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
s
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 Load Distribution Factor, Kma 每英寸长度上不对中度 0.001 0.002 0.004 0.008 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.
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 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 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 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： 4TKaKmSs? （ 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。 2TKaKm? （ For flexible splines,对于柔性花键 S c 4 ） DNLehKw
2TKaKm For fixed splines, 对于固定花键 S c ? （ 5）
9DNLhK e 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，
2221.6556?(rpm)(Doi?0.212Dri)Centrifugal tensile stress, 离心拉伸应力 S2?1,000,000(7)
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