Program 60-740—Steel Involute Spur Spline Load and Stress Analysis Introduction€¦ · ·...

Program 60-740—Steel Involute Spur Spline Load and Stress Analysis

Introduction This model will calculate the stress and/or spline life from the geometry and load data for steel spur involute splines. Fixed, flexible straight and flexible crowned splines are included. Fixed splines have no relative motion between the external and internal members and no misalignment. The effective fit may have clearance or interference. Fixed splines usually fail from: Shaft Shear Tooth Shear Bursting of the Internal Ring Fretting Corrosion (Loose fits with vibration) Flexible splines have a clearance fit and the shafts are misaligned. There is always relative motion between the external and internal members. Flexible splines usually fail from: Shaft Shear Tooth Wear Bursting of the Internal Ring The life of the spline determined by shear cycles (shaft or tooth) and compressive cycles on fixed splines depends on the number of on-off torque cycles applied, not on the number of revolutions. The life of a flexible spline determined by compressive cycles depends on the number of revolutions of the spline. The load transmitted by a splined connection is not always uniform and an application factor (Ka on the TK Solver model Variable Sheet) must be applied. Table 1 contains some suggested factors that may be used if more accurate information for the application is not available. (Table 1 is contained in the TK Solver model on the table sheets, “Ka”.)

UTS Integrated Gear Software

2

Table 1

The ability of a spline to withstand transmitted load is dependent on the materials from which the splines are made. The model contains allowable stress data for five different materials, Tables 2 (psi) and 3 (kPa) show the allowable stresses used in the model. This table is also in the model with the name “matl”.

60-740—Steel Involute Spur Spline Load And Stress Analysis

3

Table 2

Table 3


4

Examples

Example 1

This is a fixed, 26 tooth, 10/20 pitch, 30 deg pressure angle with a face width of 1.5 inches. The spline must transmit 2500 horsepower at 3000 RPM. The spline members will be made of surface hardened steel at 48 to 53 Rc/C. The power source is a turbine and the driven load will produce light shock loading. An application factor of 1.2 will be applied. The load is always in the same direction and does not reverse.

Open a new analysis in 60-740 and enter the data in the data entry form as shown in Figure 1-1. The solved model is shown in Report 1-1.

Fig. 1-1


5

Report 1-1

Model Title : Program 60-740 Unit System: US GEOMETRY

Number of Teeth 26

Diametral Pitch 10.000000 1/in `

Module 2.540000 mm `

Pressure Angle 30.000000 deg

Pitch Diameter 2.600000 in

Radial Contact Height 0.0980 in

Face Width 1.5000 in

Effective Face Width 1.5000 in

Type of Spline Connection Fixed

Misalignment 0.0000 in/in

Internal Spline

Outside Dia of Hub 3.2000 in

Major Diameter 2.8000 in

Effective_Minor (Inside) Diameter 2.5020 in

Wall Thickness 0.2000 in

Tooth Thickness @ PD 0.1547 in

Space Width @ PD 0.1595 in

External Spline

Effective_Major (Outside) Diameter 2.6980 in

Minor (Root) Diameter 2.3990 in


6

Model Title : Program 60-740 Unit System: US Inside (Bore) Diameter of Shaft 1.0000 in



Height of Crown on Tooth 0.0000 in

Crown Radius _ in

Axial Plane Generating Radius _ in

LOAD

Power 2500.00 hp

Torque 52520.83 lbf-in

Unidirectional / Fully-reversed u

Rotation Speed 3000 rpm

Application Factor, Ka 1.20

Face_Load Distribution Factor, Km 1.0000 STRESS/LIFE INTERNAL

Material # 4.0000

Allowable_Shear Stress 40000.0000 psi

Allowable_Compressive Stress 4000.0000 psi

Max Allowable Tensile Stress 45000.0000 psi STRESS/LIFE

Tooth_Shear Stress 13404.0000 psi

Life_Factor 0.4000

Shear On-Off Torque Cycles 950000.0000

Tooth_Compressive Stress 10571.0000 psi

Fixed_Spline Life Factor 0.3500


7

Model Title : Program 60-740 Unit System: US Compressive On-Off Torque Cycles 3000000.0000

