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Machinerys Handbook 28th Edition INVOLUTE SPLINES Page 40 of 40翻译：朱晓峰 节选至美国机械工程师手册第28版，有错之处，请指正。SPLINES AND SERRATIONSA splined shaft is one having a series of parallel keys formed integrally with the shaft and mating with corresponding grooves cut in a hub or fitting; this arrangement is in contrast to a shaft having a series of keys or feathers fitted into slots cut into the shaft. The latter construction weakens the shaft to a considerable degree because of the slots cut into it and consequently, reduces its torque-transmitting capacity.花键轴是一种具有“一系列相互平行的齿、并且齿与轴整体成型”的轴，它与在轮毂上或者装配体上开的键槽相配合。这种装置与“在轴上开槽并且与一组销子或者楔键相配合”的结构相反。后者的结构由于在轴上开槽大大降低了轴（的强度），降低了传递扭矩的能力。Splined shafts are most generally used in three types of applications: 1 ) for coupling shafts when relatively heavy torques are to be transmitted without slippage; 2) for transmitting power to slidably-mounted or permanently-fixed gears, pulleys, and other rotating members; and 3) for attaching parts that may require removal for indexing or change in angular position.花键轴主要用在以下三种情况：1）需要在无滑动的联轴器上传递大的扭矩；2）用于向“可滑动的装配组件”或者“固定装配的齿轮组或滑轮副”传递动力，3）用于“要求指定滑移量或转角位置”的配件上。译注A1：“slidably-mounted”例如球笼式等速万向节，万向节同时能转动一定角度；“ermanently-fixed gears”例如齿轮变速箱。（凡是带“译注”的，表示译者的理解，下同）Splines having straight-sided teeth have been used in many applications (see SAE Parallel Side Splines for Soft Broached Holes in Fittings); however, the use of splines with teeth of involute profile has steadily increased since 1) involute spline couplings have greater torque-transmitting capacity than any other type; 2) they can be produced by the same techniques and equipment as is used to cut gears; and 3) they have a self-centering action under load even when there is backlash between mating members.具有“直边式齿形”的花键已经适用于多种场合（请查看“用于软拉削加工成型的直边式花键”）；然而，“齿侧具有渐开线形状的花键”的使用正在逐步的增长，原因如下：1）渐开线花键传递扭矩的性能超过其他形式；2）可用加工齿轮的技术或设备来加工；3）在内齿和外齿配合情况下产生的反作用力具有自定心功能。译注A2：“Parallel Side Splines”指的是矩形花键，文中翻译成“直边式花键”，见GB/T 1144 矩形花键尺寸、公差和检验；译注A3：“SAE Parallel Side Splines for Soft Broached Holes in Fittings”指SAE J499A，一种类似GB/T 1144的标准。Involute SplinesAmerican National Standard Involute Splines*. These splines or multiple keys are similar in form to internal and external involute gears. The general practice is to form the external splines either by hobbing, rolling, or on a gear shaper, and internal splines either by broaching or on a gear shaper. The internal spline is held to basic dimensions and the external spline is varied to control the fit. Involute splines have maximum strength at the base, can be accurately spaced and are self-centering, thus equalizing the bearing and stresses, and they can be measured and fitted accurately.美国渐开线标准：这种花键的成型和齿轮的内外花键类似。通常的成型加工方法是外花键用滚铣刀、搓齿或插齿刀，内花键用拉削、齿轮插齿刀。内花键的尺寸是固定的，外花键根据不同的配合采用不同的尺寸。渐开线花键在近跟处有最大的强度，（键齿）能精确分布和自定心，这样就有相同的支撑力和应力，同时能准确地配合和测量。译注A4：内花键尺寸不变，外花键变，原理等同于基孔制。 In American National Standard ANSI B92.1-1970 (R 1993), many features of the 1960 standard are retained; plus the addition of three tolerance classes, for a total of four. The term “involute serration,” formerly applied to involute splines with 45-degree pressure angle, has been deleted and the standard now includes involute splines with 30-, 37.5-, and 45-degree pressure angles. Tables for these splines have been rearranged accordingly. The term “serration” will no longer apply to splines covered by this Standard.