WO2016197909A1 - 非完全对称渐开线齿轮及其加工方法 - Google Patents
非完全对称渐开线齿轮及其加工方法 Download PDFInfo
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- WO2016197909A1 WO2016197909A1 PCT/CN2016/085111 CN2016085111W WO2016197909A1 WO 2016197909 A1 WO2016197909 A1 WO 2016197909A1 CN 2016085111 W CN2016085111 W CN 2016085111W WO 2016197909 A1 WO2016197909 A1 WO 2016197909A1
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- involute
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- involute gear
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0806—Involute profile
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/17—Toothed wheels
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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
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23H—WORKING OF METAL BY THE ACTION OF A HIGH CONCENTRATION OF ELECTRIC CURRENT ON A WORKPIECE USING AN ELECTRODE WHICH TAKES THE PLACE OF A TOOL; SUCH WORKING COMBINED WITH OTHER FORMS OF WORKING OF METAL
- B23H9/00—Machining specially adapted for treating particular metal objects or for obtaining special effects or results on metal objects
- B23H9/003—Making screw-threads or gears
Definitions
- the invention relates to the technical field of involute gears, and relates to a non-completely symmetric involute gear and a processing method thereof, and a milling cutter for machining the incompletely symmetric involute gear.
- Gear transmission systems are commonly used for gears that mesh with two gears at the same time, such as intermediate idlers or planetary gears. Since their teeth are subjected to biaxial bending loads, the roots of the gears are most prone to bending and breaking, for example in GB/T 3480. -1997 "Involute Cylindrical Gear Load Capacity Calculation Method" P56 stipulates: For gears that are symmetrically bi-directionally curved (such as intermediate wheels or planetary gears), the bending fatigue limit of the gear should be multiplied by a factor of 0.7 when designing. The bending fatigue limit that such gears can withstand.
- the left and right tooth surfaces of the intermediate idler gear or the planetary gear are respectively meshed with two different gears. Therefore, the bending strengths of the left and right tooth surfaces of the intermediate idler gear or the planetary gear are respectively different, and the tooth surface involute is required for meshing. The starting point is also different.
- the traditional involute gear does not consider the difference between the starting point of the involute of the left and right tooth surfaces.
- the designed tooth profile is completely symmetrical for the left and right tooth faces and the tooth root. See GB/T 1356-2001 "General Machinery and The standard basic rack tooth profile of cylindrical gears for heavy machinery, which reveals that the involute gear has a completely symmetrical tooth profile, therefore, in order to ensure that the starting points of the left and right flank involutes are the same and have sufficient involute length to participate Engagement makes the curvature radius of the left and right tooth root curve small, which further reduces the root bending strength of the intermediate idler or planetary gear.
- a non-fully symmetric involute gear (200, 400), the tooth profile of the face tooth groove comprising an involute segment AB and an arc of the first side tooth profile (210, 410) The segment BC and the involute segment FE and the arc segment DE of the second side tooth profile (230, 430), wherein the point B is the first side of the face tooth groove of the asymmetric involute gear (200, 400)
- the involute starting point of the tooth profile (210, 410) and its involute starting point diameter is r b
- the point E being the second side tooth of the face tooth slot of the asymmetric involute gear (200, 400)
- the involute starting point of the profile (230, 430) and its involute starting point diameter is r e ;
- the involute starting point diameter r b is not equal to the involute starting point diameter r e such that the involute segment AB and the involute segment FE are not completely symmetrical with respect to the axis (III), wherein An axis III is an angle bisector of a central angle corresponding to a face groove width of the incompletely symmetric involute gear (200, 400);
- the arc curvature radius r 1 of the arc segment BC is not equal to the arc curvature radius r 2 of the arc segment DE.
- the involute segment AB, the arc segment BC, the arc segment DE and the involute segment EF are used as the cutting tooth shape of the forming milling cutter, and the tooth milling is formed by using the milling cutter to divide the tooth to be machined by the indexing.
- the incompletely symmetric involute gear (200, 400) is thus produced.
- a third aspect of the present invention there is still further a method of processing the above-described incompletely symmetric involute gear (200, 400), wherein the teeth of the face groove of the incompletely symmetric involute gear (200, 400) are The involute segment AB, the arc segment BC, the arc segment DE and the involute segment EF of the profile are used as the cutting path of the wire cutting, and the indexing of the workpiece to be machined by the indexing line forms a tooth groove, thereby producing the incomplete symmetry Open gear (200,400).
- a milling cutter characterized in that the involute section AB, the arc segment BC, and the circle of the tooth profile of the face tooth groove of the incompletely symmetric involute gear described above are provided.
