ANSI B92.1-1970(R1993) SAE美国渐开线花键-中文翻译完整版0429

ANSI B92.1-1970(R1993) SAE美国渐开线花键-中文翻译完整版0429 - 图文下载本文

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Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 1 of 38 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 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

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 2 of 38 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+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:

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INVOLUTE SPLINES Page 3 of 38 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“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。

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INVOLUTE SPLINES Page 4 of 38

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）

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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.

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INVOLUTE SPLINES Page 6 of 38 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 （λ）”。λ=（Total Profile deviation + Total Index deviation+ Total helix deviation）

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 7 of 38 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。

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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 (Φ) 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（Φ）：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 (ΦD) is the pressure angle at the specified pitch diameter. 标准压力角（ΦD）（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 + λ) is the machining tolerance plus the variation allowance. 总公差（m +λ）：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+λ。

Variation Allowance (λ) is the permissible effective variation. 综合公差（λ）：作用偏差(effective variation)的公差值允许范围。

Tooth Proportions.— There are 17 pitches: 2.5/5, 3/6, 4/8,5/10, 6/12, 8/16, 10/20,12/24, 16/32, 20/40, 24/48, 32/64, 40/80, 48/96, 64/128, 80/160, and 128/256. The numerator in this fractional designation is known as the diametral pitch and controls the pitch diameter; the denominator, which is always double the numerator, is known as the stub pitch and controls the tooth depth. For convenience in calculation, only the numerator is used in the formulas given

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and is designated as P. Diametral pitch, as in gears, means the number of teeth per inch of pitch diameter.

齿比—共有17种齿比：2.5/5，3/6，4/8，5/10，6/12，8/16，10/20，12/24，16/32，20/40，24/48，32/64，40/80，48/96，64/128，80/160和128/256。在这一系列的分数中的分子是（节圆）径节，径节决定了节圆的直径；分数中的分母通常是分子的两倍，分母是齿根径节，齿根径节决定了齿高。为了方便计算，在公式中都使用分子作为计算参数，指定节圆直径，并且与齿轮的表示方式一样定义为径节P尺寸，也就是在节圆上，每英寸长度上的齿数。

译注B17：设计了这17中之外的齿比，本人认为是不合理的。

Table 1 shows the symbols and Table 2 the formulas for basic tooth dimensions of involute spline teeth of various pitches. Basic dimensions are given in Table 3.

表1列出了符号意思，表2列出了各种不同径节的花键公式。表3列出了基本值。

Table 1. American National Standard Involute Spline Symbols

ANSI B92.1-1970, R1993 cv cF D Db Dci Dce DFe DFi Di Do Dre Dri de di Ke Ki L La Lg m Me effective clearance 作用侧隙 form clearance 齿形裕度 pitch diameter 节圆直径 base diameter 基圆直径 pin contact diameter, internal spline 针规触点直径，内花键 pin contact diameter, external spline 针规触点直径，外花键 form diameter, external spline 渐开线起点直径（外花键） form diameter, internal spline 渐开线终点直径（内花键） minor diameter, internal spline 内花键小径 major diameter, external spline 外花键大径 minor diameter, external spline(root) 外花键小径 major diameter, internal spline(root) 内花键大径外花键用测量针规直径 diameter of measuring pin for internal spline 内花键用测量针规直径 change factor for external spline 外花键变量（见ISO 4156-3） change factor for internal spline 内花键变量（见ISO 4156-3） spline length 花键长度 active spline length 有效花键长度 length of engagement 配合长度 machining tolerance 加工公差 measurement over pins, external 跨棒距外花键 Mi N P Ps p rf s sv sc ss t tv λ ∈ Φ measurement between pins, internal spline 棒间距内花键 number of teeth 齿数 diametral pitch 径节 stub pitch 齿根径节 circular pitch 周节 fillet radius 圆角半径 actual space width, circular 实际弧齿槽宽 effective space width, circular 作用弧齿槽宽 allowable compressive stress, psi 允许压缩应力 allowable shear stress, psi 允许剪切应力 actual tooth thickness, circular 实际弧齿厚 effective tooth thickness, circular 作用弧齿厚 variation allowance 综合公差 involute roll angle 渐开线旋转角 pressure angle 压力角 standard pressure angle 标准压力角内花键针规触点压力角 diameter of measuring pin for external spline ΦD Φci pressure angle at pin contact diameter, internal spline Φce pressure angle at pin contact diameter, external spline 外花键针规触点压力角 Φi pressure angle at pin center, internal spline 内花键针规中心压力角 Φe pressure angle at pin center, external spline 外花键针规中心压力角渐开线构成圆处压力角 ΦF pressure angle at form diameter 译注B18：PSI这里为应力单位，Pound-Per-Square Inch 磅每平方英寸。

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Table 2. Formulas for Involute Spline Basic Dimensions ANSI B92.1-1970, R199 30 deg ΦD Flat Root Side Fit 平齿根齿侧配合 2.5 /5-32 /64 Pitch Stub Pitch 齿根径节 Pitch Diameter节圆直径 Base Diameter基圆直径 Circular Pitch Minimum Effective Space Width最小作用弧齿槽宽 Major Diameter, Internal 内花键大径 Major Diameter, External 外花键大径 Minor Diameter, Internal 内花键小径 Minor 2.5/5 thru 12/24 pitch Dia. Ext. 16/32 pitch and 外花finer 键小10/20 pitch and 径 finer Form Diameter, Internal 内花键终止圆直径 Form Diameter, External 外花键起始圆直径 Form Clearance (Radial) 齿形裕度 37.5 deg ΦD Fillet Root Side Fit 圆齿根齿侧配合 2.5/5-48/96 Pitch 2P N/P D cos ΦD π/P π/(2P ) (N+1.8 )/P (N+1)/ P (N-1)/ P (N-1.8 )/P (N – 2 )/P … (N+1)/P + 2 cF (N– 1)/P– 2 cF Fillet Root Side Fit 圆齿根齿侧配合 2.5/5-48-/96 Pitch 2P N/P D cos ΦD π/P (0.5 π + 0.1 )/P (N+1.6 )/P (N+1)/ P (N-0.8 )/P (N-1.3 )/P (N-1.3 )/P (N-1.3 )/P (N+1)/ P + 2 cF (N-0.8 ) /P – 2cF 45 deg ΦD Fillet Root Side Fit 圆齿根齿侧配合 10/20–128/256 Pitch 2P N/P D cos ΦD π/P (0.5 π + 0.2 )/P (N+1.4 )/P (N+1)/ P (N-0.6 )/P … … (N-1)/ P (N+1)/ P + 2 cF (N– 0.6 )/P–2cF Symbol Term 术语 Flat Root Major Dia Fit 平齿根外径配合 3 /6-16 /32 Pitch 2P N/P D cos ΦD π/P π/(2 P ) (N+1)/ P (N+1)/ P (N-1)/ P (N-1.35 )/P (N-1.35 )/P (N-1.35 )/P (N+0.8)/P–0.004+2cF (N-1)/ P – 2 cF Ps D Db p sv Dri Do Di 2P N/P D cos ΦD π/P π/(2 P ) (N+1.35 )/P (N+1)/ P (N-1)/ P (N-1.35 )/P Dre (N-1.35 )/P (N-1.35 )/P DFi DFe cF (N+1)/P + 2cF (N-1)/P – 2 cF 0.001 D, with max of 0.010, min of 0.002 最大0.01，最小0.002 π = 3.1415927 Note: All spline specification table dimensions in the standard are derived from these basic formulas by application of tolerances. 注：按本表规定的基本公式，应用不同的公差等级，可得到所有其他表中的尺寸。

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Table 3. Basic Dimensions for Involute Splines ANSI B92.1-1970, R1993

渐开线花键基本尺寸 Pitch, P/Ps Circular Pitch, p 2.5 ?5 3 ?6 4 ?8 5 ?10 6 ?12 8 ?16 10 ?20 12 ?24 16 ?32 1.2566 1.0472 0.7854 0.6283 0.5236 0.3927 0.3142 0.2618 0.1963 Min Effective Space Width (BASIC), Sv min 最小作用弧齿槽宽（基本值） 30 deg Φ 0.6283 0.5236 0.3927 0.3142 0.2618 0.1963 0.1571 0.1309 0.0982 37.5degΦ 0.6683 0.5569 0.4177 0.3342 0.2785 0.2088 0.1671 0.1392 0.1044 45 deg Φ … … … … … … 0.1771 0.1476 0.1107 20 ?40 24 ?48 32 ?64 40 ?80 48 ?96 64 ?128 80 ?160 128 ?256 … 0.1571 0.1309 0.0982 0.0785 0.0654 0.0491 0.0393 0.0246 … Pitch, P/Ps Circular Pitch, p 30 deg Φ 0.0785 0.0654 0.0491 0.0393 0.0327 … … … … 37.5 deg Φ 0.0835 0.0696 0.0522 0.0418 0.0348 … … … … 45 deg Φ 0.0885 0.0738 0.0553 0.0443 0.0369 0.0277 0.0221 0.0138 … Min Effective Space Width (BASIC), Sv min Tooth Numbers.— The American National Standard covers involute splines having tooth numbers ranging from 6 to 60 with a 30- or 37.5-degree pressure angle and from 6 to 100 with a 45-degree pressure angle. In selecting the number of teeth for a given spline application, it is well to keep in mind that there are no advantages to be gained by using odd numbers of teeth and that the diameters of splines with odd tooth numbers, particularly internal splines, are troublesome to measure with pins since no two tooth spaces are diametrically opposite each other.

美国国家表准规定的渐开线花键压力角30度或37.5度的齿数范围是6到60齿，压力角45度的齿数范围是6到100齿。在选择花键齿数应用上，必须牢记的是：由于奇数齿两测量针规的中心连线距离不是（通过渐开线圆心的）直径值，所以选择奇数齿比选择偶数齿更为不利，特别是内花键。

译注C1：偶数齿的形状是对称的，一边的齿中心和相对的另一边齿中心的连线，通过渐开线花键的圆心（节圆的圆心）。而奇数齿是不通过圆心的，所以奇数齿的测量难度更高。

Types and Classes of Involute Spline Fits.— Two types of fits are covered by the American National Standard for involute splines, the side fit, and the major diameter fit. Dimensional data for flat root side fit, flat root major diameter fit, and fillet root side fit splines are tabulated in this standard for 30-degree pressure angle splines; but for only the fillet root side fit for 37.5- and 45-degree pressure angle splines.

渐开线花键的配合类型和公差等级—本标准规定两种配合类型：齿侧配合和外径配合。30度压力角时，有平齿根齿侧配合、平齿根外径配合、圆齿根齿侧配合；37.5和45度压力角只有圆齿根齿侧配合。（见表2）

Side Fit: In the side fit, the mating members contact only on the sides of the teeth; major and minor diameters are clearance dimensions. The tooth sides act as drivers and centralize the mating splines.

