Codeofchina.com is in charge of this English translation. In case of any doubt about the English translation, the Chinese original shall be considered authoritative.
This standard is developed in accordance with the rules given in GB/T 1.1-2009.
This standard replaces GB/T 17855-1999 Calculation of load capacity of spline. The following main technical changes have been made with respect to GB/T 17855-1999:
——Figures 6 and 7 in the standard are modified.
This standard was proposed by and is under the jurisdiction of SAC/TC109 National Technical Committee on Shafts for Machinery and Accessories of Standardization Administration of China.
The previous edition of this standard is as follows:
——GB/T 17855-1999.
Calculation of load capacity of spline
1 Scope
This standard specifies the calculation of load capacity of straight cylindrical involute splines and cylindrical straight-sided splines (hereinafter referred to as “splines”).
This standard is applicable to splines manufactured according to GB/T 1144 and GB/T 3478.1. It may be used as reference for other types of splines.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
GB/T 1144 Straight-sided spline - Dimensions, tolerances and verification
GB/T 3478.1-2008 Straight cylindrical involute splines - Metric module side fit - Part 1: Generalities
3 Terms and symbols
See Table 1 for the terms and symbols.
Table 1 Terms and symbols
S.N. Term Symbol Unit Remark
1 Input torque T N·m Torque input to spline pair
2 Input power P kW Power input to spline pair
3 Rotating speed n r/min Rotating speed of spline pair
4 Nominal tangential force Ft N Nominal tangential force on spline pair
5 Pitch circle diameter D mm Pitch circle diameter of involute splines
6 Average circle diameter dm mm Half of the sum of major and minor diameters of straight-sided splines
7 Unit load W N/mm Normal load on a single spline tooth per unit length [see Equations (4) and (5)]
8 Number of teeth Z - Number of spline teeth
9 Length of fit l mm Length of fitting part between internal and external splines (counted by nominal value)
10 Force acting on shaft F N Radial force on spline pair, which is perpendicular to the axis
11 Standard pressure angle αD (°) Pressure angle on pitch circle with a shape of involute spline tooth
12 Bending moment Mb N·m Bending moment acting on spline pair
13 Module m mm Module of involute splines
14 Use coefficient K1 - Coefficient for which the influence of dynamic overload caused by external factors of transmission system is mainly considered
15 Backlash coefficient K2 - Coefficient for weighing the influence of the fit clearance (interference) at the tooth flank of spline pair on the load on each spline tooth when the spline pair bears the force acting on shaft
16 Distribution coefficient K3 - Coefficient for weighing the uneven load distribution of each spline tooth due to the cumulative error (indexing error) of the spline pitch
17 Axial eccentric load coefficient K4 - Coefficient for weighing the influence on the uneven load of each spline tooth along the axial direction due to the tooth orientation error of the spline, the coaxiality error of the spline pair after installation and the torsional deformation of the spline after loading
18 Compressive stress on the tooth surface σH MPa Average contact compressive stress calculated on the surface of spline teeth
19 Working depth hw mm Working depth of spline teeth, hw=(Dee−Dii)/2
20 Major diameter of external spline Dee mm Basic dimension of major diameter of external spline
21 Minor diameter of internal spline Dii mm Basic dimension of minor diameter of internal spline
22 Calculated safety factor of tooth surface contact strength SH - Generally, SH is taken from the range of 1.25~1.50;
The larger value shall be taken for the more important and quenched splines, and smaller value shall be taken for the general unquenched splines
23 Allowable compressive stress of tooth surface [σH] MPa
24 Yield strength of material σ0.2 MPa Yield limit of spline material (taking values based on surface layer)
25 Tooth root bending stress σF MPa Calculated bending stress of spline tooth root
26 Whole depth h mm Whole depth of splines, h=(Dee−Die)/2
27 Chord tooth thickness SFn mm Chord tooth thickness of dangerous section (at the maximum bending stress) of spline tooth root
28 Allowable tooth root bending stress [σF] MPa
29 Tensile strength of materials σb MPa
30 Calculated safety factor of bending strength SF - 1.25~2.00 for straight-sided splines;
1.00~1.50 for involute splines
31 Maximum shear stress of tooth root τFmax MPa
32 Shear stress τtn MPa Shear stress near the end of spline
33 Stress concentration factor αtn -
34 Minor diameter of external spline Die mm Basic dimension of minor diameter of external spline
35 Functional diameter dh mm The diameter at equivalent stress, which is equivalent to the diameter of smooth torsion bar, see Equation (19) in 6.5.1