在美国渐开线标准ANSI B92.1-1970 (R 1993)中，保留了许多1960版本的特征；增加了三种公差等级，现一共有四种公差等级。前版中45度压力角使用的术语“渐开线锯齿involute serration”，本版本已经删除。现在版本包含了30度、37.5度和40度压力角的渐开线花键。相对应的表格也做了更新。术语“involute serration”不再适用本标准。The Standard has only one fit class for all side fit splines; the former Class 2 fit. Class 1 fit has been deleted because of its infrequent use. The major diameter of the flat root side fit spline has been changed and a tolerance applied to include the range of the 1950 and the 1960 standards. The interchangeability limitations with splines made to previous standards are given later in the section entitled “Interchangeability.”本标准中只有一种齿侧配合情况:第二种情况。在旧标准中的第一种情况由于不太使用已经被删除。平齿根齿侧配合中的大径已经有所变化，并且应用了包含1950和1960版本范围的公差。旧版本的花键术语“interchangeability limitations”已经被新版本的“Interchangeability”代替。译注A5：旧版中的配合第一种情况是“较松配合”，第二种情况是“较紧配合”。参数是Cvmin，较松配合的Cvmin的值见旧版，这里不讨论，较紧配合的Cvmin=0。原来“最大实际弧齿槽宽”的计算公式为：Smax=Smin+Cvmin+m+（具体参数意思看后面章节），删除第一种情况后Smax=Smin+m+。There have been no tolerance nor fit changes to the major diameter fit section外径配合部分，（与旧版相比）公差和配合情况没有改变。The Standard recognizes the fact that proper assembly between mating splines is dependent only on the spline being within effective specifications from the tip of the tooth to the form diameter. Therefore, on side fit splines, the internal spline major diameter now is shown as a maximum dimension and the external spline minor diameter is shown as a minimum dimension. The minimum internal major diameter and the maximum external minor diameter must clear the specified form diameter and thus do not need any additional control.本标准认为影响花键合理装配的作用区域是从齿顶（外花键大圆或内花键小圆）到“渐开线构成圆”之间的那段范围，因此在齿侧配合情况下，内花键大径以“最大尺寸值”出现，外花键小径以“最小尺寸值”出现。“内花键大径的最小值”应大于“渐开线构成圆”的直径，“外花键小径的最大值”应小于“渐开线构成圆”的直径（见后面“Form Circle”的定义）。此外，没必要指定额外的控制条件（见“译注B7”）。The spline specification tables now include a greater number of tolerance level selections. These tolerance classes were added for greater selection to suit end product needs. The selections differ only in the tolerance as applied to space width and tooth thickness.花键的规格表中，提供了多种公差水平的选择，以适应最终装配需求。选择不同的公差在“弧齿槽宽”和“弧齿厚”中应用。* See American National Standard ANSI B92.2M-1980 (R1989), Metric Module Involute Splines; also see page 2177.见美国国家标准ANSI B92.2M-1980 (R1989) 公制模数渐开线花键，可也参见（原版的）第2177页。译注A6：渐开线花键（也包括渐开线齿轮）所定义的“齿宽”、“齿厚”，都是指弧度方向上的长度。The tolerance class used in ASA B5.15-1960 is the basis and is now designated as tolerance Class 5. The new tolerance classes are based on the following formulas:在ASA B5.15-1960中使用的基本公差，已经被本标准中公差等级5代替，各关系见下表：Tolerance Class 4（公差等级4）= Tolerance Class 5（公差等级5） 0.71Tolerance Class 6（公差等级6）= Tolerance Class 5（公差等级5） 1.40Tolerance Class 7（公差等级7）= Tolerance Class 5（公差等级5） 2.00All dimensions listed in this standard are for the finished part. Therefore, any compensation that must be made for operations that take place during processing, such as heat treatment, must be taken into account when selecting the tolerance level for manufacturing.本标准罗列的所有尺寸为最终成品尺寸。因此，在加工过程中必须考虑修正系数，慎重选择加工的公差等级。