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
中華人民共和國國家標準
GB/T 17855—2017
代替GB/T 17855—1999
花鍵承載能力計算方法
Calculation of load capacity of spline
2017-09-07發布 2018-04-01實施
中華人民共和國國家質量監督檢驗檢疫總局
中國國家標準化管理委員會
發布
?
前言
本標準按照GB/T 1.1—2009給出的規則起草。
本標準代替GB/T 17855—1999《花鍵承載能力計算方法》。本標準與GB/T 17855—1999相比，主要技術變化如下：
——修改標準中的圖6、圖7。
本標準由全國機器軸與附件標準化技術委員會(SAC/TC109)提出并歸口。
本標準所代替標準的歷次發布版本情況為：
——GB/T 17855—1999。
花鍵承載能力計算方法
1范圍
本標準規定了圓柱直齒漸開線花鍵和圓柱矩形齒花鍵(以下簡稱花鍵)的承載能力計算方法。
本標準適用于按GB/T 1144和GB/T 3478.1制造的花鍵。其他類型的花鍵也可參照使用。
2規范性引用文件
下列文件對于本文件的應用是必不可少的。凡是注日期的引用文件，僅注日期的版本適用于本文件。凡是不注日期的引用文件，其最新版本(包括所有的修改單)適用于本文件。
GB/T 1144矩形花鍵尺寸、公差和檢驗
GB/T 3478.1—2008圓柱直齒漸開線花鍵(米制模數齒側配合)第1部分：總論
3術語和代號
術語和代號見表1。
表1術語和代號
序號 術語 代號 單位 說明
1 輸入轉矩 T N·m 輸入給花鍵副的轉矩
2 輸入功率 P kW 輸入給花鍵副的功率
3 轉速 n r/min 花鍵副的轉速
4 名義切向力 Ft N 花鍵副所受的名義切向力
5 分度圓直徑 D mm 漸開線花鍵分度圓直徑
6 平均圓直徑 dm mm 矩形花鍵大徑與小徑之和的一半
7 單位載荷 W N/mm 單一鍵齒在單位長度上所受的法向載荷[見公式(4)和公式(5)]
8 齒數 Z - 花鍵的齒數
9 結合長度 l mm 內花鍵與外花鍵相配合部分的長度(按名義值)
10 壓軸力 F N 花鍵副所受的與軸線垂直的徑向作用力
11 標準壓力角 αD (°) 漸開線花鍵齒形分度圓上的壓力角
12 彎矩 Mb N·m 作用在花鍵副上的彎矩
13 模數 m mm 漸開線花鍵的模數
14 使用系數 K1 - 主要考慮由于傳動系統外部因素而產生的動力過載影響的系數
15 齒側間隙系數 K2 - 當花鍵副承受壓軸力時，考慮花鍵副齒側配合間隙(過盈)對各鍵齒上所受載荷影響的系數
16 分配系數 K3 - 考慮由于花鍵的齒距累積誤差(分度誤差)影響各鍵齒載荷分配不均的系數
17 軸向偏載系數 K4 - 考慮由于花鍵的齒向誤差和安裝后花鍵副的同軸度誤差、以及受載后花鍵扭轉變形，影響各鍵齒沿軸向受載不均勻的系數
18 齒面壓應力 σH MPa 鍵齒表面計算的平均接觸壓應力
19 工作齒高 hw mm 鍵齒工作高度，hw=(Dee?Dii)/2
20 外花鍵大徑 Dee mm 外花鍵大徑的基本尺寸
21 內花鍵小徑 Dii mm 內花鍵小徑的基本尺寸
22 齒面接觸強度的計算安全系數 SH - SH值一般可取1.25～1.50；
較重要的及淬火的花鍵取較大值，一般的未經淬火的花鍵取較小值
23 齒面許用壓應力 [σH] MPa
24 材料的屈服強度 σ0.2 MPa 花鍵材料的屈服極限(按表層取值)
25 齒根彎曲應力 σF MPa 花鍵齒根的計算彎曲應力
26 全齒高 h mm 花鍵的全齒高，h=(Dee?Die)/2
27 弦齒厚 SFa mm 花鍵齒根危險截面(最大彎曲應力處)的弦齒厚