36 Fillet radius of tooth root ρ mm Generally, it refers to the minimum curvature radius of tooth root arc of external spline
37 Allowable shear stress [τF] MPa
38 Allowable compressive stress for wear of tooth surface [σH1] MPa Allowable compressive stress of spline pair in case of working at 108 cycles
39 Allowable compressive stress for wear of tooth surface [σH2] MPa Allowable compressive stress of spline pair in case of long-term working without wear
40 Equivalent stress σV MPa The composite stress of shear stress and bending stress in case of calculating the torsional and bending strengths of splines
41 Bending stress σFn MPa The bending stress in case of calculating the torsional and bending strengths of splines
42 Conversion coefficient K - The conversion coefficient used for determining the functional diameter (dh) (see Table 6)
43 Allowable stress [σV] MPa Allowable stress in calculating torsional and bending strengths of spline
44 Effective clearance CV mm Full backlash of spline pair
45 Displacement e0 mm Relative radial displacement between two axes of internal and external splines of spline pair
4 Load analysis and calculation
4.1 Load analysis
4.1.1 No-load
Since spline pairs are coaxial couples connected with each other, for error-free spline joints, the center line (or symmetry plane) of each tooth space of internal spline coincides with that of each spline tooth of external spline when such joints are in no-load state (excluding dead weight, the same below). At this time, the clearance (or interference) on both sides of the spline teeth is equal, which is half of the backlash (see Figure 1).
Figure 1 Theoretical positions of involute spline joint (left) and straight-sided spline joint (right) with no load and clearance
4.1.2 Torque load purely borne
For error-free spline joints, when they only transmit the torque (T) but do not transit the force acting on shaft (F), the tooth surfaces on one side are in contact with each other under the action of torque, the backlash is equal, and the two axes of internal and external splines are still coaxial (see Figure 2). All the spline teeth bear the same load (see Figure 3) when they transit the torque.
Figure 2 Theoretical positions of involute spline joint (left) and straight-sided spline joint (right) with load and clearance
Figure 3 Load distribution in case of transmitting the torque (T) and without the force acting on shaft (F)
4.1.3 Force load acting on shaft purely borne
For error-free spline joints, the two axes of the internal and external splines are heteroaxial when such joints only bear the force acting on shaft (F) while not bearing the torque (T), and a relative displacement (e0) (see Figure 4) appears. This relative displacement is caused by the disappearance of partial backlash of spline pairs and the elastic deformation of partial spline teeth. The elastic deformation of spline teeth is mainly related to such factors as their force size and position, the elastic modulus of backlash (clearance or interference) and the number of spline teeth.
When the spline pair rotates, the load on both sides of each spline tooth changes periodically, as shown in Figure 5. In this case, the spline pair is easy to wear.
Figure 4 Positions of internal spline and external spline in case of bearing the force acting on shaft (F) and without bearing the torque (T)
Figure 5 Load distribution in case of bearing the force acting on shaft (F) and without bearing the torque (T)
4.1.4 Under two loads: torque and force acting on shaft
For error-free spline joints, the relative position of the internal spline and external spline and the magnitude and direction of the load on each spline tooth depend on the magnitude and ratio of the torque (T) and the force acting on shaft (F).
If the load on the spline pair is mainly the torque (T) and the force acting on shaft (F) is minor or very small, the position of each spline tooth is similar to that in Figure 2 after the spline pair rotates, and the stress state of both sides of each spline tooth changes periodically, as shown in Figure 6.
If the load on the spline pair is mainly the force acting on shaft (F) and the torque (T) is minor or very small, the position of each spline tooth is similar to that in Figure 4 after the spline pair rotates, and the stress state of both sides of each spline tooth changes periodically, as shown in Figure 7. In this case, the spline pair is also easy to wear.
Figure 6 Load distribution in case of bearing both the force acting on shaft (F) and the torque (T) while the latter is dominant
Figure 7 Load distribution in case of bearing the force acting on shaft (F) and the torque (T) while the former is dominant
For spline joints with errors, their load distribution and the eccentric state are respectively shown in Figures 8 and 9 under the simultaneous action of the torque (T) and the force acting on shaft (F).