The standard has the same internal minimum effective space width and external maximum effective tooth thickness for all tolerance classes and has two types of fit. For tooth side fits, the minimum effective space width and the maximum effective tooth thickness are of equal value. This basic concept makes it possible to have interchangeable assembly between mating splines where they are made to this standard regardless of the tolerance class of the individual members. A tolerance class “mix” of mating members is thus allowed, which often is an advantage where one member is considerably less difficult to produce than its mate, and the “average” tolerance applied to the two units is such that it satisfies the design need. For instance, assigning a Class 5 tolerance to one member and Class 7 to its mate will provide an assembly tolerance in the Class 6 range. The maximum effective tooth thickness is less than the minimum effective space width for major diameter fits to allow for eccentricity variations.本标准中，所有公差等级的“内花键最小作用弧齿槽宽”和“外花键最大作用弧齿厚”的值是相同的，并且有两种配合类型。齿侧配合类，“内花键最小作用弧齿槽宽”和“外花键最大作用弧齿厚”的值相等。这一理念使得根据本标准制造的各种公差等级的单个花键能够互配。一个“混合”公差等级的配合是允许的，这样的优点是在于，一个配合零件的制造难度更小于与它相配的另一个零件。并且，“平均”的公差，也是设计需要。例如，将一个5级和7级公差的零件配合，可以得到一个范围为6级公差的配合。外径配合类，“外花键最大作用弧齿厚”比“内花键最小作用弧齿槽宽”要小，这种配合适用（装配后）的偏心情况。译注A7：“两种配合类型”指的是“齿侧配合”和“外径配合”。（也有的参考翻译成“齿形定心”和“大径定心”）In the event the fit as provided in this standard does not satisfy a particular design need and a specific amount of effective clearance or press fit is desired, the change should be made only to the external spline by a reduction or an increase in effective tooth thickness and a like change in actual tooth thickness. The minimum effective space width, in this standard, is always basic. The basic minimum effective space width should always be retained when special designs are derived from the concept of this standard.如果本标准规定的配合不能满足特殊的作用侧隙或压力配合的设计需要，设计更改应只改变（减少或增加）“外花键的作用弧齿厚”或“实际弧齿厚”。本标准的理念就是“内花键最小作用弧齿槽宽”是基本值（不变的）。Terms Applied to Involute Splines. The following definitions of involute spline terms, here listed in alphabetical order, are given in the American National Standard. Some of these terms are illustrated in the diagram in Table 6.渐开线花键术语下列美国国家标准中规定的渐开线花键术语按字母顺序排列，部分术语可参见表6中的图形。Active Spline Length (La) is the length of spline that contacts the mating spline. On sliding splines, it exceeds the length of engagement.有效花键长度：花键配合部分的长度。滑动情况下，这个长度长于配合的部分。Actual Space Width (s) is the circular width on the pitch circle of any single space considering an infinitely thin increment of axial spline length.实际弧齿槽宽：在内花键节圆（分度圆）上，各齿槽间的弧长度。译注B1：“infinitely thin increment”表示将圆弧进行无限的分割（使之成为直线），微积分概念。Actual Tooth Thickness (t) is the circular thickness on the pitch circle of any single tooth considering an infinitely thin increment of axial spline length.实际弧齿厚：在外花键节圆（分度圆）上，各齿上的弧长度。Alignment Variation is the variation of the effective spline axis with respect to the reference axis (see Fig. 1c).同心度偏差：实际花键轴心和参考轴心之间的偏差。（见图1c）译注B2： 本译文中的“Variation”翻译为“偏差”，“Tolerance”翻译为“公差”。因为按照字面理解，“Variation”指的是实际与理论的相差状态，“Tolerance”指的是相差的具体数值和范围。Base Circle is the circle from which involute spline tooth profiles are constructed.基圆：渐开线齿形开始形成处的假象圆。Base Diameter (Db) is the diameter of the base circle.基圆直径：基圆所在处的直径。