- the arc segment DE and the involute segment EF serve as the cutting tooth profile of the milling cutter.
- FIG. 1 is a schematic view showing a tooth profile of a face of a non-completely symmetric involute gear engaged with a first involute gear and a second involute gear, in accordance with an embodiment of the present invention.
- FIG. 2 is a schematic view showing the shape of two teeth of a non-completely symmetric involute gear according to an embodiment of the present invention.
- FIG. 3 is a schematic view showing a tooth profile of a face tooth groove of a non-completely symmetric involute gear according to an embodiment of the present invention.
- FIG. 4 is a schematic view showing a tooth profile of a face tooth groove of a non-completely symmetric involute gear according to still another embodiment of the present invention.
- incompletely symmetric means that one of the two objects is symmetrically disposed about a portion of the other object, and another portion of the other component is asymmetrically disposed about another portion of the other object.
- the tooth profile of the face tooth groove of the incompletely symmetric involute gear 200/400 includes an involute segment AB, a circular arc segment BC and a straight segment CD, a circular arc segment DE, and an involute segment EF.
- the involute segment AB and the arc segment BC can be used to form the left tooth profile 210/410
- the arc segment DE and the involute segment EF can be used to form the right tooth profile 230/430.
- the straight line segment CD is tangent to the arc segment BC and the arc segment DE, respectively, to points C and D.
- the involute segment AB and the involute segment EF are not completely symmetrical with respect to the axis III, wherein the axis III is the face cogging width M of the incompletely symmetric involute gear 200/400.
- point A and point F are the tooth vertices of the left and right tooth faces of the face groove of the incompletely symmetric involute gear 200/400, respectively;
- point B is the incompletely symmetric involute
- the involute starting point of the left side tooth profile 210/410 of the face tooth groove of the gear 200/400, r b is the gradual change of the left side tooth profile 210/410 of the face tooth groove of the incompletely symmetric involute gear 200/400
- the point E is the involute starting point of the right side tooth profile 230/430 of the face tooth groove of the incompletely symmetric involute gear 200/400, and
- r e is the incompletely symmetric involute gear 200/
- the straight line segment CD is perpendicular to the axis III and is tangent to the root circle
- the arc segment BC is tangent to the straight line segment CD and the straight line I
- the arc segment DE is simultaneously tangent to the straight line segment CD and the straight line II
- the straight line I is a tangent that passes through point B and is tangent to the involute segment AB
- the straight line II is a tangent that passes through the point E and is tangent to the involute segment EF.
- the y-axis is established along the axis III, and the x-axis is established with a line perpendicular to the y-axis and tangential to the root circle.
- the coordinates of the defined point B are (-x b , y b )
- the coordinates of the defined point E are (x e , y e )
- the radius of curvature of the arc of the arc segment BC is r 1
- the circle of the arc segment DE The radius of curvature of the arc is r 2 and r 1 ⁇ r 2 .
- r 2 > r 1 in the embodiment shown in Fig. 4, r 2 < r 1 .
- the radius of the arc of curvature of the arc segment BC relationship arc radius r 1 of curvature of the arc segment DE and r 2 is:
- the involute segment AB of the left tooth profile 210 is longer than the involute segment EF of the right tooth profile 230, and the involute segment AB is composed of the involute segment AE' and the involute segment E'B, and the involute segment AE' It is completely symmetrical with respect to the involute segment EF with respect to the axis III, wherein the point E' is the boundary point of the circumference of the involute segment AB corresponding to the diameter r e .
- the radius of curvature of the arc of the arc segment BC r 1 and the arc is:
- the involute segment AB of the left tooth profile 410 is shorter than the involute segment EF of the right tooth profile 430, and the involute segment EF is composed of the involute segment EB' and the involute segment B'F, and the involute segment B' F and the involute segment AB are completely symmetrical about the axis III, wherein the point B' is the boundary point of the circumference of the involute segment EF corresponding to the diameter r b .
- the involute segment AB of the left side tooth profile 210 of the face groove of the incompletely symmetric involute gear 200/400 is a non-completely symmetric involute gear.
- the involute section of the 200/400 end face tooth shape meshing with the end face tooth profile of the first involute gear 100, the involute section EF of the right side tooth profile of the face groove of the incompletely symmetric involute gear 200 is incomplete
- the involute starting point of the left and right tooth surfaces and the curvature radius of the left and right tooth root arcs are different, so the left and right teeth of the entire tooth of the incompletely symmetric involute gear
- the starting point of the involute and the radius of curvature of the left and right root arcs are different.
