应为考虑齿面精度特性的精加工方法，(b)图对应为传统的基于等残高差法的精加工方法。
1.齿轮工件；2.立铣刀。
具体实施方式
下面结合附图以及具体实施例对本发明作进一步的说明，但本发明的保护范围并不限于此。
本发明以某传动机构采用的渐开线圆柱齿轮件为例详细说明本发明的一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，齿轮类型为直齿，齿数z＝44，模数m n＝20mm，分度圆压力角α n＝20，变位系数x n＝0，齿宽b＝160mm，精度要求为ISO1328-2：1997的6级，其中，节圆处精度要求达到ISO 3级。对于该齿轮，当加工精度为ISO 6级时，齿廓总偏差为27.42μm；当加工精度为ISO 3级时，齿廓总偏差为9.69μm。已有的加工设备为一台四轴车铣复合加工中心，如图2所示，三个直线轴分别为X轴、Y轴、Z轴，一个回转轴为C轴，工件安装在C轴工作台上，刀具安装在主轴SP上，且Z轴和C轴能实现两轴联动。
根据本发明实施例的一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，具体包括以下步骤：
S01：选择刀具
对渐开线圆柱齿轮的铣削加工宜选用平头立铣刀2，其刀具参数如下，
平头立铣刀2的刀具直径D t：根据齿轮工件1的参数，计算出最小的齿槽宽度为21.9mm，为了保证刀具切削时具有足够的线速度，刀具直径D t选取φ18mm；
平头立铣刀2的刀具切削刃长度L t：根据齿轮工件1的参数，刀刃长度L t选取38mm；
S02：确定刀具偏心量
当加工设备为一台四轴车铣复合加工中心，需要采用偏心铣削方式进行加工，如图2，此时，计算立铣刀2的刀具的动态偏心量e i：
Figure PCTCN2020073343-appb-000012
式中，r b为齿轮基圆半径；σ 0为基圆齿槽半角；u i为渐开线展开角度；
Figure PCTCN2020073343-appb-000013
为与齿轮固连的回转工作台的转动角度，即C轴转动角度，且
Figure PCTCN2020073343-appb-000014
D t为立铣刀2的直径。
S03：计算刀位点
根据齿轮的齿面主要啮合区域的精度要求，通过构建齿廓方向走刀步长公式，求解走刀步长沿齿廓方向的最大间距Δl max，求解两个刀位点的相邻步长间距Δl i，求解齿面上各刀位点对应的渐开线展开角度u i，构建渐开线齿廓展开角度与齿面残高差之间的曲线 方程Δt i＝f(Δu i)，最终确定加工刀位点。所述S03步骤具体为：
S03.1构建齿廓方向走刀步长公式
将立铣刀2沿齿轮齿廓方向的刀位点等分成n＝20等份，齿面上各刀位点按照抛物线方程分布，假设走刀步长沿齿廓方向的最大间距为Δl max，最小间距为Δl min＝Δl max/5，两个刀位点的相邻步长间距为Δl i，如图1所示，此时，刀具沿齿廓方向的走刀步长满足公式(2)：
Figure PCTCN2020073343-appb-000015
S03.2求解走刀步长沿齿廓方向的最大间距为Δl max
对于给定的齿轮工件1，可知齿面渐开线沿径向高度为H＝45mm，由公式(3)可以求解出走刀步长沿齿廓方向的最大间距Δl max＝6.415mm。
Figure PCTCN2020073343-appb-000016
S03.3求解齿轮的齿面上各刀位点对应的步长间距为Δl i
将S03.2步骤中求解得到Δl max代入公式(2)中，遍历走刀数目i∈[0,20]，依次得到齿面上各点的步长间距为Δl i。
S03.4求解齿面上各刀位点对应的渐开线展开角度u i
已知Δl max＝6.415mm和当前总的走刀数目n＝20，由公式(4)，得到抛物线方程上每一个刀位点(x p，y p)对应的齿面上渐开线展开角度u i：
Figure PCTCN2020073343-appb-000017
式中，齿根圆半径r f＝415mm；基圆半径为r b＝413.645mm；基圆齿槽半角为σ 0＝1.192°。
S03.5构建渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程
假设渐开线上两个相邻的刀位点A和B的坐标分别为(x A,y A)和(x B,y B)，A和B相交于C点，则C点为相邻刀位点之间的最大残高差，假设C点坐标为(x C,y C)，假设渐开线上两个相邻的刀位点A和B的斜率分别为k A和k B，由A、B、C三点的几何关系可得到方程组(5)：
Figure PCTCN2020073343-appb-000018
由渐开线的特性可知，渐开线上两个相邻的刀位点A和B的斜率k A和k B分别为：
Figure PCTCN2020073343-appb-000019
式中，u A和u B分别为两个相邻的刀位点A和B的渐开线展开角度，可以由公式(4)得到。
且两个相邻的刀位点A和B的渐开线方程分别为：