Basic Space Width is the basic space width for 30-degree pressure angle splines; half the circular pitch. The basic space width for 37.5- and 45-degree pressure angle splines, however, is greater than half the circular pitch. The teeth are proportioned so that the external tooth, at its base, has about the same thickness as the internal tooth at the form diameter. This proportioning results in greater minor diameters than those of comparable involute splines of 30-degree pressure angle.基本弧齿槽宽：压力角30度下，为周节的一半。压力角37.5度和45度下，要大于周节的一半。这样，在基圆处的外花键弧齿厚和在 “内花键渐开线构成圆的弧齿厚”是相等的。这种比例引起了“压力角37.5度和45度的小径”要大于“压力角30度”的小径。Circular Pitch (p) is the distance along the pitch circle between corresponding points of adjacent spline teeth.周节：节圆（分度圆）上相邻同侧齿形之间的弧长。Depth of Engagement is the radial distance from the minor circle of the internal spline to the major circle of the external spline, minus corner clearance and/or chamfer depth.啮合深度：从内花键小径到外花键大径之间的，并减去“conrner clearance拐角裕度”和（或）倒角的径向距离。译注B3： conrner clearance，见图2.Diametral Pitch (P) is the number of spline teeth per inch of pitch diameter. The diametral pitch determines the circular pitch and the basic space width or tooth thickness. In con- junction with the number of teeth, it also determines the pitch diameter. (See also Pitch.)径节：在节圆上，每英寸的花键齿数。他决定了周节和基本弧齿槽宽或弧齿厚。它和齿数共同确定了节圆直径。Effective Clearance (cv) is the effective space width of the internal spline minus the effective tooth thickness of the mating external spline.作用侧隙：内花键作用弧齿槽宽减去与之相配的内花键作用弧齿厚。（正值为间隙，负值为过盈）Effective Space Width (Sv) of an internal spline is equal to the circular tooth thickness on the pitch circle of an imaginary perfect external spline that would fit the internal spline without looseness or interference considering engagement of the entire axial length of the spline. The minimum effective space width of the internal spline is always basic, as shown in Table 3. Fit variations may be obtained by adjusting the tooth thickness of the external spline.作用弧齿槽宽(Sv)：数值等于一与之在全齿长上配合（无间隙且无过盈）的“理想全齿外花键节圆弧齿厚”的弧齿槽宽。“内花键最小作用弧齿槽宽”是基本值，其值在表3中列出。用改变外花键的弧齿厚来获得各种不同的配合。译注B4： Effective Space Width (Sv)，国标GB/T 3478.1-2008 圆柱直齿渐开线花键（以下简称GB 3478.1）中的缩写为Ev。Three Types of Involute Spline Variations三种渐开线花键偏差 Center Lines of Teeth 齿中心线Reference Axis8 参考轴图 1a. Lead Variation（齿向偏差） Center Lines of Teeth 齿中心线Reference Axis 参考轴图 1b. Parallelism Variation（平行度偏差） Effective Spline Axis齿中心线Reference Axis 参考轴图 1c. Alignment Variation（同轴度偏差）Effective Tooth Thickness (tv) of an external spline is equal to the circular space width on the pitch circle of an imaginary perfect internal spline that would fit the external spline without looseness or interference, considering engagement of the entire axial length of the spline.作用弧齿厚(tv)：数值等于一与之在全齿长上配合（无间隙且无过盈）的“理想全齿外花键节圆弧齿厚”的弧齿槽宽。译注B5： Effective Tooth Thickness (tv)，国标GB 3478.1中的缩写为Sv。Effective Variation is the accumulated effect of the spline variations on the fit with the mating part.作用偏差：配合渐开线花键上的各种偏差的累积。External Spline is a spline formed on the outer surface of a cylinder.外花键：在圆柱外表面形成的花键。Fillet is the concave portion of the tooth profile that joins the sides to the bottom of the space.齿根圆弧：联结齿形处和底部（小圆）的凹处部分。Fillet Root Splines are those in which a single fillet in the general form of an arc joins the sides of adjacent teeth.