- the designer can design different curvature curves of the left and right root curves according to the position of the starting point of the involute of the left and right tooth surfaces, so that the left and right sides of the tooth obtain different roots.
- the bending strength ensures that the gear of the present invention can better adapt to the effect of the biaxial bending load, thereby improving the reliability of the gear.
- the invention is particularly applicable to intermediate idlers or planet gears in which the teeth are subjected to a bi-directional bending load.
- ⁇ 1 represents the central angle of the groove width on the circumference corresponding to the diameter r b , which is calculated by the following formulas (1-3) to (1-7):
- m and ⁇ respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400
- a 1 represents the first involute gear 100 of the incompletely symmetric involute gear 200/400 meshing therewith
- the center distance, r a1 represents the tip circle diameter of the first involute gear 100
- z 1 represents the number of teeth of the first involute gear 100.
- r e is the involute starting point diameter of the right side tooth profile 230/430 of the face tooth groove of the asymmetric involute gear 200/400
- r f is the root circle of the asymmetric involute gear 200/400
- ⁇ 2 represents the central angle of the groove width on the circumference corresponding to the diameter r e , which is calculated by the following formulas (2-3) to (2-7):
- m and ⁇ respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400
- a 2 represents the second involute gear 300 of the incompletely symmetric involute gear 200/400 meshing therewith.
- the center distance, r a2 represents the tip circle diameter of the second involute gear 300
- z 2 represents the number of teeth of the second involute gear 300.
- r 1 represents the radius of curvature of the arc segment BC, which is calculated by the following formula and equation:
- ⁇ 1 represents the central angle of the tooth groove width on the circumference corresponding to the diameter r b , which can be calculated by the above formula (1-3), and x b and y b respectively represent the x coordinate and the y coordinate of the point B, It can be calculated by the above formula (1-1), ⁇ b is calculated by the above formula (1-4), and s 1 is the maximum value of the solution of equation (3-3).
- r 2 represents the radius of curvature of the arc segment DE, which is calculated by the following formula and equation:
- ⁇ 2 represents the central angle of the cogging width on the circumference corresponding to the diameter r e , which can be calculated by the above formula (2-3), and x e and y e respectively represent the x coordinate and y of the E point.
- the coordinates can be calculated by the above formula (2-1), ⁇ e is calculated by the above formula (2-4), and s 2 is the minimum value of the solution of equation (4-3).
- m and ⁇ respectively represent the end face modulus and the end face pressure angle of the incompletely symmetric involute gear 200/400; z, z 1 , and z 2 are respectively represented as the incomplete symmetry.
- the top circle diameter; a 1 , a 2 respectively represent the center distance of the incompletely symmetric involute gear 200/400 and the first involute gear 100 and the incompletely symmetric involute gear 200/400 and the second involute
- the center distance of the line gear 300; r b , r e , r f respectively represent the starting point radius of the left flank involute of the face tooth profile of the incompletely symmetric involute gear 200/400, and the face tooth
- the present invention also provides a method of processing a non-completely symmetric involute gear as shown in Figures 3 and 4.
- the involute segment AB, the arc segment BC, the straight segment CD, the arc segment DE, and the involute segment EF of the face tooth profile of the incompletely symmetric involute gear 200/400 are used as forming milling
- the cutting tooth profile of the tooth cutter is formed by pitching the tooth to be machined to form a tooth groove, and a non-completely symmetric involute gear 200/400 is obtained. This processing method is highly efficient and is very suitable for mass production.
- the involute segment AB, the arc segment BC, the straight segment CD, the arc segment DE, and the involute segment EF of the face tooth tooth profile of the incompletely symmetric involute gear 200/400 are taken as a line
- the cutting path of the cutting, the indexing of the workpiece to be machined to form a tooth groove, and a non-completely symmetric involute gear 200/400 is obtained.
- special tools are not required, but the efficiency is low, suitable for single or small batch production. This eliminates the need for special tools, but is relatively inefficient and suitable for single or small batch production.
- a coordinate system is established, with the axis of symmetry of the cogging being the y-axis, and the line perpendicular to the y-axis and tangential to the root circle being the x-axis.
- the coordinates of the point B (-x b , y b ), the coordinates of the point E (x e , y e ), and the curve equation of the arc segment BC and the arc segment DE are determined as follows.