齿侧配合：配合的零件只通过齿的侧面配合，大小径之间存在间隙。齿侧配合同时具有驱动和自定心功能。

Major Diameter Fit: Mating parts for this fit contact at the major diameter for centralizing. The sides of the teeth act as drivers. The minor diameters are clearance dimensions. 外径配合：用大径来定心，用侧面来驱动。小径具有间隙。

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The major diameter fit provides a minimum effective clearance that will allow for contact and location at the major diameter with a minimum amount of location or centralizing effect by the sides of the teeth. The major diameter fit has only one space width and tooth thickness tolerance which is the same as side fit Class 5.

外径配合规定了一个最小作用侧隙，以用来连接或定位大径。跟齿侧一起，能得到一个小间隙和同心的效果。外径配合只有一个弧齿槽宽和弧齿厚公差，等同于齿侧配合中公差等级为5的公差值。

A fillet root may be specified for an external spline, even though it is otherwise designed to the flat root side fit or major diameter fit standard. An internal spline with a fillet root can be used only for the side fit.

外花键一般用圆齿根，也有其它情况采用平齿根的齿侧配合或外径配合。内花键圆齿根只适用于齿侧配合。

Classes of Tolerances.— This standard includes four classes of tolerances on space width and tooth thickness. This has been done to provide a range of tolerances for selection to suit a design need. The classes are variations of the former single tolerance which is now Class5 and are based on the formulas shown in the footnote of Table 4. All tolerance classes have the same minimum effective space width and maximum effective tooth thickness limits so that a mix of classes between mating parts is possible.

公差等级—弧齿槽宽和弧齿厚规定了四种公差等级。这样就满足了设计是选择不同公差等级的需要。旧版中只有一种等级的公差，在本标准中规定为等级5，作为基本等级，见表4。各公差等级的最小作用弧齿宽和最大作用弧齿厚的值是相等的，这样允许不同公差等级的花键互配。

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INVOLUTE SPLINES Page 13 of 38 Table 4. Maximum Tolerances for Space Width and Tooth Thickness of Tolerance

Class 5 Splines ANSI B92.1-1970, R1993

(Values shown in ten thousandths; 20 = 0.0020 表中20=0.0020英寸)

Pitch, P/Ps 6 ?12 and 10?20 and 16?32 and 24?48 and 64 ?128 128 ?256 8 ?16 12 ?24 20 ?40 48 ?96 and 80?160 Machining Tolerance, m 加工公差 12.5 12 11.7 11.7 9.6 9.5 14 13 12.4 12.4 10.2 10 15.5 14 13.1 13.1 10.8 10.5 17 15 13.8 13.8 11.4 — 18.5 16 14.5 14.5 — — 20 17 15.2 15.2 — — — 18 15.9 15.9 — — — 19 16.6 16.6 — — — 20 17.3 17.3 — — — 21 18 18 — — Variation Allowance, λ 综合公差 17 15.7 14.2 12.2 11 9.8 19 17.4 15.4 13.4 12 10.6 21 19.1 16.6 14.6 13 11.4 23 21.6 17.8 15.8 14 — 25 22.5 19 17 — — 27 24.2 20.2 18.2 — — — 25.9 21.4 19.4 — — — 27.6 22.6 20.6 — — — 29.3 23.8 21.8 — — — 31 25 23 — — Total Index Variation 齿距累积偏差 15 15 14 12 11 10 18 17 15 13 12 11 20 19 16 15 14 13 22 20 18 16 15 — 25 22 19 17 — — 27 24 20 18 — — — 26 21 20 — — — 28 22 21 — — — 29 24 23 — — — 31 25 24 — — Profile Variation 齿形偏差 +5 +4 +3 +2 +2 +2 ?7 ?6 ?5 ?4 ?4 ?4 Lead Variation 齿向偏差 Lg, in.配合长度英寸 Variation偏差值 0.3 2 0.5 3 1 4 2 5 3 6 4 7 5 8 6 9 7 10 8 11 9 12 10 13 No.of 2.5 ?5 and 4 ?8 and Teeth 3 ?6 5 ?10 N 10 15.8 14.5 20 17.6 16 30 18.4 17.5 40 21.8 19 50 23 20.5 60 24.8 22 70 — — 80 — — 90 — — 100 — — N 10 23.5 20.3 20 27 22.6 30 30.5 24.9 40 34 27.2 50 37.5 29.5 60 41 31.8 70 — — 80 — — 90 — — 100 — — N 10 20 17 20 24 20 30 28 22 40 32 25 50 36 27 60 40 30 70 — — 80 — — 90 — — 100 — — N +7 +6 All ?10 ?8

For other tolerance classes: Class 4 = 0.71 × Tabulated value 等级4=0.71×基本值 Class 5 = As tabulated in table 等级5=定义为基本值 Class 6 = 1.40 × Tabulated value 等级6=1.40×基本值 Class 7 = 2.00 × Tabulated value 等级7=2.00×基本值

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INVOLUTE SPLINES Page 14 of 38 Fillets and Chamfers.— Spline teeth may have either a flat root or a rounded fillet root. 圆角和倒角—花键齿可以采用圆齿根或平齿根。

Flat Root Splines: are suitable for most applications. The fillet that joins the sides to the bottom of the tooth space, if generated, has a varying radius of curvature. Specification of this fillet is usually not required. It is controlled by the form diameter, which is the diameter at the deepest point of the desired true involute form (sometimes designated as TIF).

平齿根花键：能够应用在大多数场合。在花键同一齿槽上，两侧渐开线齿形各由一段过渡曲线与齿根（直径圆）相连接的花键。若用滚齿加工（展成法），这个圆弧的曲率是变化的。没必要指定这个圆弧的大小，它的范围通常用“构成圆”来决定，“构成圆”在渐开线配合范围的极限处。（有是候设计简称TIF）

When flat root splines are used for heavily loaded couplings that are not suitable for fillet root spline application, it may be desirable to minimize the stress concentration in the flat root type by specifying an approximate radius for the fillet.

若某种重载的场合不适用圆齿根，而采用平齿根时，应在平齿根的拐角处设计一个近似的圆弧，以减少接触应力。

Because internal splines are stronger than external splines due to their broad bases and high pressure angles at the major diameter, broaches for flat root internal splines are normally made with the involute profile extending to the major diameter.

由于内花键在齿根处的材料基体更多、压力角更大，所以内花键强度要大于外花键，在拉削加工（内花键）时，渐开线花键的齿形一般延伸到大径处。

Fillet Root Splines: are recommended for heavy loads because the larger fillets provided reduce the stress concentrations. The curvature along any generated fillet varies and can not be specified by a radius of any given value.

圆齿根花键：推荐在重载荷情况下使用。它的圆角（比平齿根）更大，能有效减少应力集中。若用滚齿加工（展成法），这个圆弧的曲率是变化的，不能指定某一固定值。

External splines may be produced by generating with a pinion-type shaper cutter or with a hob, or by cutting with no generating motion using a tool formed to the contour of a tooth space. External splines are also made by cold forming and are usually of the fillet root design. Internal splines are usually produced by broaching, by form cutting, or by generating with a shaper cutter. Even when full-tip radius tools are used, each of these cutting methods produces a fillet contour with individual characteristics. Generated spline fillets are curves related to the prolate epicycloid for external splines and the prolate hypocycloid for internal splines. These fillets have a minimum radius of curvature at the point where the fillet is tangent to the external spline minor diameter circle or the internal spline major diameter circle and a rapidly increasing radius of curvature up to the point where the fillet comes tangent to the involute profile.

外花键可以用“插齿成型刀”加工，或者用滚铣刀，或者非滚齿的、与外花键齿形一致的内花键工具。圆齿根的外花键也可以采用冷作成型的方式加工。内花键通常用拉削、成型切削、插齿刀成型等来加工。即使使用的这些“圆角全一致的工具”，加工出来的单个齿形仍然是不同的。用展成法加工的倒圆角，关系到外花键的外摆线和内花键的内摆线。这些圆弧曲率半径是变化的，在圆弧与外花键小圆（或内花键大圆）相切点为最小，沿圆弧逐渐增加，至外花键渐开线起点（或内花键渐开线终点）附近为最大。

译注C2：冷作成型指的是不去除材料的方式，比如搓齿机成型。译注C3：曲率变化见《3478.1-2008中》5 基本齿廓 5.5注

Chamfers and Corner Clearance: In major diameter fits, it is always necessary to provide corner clearance at the major diameter of the spline coupling. This clearance is usually effected

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by providing a chamfer on the top corners of the external member. This method may not be possible or feasible because of the following:

在外径配合情况下，在（内花键）大径处总是有必要指定一个“拐角裕度”。这种形式也通常用“在（外花键）齿顶处作一个倒角”来代替。然而，代替的这种情况，若有以下几个方面就不适合了：

a) If the external member is roll formed by plastic deformation, a chamfer cannot be pro- vided by the process.

外花键如果滚动成型、是塑性变形的，倒角就无法加工 b) A semitopping cutter may not be available. 半圆形刀具也无法加工倒角

c) When cutting external splines with small numbers of teeth, a semitopping cutter may reduce the width of the top land to a prohibitive point.

当分半切削小齿数的外花键时，半圆形刀具的加工容易使齿顶平面产生过切现象。

In such conditions, the corner clearance can be provided on the internal spline, as shown in Fig. 2.

若有以上情况，可用图2中的方法。

When this option is used, the form diameter may fall in the protuberance area. 如采用这个方法，“构成圆”的直径线，会被这个“corner‖“掩盖”掉。

译注C4：图中的“Form Circle”为译者增加。

Form Circle Fig. 2. Internal corner clearance

Spline Variations.— The maximum allowable variations for involute splines are listed in Table 4.

花键偏差—花键最大综合偏差值见表4。

Profile Variation: The reference profile, from which variations occur, passes through the point used to determine the actual space width or tooth thickness. This is either the pitch point or the contact point of the standard measuring pins.

齿形偏差：用齿廓上发生偏差的一个点，来定义实际弧齿槽宽或实际弧齿厚。这个点可以是节圆（和齿廓）的交点，也可以是测量针规（和齿廓）的交点。

译注C5：在《ISO 4156-1》中，有图形说明，请参照图形理解。另在《3478.1-2008》表1中有定义。

Profile variation is positive in the direction of the space and negative in the direction of the tooth. Profile variations may occur at any point on the profile for establishing effective fits and are shown in Table 4.

齿形偏差是弧齿槽宽的正方向或者是弧齿厚的反方向。实际装配的时候，齿廓的任何点上都有可能发生偏差。

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Lead Variations: The lead tolerance for the total spline length applies also to any portion thereof unless otherwise specified.

齿向偏差：指的是花键全齿长上或者指定长度方向上的偏差。

Out of Roundness: This condition may appear merely as a result of index and profile variations given in Table 4 and requires no further allowance. However, heat treatment and deflection of thin sections may cause out of roundness, which increases index and profile variations. Tolerances for such conditions depend on many variables and are therefore not tabulated. Additional tooth and/or space width tolerance must allow for such conditions.

