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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 SERRATIONS

A 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 Splines

American 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，花键用拉削、齿轮插齿刀。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：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+λ（具体参数意思看后面章节），删除第一种情况后Smax=Smin+m+λ。

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（外花键大圆或花键小圆）到“渐开线构成圆”之间的那段围，因此在齿侧配合情况下，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。“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）× 0.71 Tolerance Class 6（公差等级6）= Tolerance Class 5（公差等级5）× 1.40 Tolerance Class 7（公差等级7）= Tolerance Class 5（公差等级5）× 2.00

All 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“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，“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“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“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 “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：花键作用弧齿槽宽减去与之相配的花键作用弧齿厚。（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。“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.