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Abstract
一种非完全对称渐开线齿轮及其加工方法和加工刀具,该非完全对称渐开线齿轮端面齿槽的齿廓包括第一侧齿廓的渐开线段AB和圆弧段BC以及第二侧齿廓的渐开线段FE和圆弧段DE,其中点B为非对称渐开线齿轮的端面齿槽的第一侧齿廓的渐开线起始点并且其渐开线起始点直径为rb,点E为非对称渐开线齿轮的端面齿槽的第二侧齿廓的渐开线起始点并且其渐开线起始点直径为re,rb≠re,使得渐开线段AB与渐开线段FE关于轴线Ⅲ非完全对称,该非完全对称渐开线齿轮的齿牙两侧可以获得不同的齿根弯曲强度。
Description
本发明涉及渐开线齿轮技术领域,涉及非完全对称渐开线齿轮及其加工方法、以及用于加工该非完全对称渐开线齿轮的铣齿刀具。
齿轮传动***常用到同时与两个齿轮啮合的齿轮,例如中间惰轮或行星轮,由于它们的齿牙受双向弯曲载荷作用,该齿轮的齿根最容易出现弯曲折断,例如在GB/T 3480-1997《渐开线圆柱齿轮承载能力计算方法》P56中规定:对于受对称双向弯曲的齿轮(如中间轮或行星轮),在设计时,应将齿轮的弯曲疲劳极限值乘上系数0.7作为这类齿轮所能承受的弯曲疲劳极限。
另外,中间惰轮或行星轮的左右齿面分别与两个不同的齿轮啮合,因此,中间惰轮或行星轮的齿牙左右齿面分别承受的弯曲强度不同,啮合所需齿面渐开线的起始点也不同。
然而,传统的渐开线齿轮不考虑左、右齿面渐开线起始点的差异,设计的齿形为左、右齿面及齿根完全对称,参见GB/T 1356-2001《通用机械和重型机械用圆柱齿轮标准基本齿条齿廓》,其揭示的渐开线齿轮具有完全对称齿廓,因此,为了保证左、右齿面渐开线起始点相同且具有足够的渐开线长度参与啮合,使得左右齿廓齿根曲线曲率半径均很小,这进一步降低了中间惰轮或行星轮的齿根弯曲强度。
发明内容
按照本发明的第一方面,提供一种非完全对称渐开线齿轮(200,400),其端面齿槽的齿廓包括第一侧齿廓(210,410)的渐开线段AB和圆弧段BC以及第二侧齿廓(230,430)的渐开线段FE和圆弧段DE,其中,点B为所述非对称渐开线齿轮(200,400)的端面齿槽的第一侧齿廓(210,410)的渐开线起始点并且其渐开线起始点直径为rb,点E为所述非对称渐开线齿轮(200,400)的端面齿槽的第二侧齿廓(230,430)的渐开线起始点并且其渐开线起始点直径为re;
其中,所述渐开线起始点直径rb不等于渐开线起始点直径re,使
得所述渐开线段AB与所述渐开线段FE关于轴线(Ⅲ)非完全对称,其中,所述轴线Ⅲ为所述非完全对称渐开线齿轮(200,400)的端面齿槽宽所对应的圆心角的角平分线;
并且,圆弧段BC的圆弧曲率半径r1不等于圆弧段DE的圆弧曲率半径r2。
按照本发明的第二方面,提供一种上述非完全对称渐开线齿轮(200,400)的加工方法,其中,将所述非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为成形铣齿刀具的切削齿形,并使用该铣齿刀具、采用分度逐齿铣削待加工件形成齿槽,从而制得所述非完全对称渐开线齿轮(200,400)。
按照本发明的第三方面,提供又一种上述非完全对称渐开线齿轮(200,400)的加工方法,其中,将所述非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为线切割的切割路径,分度逐齿线切割待加工件形成齿槽,从而制得所述非完全对称渐开线齿轮(200,400)。
按照本发明的第四方面,提供一种铣齿刀具,其特征在于,将以上所述的非完全对称渐开线齿轮的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为该铣齿刀具的切削齿形。
根据以下描述和附图本发明的以上特征和操作将变得更加显而易见。
从结合附图的以下详细说明中,将会使本发明的上述和其他目的及优点更加完整清楚,其中,相同或相似的要素采用相同的标号表示。
图1是按照本发明一实施例的非完全对称渐开线齿轮与第一渐开线齿轮和第二渐开线齿轮啮合的端面齿形示意图。