圆度（偏差）：（理论上）仅仅由于表4中规定的齿距偏差和齿形偏差引起。但是，热处理和薄壁零也会产生圆度（偏差），从而增大齿距偏差和齿形偏差。这种公差大小涉及到多种因素，无法一一指明。弧齿槽宽和弧齿厚必须允许这种变化量。译注D1：工艺编制时，应着重考虑热处理对弧齿槽宽和弧齿厚的影响。

Eccentricity: Eccentricity of major and minor diameters in relation to the effective diameter of side fit splines should not cause contact beyond the form diameters of the mating splines, even under conditions of maximum effective clearance. This standard does not establish specific tolerances.

偏心距：齿侧配合时，大径和小径配合引起的偏心距离，不得超过构成圆直径范围，特别是在最大作用侧隙时。本标准没有规定（偏心距）的公差值。

Eccentricity of major diameters in relation to the effective diameters of major diameter fit splines should be absorbed within the maximum material limits established by the tolerances on major diameter and effective space width or effective tooth thickness.

大径配合时引起的偏心距，应该在“大径本身和作用弧齿槽宽或弧齿厚”形成的“最大实体状态”范围内。

译注D2：最大实体含义请查阅相关的形状和位置公差书籍。本段的含义理解为：若偏心距过大，超过了最大实体范围，可能就无法装配。

If the alignment of mating splines is affected by eccentricity of locating surfaces relative to each other and/or the splines, it may be necessary to decrease the effective and actual tooth thickness of the external splines in order to maintain the desired fit condition. This standard does not include allowances for eccentric location.

如果配合花键的同心度，由于受到“相对应的配合表面产生的偏心距”的影响，就有必要减少外花键作用和实际弧齿厚，以保持原有的配合状态。本标准没有规定（偏心距）位置度公差值。

Effect of Spline Variations.— Spline variations can be classified as index variations, profile variations, or lead variations.

花键的作用偏差—可分为：齿距偏差、齿形偏差和齿向偏差。

Index Variations: These variations cause the clearance to vary from one set of mating tooth sides to another. Because the fit depends on the areas with minimum clearance, index variations reduce the effective clearance.

齿距偏差：导致每个齿与齿的配合的间隙都是不同的。最小间隙决定了配合状况，齿距偏差减少了作用侧隙的范围。

译注D3：“Index Variations”在《ISO 4156》中也称为“Pitch Deviation‖。

Profile Variations: Positive profile variations affect the fit by reducing effective clearance. Negative profile variations do not affect the fit but reduce the contact area.

齿形偏差：正向的齿形偏差减少了作用侧隙，反向的齿形偏差只减少接触面积不影响装配。

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Lead Variations: These variations will cause clearance variations and therefore reduce the effective clearance.

齿向偏差：齿向偏差导致侧隙偏差的改变，从而减少作用侧隙。

Variation Allowance: The effect of individual spline variations on the fit (effective variation) is less than their total, because areas of more than minimum clearance can be altered without changing the fit. The variation allowance is 60 percent of the sum of twice the positive profile variation, the total index variation and the lead variation for the length of engagement. The variation allowances in Table 4 are based on a lead variation for an assumed length of engagement equal to one-half the pitch diameter. Adjustment may be required for a greater length of engagement. 综合公差（允许值）：单个花键对配合的影响（作用偏差）小于它们的总和。在不改变配合的情况下，（由于总和的影响）这些大于最小间隙的接触区域也会发生改变。在配合长度上，综合公差等于“齿形偏差、总齿距偏差和齿向偏差之和”两倍的60%。表4中的值，是按花键配合长度为其节圆直径一半的齿向公差来计算的。若长度不同，必要时可调整λ。译注D4：关于“Variation Allowance”，在《ISO 4156》中，9.2更为合理和容易理解。本标准中定义的公式与美国米制公式《B92.2M》不同。

Effective and Actual Dimensions.— Although each space of an internal spline may have the same width as each tooth of a perfect mating external spline, the two may not fit because of variations of index and profile in the internal spline. To allow the perfect external spline to fit in any position, all spaces of the internal spline must then be widened by the amount of interference. The resulting width of these tooth spaces is the actual space width of the internal spline. The effective space width is the tooth thickness of the perfect mating external spline. The same reasoning applied to an external spline that has variations of index and profile when mated with a perfect internal spline leads to the concept of effective tooth thickness, which exceeds the actual tooth thickness by the amount of the effective variation.

由于内花键有误差，所以该外花键即使每个弧齿厚与内花键每个弧齿槽宽想的，也不能装入内花键。若要使理想的外花键在任意位置上都可以装入内花键，且作用侧隙为零，则该内花键所有弧齿槽宽均需按最大干涉量加宽。这些加宽后的弧齿槽宽即是内花键的各实际弧齿槽宽。与之相配的理想外花键的弧齿厚即是内花键的作用弧齿槽宽。反之也应用在外花键上。有齿距误差和齿形误差的外花键，与理想的内花键的弧齿槽宽相配和的弧齿厚，即是作用弧齿厚，作用弧齿厚是由实际弧齿厚按照作用偏差往外扩大得到的。

The effective space width of the internal spline minus the effective tooth thickness of the external spline is the effective clearance and defines the fit of the mating parts. (This statement is strictly true only if high points of mating parts come into contact.) Positive effective clearance represents looseness or backlash. Negative effective clearance represents tightness or interference.

内花键的作用弧齿槽宽减去外花键的作用弧齿厚即为作用侧隙，它决定了配合形式（这一定义只有在配合的极限点是接触的状态下才严格成立）。（相减后）正值的作用侧隙形成松配或间隙配合；负值的作用侧隙形成紧配或过盈配合。

Space Width and Tooth Thickness Limits.— The variation of actual space width and actual tooth thickness within the machining tolerance causes corresponding variations of effective dimensions, so that there are four limit dimensions for each component part. These variations are shown diagrammatically in Table 5.

弧齿槽宽和弧齿厚的极限—由制造时产生的实际弧齿槽宽和实际弧齿厚，由于各种偏差就产生了作用偏差尺寸。所以对每个配合零件，共有四种极限尺寸。各种偏差见表5。

译注E1：对于内花键，实际弧齿槽宽大于作用弧齿槽宽；对于外花键，作用弧齿厚大于实际弧齿厚。

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Table 5. Specification Guide for Space Width and Tooth Thickness

ANSI B92.1-1970, R1993

译注E2：综合公差和制造公差的值，在后面的计算举例中，是采用查表的方法。在B92.1-1996版本中，可以采用以下公式计算：

Spine Pitche P/PS 2.5/5 and 3/6 4/8 and 5/10 6/12 and 8/16 10/20 and 12/24 16/32 and 20/40 24/48 thru 48/96 64/128 and 80/160 128/256 λ 0.35N+20 0.23N+18 0.20N+15 0.17N+14 0.12N+13 0.12N+11 0.10N+10 0.08N+9 m 0.18N+14 0.15N+13 0.15N+11 0.10N+11 0.07N+11 0.07N+11 0.06N+9 0.05N+9

The minimum effective space width is always basic. The maximum effective tooth thickness is the same as the minimum effective space width except for the major diameter fit. The major diameter fit maximum effective tooth thickness is less than the minimum effective space width by an amount that allows for eccentricity between the effective spline and the major diameter. The permissible variation of the effective clearance is divided between the internal and external splines to arrive at the maximum effective space width and the minimum effective tooth thickness. Limits for the actual space width and actual tooth thickness are constructed from suitable variation allowances.

最小作用弧齿槽宽总是为基本值。除了外径配合形式外，“最大作用弧齿厚”和“最小作用弧齿槽宽”的值相等。外径配合情况，由于齿侧和大径（与各自相配的零件）相配合后存在偏心，这时要求“最大作用弧齿厚”要小于“最小作用弧齿槽宽”。（实际弧齿厚）去掉“作用侧隙”的影响，在内花键上得到“最大作用弧齿槽宽”，在外花键上得到“最小作用弧齿厚”。“实际弧齿槽宽”和“实际弧齿厚”的极限值来源于“综合公差”。

Use of Effective and Actual Dimensions.— Each of the four dimensions for space width and tooth thickness shown in Table 5 has a definite function.

作用和实际尺寸的使用—表5中显示的四个齿槽宽和齿厚，每一个尺寸都特定的作用。

Minimum Effective Space Width and Maximum Effective Tooth Thickness: These dimensions control the minimum effective clearance, and must always be specified.

最小作用弧齿槽宽和最大作用弧齿厚：这些尺寸控制最小作用侧隙，必须指定。

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Minimum Actual Space Width and Maximum Actual Tooth Thickness: These dimensions cannot be used for acceptance or rejection of parts. If the actual space width is less than the minimum without causing the effective space width to be undersized, or if the actual tooth thickness is more than the maximum without causing the effective tooth thickness to be oversized, the effective variation is less than anticipated; such parts are desirable and not defective. The specification of these dimensions as processing reference dimensions is optional. They are also used to analyze undersize effective space width or oversize effective tooth thickness conditions to determine whether or not these conditions are caused by excessive effective variation.

最小实际弧齿槽宽和最大实际弧齿厚：这些尺寸不能用于作为接收或拒收零件的标准。如果实际弧齿槽宽小于最小值，但没有影响最小作用弧齿槽宽，或者如果实际弧齿厚大于最大值，但没有影响到最大作用弧齿厚，这种偏差小于期望值的零件是可用的，不应判定为不合格品。这些尺寸在工艺中仅作为非强制性的参考尺寸。它们也可以用于分析过小作用弧齿槽宽或过大作用弧齿厚的情况，以判定这些情况是否由于超差的作用误差造成的。

Maximum Actual Space Width and Minimum Actual Tooth Thickness: These dimensions control machining tolerance and limit the effective variation. The spread between these dimensions, reduced by the effective variation of the internal and external spline, is the maximum effective clearance. Where the effective variation obtained in machining is appreciably less than the variation allowance, these dimensions must be adjusted in order to maintain the desired fit.

最大实际弧齿槽宽和最小实际弧齿厚：这些尺寸控制加工误差和作用误差的极限。这些尺寸范围，由于内花键和外花键的作用偏差而减少，得到最大的作用侧隙。加工中的作用偏差（值）略小于综合公差时，这些尺寸必须经过适当调整以保证预期的配合。

Maximum Effective Space Width and Minimum Effective Tooth Thickness: These dimensions define the maximum effective clearance but they do not limit the effective variation. They may be used, in addition to the maximum actual space width and minimum actual tooth thickness, to prevent the increase of maximum effective clearance due to reduction of effective variations. The notation ―inspection optional‖ may be added where maximum effective clearance is an assembly requirement, but does not need absolute control. It will indicate, without necessarily adding inspection time and equipment, that the actual space width of the internal spline must be held below the maximum, or the actual tooth thickness of the external spline above the minimum, if machining methods result in less than the allowable variations. Where effective variation needs no control or is controlled by laboratory inspection, these limits may be substituted for maximum actual space width and minimum actual tooth thickness.