Figure 8 Load distribution of involute spline pair with 46 teeth under the action of the force acting on shaft (F) and torque (T)
Figure 9 Eccentric state of involute spline pair with clearance fit and 46 teeth under the action of the force acting on shaft (F) and torque (T)
4.2 Load calculation
4.2.1 The input torque (T) shall be calculated using Equation (1):
T=9549·P/n (1)
4.2.2 The nominal tangential force (Ft) shall be calculated using Equations (2) and (3):
For involute splines: Ft=2000·T/D (2)
For straight-sided splines: Ft=2000·T/dm (3)
4.2.3 The unit load (W) shall be calculated using Equations (4) and (5):
For involute splines: W=Ft/(Z·l·cosαD) (4)
For straight-sided splines: W=Ft/(Z·l) (5)
4.2.4 Calculation of force acting on shaft (F) and bending moment (Mb):
The force acting on shaft (F) and bending moment (Mb) of spline pairs shall be calculated after stress analysis based on specific transmission structure.
5 Coefficients
5.1 Use coefficient (K1)
The use coefficient (K1) is mainly a coefficient considering the influence of dynamic overload caused by external factors of the transmission system. The influence of overload depends on such factors as the characteristics and mass ratio of the prime mover (input end) and working machine (output end), the fitting property and accuracy of the spline pair, and the running state.
The coefficient may be obtained by precise measurement, and may also be determined after analyzing the whole system. If both of the methods are not available, values may be taken with reference to Table 2.
Foreword i
1 Scope
2 Normative references
3 Terms and symbols
4 Load analysis and calculation
5 Coefficients
6 Calculation of load capacity
7 Examples
ICS 21.100.20
J 18
中华人民共和国国家标准
GB/T 17855—2017
代替GB/T 17855—1999
花键承载能力计算方法
Calculation of load capacity of spline
2017-09-07发布 2018-04-01实施
中华人民共和国国家质量监督检验检疫总局
中国国家标准化管理委员会
发布
前言
本标准按照GB/T 1.1—2009给出的规则起草。
本标准代替GB/T 17855—1999《花键承载能力计算方法》。本标准与GB/T 17855—1999相比，主要技术变化如下：
——修改标准中的图6、图7。
本标准由全国机器轴与附件标准化技术委员会(SAC/TC109)提出并归口。
本标准所代替标准的历次发布版本情况为：
——GB/T 17855—1999。
花键承载能力计算方法
1范围
本标准规定了圆柱直齿渐开线花键和圆柱矩形齿花键(以下简称花键)的承载能力计算方法。