图2是本发明一实施例的非完全对称渐开线齿轮的其中两个齿牙形状示意图。
图3是本发明一实施例的非完全对称渐开线齿轮的端面齿槽的齿廓型线示意图。
图4是本发明又一实施例的非完全对称渐开线齿轮的端面齿槽的齿廓型线示意图。
下面介绍的是本发明的多个可能实施例中的一些,旨在提供对本发明的基本了解,并不旨在确认本发明的关键或决定性的要素或限定所要保护的范围。容易理解,根据本发明的技术方案,在不变更本发明的实质精神下,本领域的一般技术人员可以提出可相互替换的其他实现方式。因此,以下具体实施方式以及附图仅是对本发明的技术方案的示例性说明,而不应当视为本发明的全部或者视为对本发明技术方案的限定或限制。
在描述中,使用方向性术语(例如“左”、“右”等)以及类似术语描述的各种实施方式的部件表示附图中示出的方向或者能被本领域技术人员理解的方向。这些方向性术语用于相对的描述和澄清,而不是要将任何实施例的定向限定到具体的方向或定向,其可以随着滚刀或齿轮的所放置的方位的变化而相应地发生变化,例如,非完全对称渐开线齿轮的齿牙按附图中方位定义“左侧”和“右侧”,在非完全对称渐开线齿轮沿轴向掉头后,原来的齿牙的“左侧”将对应新的方位的齿牙的“右侧”,原来的齿牙的“右侧”将对应新的方位的齿牙的“左侧”。
在本文中,“非完全对称”是指两个对象中其中一个对象的一部分是关于另一对象的一部分是对称设置的、一个对象的另一部分是关于另一对象的另一部分是不对称设置的。
如图1至图4所示,非完全对称渐开线齿轮200/400的端面齿槽的齿廓包括渐开线段AB、圆弧段BC和直线段CD、圆弧段DE和渐开线段EF,其中,渐开线段AB和圆弧段BC可以用来形成左侧齿廓210/410,圆弧段DE和渐开线段EF可以用来形成右侧齿廓230/430。直线段CD与圆弧段BC和圆弧段DE分别相切于C点和D点。
从图3和图4中可以看到,渐开线段AB和渐开线段EF相对于轴线Ⅲ非完全对称,其中,轴线Ⅲ为非完全对称渐开线齿轮200/400的端面齿槽宽M⌒N所对应的圆心角的角平分线;点A和点F分别是非完全对称渐开线齿轮200/400的端面齿槽的左、右齿面的齿顶点;点B为非完全对称渐开线齿轮200/400的端面齿槽的左侧齿廓210/410的渐开线
起始点,rb为非完全对称渐开线齿轮200/400的端面齿槽的左侧齿廓210/410的渐开线起始点直径;点E为非完全对称渐开线齿轮200/400的端面齿槽的右侧齿廓230/430的渐开线起始点,re为非完全对称渐开线齿轮200/400的端面齿槽的右侧齿廓230/430的渐开线起始点直径。
其中,直线段CD与轴线Ⅲ垂直且与齿根圆相切,圆弧段BC同时与直线段CD和直线Ⅰ相切,圆弧段DE同时与直线段CD和直线Ⅱ相切,其中,直线Ⅰ是过点B且与渐开线段AB相切的切线,直线Ⅱ是过点E且与渐开线段EF相切的切线。
为方便说明齿廓中各点的坐标位置关系,如图3和图4所示,沿轴线Ⅲ建立y轴,以垂直于y轴且与齿根圆相切的直线建立x轴。进一步,定义点B的坐标为(-xb,yb),定义点E的坐标为(xe,ye),圆弧段BC的圆弧曲率半径为r1,圆弧段DE的圆弧曲率半径r2,且r1≠r2。其中,在图3所示实施例中,r2>r1,在图4所示实施例中,r2<r1。
如图3所示,当yb<ye时,此时,rb<re,圆弧段BC的圆弧曲率半径r1与圆弧段DE的圆弧曲率半径r2的关系为:并且,左侧齿廓210的渐开线段AB相对右侧齿廓230的渐开线段EF较长,渐开线段AB由渐开线段AE'和渐开线段E'B组成,渐开线段AE'与渐开线段EF关于轴线Ⅲ完全对称,其中点E'是渐开线段AB与直径re对应的圆周的交界点。
当yb>ye时(如图4所示实施例的非完全对称渐开线齿轮400中),此时,rb>re,圆弧段BC的圆弧曲率半径r1与圆弧段DE的圆弧曲率半径r2的关系为:并且,左侧齿廓410的渐开线段AB相对右侧齿廓430的渐开线段EF较短,渐开线段EF由渐开线段EB'和渐开线段B'F组成,渐开线段B'F和渐开线段AB关于轴线Ⅲ完全对称,其中,点B'是渐开线段EF与直径rb对应的圆周的交界点。
继续如图1、图3和图4所示,非完全对称渐开线齿轮200/400的端面齿槽的左侧齿廓210的渐开线段AB为非完全对称渐开线齿轮