最大作用弧齿槽宽和最小作用弧齿厚：这些尺寸定义了最大的作用侧隙，但它们不能限定作用偏差。它们可用作为“最大实际弧齿槽宽”和“最小实际弧齿厚”的附加（检验或控制方式），以防止由于减少作用偏差而引起的“最大作用侧隙”变大（超过最大值）。“非强制的检测”一词可以作为装配要求附加在那些“最大作用侧隙”上，但不要求完全控制的情况。它的意思是：如果加工方法（产生的偏差）小于综合公差，不增加这些“非强制的检验”，那么“内花键实际弧齿槽宽”必须控制在最大以内，或者“外花键实际弧齿厚”必须控制在最小值以上。如果不要求控制作用偏差或者这个靠实验室检测控制，那么这些限制可以代替“最大实际弧齿槽宽”和“最小作用弧齿厚”。

译注E3：此项检验方法，请参照《GB3478.1-2008》中图6的检验图解。意思是：内花键，用止规检验“最大实际弧齿宽”，能止住，就表示“最大作用弧齿槽宽”是公差范围内的；外花键，用止规检验最小实际弧齿槽宽，能止住，就表示“最小作用弧齿宽”是公差范围内的。这个前提是加工公差要很小。这个代替检验的原因是实际的弧齿槽宽和弧齿厚难以检验。

Combinations of Involute Spline Types.— Flat root side fit internal splines may be used with fillet root external splines where the larger radius is desired on the external spline for

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control of stress concentrations. This combination of fits may also be permitted as a design option by specifying for the minimum root diameter of the external, the value of the minimum root diameter of the fillet root external spline and noting this as ―optional root.‖

渐开线花键种类的混合使用—当外花键需要控制应力集中，而采用大的圆角半径时，平齿根齿侧配合的内花键和圆齿根外花键可以混合使用。这种配合也可指定在外花键的最小齿根圆直径，这个值标明是一个“可选值”。

A design option may also be permitted to provide either flat root internal or fillet root internal by specifying for the maximum major diameter, the value of the maximum major diameter of the fillet root internal spline and noting this as ―optional root.‖ 还有一种允许的设计选择是，指定内花键平齿根或者是内花键圆齿根的最大值，也是“可选值”。

Interchangeability.— Splines made to this standard may interchange with splines made to older standards. Exceptions are listed below.

互换性。－按本标准制造的花键与按旧标准制造的花键具有互换性。例外情况如下。

External Splines: These external splines will mate with older internal splines as follows: 外花键：这些外花键与老旧标准内花键相配情况如下：

Year年代 1946 1950b 1950C 1957 SAE 1960 Major Dia.Fit Flat Root Side Fit Fillet Root Side Fit 外径配合平齿根齿侧配合圆齿根齿侧配合可以不可以（A）a 不可以（A）可以（B）可以（B）可以（C）可以（B）不可以（A）可以（C）可以不可以（A）可以（C）可以不可以（A）可以（C） a For exceptions A, B, C, see the paragraph on Exceptions that follows. 对于ABC例外情况见后面解释。

b Full dedendum. 全齿根 c Short dedendum. 短齿根

Internal Splines: These will mate with older external splines as follows: 内花键：这些花键按如下情况与旧标准外花键相配情况如下：

Major Dia.Fit Flat Root Side Fit Fillet Root Side Fit Year年代外径配合平齿根齿侧配合圆齿根齿侧配合 1946 不可以（D）a 不可以（E）不可以（D） 1950 可以（F）可以可以（C） 1957 SAE 可以（G）可以可以 1960 可以（G）可以可以 a For exceptions C, D, E, F, G, see the paragraph on Exceptions that follows. 对于 C、D、E、F、G，见下后面解释。

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Root Side Fit ANSI B92.1-1970, R1993 30-Deg Pressure Angle The fit shown is used in restricted areas (as with tubular parts with wall thickness too small to permit use of fillet roots, and to allow hobbing closer to shoulders, etc.) and for economy (when hobbing, shaping, etc., and using shorter broaches for the internal member). 图中表示只适用限定的范围（比如不允许圆角的管状壁厚，或者滚铣接近基体等），也更经济。 Press fits are not tabulated because their design depends on the degree of tightness desired and must allow for such factors as the shape of the blank, wall thickness, material, hardness, thermal expansion, etc. Close tolerances or selective size grouping may be required to limit fit variations. 过盈配合未列出，因为设计要根据紧配的角度、毛坯形状、壁厚、材料硬度、热膨胀等个因素。应才用最接近或者标准化的尺寸用于限制配合偏差。 Drawing Data 图纸参数 Internal Involute Spline Data Flat Root Side Fit Number of Teeth xx Pitch xx/xx Pressure Angle 30° Base Diameter x.xxxxxx Ref Pitch Diameter x.xxxxxx Ref Major Diameter x.xxx max Form Diameter x.xxx Minor Diameter x.xxx/x.xxx Circular Space Width Max Actual x.xxxx Min Effective x.xxxx The following information may be added as required: Max Measurement Between Pins x.xxx Ref Pin Diameter x.xxxx The following information may be added as required: Min Measurement Over Pins x.xxxx Ref Pin Diameter x.xxxx Circular Tooth Thickness Max Effective x.xxxx Min Actual x.xxxx External Involute Spline Data Flat Root Side Fit Number of Teeth xx Pitch xx/xx Pressure Angle 30° Base Diameter x.xxxxxx Ref Pitch Diameter x.xxxxxx Ref Major Diameter x.xxx/x.xxx Form Diameter x.xxx Minor Diameter x.xxx min The above drawing data are required for the spline specifications. The standard system is shown; for alternate systems, see Table 5. Number of x's indicates number of decimal places normally used. 上表的参数是花键必须指定的。不同（使用）情况见表5。表中x.x表示小数位数。

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INVOLUTE SPLINES Page 22 of 38 Exceptions:

a) The external major diameter, unless chamfered or reduced, may interfere with the internal form diameter on flat root side fit splines. Internal splines made to the 1957 and 1960 standards had the same dimensions as shown for the major diameter fit splines in this standard.

除非倒角或减小尺寸，外花键大径可能与平根齿侧配合内花键在“渐开线构成圆”处产生干涉。按1957和1960版制造的外径配合的内花键，与本标准尺寸相同。

b) For 15 teeth or less, the minor diameter of the internal spline, unless chamfered, will interfere with the form diameter of the external spline. 小于或等于15齿的内花键小径，除非倒角，否则可能和外花键的渐开线构成圆产生干涉。 c) For 9 teeth or less, the minor diameter of the internal spline, unless chamfered, will interfere with form diameter of the external spline.

小于或等于9齿的内花键小径，除非倒角，否则可能和外花键的渐开线构成圆产生干涉。 d) The internal minor diameter, unless chamfered, will interfere with the external form diameter.

除非倒角，内花键的小径将与外花键的渐开线构成圆产生干涉。

e) The internal minor diameter, unless chamfered, will interfere with the external form diameter.

除非倒角，内花键的小径将与外花键的渐开线构成圆产生干涉。

f) For 10 teeth or less, the minimum chamfer on the major diameter of the external spline may not clear the internal form diameter.

小于或等于10齿的外花键大径的最小倒角尺寸应保证不可以超过内花键渐开线构成圆。 g) Depending upon the pitch of the spline, the minimum chamfer on the major diameter may not clear the internal form diameter.

G）依据花键的径节，大径的最小倒角不可以超过内花键的渐开线构成圆。

Drawing Data.— It is important that uniform specifications be used to show complete information on detail drawings of splines. Much misunderstanding will be avoided by following the suggested arrangement of dimensions and data as given in Table 6. The number of x's indicates the number of decimal places normally used. With this tabulated type of spline specifications, it is usually not necessary to show a graphic illustration of the spline teeth. 图纸参数－统一规范花键图面上的完整信息是很重要的。按表6中给出的推荐的参数（在图纸上列表）可以避免很多误解。X的数量表示小数常用的位数。利用表中花键规范，一般不再需要再示例一个花键齿的图形。

Spline Data and Reference Dimensions.— Spline data are used for engineering and manufacturing purposes. Pitch and pressure angle are not subject to individual inspection. As used in this standard, reference is an added notation or modifier to a dimension, specification, or note when that dimension, specification, or note is:

花键参数和参考尺寸。－花键参数用于工程和制造。径节和压力角不可以单独检测。本标准中，参考尺寸是一个增加的符号或修改的尺寸、规范或注解，如下： 1) Repeated for drawing clarification. 使图纸更清晰明确地表示。

2) Needed to define a nonfeature datum or basis from which a form or feature is generated. 需要为形状或特征的生成而定义一个非特征基准面或基准（系）。

3) Needed to define a nonfeature dimension from which other specifications or dimensions are developed.

需要为其它规范或尺寸的衍生而定义一个非特征尺寸

4) Needed to define a nonfeature dimension at which toleranced sizes of a feature are specified.

需要为指定特征的公差而定义一个非特征尺寸

译注F1：一般在图纸中还应标明公差。

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INVOLUTE SPLINES Page 23 of 38

5) Needed to define a nonfeature dimension from which control tolerances or sizes are developed or added as useful information.

需要为延伸或额外的尺寸或公差控制而定义一个非特征尺寸

Any dimension, specification, or note that is noted ―REF‖ should not be used as a criterion for part acceptance or rejection.

任何标明为“参考”的尺寸、规范或注解都不应当作为零件接收或拒收的标准。

Estimating Key and Spline Sizes and Lengths.— Fig. 3 may be used to estimate the size of American Standard involute splines required to transmit a given torque. It also may be used to find the outside diameter of shafts used with single keys. After the size of the shaft is found, the proportions of the key can be determined from Table 1 on page 2385. 估计齿、花键大小和长度－图3可以估计在一个给定传递扭矩的条件下，美国标准渐开线花键的尺寸。它也可以用于估计带单键的轴的外径。在确定轴的尺寸后，键槽的比例可以在2385页（原件）中的表1确定。

Curve A is for flexible splines with teeth hardened to Rockwell C 55–65. For these splines, lengths are generally made equal to or somewhat greater than the pitch diameter for diameters below 11?4 inches; on larger diameters, the length is generally one-third to two-thirds the pitch diameter. Curve A also applies for a single key used as a fixed coupling, the length of the key being one to one and one-quarter times the shaft diameter. The stress in the shaft, neglecting stress concentration at the keyway, is about 7500 pounds per square inch. See also Effect of Keyways on Shaft Strength starting on page 302.

曲线A是用于花键齿硬度为HRC55~65 柔性花键。对于直径低于1.25英寸的花键，这些花键的键的长度一般制成等于或略大于节圆直径；对于大直径的花键，花键长度一般为节圆直径的 1/3 到2/3。曲线 A 也可以用于一个固定联轴器的单键。键的长度是轴径的1到1 1/4倍。轴上的压力，不考虑键槽处的应力集中，大约为7500磅每平方英寸。可见从302页（原件）开始“键槽对轴强度的影响”。

Curve B represents high-capacity single keys used as fixed couplings for stresses of 9500 pounds per square inch, neglecting stress concentration. Key-length is one to one and one- quarter times shaft diameter and both shaft and key are of moderately hard heat-treated steel. This type of connection is commonly used to key commercial flexible couplings to motor or generator shafts.