Figure PCTCN2020073343-appb-000020
Figure PCTCN2020073343-appb-000021
将公式(6)(7)(8)代入公式(5)中可以得到C点坐标(x C,y C)。
计算C点的残高差：
Figure PCTCN2020073343-appb-000022
根据公式(9)，可以依次得到相邻刀位点之间的齿面残高差Δt i，由已知的渐开线齿廓展开角度Δu i，如图4所示，构建出渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程为：
Δt i＝f(Δu i)      式(10)
S03.6根据公式(10)，使刀路轨迹从齿面节圆至上下两端齿廓分别呈现由密到疏的分布，即实现了靠近节圆附近的主要啮合区域的齿面残高差Δt i最小，距离节圆较远的次要啮合区域的齿面残高差Δt i逐渐增大，且靠近齿根和齿顶部分的非啮合区域齿面残高差Δt i最大。
S04：规划走刀路径
加工过程中，刀具从齿顶部分的一侧端面开始，首先沿着齿向方向走第1刀，完成对整个齿宽b的铣削；
沿着渐开线齿廓向齿槽方向进给Δu i的长度；
再沿着齿向方向走第2刀；
依次类推，直至完成对齿个齿面的包络铣削。
在整个铣削过程中，将加工步距与齿面精度之间按照特定的算法执行控制，即可实现对渐开线圆柱齿轮的高精度、高效率的包络铣削加工。
如图5所示，是渐开线齿面的刀具包络刀位点同为20个时，通过CAM软件模拟出的渐开线齿面包络刀位点。图5(a)是采用本发明的考虑齿面精度特性的精加工方法，齿面刀位点主要集中于精度要求较高的节圆附近。图5(b)是采用传统的基于等残高法的精加工方法，齿面刀位点沿齿根向齿顶呈由密到疏的趋势。
如图6所示，是渐开线齿面的径向长度与残高差之间关系。图6(a)是采用本发明的考虑齿面精度特性的精加工方法，得到的齿面残高差沿节圆分别向齿顶和齿根两端呈增大趋势，节圆附近(435mm<r v<445mm)的残高差Δt<2.5μm。图6(b)是采用传统的基于等残高法的精加工方法，得到的齿面残高差沿齿面分布均匀一致，即节圆处的残高差与齿顶、齿根部分的残高差Δt＝6μm，而对于渐开线齿轮来说，齿面上靠近节圆附近才是主要啮合区域，而接近齿根和齿顶部分几乎不参与啮合，基于等残高差法的渐开线齿面精加工方法造成了在齿根和齿顶部分的大量冗余走刀，不仅降低了加工效率，而且没能考虑节圆处啮合区域的精度要求。因此，本发明提出的一种考虑齿面精度特性的渐开线圆柱齿轮包络络铣削加工方法，不仅能提高齿轮的包络铣削加工效率，而且使齿面具有更好的啮合性能。
所述实施例为本发明的优选的实施方式，但本发明并不限于上述实施方式，在不背离本发明的实质内容的情况下，本领域技术人员能够做出的任何显而易见的改进、替换或变型均属于本发明的保护范围。

Claims (7)

  1. 一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，包括：
    S01：根据待加工齿轮工件参数，选择刀具，确定刀具直径和刀具切削刃长度；
    S02：采用偏心铣削方式进行加工，确定刀具轴线相对于齿轮轴线的动态偏心量e i；
    S03：根据齿轮的齿面主要啮合区域的精度要求，通过构建齿廓方向走刀步长公式，求解走刀步长沿齿廓方向的最大间距Δl max、两个刀位点的相邻步长间距Δl i以及齿面上各刀位点对应的渐开线展开角度u i，构建渐开线齿廓展开角度与齿面残高差之间的曲线方程Δt i＝f(Δu i)，最终确定加工刀位点；
    S04：根据刀位点规划走刀路径。
  2. 根据权利要求1所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述步骤S01中，对于中小模数渐开线圆柱齿轮选用立铣刀或棒铣刀，对于大模数渐开线圆柱齿轮选用圆锥盘形铣刀或棒铣刀。
  3. 根据权利要求2所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述步骤S01中，刀具直径D t≥φ10mm，刀刃长度L t≥20mm。
  4. 根据权利要求1所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述偏心量e i的计算公式为：
    Figure PCTCN2020073343-appb-100001
    式中，r b为齿轮基圆半径；σ 0为基圆齿槽半角；u i为齿面上各刀位点对应的渐开线展开角度；
    Figure PCTCN2020073343-appb-100002
    为与齿轮固连的回转工作台转动角度，且
    Figure PCTCN2020073343-appb-100003
    D t为刀具直径。
  5. 根据权利要求1所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述S03步骤具体为：