200/400的端面齿形与第一渐开线齿轮100的端面齿形相啮合的渐开线段,非完全对称渐开线齿轮200的端面齿槽的右侧齿廓的渐开线段EF为非完全对称渐开线齿轮200/400的端面齿形与第二渐开线齿轮300的端面齿形相啮合的渐开线段。因此,本发明实施例的非完全对称渐开线齿轮200/400的左右齿面分别啮合两个不同的齿轮,其具体可以用作为中间惰轮或行星轮等。
本发明的非完全对称渐开线齿轮的端面齿槽齿形左右齿面渐开线起始点和左右齿根圆弧曲率半径不同,因此所述非完全对称渐开线齿轮整个齿牙的左右齿面渐开线起始点和左右齿根圆弧曲率半径不同,设计者可根据左右齿面渐开线起始点的位置设计不同的左右齿根曲线曲率半径,使齿牙左右侧获得不同的齿根弯曲强度,确保本发明的齿轮能够更好地适应双向弯曲载荷的作用,从而提高齿轮的可靠性。本发明特别适用于齿牙受双向弯曲载荷作用的中间惰轮或行星轮。
以下进一步说明本发明实施例的非完全对称渐开线齿轮200/400的端面齿槽的齿廓的具体示例形状。
(1)点B的坐标(-xb,yb)满足如下公式(1-1)和(1-2):
其中,rb为非对称渐开线齿轮200/400的端面齿槽的左侧齿廓210的渐开线起始点直径,rf为非对称渐开线齿轮200/400的齿根圆半径,β1表示直径rb对应的圆周上的齿槽宽所对圆心角,其通过以下公式(1-3)至(1-7)计算:
其中,m、α分别表示非完全对称渐开线齿轮200/400的端面模数和端面压力角,a1表示非完全对称渐开线齿轮200/400与其啮合的第一渐开线齿轮100的中心距,ra1表示第一渐开线齿轮100齿顶圆直径,z1表示第一渐开线齿轮100的齿数。
(2)点E的坐标(xe,ye)满足如下公式(2-1)和(2-2):
其中,re为非对称渐开线齿轮200/400的端面齿槽的右侧齿廓230/430的渐开线起始点直径,rf为非对称渐开线齿轮200/400的齿根圆半径,β2表示直径re对应的圆周上的齿槽宽所对圆心角,其通过以下公式(2-3)至(2-7)计算:
其中,m、α分别表示非完全对称渐开线齿轮200/400的端面模数和端面压力角,a2表示非完全对称渐开线齿轮200/400与其啮合的第二渐开线齿轮300的中心距,ra2表示第二渐开线齿轮300齿顶圆直径,z2表示第二渐开线齿轮300的齿数。
(3)圆弧段BC的曲线坐标(x,y)通过以下方程式(3-1)确定:
其中,r1表示圆弧段BC的曲率半径,其通过以下公式和方程式计
算得到:
其中,β1表示直径rb对应的圆周上的齿槽宽所对圆心角,其可以通过以上公式(1-3)计算得到,xb、yb分别表示点B的x坐标和y坐标,可以通过以上公式(1-1)计算得到,αb通过以上公式(1-4)计算得到,s1取方程式(3-3)的求解最大值。
(4)圆弧段DE的曲线坐标(x,y)通过以下方程式(4-1)确定:
其中,r2表示圆弧段DE的曲率半径,其通过以下公式和方程式计算得到:
其中,其中,β2表示直径re对应的圆周上的齿槽宽所对圆心角,其可以通过以上公式(2-3)计算得到,xe、ye分别表示E点的x坐标和y坐标,可以通过以上公式(2-1)计算得到,αe通过以上公式(2-4)计算得到,s2取方程式(4-3)的求解最小值。
具体地,上述公式、方程式中,m、α分别表示所述非完全对称渐开线齿轮200/400的端面模数和端面压力角;z、z1、z2分别表示为所述非完全对称渐开线齿轮200/400、第一渐开线齿轮100和第二渐开线齿轮300的齿数;ra1、ra2分别表示第一渐开线齿轮100和第二渐开线齿轮300的齿顶圆直径;a1、a2分别表示所述非完全对称渐开线齿轮200/400与第一渐开线齿轮100的中心距和非完全对称渐开线齿轮200/400与第二渐开线齿轮300的中心距;rb、re、rf分别表示所述非完全对称渐开线齿轮200/400的端面齿槽齿形的左齿面渐开线起始点
半径、端面齿槽齿形的右齿面渐开线起始点半径和齿根圆半径;r1、r2分别表示圆弧段BC和圆弧段DE的曲率半径。
进一步地,非完全对称渐开线齿轮200/400的渐开线段AB和渐开线段EF上的点坐标方程可由机械工业出版社1977年出版的《磨齿工作原理》中的公式1-27确定。