曲线 B 代表使用于固定联轴器，应力为 9500 磅每平方英寸的高强度单键，不考虑应力集中。键的长度是轴径的1到1 1/4倍。轴和键都是中等硬度热处理钢。这种连接形式一般用于商用柔性联轴器与电机或与发电机的轴连接。

Curve C is for multiple-key fixed splines with lengths of three-quarters to one and one- quarter times pitch diameter and shaft hardness of 200–300 BHN.

曲线 C 用于长度为节圆直径为 3/4 到 1 1/4，轴硬度为200－300HB的多键固定花键。

Curve D is for high-capacity splines with lengths one-half to one times the pitch diameter. Hardnesses up to Rockwell C 58 are common and in aircraft applications the shaft is generally hollow to reduce weight.

曲线 D 用于长度为1/2 到1倍节圆直径的高强度花键。硬度一般为HRC58，在航空应用中，轴一般为中空以减少重量。

Curve E represents a solid shaft with 65,000 pounds per square inch shear stress. For hollow shafts with inside diameter equal to three-quarters of the outside diameter the shear stress would be 95,000 pounds per square inch.

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INVOLUTE SPLINES Page 24 of 38

曲线E代表剪切应力为65000 磅每平方英寸的实心轴。对于内径为外径3/4的空心轴，剪切应力为95000磅每平方英寸。

Torque, lb-inches

Fig. 3. Chart for Estimating Involute Spline Size Based on Diameter-Torque Relationships

Pitch Diameter inches

Maximum Effective Length Le, inches

Fig. 4. Maximum Effective Length for Fixed and Flexible Spline

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INVOLUTE SPLINES Page 25 of 38

Length of Splines: Fixed splines with lengths of one-third the pitch diameter will have the same shear strength as the shaft, assuming uniform loading of the teeth; however, errors in spacing of teeth result in only half the teeth being fully loaded. Therefore, for balanced strength of teeth and shaft the length should be two-thirds the pitch diameter. If weight is not important, however, this may be increased to equal the pitch diameter. In the case of flexible splines, long lengths do not contribute to load carrying capacity when there is misalignment to be accommodated. Maximum effective length for flexible splines may be approximated from Fig. 4. 花键长度：假定花键齿均匀受载，长度为节圆直径1/3的固定式花键将具有与轴等同的剪切应力；但花键齿齿槽的误差会导致只有一半的花键齿全部受载。因此，为平衡花键齿和轴的受力，长度应当等于节圆直径的2/3。如果重量不重要，就可以增加至等于节圆直径的长度。对于柔性花键，当存在不同心的情况下，增加长度并不能带来更多负载能力。柔性花键的最大作用长度可以按图4选择近似值。

Formulas for Torque Capacity of Involute Splines.— The formulas for torque capacity of 30-degree involute splines given in the following paragraphs are derived largely from an article ―When Splines Need Stress Control‖ by D. W. Dudley, Product Engineering, Dec.23, 1957.

渐开线花键扭矩能力公式—下列段落中给出的 30 度渐开线花键公式大部分来源于文章“花键何时需要应力控制”（作者 D.W.Dudley，制造工程，1957-12-23）。

In the formulas that follow the symbols used are as defined on page 2161 with the following additions: Dh = inside diameter of hollow shaft, inches; Ka = application factor from Table 7; Km = load distribution factor from Table 8; Kf = fatigue life factor from Table 9; Kw= wear life factor from Table 10; Le = maximum effective length from Fig. 4, to be used in stress formulas even though the actual length may be greater; T = transmitted torque, pound-inches. For fixed splines without helix modification, the effective length Le should never exceed 5000 D3.5 ÷ T. 公式中的符号在 2161页上定义的，下列为增加的补注：Dh=空心轴的内孔直径，英寸；Ka=应用系数，从表7中选择；Km＝负荷分布系数，从表8中选择；Kf＝疲劳寿命系数，从表9中选取；Kw＝磨损寿命系数，从表10中选取；Le＝图4中的最大作用长度，尽管实际长度可能更长一些，仍可使用应力公式；T＝传递扭矩，磅-英寸。对于没有螺旋线变位的固定式花键，有效长度Le应当不超过 5000 D3.5÷T。

Table 7. Spline Application Factors, Ka Power Source 动力源 Type of Load载荷种类 Light Shock Intermittent Shock Uniform (Oscillating (Actuating Pumps, (Generator, Fan) Pumps, etc.) 轻微etc.) 间歇冲击（加速平稳（发电机风扇）冲击（振动泵等）泵等） Application Factor, Ka使用系数 1.0 1.2 2.0 1.2 1.3 2.2 1.5 1.8 2.4 Heavy Shock (Punches, Shears, etc.) 重冲击（冲床，剪子等） 1.8 2.1 2.8 Uniform (Turbine, Motor) 同步机（涡轮机，电机） Light Shock (Hydraulic Motor) 轻微冲击（液压马达） Medium Shock (Internal Combustion, Engine)中等冲击（内燃机，引擎） Table 8. Load Distribution Factors, Km, for Misalignment of Flexible Splines Misalignment, inches per inch 每英寸长度上不对中度 0.001 0.002 0.004 0.008 Load Distribution Factor, Kma 1/2-in. Face Width2 1 1 1 1 1/2 1-in. Face Width 1 1 1 1/2 2 2-in. Face Width 1 1 1/2 2 2 1/2 4-in. Face Width 1 1/2 2 2 1/2 3 a

For fixed splines, 对于固定的花键Km=1.

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INVOLUTE SPLINES Page 26 of 38

Table 9. Fatigue-Life Factors, Kf, for Splines No. of Torque Cyclesa a扭矩循环周期 1,000 10,000 100,000 1,000,000 10,000,000 a

Fatigue-Life Factor, Kf疲劳寿命系数 Unidirectional单一方向 1.8 1.0 0.5 0.4 0.3 Fully-reversed双向 1.8 1.0 0.4 0.3 0.2 A torque cycle consists of one start and one stop, not the number of revolutions. 一个扭矩循环周期包括一个起停，不是回转的数量。

Table 10. Wear Life Factors, Kw, for Flexible Splines Number of Revolutions of Spline 花键运转数量 10,000 100,000 1,000,000 10,000,000 Life Factor,，Kw 寿命系数 4.0 2.8 2.0 1.4 Number of Revolutions of Spline 100,000,000 1,000,000,000 10,000,000,000 … Life Factor, Kw 1.0 0.7 0.5 …

Wear life factors, unlike fatigue life factors given in Table 9, are based on the total number of revolutions of the spline, since each revolution of a flexible spline results in a complete cycle of rocking motion which contributes to spline wear.

磨损寿命系数，不是基于花键的运转总数量，如表9中的疲劳系数。因为柔性花键的每一转的冲击都会造成花键的磨损。

Definitions: A fixed spline is one which is either shrink fitted or loosely fitted but piloted with rings at each end to prevent rocking of the spline which results in small axial movements that cause wear. A flexible spline permits some rocking motion such as occurs when the shafts are not perfectly aligned. This flexing or rocking motion causes axial movement and consequently wear of the teeth. Straight-toothed flexible splines can accommodate only small angular misalignments (less than 1 deg.) before wear becomes a serious problem. For greater amounts of misalignment (up to about 5 deg.), crowned splines are preferable to reduce wear and end-loading of the teeth.

定义：一个固定花键可以是紧配合或松配合，但在每一端都用环固定以防止由于花键的磨损引起轴向的移动而产生的跳动。一个柔性花键允许一些在轴没有准确对中时产生的跳动。这些屈挠或跳动引起轴向位移，从而磨损齿形。直齿柔性花键的只有在很小的偏心角度状态（小于1度），磨损才不会很严重。对于更多的偏心情况（大于5度），鼓形齿花键可以更好地减小磨损和花键齿端部受载。

Shear Stress Under Roots of External Teeth: For a transmitted torque T, the torsional shear stress induced in the shaft under the root diameter of an external spline is:

外花键齿根部的剪切应力：对于一个给定的传递扭矩T，在外花轴齿根处产生的扭转剪切应力为：

16TKafor a solid shaft 用于实心轴 S s ? 3 （1）

?DreKf

16TDreKafor a hollow shaft 用于空心轴 S s ? 4（2）

?(Dre?Dh4)Kf

The computed stress should not exceed the values in Table 11. 计算应力值不能超过表11中的值。

Table 11. Allowable Shear, Compressive, and Tensile Stresses for Splines

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 27 of 38 Material 材料 Max. Allowable Stress 最大允应力 Compressive Stress, psi Shear Stress, psi Tensile Stress, psi 压缩应力剪切应力拉升应力 Brinell布氏 Rockwell C洛氏 Straight直的 Crowned鼓的 Hardness 硬度 160–200 230–260 302–351 — — — — — 33–38 48–53 58–63 42–46 20,000 30,000 40,000 40,000 50,000 45,000 1,500 2,000 3,000 4,000 5,000 — 6,000 8,000 12,000 16,000 20,000 — 22,000 32,000 45,000 45,000 55,000 50,000 Steel 钢 Surface-hardened Steel 表面淬硬钢 Case-hardened Steel 表面渗碳硬化钢 Through-hardened Steel (Aircraft Quality) 整体淬硬钢(航空质量) Shear Stress at the Pitch Diameter of Teeth: The shear stress at the pitch line of the teeth for a transmitted torque T is:

齿节圆处的剪切应力：对于一个给定的传递扭矩 T，齿节节圆处的剪切应力为： 4TKaKm S s ? （ 3 ）

DNLetKf

The factor of 4 in (3) assumes that only half the teeth will carry the load because of spacing errors. For poor manufacturing accuracies, change the factor to 6.

公式（3）中系数4是假设由于齿槽的间隙而只有一半花键齿承载。对于更低等级的制造精度，将系数改为 6。

The computed stress should not exceed the values in Table 11. 计算应力值不能超过表11中值。

Compressive Stresses on Sides of Spline Teeth: Allowable compressive stresses on splines are very much lower than for gear teeth since non-uniform load distribution and misalignment result in unequal load sharing and end loading of the teeth.

花键齿侧压缩应力：由于不均匀的载荷分布和偏心造成的不均负载和齿端受载，花键的许用压缩应力值比（理论值）要小得多。

2TKK For flexible splines,对于柔性花键 S c （ 4 ） ? a mDNLehKw

2TKaKm

For fixed splines, 对于固定花键 S c ? （5）

9DNL e hK f

In these formulas, h is the depth of engagement of the teeth, which for flat root splines is 0.9/P and for fillet root splines is 1/P, approximately.