    S03.1将刀具沿齿轮齿廓方向的刀位点等分成n等份，齿面上各刀位点按照抛物线方程分布，设走刀步长沿齿廓方向的最大间距为Δl max，最小间距为Δl min＝Δl max/5，两个刀位点的相邻步长间距为Δl i，刀具沿齿廓方向的走刀步长满足下式：
    Figure PCTCN2020073343-appb-100004
    S03.2根据给定的齿轮工件，得到齿面渐开线沿径向高度为H，由公式(3)可以求解出走刀步长沿齿廓方向的最大间距Δl max：
    Figure PCTCN2020073343-appb-100005
    S03.3将S03.2步骤中求解得到的Δl max代入公式(2)中，遍历走刀数目i∈[0,n]，依次得到齿面上各刀位点对应的的步长间距为Δl i；
    S03.4已知Δl max和当前走刀数目i，由公式(4)，得到抛物线方程上每一个刀位点(x p，y p)对应的齿面上渐开线展开角度u i：
    Figure PCTCN2020073343-appb-100006
    式中，r f为齿根圆半径；r b为基圆半径；σ 0为基圆齿槽半角；
    S03.5假设渐开线上两个相邻的刀位点A和B的坐标分别为(x A,y A)和(x B,y B)，A和B相交于C点，则C点为相邻刀位点之间的最大残高差，假设C点坐标为(x C,y C)，假设渐开线上两个相邻的刀位点A和B的斜率分别为k A和k B，由A、B、C三点的几何关系可得到下式：
    Figure PCTCN2020073343-appb-100007
    由渐开渐的特性可知，渐开线上两个相邻的刀位点A和B的斜率k A和k B分别为：
    Figure PCTCN2020073343-appb-100008
    式中，u A和u B分别为两个相邻的刀位点A和B的渐开线展开角度；
    且两个相邻的刀位点A和B的渐开线方程分别为：
    Figure PCTCN2020073343-appb-100009
    Figure PCTCN2020073343-appb-100010
    将公式(6)(7)(8)代入公式(5)中可以得到C点坐标(x C,y C)，
    计算C点的残高差：
    Figure PCTCN2020073343-appb-100011
    根据公式(9)，可以依次得到相邻刀位点之间的齿面残高差Δt i，由已知的渐开线齿廓展开角度Δu i，构建出渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程为：
    Δt i＝f(Δu i)       式(10)
    S03.6根据渐开线齿廓展开角度Δu i与齿面残高差Δt i之间的曲线方程，确定加工刀位点。
  6. 根据权利要求5所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述步骤S03.6中确定加工刀位点的具体方法为：使刀路轨迹从齿面节圆至上下两端齿廓分别呈现由密到疏的分布，即使靠近节圆附近的主要啮合区域的齿面残高差Δt i最小，距离节圆较远的次要啮合区域的齿面残高差Δt i逐渐增大，且靠近齿根和齿顶部分的非啮合区域齿面残高差Δt i最大。
  7. 根据权利要求1所述的考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法，其特征在于，所述S04步骤具体为：
    刀具从齿顶部分的一侧端面开始，首先沿着齿向方向走第一刀，完成对整个齿宽b的铣削；
    沿着渐开线齿廓向齿槽方向进给Δu i的长度；
    再沿着齿向方向走第2刀；
    依此类推，直至完成对齿个齿面的包络铣削。
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CN110125490B (zh) * 2019-05-17 2020-05-22 淮阴工学院 一种平底锥度铣刀全刀刃侧刃精铣尼曼蜗轮齿面的方法
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CN111687495B (zh) * 2020-05-25 2022-04-22 西安交通大学 一种窄空刀槽人字齿轮阶梯进刀粗切方法
CN114043012A (zh) * 2021-09-15 2022-02-15 南京工业大学 一种铣齿刀盘刀具路径的柔性包络加工方法
CN114309820B (zh) * 2022-01-04 2022-08-02 南京工业大学 一种定制刀具与特定路径结合的齿轮单边成形加工方法

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101069935A (zh) * 2007-06-22 2007-11-14 武汉船用机械有限责任公司 一种大模数齿轮齿廓的范成加工方法