28 許用齒根彎曲應力 [σF] MPa
29 材料的拉伸強度 σh MPa
30 彎曲強度的計算安全系數 SF - 對矩形花鍵1.25～2.00；
對漸開線花鍵1.00～1.50
31 齒根最大剪切應力 τFmax MPa
32 剪切應力 τtn MPa 靠近花鍵收尾處的剪應力
33 應力集中系數 αtn -
34 外花鍵小徑 Die mm 外花鍵小徑的基本尺寸
35 作用直徑 dh mm 當量應力處的直徑，相當于光滑扭棒的直徑，見6.5.1的公式(19)
36 齒根圓角半徑 ρ mm 一般指外花鍵齒根圓弧最小曲率半徑
37 許用剪切應力 [τF] MPa
38 齒面磨損許用壓應力 [σH1] MPa 花鍵副在108次循環數以下工作時的許用壓應力
39 齒面磨損許用壓應力 [σH2] MPa 花鍵副長期工作無磨損的許用壓應力
40 當量應力 σV MPa 計算花鍵扭轉與彎曲強度時，剪切應力與彎曲應力的合成應力
41 彎曲應力 σpa MPa 計算花鍵扭轉與彎曲強度時的彎曲應力
42 轉換系數 K - 確定作用直徑dh的轉換系數(見表6)
43 許用應力 [σV] MPa 計算花鍵扭轉與彎曲強度時的許用應力
44 作用側隙 CV mm 花鍵副的全齒側隙
45 位移量 ea mm 花鍵副的內外花鍵兩軸線的徑向相對位移量
4受載分析與計算
4.1受載分析
4.1.1無載荷
由于花鍵副是相互聯結的同軸偶件，所以對于無誤差的花鍵聯結，在其無載荷狀態時(不計自重，下同)，內花鍵各齒槽的中心線(或對稱面)與外花鍵各鍵齒的中心線(或對稱面)是重合的。此時，鍵齒兩側的間隙(或過盈)相等，均為側隙之半(見圖1)。
圖1無載荷、有間隙的漸開線花鍵聯結(左邊)和矩形花鍵聯結(右邊)的理論位置
4.1.2受純轉矩載荷
對無誤差的花鍵聯結，在其只傳遞轉矩T而無壓軸力F時，一側的各齒面在轉矩的作用下，彼此接觸、側隙相等，內花鍵與外花鍵的兩軸線仍是同軸的(見圖2)。所有鍵齒傳遞轉矩，承受同樣大小的載荷(見圖3)。
圖2有載荷、有間隙的漸開線花鍵聯結(左)和矩形花鍵聯結(右)的理論位置
圖3只傳遞轉矩T而無壓軸力F時的載荷分配
4.1.3受純壓軸力載荷
對無誤差的花鍵聯結，在其只承受壓軸力F、不受轉矩T時，內花鍵與外花鍵的兩軸線不同軸，出現一個相對位移量e0(見圖4)。這個相對位移量是由花鍵副的部分側隙消失和部分鍵齒彈性變形造成的。鍵齒的彈性變形主要與它們的受力大小和位置、側隙(間隙或過盈)彈性模量和花鍵齒數等因素有關。
當花鍵副回轉時，各鍵齒兩側面所受載荷的大小按圖5周期性變化。在這種情況下，花鍵副容易磨損。
圖4只承受壓軸力F、無轉矩T時，內花鍵與外花鍵的位置
圖5只承受壓軸力下而無轉矩T時的載荷分配
4.1.4受轉矩和壓軸力兩種載荷
對無誤差的花鍵聯結，在其承受轉矩T和壓軸力F兩種載荷時，內花鍵與外花鍵的相對位置和各鍵齒所受載荷的大小和方向，決定于所受轉矩T和壓軸力F的大小及兩者的比例。
當花鍵副所受的載荷主要是轉矩T，壓軸力F是次要的或很小時，該花鍵副回轉后，各鍵齒的位置近似圖2，各鍵齒兩側面的受力狀態發生周期性變化，見圖6。
當花鍵副所受的載荷主要是壓軸力F，轉矩T是次要的或很小時，該花鍵副回轉后，各鍵齒的位置近似圖4，各鍵齒兩側面的受力狀態發生周期性變化，見圖7。在這種情況下，花鍵副也容易磨損。
圖6同時承受壓軸力F和轉矩T，而轉矩占優勢時的載荷分配
圖7同時承受壓軸力F和轉矩T，而壓軸力占優勢時的載荷分配
對有誤差的花鍵聯結，在轉矩T和壓軸力F同時作用下，其載荷分配見圖8，偏心狀態見圖9。
圖8在壓軸力F和轉矩T的作用下，齒數為46的漸開線花鍵副的載荷分配
圖9間隙配合、齒數為46的漸開線花鍵副在壓軸力F和轉矩T作用下的偏心狀態