公式中，h 是花键齿的接合长度，对于平齿根花键，h约为 0.9/P，对于圆齿根花键，h约为1/P。

The stresses computed from Formulas (4) and (5) should not exceed the values in Table 11. 公式（4）和公式（5）中计算出的应力值不能够超过表11中的值。

Bursting Stresses on Splines: Internal splines may burst due to three kinds of tensile stress: 1) tensile stress due to the radial component of the transmitted load; 2) centrifugal tensile stress; and 3) tensile stress due to the tangential force at the pitch line causing bending of the teeth. 花键的抗裂应力：内花键可能由于下列三种拉应力而破坏：1）传递扭矩中产生的径向分

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 28 of 38 解力引起的拉伸力；2）离心力； 3）节圆线上由于齿弯曲而造成的拉伸力。

Ttan?Radial load tensile stress, 径向负荷拉伸应力， (6) S1? ? Dt w L

where tw = wall thickness of internal spline = outside diameter of spline sleeve minus spline major diameter, all divided by 2. L = full length of spline.

这里，tW=内花键的壁厚＝内花键筒的外径减去花键大径，后再除 2。L＝花键的总长，

1.6556?(rpm)2(Doi2?0.212Dri2)Centrifugal tensile stress, 离心拉伸应力 (7) S2? 1 ,000,000

where Doi = outside diameter of spline sleeve. Doi＝花键套筒的外径。

4TBeam loading tensile stress, 梁拉伸应力， (8) S3?2DLeY

In Equation (8), Y is the Lewis form factor obtained from a tooth layout. For internal splines of 30-deg. pressure angle a value of Y= 1.5 is a satisfactory estimate. The factor 4 in (8) assumes that only half the teeth are carrying the load.

在这个等式（8）中，Y是花键设计得到的一个刘易斯形状系数。对于 30 度压力角的内花键Y＝1.5是一个很保守的估计值。系数4假定只有一半花键齿承受载荷。

The total tensile stress tending to burst the rim of the external member is: and should be less than those in Table 11.

造成外花键的轮缘破坏的总的拉伸应力是： St = [KaKm (S1 + S3) + S2]/Kf; 并且该值应小于表11中值。

Crowned Splines for Large Misalignments.— As mentioned on page 2173, crowned splines can accommodate misalignments of up to about 5 degrees. Crowned splineshave considerably less capacity than straight splines of the same size if both are operating with precise alignment. However, when large misalignments exist, the crowned spline has greater capacity.

大偏心鼓形齿花键。－正如第 2173页中提到的，鼓形齿花键能够允许最大5度的偏心。如果在运转时，同尺寸的鼓形齿花键和直齿花键都精确对中，那么鼓形齿花键的性能要比直齿花键要小，当偏心较大，那么性能就大。

American Standard tooth forms may be used for crowned external members so that they may be mated with straight internal members of Standard form.

美国标准花键齿形状可以用于鼓形齿的外花键，这样它们就可以与美国标准的直齿的内花键相配合。

The accompanying diagram of a crowned spline shows the radius of the crown r1; the radius of curvature of the crowned tooth, r2; the pitch diameter of the spline, D; the face width, F; and the relief or crown height A at the ends of the teeth. The crown height A should always be made somewhat greater than one-half the face width multiplied by the tangent of the

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 29 of 38 misalignment angle. For a crown height A, the approximate radius of curvature r2 is F2 ÷ 8A, and r1 = r2 tan Φ, where Φ is the pressure angle of the spline.

附图说明了美国标鼓形半径 r1，曲率半径 r2，节圆直径D，齿向宽F，齿端的鼓形量A。鼓形量A制造时应总是大于“齿向宽的一半乘以偏心角的正切”。曲率半径r2的近似值为F2 ÷ 8A，并且r1 = r2 tan Φ，Φ表示压力角。

For a torque T, the compressive stress on the teeth is: 对于一个给定的扭矩 T，花键齿的压缩应力为： Sc?22902T?DNhr2

and should be less than the value in Table 11. 并且，该值不能超过表11中的值。

Fretting Damage to Splines and Other Machine Elements.— Fretting is wear that occurs when cyclic loading, such as vibration, causes two surfaces in intimate contact to undergo small oscillatory motions with respect to each other. During fretting, high points or asperities of the mating surfaces adhere to each other and small particles are pulled out, leaving minute, shallow pits and a powdery debris. In steel parts exposed to air, the metallic debris oxidizes rapidly and forms a red, rustlike powder or sludge; hence, the coined designation ―fretting corrosion.‖

周期负载形成了磨损，如振动，在小幅振动下，造成了（内齿和外齿）两面的直接紧密的接触。在摩擦中，（表面的最高的）极限点或粗糙部，相互作用，就形成了微小颗粒，一段时间后，就会有小的坑或粉状碎片存在。金属部件暴露在空气中，金属碎片就会很快氧化成一个个红色的、铁锈色的粉末或泥状物。由此，产生叫“fretting corrosion”（磨损腐蚀）的名词。

Fretting is mechanical in origin and has been observed in most materials, including those that do not oxidize, such as gold, platinum, and nonmetallics; hence, the corrosion accompanying fretting of steel parts is a secondary factor.

磨损的机械中固有的，大多数材料都会发生，包括那些不会被氧化的物质，如：金、铂和非金属类；所以金属件的腐蚀是第二位的特性。

Fretting can occur in the operation of machinery subject to motion or vibration or both. It can destroy close fits; the debris may clog moving parts; and fatigue failure may be accelerated because stress levels to initiate fatigue in fretted parts are much lower than for undamaged material. Sites for fretting damage include interference fits; splined, bolted, keyed, pinned, and riveted joints; between wires in wire rope; flexible shafts and tubes; between leaves in leaf springs; friction clamps; small amplitude-of-oscillation bearings; and electrical contacts.

磨损可发生在机械设备的运作时的转动或振动或者两者兼之。它可以破坏紧配合，碎片可以阻碍零件运动；由于发生磨损的零件比没损坏的零件的疲劳承受能力要低很多，所以磨损会加速疲劳失效。发生磨损破坏的地方有接触面，花键、螺栓、键、销和铆钉连接；线丝和线圈；柔性轴和管；触片和片簧；磨擦钳；小的摆动轴承和电接触零件。

Vibration or cyclic loadings are the main causes of fretting. If these factors cannot be eliminated, greater clamping force may reduce movement but, if not effective, may actually worsen the damage. Lubrication may delay the onset of damage; hard plating or surface hardening methods may be effective, not by reducing fretting, but by increasing the fatigue strength of the material. Plating soft materials having inherent lubricity onto contacting surfaces is effective until the plating wears through.

振动和周期负荷是磨损的主要产生原因。如果这样因素不能消除，使用更大的夹紧力可以减小位移，但如果它不起作用，反而会使损坏情况更严重。润滑可以减缓损坏的过程；硬平板或表面硬化方法可以起作用，这些方法不能减小磨损，只是增加了材料的疲劳延伸强度。具有内在自润滑功能的平板软材料在磨穿前能够起到（减少磨损）作用。

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Involute Spline Inspection Methods.— Spline gages are used for routine inspection of production parts.

渐开线花键检测方法－花键量规可以用于零件的常规检测。

Analytical inspection, which is the measurement of individual dimensions and variations, may be required:

下列情况需要单个尺寸和偏差的分析检测：

a) To supplement inspection by gages, for example, where NOT GO composite gages are used in place of NOT GO sector gages and variations must be controlled.

作为规的附加检测，例如，使用组合通止规代替单个止规，并且误差必须控制的情况。 b) To evaluate parts rejected by gages。评价用规检测拒收的零件。 c) For prototype parts or short runs where spline gages are not used. 试样或短期加工不能使用规的情况。

d) To supplement inspection by gages where each individual variation must be restrained from assuming too great a portion of the tolerance between the minimum material actual and the maximum material effective dimensions.

当在“最小实体尺寸和最大作用尺寸”之间的公差区域很大，它们的当个单个偏差必须限定时，作为规的附加检测。

Inspection with Gages.— A variety of gages is used in the inspection of involute splines. 量规检测－各式的量规用于检测渐开线花键。

Types of Gages: A composite spline gage has a full complement of teeth. A sector spline gage has two diametrically opposite groups of teeth. A sector plug gage with only two teeth per sector is also known as a ―paddle gage.‖ A sector ring gage with only two teeth per sector is also known as a ―snap ring gage.‖ A progressive gage is a gage consisting of two or more adjacent sections with different inspection functions. Progressive GO gages are physical combinations of GO gage members that check consecutively first one feature or one group of features, then their relationship to other features. GO and NOT GO gages may also be combined physically to form a progressive gage.

量规的种类：一个综合花键量规具有全齿。一个单独的花键量规具有一个相对齿形成的直径。单个只有两个齿的塞规称作“叶片规”，单个只有两齿的环规叫做“环卡规”。一个递进规是一种包括相邻有二个或更多区域的，用来检测不同功能的检测量规。递进通规是能够“先检测一个或一组特征（合格与否），再检测它们相互关系的特征（合格与否）”的组合实体。通规和止规可以合并在起组成一个递进规。

Fig. 5. Space width and tooth-thickness inspection.

GO and NOT GO Gages: GO gages are used to inspect maximum material conditions (maximum external, minimum internal dimensions). They may be used to inspect an individual

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dimension or the relationship between two or more functional dimensions. They control the minimum looseness or maximum interference.

通规和止规：通规是用于检测最大实体状态（最大外径，最小内部尺寸）。它们可以用于检测一个单个尺寸，或者两个及两个以上功能性尺寸。它们控制最小间隙或最大干涉的程度。

NOT GO gages are used to inspect minimum material conditions (minimum external, maximum internal dimensions), thereby controlling the maximum looseness or minimum interference. Unless otherwise agreed upon, a product is acceptable only if the NOT GO gage does not enter or go on the part. A NOT GO gage can be used to inspect only one dimension. An attempt at simultaneous NOT GO inspection of more than one dimension could result in failure of such a gage to enter or go on (acceptance of part), even though all but one of the dimensions were outside product limits. In the event all dimensions are out- side the limits, their relationship could be such as to allow acceptance.

止规是用于检测最小实体状态（最小外径、最大内部尺寸），这样控制最大的间隙或最小干涉程度。除非达成共识，一个产品只有在止规不能够进入或穿过零件时才可接受。一个止规只能用于检测一个尺寸。用一个“组合”的止规，来检验多个尺寸，会导致这止规不能进入或通过（合格的部分），因为仅仅一个尺寸超差，止规就不能进入或通过产品。更甚者，所有尺寸都超差，但它们的“组合关系”确实合格的（尺寸超差，止规却能止住）。

译注G1：例如一个零件是2个尺寸，那么通止规是：1通2止。在国标《GB/T 3478.1》中，基本方法是综合通端量规+非全齿止端量规，而不是“全齿止规”。只有在加入其它方法后，才可以使用综合止规。例如方法A和方法B。 .

Effective and Actual Dimensions: The effective space width and tooth thickness are inspected by means of an accurate mating member in the form of a composite spline gage. The actual space width and tooth thickness are inspected with sector plug and ring gages, or by measurements with pins.

作用和实际尺寸：作用弧齿槽宽和弧齿厚是通过一个在构成圆上精确的配对的复合量规来检验。实际弧齿槽宽和弧齿厚是通单独的通规或环规来检验，或者通过量棒来测量。

Measurements with Pins.— The actual space width of internal splines, and the actual tooth thickness of external splines, may be measured with pins. These measurements do not determine the fit between mating parts, but may be used as part of the analytic inspection of splines to evaluate the effective space width or effective tooth thickness by approximation.