本标准适用于按GB/T 1144和GB/T 3478.1制造的花键。其他类型的花键也可参照使用。
2规范性引用文件
下列文件对于本文件的应用是必不可少的。凡是注日期的引用文件，仅注日期的版本适用于本文件。凡是不注日期的引用文件，其最新版本(包括所有的修改单)适用于本文件。
GB/T 1144矩形花键尺寸、公差和检验
GB/T 3478.1—2008圆柱直齿渐开线花键(米制模数齿侧配合)第1部分：总论
3术语和代号
术语和代号见表1。
表1术语和代号
序号 术语 代号 单位 说明
1 输入转矩 T N·m 输入给花键副的转矩
2 输入功率 P kW 输入给花键副的功率
3 转速 n r/min 花键副的转速
4 名义切向力 Ft N 花键副所受的名义切向力
5 分度圆直径 D mm 渐开线花键分度圆直径
6 平均圆直径 dm mm 矩形花键大径与小径之和的一半
7 单位载荷 W N/mm 单一键齿在单位长度上所受的法向载荷[见公式(4)和公式(5)]
8 齿数 Z - 花键的齿数
9 结合长度 l mm 内花键与外花键相配合部分的长度(按名义值)
10 压轴力 F N 花键副所受的与轴线垂直的径向作用力
11 标准压力角 αD (°) 渐开线花键齿形分度圆上的压力角
12 弯矩 Mb N·m 作用在花键副上的弯矩
13 模数 m mm 渐开线花键的模数
14 使用系数 K1 - 主要考虑由于传动系统外部因素而产生的动力过载影响的系数
15 齿侧间隙系数 K2 - 当花键副承受压轴力时，考虑花键副齿侧配合间隙(过盈)对各键齿上所受载荷影响的系数
16 分配系数 K3 - 考虑由于花键的齿距累积误差(分度误差)影响各键齿载荷分配不均的系数
17 轴向偏载系数 K4 - 考虑由于花键的齿向误差和安装后花键副的同轴度误差、以及受载后花键扭转变形，影响各键齿沿轴向受载不均匀的系数
18 齿面压应力 σH MPa 键齿表面计算的平均接触压应力
19 工作齿高 hw mm 键齿工作高度，hw=(Dee−Dii)/2
20 外花键大径 Dee mm 外花键大径的基本尺寸
21 内花键小径 Dii mm 内花键小径的基本尺寸
22 齿面接触强度的计算安全系数 SH - SH值一般可取1.25～1.50；
较重要的及淬火的花键取较大值，一般的未经淬火的花键取较小值
23 齿面许用压应力 [σH] MPa
24 材料的屈服强度 σ0.2 MPa 花键材料的屈服极限(按表层取值)
25 齿根弯曲应力 σF MPa 花键齿根的计算弯曲应力
26 全齿高 h mm 花键的全齿高，h=(Dee−Die)/2
27 弦齿厚 SFa mm 花键齿根危险截面(最大弯曲应力处)的弦齿厚
28 许用齿根弯曲应力 [σF] MPa
29 材料的拉伸强度 σh MPa
30 弯曲强度的计算安全系数 SF - 对矩形花键1.25～2.00；
对渐开线花键1.00～1.50
31 齿根最大剪切应力 τFmax MPa
32 剪切应力 τtn MPa 靠近花键收尾处的剪应力
33 应力集中系数 αtn -
34 外花键小径 Die mm 外花键小径的基本尺寸
35 作用直径 dh mm 当量应力处的直径，相当于光滑扭棒的直径，见6.5.1的公式(19)
36 齿根圆角半径 ρ mm 一般指外花键齿根圆弧最小曲率半径
37 许用剪切应力 [τF] MPa
38 齿面磨损许用压应力 [σH1] MPa 花键副在108次循环数以下工作时的许用压应力
39 齿面磨损许用压应力 [σH2] MPa 花键副长期工作无磨损的许用压应力
40 当量应力 σV MPa 计算花键扭转与弯曲强度时，剪切应力与弯曲应力的合成应力
41 弯曲应力 σpa MPa 计算花键扭转与弯曲强度时的弯曲应力
42 转换系数 K - 确定作用直径dh的转换系数(见表6)
43 许用应力 [σV] MPa 计算花键扭转与弯曲强度时的许用应力
44 作用侧隙 CV mm 花键副的全齿侧隙
45 位移量 ea mm 花键副的内外花键两轴线的径向相对位移量
4受载分析与计算
4.1受载分析
4.1.1无载荷
由于花键副是相互联结的同轴偶件，所以对于无误差的花键联结，在其无载荷状态时(不计自重，下同)，内花键各齿槽的中心线(或对称面)与外花键各键齿的中心线(或对称面)是重合的。此时，键齿两侧的间隙(或过盈)相等，均为侧隙之半(见图1)。
图1无载荷、有间隙的渐开线花键联结(左边)和矩形花键联结(右边)的理论位置
4.1.2受纯转矩载荷
对无误差的花键联结，在其只传递转矩T而无压轴力F时，一侧的各齿面在转矩的作用下，彼此接触、侧隙相等，内花键与外花键的两轴线仍是同轴的(见图2)。所有键齿传递转矩，承受同样大小的载荷(见图3)。
图2有载荷、有间隙的渐开线花键联结(左)和矩形花键联结(右)的理论位置
图3只传递转矩T而无压轴力F时的载荷分配
4.1.3受纯压轴力载荷
对无误差的花键联结，在其只承受压轴力F、不受转矩T时，内花键与外花键的两轴线不同轴，出现一个相对位移量e0(见图4)。这个相对位移量是由花键副的部分侧隙消失和部分键齿弹性变形造成的。键齿的弹性变形主要与它们的受力大小和位置、侧隙(间隙或过盈)弹性模量和花键齿数等因素有关。