本发明还提供如图3和图4所示的非完全对称渐开线齿轮的加工方法。
在一实施例中,将非完全对称渐开线齿轮200/400的端面齿槽齿形的渐开线段AB、圆弧段BC、直线段CD、圆弧段DE和渐开线段EF作为成形铣齿刀具的切削齿形,采用分度逐齿铣削待加工件形成齿槽,制得非完全对称渐开线齿轮200/400。这种加工方法生产效率很高,非常适合大批量生产。
在又一实施例中,将非完全对称渐开线齿轮200/400的端面齿槽齿形的渐开线段AB、圆弧段BC、直线段CD、圆弧段DE和渐开线段EF作为线切割的切割路径,分度逐齿线切割待加工件形成齿槽,制得非完全对称渐开线齿轮200/400。这样,就不需要采用专门刀具,但效率偏低,适合单件或小批量生产。这样,不需要采用专门刀具,但是,效率相对较低,适合单件或小批量生产。
以下具体示例说明的非完全对称渐开线齿轮400的端面齿槽的齿廓AB、BC、CD、DE、EF的设计确定过程。
非完全对称渐开线齿轮400及相啮合的第一渐开线齿轮100和第二渐开线齿轮300,它们的主要参数值为:m=7、α=20°、z=26、z1=17、z2=89、ra1=69.37、ra2=314.37、a1=157、a2=402,rf=85.88。
第一步,建立坐标系,以齿槽的对称轴线为y轴,垂直于y轴且与齿根圆相切的直线为x轴。
第二步,按如下过程确定点B的坐标(-xb,yb)、点E的坐标(xe,ye)及圆弧段BC和圆弧段DE的曲线方程。
(一)点B的坐标(-xb,yb)按以上公式(1-1)至(1-6)计算,将相应的参数值分别代入公式(1-1)至(1-6)计算得出:
因此,得到点B的坐标(-xb,yb)为(-4.977,3.692)。
(二)点E的坐标(-xb,yb)按以上公式(2-1)至(2-6)计算,将相应的参数值分别代入公式(2-1)至(2-6)计算得出:
因此,计算得到点E的坐标(xe,ye)为(4.464,2.187)。
(三)圆弧段BC的曲线方程按方程式(3-1)确定,按以上公式(3-3)、公式(3-4)和方程式(3-3)计算:
s1取上述方程的求解最大值为7.525;
从而,确定圆弧段BC的曲线方程(x-7.525)2+(y-2.725)2=7.425。
(四)圆弧段DE的曲线方程按方程式(4-1)确定,按以上公式(4-3)、公式(4-4)和方程式(4-3)计算:
其中,s2取上述方程的求解最小值为4.137;
从而,确定圆弧段DE的曲线方程:(x-4.137)2+(y-1.121)2=1.254
(五)计算得到:
此时,圆弧段BC的圆弧曲率半径r1是圆弧段DE的圆弧曲率半径r2的2.43倍,因此,该非完全对称渐开线齿轮的齿牙左右侧具有不同的齿根弯曲强度,且圆弧段BC所在一侧所在的齿牙侧具有更高的齿根弯曲强度。
以上例子主要说明了本发明的非完全对称渐开线齿轮及其加工方法。尽管只对其中一些本发明的实施方式进行了描述,但是本领域普通技术人员应当了解,本发明可以在不偏离其主旨与范围内以许多其他的形式实施。因此,所展示的例子与实施方式被视为示意性的而非限制性的,在不脱离如所附各权利要求所定义的本发明精神及范围的情况下,本发明可能涵盖各种的修改与替换。
Claims (13)
- 一种非完全对称渐开线齿轮(200,400),其端面齿槽的齿廓包括第一侧齿廓(210,410)的渐开线段AB和圆弧段BC以及第二侧齿廓(230,430)的渐开线段FE和圆弧段DE,其中,点B为所述非对称渐开线齿轮(200,400)的端面齿槽的第一侧齿廓(210,410)的渐开线起始点并且其渐开线起始点直径为rb,点E为所述非对称渐开线齿轮(200,400)的端面齿槽的第二侧齿廓(230,430)的渐开线起始点并且其渐开线起始点直径为re;其特征在于,所述渐开线起始点直径rb不等于渐开线起始点直径re,使得所述渐开线段AB与所述渐开线段FE关于轴线(Ⅲ)非完全对称,其中,所述轴线Ⅲ为所述非完全对称渐开线齿轮(200,400)的端面齿槽宽所对应的圆心角的角平分线;并且,圆弧段BC的圆弧曲率半径r1不等于圆弧段DE的圆弧曲率半径r2。