量棒测量。－内花键的实际弧齿槽宽和外花键的实际弧齿厚可以用量棒测量。这些测量不能够决定配合件之间的装配，但可以用于花键的一种分析检测，以近似评价作用弧齿槽宽和作用弧齿厚。

Formulas for 2-Pin Measurement Between Pins: For measurement between pins of internal splines using the symbols given on page 2161:

两个量棒检测的棒间距公式：对于内花键的棒间距使用的符号在 2161页中给出：

1) Find involute of pressure angle at pin center: 算出量棒中心的压力角： disinv?i??inv?d?

DDb

2) Find the value of Φi in degrees, in the involute function tables beginning on page 110. Find secΦi= 1/cos ineΦi in the trig tables, pages 106 through 108, using interpolation to obtain higher accuracy.

在第110页开始的渐开线函数表中查出Φi的角度值。在106到108页的三角函数表上找出secΦi= 1/ cos ineΦi 的值，可用插值法得到更高的精度，。

译注G2：渐开线函数和渐开线反函数，一般用软件查询。

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3) Compute measurement, Mi, between pins: 计算棒间距Mi For even numbers of teeth对于偶数齿: Mi = Db sec Φi ? di

For odd numbers of teeth对于奇数齿: Mi = (Db cos 90°/N) sec Φi ? di

where: di = 1.7280/P for 30° and 37.5° standard pressure angle (ΦD) splines. 30和 37.5度

di = 1.9200/P for 45° pressure angle splines. 45°压力角

Example: Find the measurement between pins for maximum actual space width of an internal spline of 30° pressure angle, tolerance class 4, 3/6 diametral pitch, and 20 teeth.

举例：用针规测量方法计算，30度压力角，公差等级4，3/6径节，20齿的棒间距来判定最大实际弧齿槽宽。

The maximum actual space width to be substituted for s in Step 1 above is obtained as follows: In Table 5, page 2167, the maximum actual space width is the sum of the minimum effective space width (second column) and λ + m (third column). The minimum effective space width sv from Table 2, page 2162, is π/2P = π/(2 × 3). The values of λ and m from Table 4, page 2164, are, for a class 4 fit, 3?6 diametral pitch, 20-tooth spline: λ =0.0027 × 0.71 = 0.00192; and m = 0.00176 × 0.71 = 0.00125, so that s = 0.52360 + 0.00192+ 0.00125 = 0.52677.

按第1步，表5，第2167页，最大实际弧齿槽宽=最小作用弧齿槽宽+（λ + m），（2列，3列），最小作用弧齿槽宽Sv从表2，地2162页，=π/2P = π/(2 × 3)。λ 和m的值从表4，第2164页等级4，径节为3/6，20齿中查询：λ =0.0027 × 0.71 = 0.00192，m = 0.00176 × 0.71 = 0.00125,可得：s = 0.52360 + 0.00192+ 0.00125 = 0.52677

Other values required for Step 1 are:步骤1所需的其它值 D= N ÷ P = 20 ÷ 3 = 6.66666

inv ΦD = inv 30° = 0.053751 from a calculator计算器计算 di = 1.7280 ?3 = 0.57600

Db =D cos ΦD = 6.66666 × 0.86603 = 5.77353 The computation is made as follows:计算值如下

1) inv Φi = 0.52677 ?6.66666 + 0.053751 ? 0.57600 ?5.77353 = 0.03300 2) From a calculator, Φi = 25°46.18 ′ and sec Φi = 1.11044 3) Mi = 5.77353 × 1.11044 ? 0.57600 = 5.8352 inches

Formulas for 2-Pin Measurement Over Pins: For measurement over pins of external splines: 对于外花键的棒间距的测量：

1）Find involute of pressure angle at pin center: 计算量棒中心的渐开线压力角： de?tinv???inv??? eDDDbN

2）Find the value of Φe and sec Φe from the involute function tables beginning on page 110. 从第110页开始的渐开线函数表中找出Φe和 secΦe 的值。

3) Compute measurement, Me, over pins: 计算跨棒距，Me For even numbers of teeth: 对于偶数齿： Me = Db sec Φe + de

For odd numbers of teeth: 对于奇数齿： Me = (Db cos 90°/N) sec Φe + de where de = 1.9200/P for all external splines 所有外花键De=1.9200/P

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 33 of 38 （以下为美国标准ANSI B92.2M-1980 渐开线花键，米制部分，一并摘录做参考。） American National Standard Metric Module Splines.— ANSI B92.2M-1980 (R1989) is the American National Standards Institute version of the International Standards Organization involute spline standard. It is not a ―soft metric‖ conversion of any previous, inch- based, standard,* and splines made to this hard metric version are not intended for use with components made to the B92.1 or other, previous standards. The ISO 4156 Standard from which this one is derived is the result of a cooperative effort between the ANSI B92 committee and other members of the ISO/TC 14-2 involute spline committee.

* A ―soft‖ conversion is one in which dimensions in inches, when multiplied by 25.4 will, after being appropriately rounded off, provide equivalent dimensions in millimeters. In a ―hard‖ system the tools of production, such as hobs, do not bear a usable relation to the tools in another system; i.e., a 10 diametral pitch hob calculates to be equal to a 2.54 module hob in the metric module system, a hob that does not exist in the metric standard.

Many of the features of the previous standard, ANSI B92.1-1970 (R1993), have been retained such as: 30-, 37.5-, and 45-degree pressure angles; flat root and fillet root side fits; the four tolerance classes 4, 5, 6, and 7; tables for a single class of fit; and the effective fit concept.

Among the major differences are: use of modules of from 0.25 through 10 mm in place of diametral pitch; dimensions in millimeters instead of inches; the ―basic rack‖; removal of the major diameter fit; and use of ISO symbols in place of those used previously. Also, pro- vision is made for calculating three defined clearance fits.

The Standard recognizes 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, the internal spline major diameter 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 require no additional control. All dimensions are for the finished part; any compensation that must be made for operations that take place during processing, such as heat treatment, must be considered when selecting the tolerance level for manufacturing.

The Standard provides the same internal minimum effective space width and external maximum effective tooth thickness for all tolerance classes. This basic concept makes possible interchangeable assembly between mating splines regardless of the tolerance class of the individual members, and permits a tolerance class ―mix‖ of mating members. This arrangement is often an advantage when one member is considerably less difficult to pro- duce than its mate, and the ―average‖ tolerance applied to the two units is such that it satisfies the design need. For example, by specifying Class 5 tolerance for one member and Class 7 for its mate, an assembly tolerance in the Class 6 range is provided.

If a fit given in this Standard does not satisfy a particular design need, and a specific clearance or press fit is desired, the change shall be made only to the external spline by a reduction of, or an increase in, the effective tooth thickness and a like change in the actual tooth thickness. The minimum effective space width is always basic and this basic width should always be retained when special designs are derived from the concept of this Standard.

Spline Terms and Definitions: The spline terms and definitions given for American National Standard ANSI B92.1-1970 (R1993) described in the preceding section, may be used in regard to ANSI B92.2M-1980 (R1989). The 1980 Standard utilizes ISO symbols in place of those used in the 1970 Standard; these differences are shown in Table 12.

Dimensions and Tolerances: Dimensions and tolerances of splines made to the 1980

Standard may be calculated using the formulas given in Table 13. These formulas are for metric module splines in the range of from 0.25 to 10 mm metric module of side-fit design and having pressure angles of 30-, 37.5-, and 45-degrees. The standard modules in the system are:

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0.25; 0.5; 0.75; 1; 1.25; 1.5; 1.75; 2; 2.5; 3; 4; 5; 6; 8; and 10. The range of from 0.5 to 10 module applies to all splines except 45-degree fillet root splines; for these, the range of from 0.25 to 2.5 module applies.

Fit Classes: Four classes of side fit splines are provided: spline fit class H/h having a minimum effective clearance, cv = es = 0; classes H/f, H/e, and H/d having tooth thickness modifications, es, of f, e, and d, respectively, to provide progressively greater effective clearance cv, The tooth thickness modifications h, f, e, and d in Table 14 are fundamental deviations selected from ISO R286, ―ISO System of Limits and Fits.‖ They are applied to the external spline by shifting the tooth thickness total tolerance below the basic tooth thickness by the amount of the tooth thickness modification to provide a prescribed mini- mum effective clearance cv.

Table 12. Comparison of Symbols Used in ANSI B92.2M-1980 (R1989) and Those in ANSI B92.1-1970, R1993 （B92.1和B92.2符号区别） Symbol B92.2M B92.1 c … theoretical clearance cv cv effective clearance cF cF form clearance D D pitch diameter DB Db base diameter pin contact diameter, dce Dce external spline pin contact diameter, dci Dci internal spline DEE DEI DFE DFI DIE DII DRE DRI hs λ INV a KE KI g gw gγ T MRE MRI Z Do Dri DFe DFi Dre Di de di … λ … Ke Ki L … … m Me Mi N major diam., ext. spline major diam., int. spline form diam., ext. spline form diam., int. spline minor diam., ext. spline minor diam., int. spline pin diam., ext. spline pin diam., int. spline see Figs. 6a, 6b, 6c, and 6d effective variation involute α=tan α? arc α change factor, ext. spline change factor, int. spline spline length active spline length length of engagement machining tolerance meas. over 2 pins, ext. spline Symbol B92.2M B92.1 m … … P … Ps Pb … p p π rfe rfi Ebsc Emax Emin Ev Sbsc Smax smin SV α αD αci αce αi αe αFe αFi es π rf rf Svmin s s Sv tvmax t t tv Φ ΦD Φci Φce Φi Φe ΦF ΦF … module diametral pitch stub pitch = 2P base pitch circular pitch 3.141592654 fillet rad.,ext.spline fillet rad., int. spline basic circular space width max. actual circular space width min. actual circular space width effective circular space width basic circular tooth thickness max. actual circular tooth thick min. actual circular tooth thick effective circular tooth thick. pressure angle standard pressure angle press. angle at pin contact diameter, internal spline press. angle at pin contact diameter, external spline press. angle at pin center, internal spline press. angle at pin center, external spline press. angle at form diameter, external spline press. angle at form diameter, internal spline ext. spline cir. tooth thick.modifi- cation for required fit class=cvmin (Table 14) tooth thick, size modifiers (called fundamental deviation in ISO R286), Table 14 space width size modifier (called fundamental deviation in ISO R286), Table 14 meas. bet. 2 pins, int. spline h,f,e,or d … number of teeth H …

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Table 13. Formulas for Dimensions and Tolerances for All Fit Classes—