圆齿根花键：两侧渐开线齿形由一段或近似一段过渡曲线与底部（小圆）相连的花键。Flat Root Splines are those in which fillets join the arcs of major or minor circles to the tooth sides.平齿根花键：两侧渐开线齿形各由一段过渡曲线与齿根圆相连接的花键。Form Circle is the circle which defines the deepest points of involute form control of the tooth profile. This circle along with the tooth tip circle (or start of chamfer circle) determines the limits of tooth profile requiring control. It is located near the major circle on the internal spline and near the minor circle on the external spline.渐开线构成圆：渐开线构成圆是用于控制齿廓上渐开线的极限距离的圆。渐开线构成圆与齿顶圆（或者倒角线的起点所在的圆）共同构成了“所要求的渐开线齿廓”的范围。渐开线构成圆的位置靠近内花键的大圆（齿根圆）或者外花键的小圆（齿根圆）。译注B6：在GB/T 3478.1-2008中，将Form Cycle定义为两个圆：键的渐开线终止圆（内花键用）和渐开线起始圆（外花键用）。而在本标准中，将这两个圆统称为Form Cycle，译者将Form Cycle翻译为渐开线构成圆。（这个圆与另外一个圆，构成了渐开线使用的范围）。具体看GB 3478.1中，表1序号17 -20和图1 渐开线花键联结。译注B7：定义Form Circle（渐开线构成圆）的原因是：在渐开线构成圆与齿顶圆（或者倒角线的起点所在的圆）之间的花键的齿形必须为渐开线齿形，其余部分不一定按照渐开线成形。译注B8：句中chamfer，并不是指真正的倒角，而是一种平滑的过渡线。（渐开线和大径或小径的过渡线）译注B9：这个范围是一个直径的范围。也就是从直径A开始到直径B为止，这中间的齿廓必须为渐开线。Form Clearance (cF) is the radial depth of involute profile beyond the depth of engagement with the mating part. It allows for looseness between mating splines and for eccentricities between the minor circle (internal), the major circle (external), and their respective pitch circles.齿形裕度：齿形裕度(cF)是相互配合的内、外花键的渐开线齿廓超过结合部分的径向距离。（定义齿形裕度的原因是）它允许相互配合的内、外花键之间存在一定间隙，而且小径（内花键）、大圆（外花键）、以及内、外花键各自的节圆之间存在一定的偏心距。译注B10：关于cF请看GB 3478.1中，图1 渐开线花键联结cF，或者本标准表6，图中cF。Form Diameter (DFe, DFi) the diameter of the form circle.渐开线构成圆直径（DFe, DFi）：渐开线构成圆所在圆的直径。（见译注B4和表6中的图）Internal Spline is a spline formed on the inner surface of a cylinder.内花键：在圆柱体的孔的内表面形成的花键。Involute Spline is one having teeth with involute profiles.渐开线花键：花键的齿形为渐开线形式的花键。Lead Variation is the variation of the direction of the spline tooth from its intended direction parallel to the reference axis, also including parallelism and alignment variations (see Fig. 1a). Note: Straight (nonhelical) splines have an infinite lead.齿向偏差：花键的键齿的实际齿线与花键的参考轴线之间的平行度偏差的最大绝对值。它包括平行度偏差（见图1b）和同轴度偏差（见图1a）。注意：直齿花键（非螺旋花键）的齿向偏差为无限长。译注B11：在ISO 4156 Straight cylindrical involute splines Metric module, side fit中，“Lead variation”定义为“Helix deviation”。国标GB 3478.1定义为“齿向公差”。本人认为ISO 4156中的定义和图形更详细和易于理解。根据ISO 4156中定义，“Form deviation”(综合形状偏差)，包括了三种：Profile deviation、Index deviation和helix deviation。“Form deviation”的值即为GB 3478.1中的“Deviation allowance （）”。=（Total Profile deviation + Total Index deviation+ Total helix deviation）Length of Engagement (Lq) is the axial length of contact between mating splines.配合长度（Lq）：配合长度是配合花键接触段轴向的长度。Machining Tolerance (m) is the permissible variation in actual space width or actual tooth thickness.加工公差（m）：加工公差是花键的实际弧齿槽宽和实际弧齿厚的允许的变动量。译注B12：在 GB 3478.1中，加工公差代号为T。Major Circle is the circle formed by the outermost surface of the spline. It is the outside circle (tooth tip circle) of the external spline or the root circle of the internal spline.大圆：大圆是花键的最大齿形面的形成的圆。它是外花键的外圆（齿顶圆），和内花键的齿根圆。Major Diameter (Do, Dri) is the diameter of the major circle.大径：大圆直径（Do, Dri）是大圆所在圆的直径。Minor Circle is the circle formed by the innermost surface of the spline. It is the root circle of the external spline or the inside circle (tooth tip circle) of the internal spline.