4.2載荷計算
4.2.1輸入轉矩T按式(1)計算：
T=9549·P/n (1)
4.2.2名義切向力Ft按式(2)和式(3)計算：
漸開線花鍵： Ft=2000·T/D (2)
矩形花鍵： Ft=2000·T/dm (3)
4.2.3單位載荷W按式(4)和式(5)計算：
漸開線花鍵： W=Ft/(Z·l·cosαD) (4)
矩形花鍵： W=Ft/(Z·l) (5)
4.2.4壓軸力F和彎矩Mb計算：
花鍵副所受的壓軸力F和彎矩Mb，應根據具體傳動結構進行受力分析后計算。
5系數
5.1使用系數K1
使用系數K1主要是考慮由于傳動系統外部因素引起的動力過載影響的系數。這種過載影響取決于原動機(輸入端)和工作機(輸出端)的特性、質量比、花鍵副的配合性質與精度，以及運行狀態等因素。
該系數可以通過精密測量獲得，也可經過對全系統分析后確定。在上述方法不能實現時，可參考表2取值。
表2使用系數K1
原動機(輸入端) 工作機(輸出端)
均勻、平穩 中等沖擊 嚴重沖擊
均勻、平穩 1.00 1.25 1.75或更大
輕微沖擊 1.25 1.50 2.00或更大
中等沖擊 1.50 1.75 2.25或更大
注1：均勻平穩的原動機：電動機、蒸汽輪機、燃氣輪機等。
注2：輕微沖擊的原動機：多缸內燃機等。
注3：中等沖擊的原動機：單缸內燃機等。
注4：均勻平穩的工作機：發電機、皮帶輸送機、通風機、透平壓縮機、均勻密度材料攪拌機等。
注5：中等沖擊的工作機：機床主傳動、非均勻密度材料攪拌機、多缸柱塞泵、航空或艦船螺旋槳等。
注6：嚴重沖擊的工作機：沖床、剪床、軋機、鉆機等。
5.2齒側間隙系數K2
當花鍵副的受力狀態如圖4所示時，漸開線花鍵或矩形花鍵的各鍵齒上所受的載荷大小，除取決于鍵齒彈性變形大小外，還取決于花鍵副的側隙大小。在壓軸力的作用下，隨著側隙的變化(一半圓周間隙增大，另一半圓周間隙減小)，內花鍵與外花鍵的兩軸線將出現一個相對位移e0，參見圖4和圖9。其位移量e0的大小與花鍵的作用側隙(間隙)大小和制造精度高低等因素有關。產生位移后，使載荷分布在較少的鍵齒上(對漸開線花鍵失去了自動定心的作用)，因而影響花鍵的承載能力。此影響用齒側間隙系數K2予以考慮。通常K2=1.1～3.0。
當壓軸力較小、花鍵副的精度較高時，可取K2=1.1～1.5；當壓軸力較大、花鍵副的精度較低時，可取K2=2.0～3.0；當壓軸力為零、只承受轉矩時(見圖2)，K2=1.0。
5.3分配系數K3
花鍵副的內花鍵和外花鍵的兩軸線在同軸狀態下，由于其齒距累積誤差(分度誤差)的影響，使花鍵副的理論側隙(單齒側隙)不同，各鍵齒所受載荷也不同。
這種影響用分配系數K3予以考慮。對于磨合前的花鍵副，當精度較高時(按GB/T 1144標準為精密級的矩形花鍵或精度等級按GB/T 3478.1—2008標準為5級或高于5級時)，K3=1.1～1.2；當精度較低時(按GB/T 1144標準為一般用的矩形花鍵或精度等級按GB/T 3478.1—2008標準低于5級時)，K3=1.3～1.6。對于磨合后的花鍵副，各鍵齒均參與工作，且受載荷基本相同時，取K3=1.0。
5.4軸向偏載系數K4
由于花鍵副在制造時產生的齒向誤差和安裝后的同軸度誤差，以及受載后的扭轉變形，使各鍵齒沿軸向所受載荷不均勻。用軸向偏載系數K4予以考慮。其值可從表3中選取。
對于磨合后的花鍵副，各鍵齒沿軸向載荷分布基本相同時，可取K4=1.0。
當花鍵的精度較高和分度圓直徑D或平均圓直徑dm較小時，表3中的軸向偏載系數K4取較小值，反之取較大值。
表3軸向偏載系數K4
系列或模數m
mm 分離圓直徑D或平均圓直徑dm
mm l//D或l/dm
≤1.0 >1.0～1.5 >1.5～2.0
輕系列或m≤2
中系列或2
