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
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.
Contents of GB/T 17855-2017
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