Metric Module Involute Splines Formula Term Symbol 30-Degree Flat Root 0.5 to 10 module Pitch Diameter Base Diameter Circular Pitch Base Pitch Tooth Thick Mod Min Maj. Diam. Int Max Maj Diam. Int. Form Diam, Int. Min Minor Diam, Int Max Minor Diam,Int Cir Space Width, Basic Min Effective Max Actual Min Actual Max Effective Max Major Diam,Extd Min Major Diam.Ext Form Diam, External Max Minor Diam,Extd Min Minor Diam,Ext Cir Tooth Thick, Basic Max Effective Min Actual Max Actual Min Effective Total Tolerance on Circular Space Width or Tooth Thickness Machining Toler- ance on Circular Space Width or Tooth Thickness Effective Variation Allowed on Circu- lar Space Width or Tooth Thickness Form Clearance Rack Dimension D DB p pb es DEI min DEI max DFI DII min DII max Ebsc EV min E max E min EV max DEEmax DEEmin DFE DIE max DIE min Sbsc SV max S min S max SV min (T + λ) mZ mZ cos αD πm πm cos αD According to selected fit class, H/h, H/f, H/e, or H/d (see Table 14) m(Z + 1.5) m(Z + 1) + 2cF m(Z + 1.8) m(Z + 1)+2cF m(Z + 1.4) m(Z+0.9)+2cF m(Z + 1.2) m(Z+0.8)+2cF DEI min + (T + λ)/tan αD (see Footnote a) DFE + 2cF (see Footnote b) DII min + (0.2m0.667 ? 0.01m?0.5) (see Footnote c) 0.5πm 0.5πm EV min + (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) EV min + λ (see text on page 2181 for λ) E max ?λ (see text on page 2181 for λ) m(Z+1)-es/tanαD m(Z+1)-es/tanαD m(Z+0.9)-es/tanαD m(Z+0.8)-es/tanαD DEE max ? (0.2m0.667 ? 0.01m?0.5)c 30-Degree Fillet Root 0.5 to 10 module 37.5-Degree Fillet Root 0.5 to 10 module 45-Degree Fillet Root 0.25 to 2.5 module 2?(0.5Db)2?[0.5Dsin?D?m(Z ?1.8)?es/tanαD hs?((0.5es)/tan?D)2]sin?Dm(Z ?1.2)?es/tanαD m(Z ?1.5)-es/tanαD 0.5πm Sbsc ? es m(Z ?1.4)?es/tanαD DIE max ? (T + λ)/tan αD (see Footnote a) SV max ? (T + λ) for classes 4, 5, 6, and 7 (see Table 15 for T + λ) SV max ?λ (see text on page 2181 for λ) S min + λ (see text on page 2181 for λ) See formulas in Table 15 T T = (T + λ) from Table 15 ?λ from text on page 2181. λ cF hs See text on page 2181. 0.1m 0.6m(see Fig. 6a) 0.6m(see Fig. 6b) 0.55m(see Fig. 6c) 0.5m(see Fig. 6d) a Use (T + λ) for class 7 from Table 15

b For all types of fit, always use the DFE value corresponding to the H/h fit.

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c Values of (0.2m0.667 ? 0.01m?0.5) are as follows: for 10 module, 0.93; for 8 module, 0.80; for 6 mod- ule, 0.66; for 5 module, 0.58; for 4 module, 0.50; for 3 module, 0.41; for 2.5 module, 0.36; for 2 mod-ule, 0.31; for 1.75 module, 0.28; for 1.5 module, 0.25; for 1.25 module, 0.22; for 1 module, 0.19; for0.75 module, 0.15; for 0.5 module, 0.11; and for 0.25 module, 0.06.d See Table 17 for values of es/tan α D.

Table 14. Tooth Thickness Modification, es, for Selected Spline Fit Classes External Splinesa External Splinesa Selected Fit Class Selected Fit Class Pitch Pitch d e f h d e f h Diameter in Diameter in Tooth Thickness Modification Tooth Thickness Modification mm, mm, (Reduction) Relative to Basic (Reduction) Relative to Basic D D Tooth Thickness at Pitch Tooth Thickness at Pitch ≤ 3 0.020 0.014 0.006 0 > 120 to 0.145 0.085 0.043 0 > 3 to 6 0.030 0.020 0.010 0 180 0.170 0.100 0.050 0 > 6 to 10 0.040 0.025 0.013 0 > 180 to 0.190 0.110 0.056 0 > 10 to 18 0.050 0.032 0.016 0 250 0.210 0.125 0.062 0 > 250 to > 18 to 30 0.065 0.040 0.020 0 0.230 0.135 0.068 0 > 30 to 50 0.080 0.050 0.025 0 315 0.260 0.145 0.076 0 > 315 to > 50 to 80 0.100 0.060 0.030 0 0.290 0.160 0.080 0 > 80 to 120 0.120 0.072 0.036 0 400 0.320 0.170 0.086 0 > 400 to a Internal splines are fit class H and have space width modification from basic space width equal to zero; thus, an H/h fit class has effective clearance cv = 0.

Note: The values listed in this table are taken from ISO R286 and have been computed on the basis of the geometrical mean of the size ranges shown. Values in boldface type do not comply with any documented rule for rounding but are those used by ISO R286; they are used in this table to comply with established international practice.

Basic Rack Profiles: The basic rack profile for the standard pressure angle splines are shown in Figs. 6a, 6b, 6c, and 6d. The dimensions shown are for maximum material condition and for fit class H/h.

Spline Machining Tolerances and Variations.— The total tolerance (T + λ), Table 15, is the sum of Effective Variation, λ, and a Machining Tolerance, T.

Table 15. Space Width and Tooth Thickness Total Tolerance, (T + λ), in Millimeters Spline Formula for Spline Tolerance Total Tolerance, Tolerance Class Class T + λ) Formula for Total Tolerance, (T + λ) In these formulas, i* and i** are tolerance units based upon pitch diameter and tooth thickness, respectively: (√ is radication) i?= 0.001 (0.45 *3√D+0.001D) for D≤500 mm i?= 0.001 (0.004D + 2.1 ) for D > 500 mm i??= 0.001 (0.45 *3 √(Sbsc) + 0.001 Sbsc ) 4 5 10i* + 40i** 16i* + 64i** 6 7 25i* + 100i** 40i* + 160i** Effective Variation: The effective variation, λ, is the combined effect that total index variation, positive profile variation, and tooth alignment variation has on the effective fit of mating involute splines. The effect of the individual variations is less than the sum of the allowable variations because areas of more than minimum clearance can have profile, tooth alignment, or index variations without changing the fit. It is also unlikely that these variations would occur in their maximum amounts simultaneously on the same spline. For this reason, total index variation, total profile variation, and tooth alignment variation are used to calculate the combined effect by the following formula:

millimeters

The above variation is based upon a length of engagement equal to one-half the pitch diameter of the spline; adjustment of λ may be required for a greater length of engagement. Formulas for values of Fp, ff, and Fβ used in the above formula are given in Table 16.

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 37 of 38

Table 16. Formulas for Fp, ff , and Fβ used to calculate λ

Spline Total Index Variation, in mm, Total Profile Variation, in mm, Total Lead Variation, in Tolerance ff mm,Fβ Fp Class 4 5 6 7 0.001(2.5*√(mZπ/2)+6.3) 0.001(3.55*√(mZπ/2)+9) 0.001(5*√(mZπ/2)+12.5) 0.001(7.1*√(mZπ/2)+18) 0.001[1.6m(1+0.0125Z)+10] 0.001[2.5m(1+0.0125Z)+16] 0.001[4m(1+0.0125Z)+25] 0.001[6.3m(1+0.0125Z)+40] 0.001(0.8*√g+4) 0.001(1.0*√g+5) 0.001(1.25*√g+6.3) 0.001(2*√g+10) g = length of spline in millimeters. Table 17. Reduction, es/tan αD, of External Spline Major and Minor Diameters

Required for Selected Fit Classes

Pitch Diameter D in mm ≤3 >3 to 6 > 6 to 10 > 10 to 18 > 18 to 30 > 30 to 50 > 50 to 80 > 80 to 120 > 120 to 180 > 180 to 250 > 250 to 315 > 315 to 400 > 400 to 500 > 500 to 630 > 630 to 800 > 800 to 1000 30 37.5 d 0.035 0.052 0.069 0.087 0.113 0.139 0.173 0.208 0.251 0.294 0.329 0.364 0.398 0.45 0.502 0.554 0.026 0.039 0.052 0.065 0.085 0.104 0.13 0.156 0.189 0.222 0.248 0.274 0.3 0.339 0.378 0.417 0.02 0.03 0.04 0.05 0.065 0.08 0.1 0.12 0.145 0.17 0.19 0.21 0.23 0.26 0.29 0.32 45 Standard Pressure Angle, in Degrees 30 37.5 45 30 Classes of Fit e es/tan αD in millimeters 0.024 0.018 0.014 0.01 0.035 0.026 0.02 0.017 0.043 0.033 0.025 0.023 0.055 0.042 0.032 0.028 0.069 0.052 0.04 0.035 0.087 0.065 0.05 0.043 0.104 0.078 0.06 0.052 0.125 0.094 0.072 0.062 0.147 0.111 0.085 0.074 0.173 0.13 0.1 0.087 0.191 0.143 0.11 0.097 0.217 0.163 0.125 0.107 0.234 0.176 0.135 0.118 0.251 0.189 0.145 0.132 0.277 0.209 0.16 0.139 0.294 0.222 0.17 0.149 37.5 f 0.008 0.013 0.017 0.021 0.026 0.033 0.039 0.047 0.056 0.065 0.073 0.081 0.089 0.099 0.104 0.112 0.006 0.01 0.013 0.016 0.02 0.025 0.03 0.036 0.043 0.05 0.056 0.062 0.068 0.076 0.08 0.086 45 All h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 These values are used with the applicable formulas in Table 13.

Machining Tolerance: A value for machining tolerance may be obtained by subtracting the effective variation, λ, from the total tolerance (T + λ). Design requirements or specific processes used in spline manufacture may require a different amount of machining tolerance in relation to the total tolerance.

Fig. 6a. Profile of Basic Rack for 30° Flat Root Spline

Machinery's Handbook 28th Edition

INVOLUTE SPLINES Page 38 of 38

Fig. 6b. Profile of Basic Rack for 30° Fillet Root Spline

Fig. 6c. Profile of Basic Rack for 37.5° Fillet Root Spline

Fig. 6d. Profile of Basic Rack for 45° Fillet Root Spline

British Standard Straight Splines.— British Standard BS 2059:1953, ―Straight-sided Splines and Serrations‖, was introduced because of the widespread development and use of splines and because of the increasing use of involute splines it was necessary to provide a separate standard for straight-sided splines. BS 2059 was prepared on the hole basis, the hole being the constant member, and provide for different fits to be obtained by varying the size of the splined or serrated shaft. Part 1 of the standard deals with 6 splines only, irrespective of the shaft diameter, with two depths termed shallow and deep. The splines are bottom fitting with top clearance.

The standard contains three different grades of fit, based on the principle of variations in the diameter of the shaft at the root of the splines, in conjunction with variations in the widths of the splines themselves. Fit 1 represents the condition of closest fit and is designed for minimum backlash. Fit 2 has a positive allowance and is designed for ease of assembly, and Fit 3 has a larger positive allowance for applications that can accept such clearances.

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