当花键副回转时，各键齿两侧面所受载荷的大小按图5周期性变化。在这种情况下，花键副容易磨损。
图4只承受压轴力F、无转矩T时，内花键与外花键的位置
图5只承受压轴力下而无转矩T时的载荷分配
4.1.4受转矩和压轴力两种载荷
对无误差的花键联结，在其承受转矩T和压轴力F两种载荷时，内花键与外花键的相对位置和各键齿所受载荷的大小和方向，决定于所受转矩T和压轴力F的大小及两者的比例。
当花键副所受的载荷主要是转矩T，压轴力F是次要的或很小时，该花键副回转后，各键齿的位置近似图2，各键齿两侧面的受力状态发生周期性变化，见图6。
当花键副所受的载荷主要是压轴力F，转矩T是次要的或很小时，该花键副回转后，各键齿的位置近似图4，各键齿两侧面的受力状态发生周期性变化，见图7。在这种情况下，花键副也容易磨损。
图6同时承受压轴力F和转矩T，而转矩占优势时的载荷分配
图7同时承受压轴力F和转矩T，而压轴力占优势时的载荷分配
对有误差的花键联结，在转矩T和压轴力F同时作用下，其载荷分配见图8，偏心状态见图9。
图8在压轴力F和转矩T的作用下，齿数为46的渐开线花键副的载荷分配
图9间隙配合、齿数为46的渐开线花键副在压轴力F和转矩T作用下的偏心状态
4.2载荷计算
4.2.1输入转矩T按式(1)计算：
T=9549·P/n (1)
4.2.2名义切向力Ft按式(2)和式(3)计算：
渐开线花键： Ft=2000·T/D (2)
矩形花键： Ft=2000·T/dm (3)
4.2.3单位载荷W按式(4)和式(5)计算：
渐开线花键： W=Ft/(Z·l·cosαD) (4)
矩形花键： W=Ft/(Z·l) (5)
4.2.4压轴力F和弯矩Mb计算：
花键副所受的压轴力F和弯矩Mb，应根据具体传动结构进行受力分析后计算。
5系数
5.1使用系数K1
使用系数K1主要是考虑由于传动系统外部因素引起的动力过载影响的系数。这种过载影响取决于原动机(输入端)和工作机(输出端)的特性、质量比、花键副的配合性质与精度，以及运行状态等因素。
该系数可以通过精密测量获得，也可经过对全系统分析后确定。在上述方法不能实现时，可参考表2取值。
表2使用系数K1
原动机(输入端) 工作机(输出端)
均匀、平稳 中等冲击 严重冲击
均匀、平稳 1.00 1.25 1.75或更大
轻微冲击 1.25 1.50 2.00或更大
中等冲击 1.50 1.75 2.25或更大
注1：均匀平稳的原动机：电动机、蒸汽轮机、燃气轮机等。
注2：轻微冲击的原动机：多缸内燃机等。
注3：中等冲击的原动机：单缸内燃机等。
注4：均匀平稳的工作机：发电机、皮带输送机、通风机、透平压缩机、均匀密度材料搅拌机等。
注5：中等冲击的工作机：机床主传动、非均匀密度材料搅拌机、多缸柱塞泵、航空或舰船螺旋桨等。
注6：严重冲击的工作机：冲床、剪床、轧机、钻机等。
5.2齿侧间隙系数K2
当花键副的受力状态如图4所示时，渐开线花键或矩形花键的各键齿上所受的载荷大小，除取决于键齿弹性变形大小外，还取决于花键副的侧隙大小。在压轴力的作用下，随着侧隙的变化(一半圆周间隙增大，另一半圆周间隙减小)，内花键与外花键的两轴线将出现一个相对位移e0，参见图4和图9。其位移量e0的大小与花键的作用侧隙(间隙)大小和制造精度高低等因素有关。产生位移后，使载荷分布在较少的键齿上(对渐开线花键失去了自动定心的作用)，因而影响花键的承载能力。此影响用齿侧间隙系数K2予以考虑。通常K2=1.1～3.0。
当压轴力较小、花键副的精度较高时，可取K2=1.1～1.5；当压轴力较大、花键副的精度较低时，可取K2=2.0～3.0；当压轴力为零、只承受转矩时(见图2)，K2=1.0。
5.3分配系数K3
花键副的内花键和外花键的两轴线在同轴状态下，由于其齿距累积误差(分度误差)的影响，使花键副的理论侧隙(单齿侧隙)不同，各键齿所受载荷也不同。
这种影响用分配系数K3予以考虑。对于磨合前的花键副，当精度较高时(按GB/T 1144标准为精密级的矩形花键或精度等级按GB/T 3478.1—2008标准为5级或高于5级时)，K3=1.1～1.2；当精度较低时(按GB/T 1144标准为一般用的矩形花键或精度等级按GB/T 3478.1—2008标准低于5级时)，K3=1.3～1.6。对于磨合后的花键副，各键齿均参与工作，且受载荷基本相同时，取K3=1.0。
5.4轴向偏载系数K4
由于花键副在制造时产生的齿向误差和安装后的同轴度误差，以及受载后的扭转变形，使各键齿沿轴向所受载荷不均匀。用轴向偏载系数K4予以考虑。其值可从表3中选取。
对于磨合后的花键副，各键齿沿轴向载荷分布基本相同时，可取K4=1.0。
当花键的精度较高和分度圆直径D或平均圆直径dm较小时，表3中的轴向偏载系数K4取较小值，反之取较大值。
表3轴向偏载系数K4
系列或模数m
mm 分离圆直径D或平均圆直径dm
mm l//D或l/dm
≤1.0 >1.0～1.5 >1.5～2.0
轻系列或m≤2
中系列或2