- 如权利要求1所述的非完全对称渐开线齿轮(200,400),其特征在于,所述非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓还包括直线段CD,所述直线段CD通过C点与所述圆弧段BC相切地连接,所述直线段CD通过D点与所述圆弧段DE相切地连接,所述直线段CD与所述轴线Ⅲ垂直且与齿根圆相切。
- 如权利要求1或4所述的非完全对称渐开线齿轮(200,400),其特征在于,所述圆弧段BC与通过点B直线Ⅰ相切,所述圆弧段DE与通过点E与直线Ⅱ相切,所述直线Ⅰ是过点B且与所述渐开线段AB相切的切线,所述直线Ⅱ是过点E且与所述渐开线段EF相切的切线。
- 如权利要求1或4所述的非完全对称渐开线齿轮(200,400),其特征在于,所述点A是所述第一侧齿廓(210,410)的齿顶点,所述点F是第二侧齿廓(230,430)的齿顶点。
- 如权利要求1所述的非完全对称渐开线齿轮(200,400),其特征在于,所述非完全对称渐开线齿轮(200,400)为用于双向啮合的中间惰轮或行星轮。
- 如权利要求2或3所述的非完全对称渐开线齿轮(200,400),其特征在于,所述非完全对称渐开线齿轮(200,400)的端面齿槽的渐开线段AB和渐开线段FE分别与第一渐开线齿轮(100)和第一渐开线齿轮(300)的齿面相啮合。
- 如权利要求8所述的非完全对称渐开线齿轮(200,400),其特征在于,所述点B的坐标(-xb,yb)满足以下公式(1-1)和(1-2):其中,rf为非对称渐开线齿轮(200,400)的齿根圆半径,β1表示 渐开线起始点直径rb对应的圆周上的齿槽宽所对圆心角,其通过以下公式(1-3)至(1-7)计算:其中,m、α分别表示所述非完全对称渐开线齿轮(200,400)的端面模数和端面压力角,a1表示所述非完全对称渐开线齿轮(200,400)与其啮合的所述第一渐开线齿轮(100)的中心距,ra1表示所述第一渐开线齿轮(100)齿顶圆直径,z1表示所述第一渐开线齿轮(100)的齿数;所述点E的坐标(xe,ye)满足如下公式(2-1)和(2-2):其中,β2表示渐开线起始点直径re对应的圆周上的齿槽宽所对圆心角,其通过以下公式(2-3)至(2-7)计算:其中,a2表示所述非完全对称渐开线齿轮(200,400)与其啮合的第二渐开线齿轮(300)的中心距,ra2表示第二渐开线齿轮(300)齿顶圆直径,z2表示第二渐开线齿轮(300)的齿数。
- 一种如权利要求1至10中任一项所述的非完全对称渐开线齿轮(200,400)的加工方法,其特征在于,将所述非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为成形铣齿刀具的切削齿形,并使用该铣齿刀具、采用分度逐齿铣削待加工件形成齿槽,从而制得所述非完全对称渐开线齿轮(200,400)。
- 一种如权利要求1至10中任一项所述的非完全对称渐开线齿轮(200,400)的加工方法,其特征在于:将所述非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为线切割的切割路径,分度逐齿线切割待加工件形成齿槽,从而制得所述非完全对称渐开线齿轮(200,400)。
- 一种铣齿刀具,其特征在于,将如权利要求1至10中任一项所述的非完全对称渐开线齿轮(200,400)的端面齿槽的齿廓的渐开线段AB、圆弧段BC、圆弧段DE和渐开线段EF作为该铣齿刀具的切削齿形。
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CN110645319B (zh) * | 2019-09-24 | 2023-01-24 | 武汉理工大学 | 一种多齿廓啮合圆柱齿轮传动 |
CN112059082B (zh) * | 2020-09-11 | 2022-08-09 | 汉德车桥(株洲)齿轮有限公司 | 渐开线花键键齿修形设计方法和加工方法及其齿轮产品 |
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