CN106774167A (zh) * 2017-02-07 2017-05-31 陕西理工学院 一种少齿数齿轮数控加工方法
EP3187294A1 (en) * 2015-12-30 2017-07-05 Bomar S.A. w upadlosci ukladowej A method of shaping a gear
CN109128391A (zh) * 2018-11-22 2019-01-04 上海电气集团股份有限公司 一种齿轮加工方法
CN109663991A (zh) * 2019-01-22 2019-04-23 江苏大学 一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10005438A1 (de) * 2000-02-08 2001-08-16 Psw Press Und Schmiedewerk Gmb Verfahren und Vorrichtung zur Herstellung von Kupplungsverzahnungen an Gangrädern für Schaltgetriebe
US7364391B1 (en) * 2005-10-04 2008-04-29 The Gleason Works Manufacturing straight bevel gears
CN101526129B (zh) * 2009-02-27 2011-07-27 南京航空航天大学 螺旋渐开线齿轮及其加工方法
CN101733482B (zh) * 2009-12-22 2012-04-25 沈阳黎明航空发动机(集团)有限责任公司 基于加工精度指标标定的圆弧端齿数控加工方法
CN101961802B (zh) * 2010-09-27 2012-05-23 西安交通大学 多圆柱非等长铣削包络的单螺杆压缩机齿面型线构成方法
CN102385347B (zh) * 2011-11-04 2013-07-10 山东大学 用于异形螺旋曲面加工的智能数控编程***
CN105499712B (zh) * 2016-01-08 2017-07-18 南京工大数控科技有限公司 一种超大模数少齿数圆柱齿轮加工方法
CN110125490B (zh) * 2019-05-17 2020-05-22 淮阴工学院 一种平底锥度铣刀全刀刃侧刃精铣尼曼蜗轮齿面的方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101069935A (zh) * 2007-06-22 2007-11-14 武汉船用机械有限责任公司 一种大模数齿轮齿廓的范成加工方法
EP3187294A1 (en) * 2015-12-30 2017-07-05 Bomar S.A. w upadlosci ukladowej A method of shaping a gear
CN106774167A (zh) * 2017-02-07 2017-05-31 陕西理工学院 一种少齿数齿轮数控加工方法
CN109128391A (zh) * 2018-11-22 2019-01-04 上海电气集团股份有限公司 一种齿轮加工方法
CN109663991A (zh) * 2019-01-22 2019-04-23 江苏大学 一种考虑齿面精度特性的渐开线圆柱齿轮包络铣削加工方法

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113283025A (zh) * 2021-05-11 2021-08-20 北京理工大学 一种包含***误差的渐开线齿廓误差建模方法
CN113283025B (zh) * 2021-05-11 2022-09-06 北京理工大学 一种包含***误差的渐开线齿廓误差建模方法
CN113885432A (zh) * 2021-10-26 2022-01-04 辽宁科技学院 一种用于少轴数控加工面齿轮的刀具路径规划方法
CN113885432B (zh) * 2021-10-26 2023-11-17 辽宁科技学院 一种用于少轴数控加工面齿轮的刀具路径规划方法
CN114770217A (zh) * 2022-05-05 2022-07-22 清华大学 非对称仿生鱼鳞型微结构的加工方法及装置
CN114770217B (zh) * 2022-05-05 2024-01-26 清华大学 非对称仿生鱼鳞型微结构的加工方法及装置
CN115657602A (zh) * 2022-12-03 2023-01-31 广西大学 一种刮齿刀具设计及修形方法
CN115657602B (zh) * 2022-12-03 2024-05-28 广西大学 一种刮齿刀具设计及修形方法

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