小圆：小圆是花键的最小齿形面的形成的圆。它是外花键的齿根圆，和内花键的内圆（齿顶圆）。Minor Diameter (Dre, Di) is the diameter of the minor circle.小圆直径：小圆直径（Dre, Di）是小圆所在圆的直径。Nominal Clearance is the actual space width of an internal spline minus the actual tooth thickness of the mating external spline. It does not define the fit between mating members, because of the effect of variations.理论侧隙：理论侧隙是“内花键的实际弧齿槽宽”减去与之相互配合的“外花键的实际弧齿厚”所得的值。由于（内、外花键）的各种实际偏差，理论侧隙不能用于确定花键的配合情况。Out of Roundness is the variation of the spline from a true circular configuration.圆度：圆度是花键与理论圆的轮廓之间的偏差。Parallelism Variation is the variation of parallelism of a single spline tooth with respect to any other single spline tooth (see Fig. 1b).平行度偏差：平行度偏差是单根键齿相对其它的单根键齿之间的平行偏差。（见图1b）Pitch (P/Ps) is a combination number of a one-to-two ratio indicating the spline proportions; the upper or first number is the diametral pitch, the lower or second number is the stub pitch and denotes, as that fractional part of an inch, the basic radial length of engagement, both above and below the pitch circle.径节（分数制）（P/Ps）：径节（分数制）是一个1比2组合分数，用于表示花键的比率。分数中第一个数（分子）表示的是花键的节圆径节，第二个数（分母）表示的是齿根径节，其中的分数用英寸表示，节圆径节表示的是在节圆上方的键齿在半径方向上的配合长度，齿根径节表示的是在节圆下方的键齿在半径方向上的配合长度。译注B13：可以理解为节圆将整个花键键齿一分为二，节圆上方的键齿的齿高为径节，节圆下方的键齿的齿高为齿根径节。在实际计算时要考虑到渐开线终止圆与修缘线所在圆对键齿有效结合齿高的影响，并将其扣除。Pitch Circle is the reference circle from which all transverse spline tooth dimensions are constructed.节圆：节圆是一个参考圆，花键的所有横向尺寸都是以节圆为基础开始计算的。译注B14：米制叫分度圆。Pitch Diameter (D) is the diameter of the pitch circle节圆直径（D）：节圆直径是节圆所在圆的直径。.Pitch Point is the intersection of the spline tooth profile with the pitch circle.节点：节点是键齿的齿廓与节圆的交点。Pressure Angle () is the angle between a line tangent to an involute and a radial line through the point of tangency. Unless otherwise specified, it is the standard pressure angle.压力角（）：压力角是花键的渐开线齿廓的切线与通过切点的半径所组成的夹角。除非有特殊说明，压力角通常是指标准压力角。Profile Variation is any variation from the specified tooth profile normal to the flank.齿形偏差：垂直于侧面的、指定的齿廓（与理论齿廓）的所有公差。译注B15：见GB 3478.1-2008表1中的“齿形公差”定义，本人认为国标从轮廓度检测方面加以解释，应更合理。Spline is a machine element consisting of integral keys (spline teeth) or keyways (spaces) equally spaced around a circle or portion thereof.花键：是一种机械零件，它由凸出的齿（花键齿）或凹下的沟（槽）组成，键齿和键槽等分一个完整的圆或圆上部分。Standard (Main) Pressure Angle (D) is the pressure angle at the specified pitch diameter. 标准压力角（D）（主压力角）：标准压力角是指特定在节圆上的压力角。Stub Pitch (Ps) is a number used to denote the radial distance from the pitch circle to the major circle of the external spline and from the pitch circle to the minor circle of the internal spline. The stub pitch for splines in this standard is twice the diametral pitch.齿根径节（Ps）：齿根径节是一个数，它用于表示节圆与外花键的大圆或内花键的小圆之间的半径差。在本标准中，花键的齿根径节是径节的2倍。Total Index Variation is the greatest difference in any two teeth (adjacent or otherwise) between the actual and the perfect spacing of the tooth profiles.齿距累计偏差：任意两个齿（相邻齿或其他情况）的实际齿廓与理论值之差的最大值。Total Tolerance (m + ) is the machining tolerance plus the variation allowance.总公差（m +）：总公差是加工公差与综合公差之和。译注B16：在GB 3478.1将总公差定义为：T+。Variation Allowance () is the permissible effective variation.综合公差（）：作用偏差(effective variation)的公差值允许范围。Tooth Proportions. There
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