Flexible/Crowned Spline Life Fact

Revolutions

Wear Life hr

Hub_Shear Stress (Torsion) 19726.0000 psi

Life_Factor 0.5900


Bursting Stress (Tensile) 31601.0000 psi STRESS/LIFE EXTERNAL

Material # 4.0000


Allowable_Compressive Stress 4000.0000 psi STRESS/LIFE


Life_Factor 0.4000



Fixed_Spline Life Factor 0.3500

Compressive On-Off Torque Cycles 3000000.0000

Flexible/Crowned Spline Life Fact

Revolutions

Wear Life hr

Shaft_Shear Stress (Torsion) 19977.0000 psi

Life_Factor 0.6000



8

The limiting stress for the internal member is the hub shear stress produced by the torque carried. The number of on-off torque cycles that the hub will withstand is about 6.6 x 104. The limiting stress for the external member is the shaft shear stress. The number of on-off torque cycles that the shaft will withstand (assuming that the smallest shaft diameter is the same as the spline root diameter is about 6.3 x 104.

Example 2 This flexible 20 pitch spline has 6 teeth, a pressure angle of 45 degrees and a face of 0.25 inch. It is required that the life be at least 1000 hours with a misalignment of 0.003 in/in. The transmitted power is 2.25 HP at 3600 RPM. The power source and the driven equipment produce no shock load and the application factor is 1.0. The load is applied on one direction only. The material has not been specified. We will first try a through hardened steel with a hardness of 302 to 351 Brinell (Rockwell C 33 to 38). Enter the data as shown in Figure 2-1. Report 2-1 shows the solved model.


9

Fig. 2-1


10

Report 2-1


Number of Teeth 6








Type of Spline Connection Flexible


Internal Spline







External Spline




11





Crown Radius _ in


LOAD

Power 2.25 hp

Torque 39.39 lbf-in





Material # 3.0000





Life_Factor 0.1300



Fixed_Spline Life Factor


12

Model Title : Program 60-740 Unit System: US Compressive On-Off Torque Cycles

Flexible/Crowned Spline Life Fact 1.4600

Revolutions 8000000.0000

Wear Life 36.9000 hr


Life_Factor 0.0600



Material # 3.0000




Life_Factor 0.1100




Compressive On-Off Torque Cycles





Life_Factor 0.3600



13

With this material the wear life is only about 37 hours. We will try a surface hardened steel with a hardness of Rockwell C 48 to 53. Change the material numbers for both internal and external members to 4 and solve the model again. The completed data input form is shown in Figure 2-2, the solved model in Report 2-2. Fig. 2-2


14

Report 2-2


Number of Teeth 6










Internal Spline







External Spline




15





Crown Radius _ in


LOAD

Power 2.25 hp

Torque 39.39 lbf-in





Material # 4.0000





Life_Factor 0.1300





16

Model Title : Program 60-740 Unit System: US Compressive On-Off Torque Cycles





Life_Factor 0.0600



Material # 4.0000




Life_Factor 0.1100









Life_Factor 0.3600



17

A change to this material increased the wear life, but it still is only about 270 hours. As a last effort, before looking at redesigning the spline, we will try a case hardened steel with a hardness of Rockwell C 58 to 63. Change the material numbers for both internal and external members to 5 and solve the model again. The completed data input form is shown in Figure 2-3, the solved model in Report 2-3. Fig. 2-3


18

Report 2-3


Number of Teeth 6










Internal Spline







External Spline




19





Crown Radius _ in

Axial Plane Generating Radius _ in LOAD

Power 2.25 hp

Torque 39.39 lbf-in





Material # 5.0000





Life_Factor 0.1000






20

Model Title : Program 60-740 Unit System: US Flexible/Crowned Spline Life Fact 0.8800




Life_Factor 0.0500



Material # 5.0000



STRESS/LIFE


Life_Factor 0.0800









Life_Factor 0.2900



21

We now have about 1200 hours life, and a spline made with this material should be satisfactory. Example 3 This is a 10 tooth, 2 mm module, 45 degree pressure angle spline. It is to be designed as a crowned flexible spline to handle a misalignment up to 0.005 radians (mm/mm). The material is to be surface hardened steel with a hardness of Rockwell C 48 to 53. We will first try a crown of 0.025 mm (about half the face width times the misalignment). Make certain you have selected metric units. The completed data input form is shown in Figure 3-1. Fig. 3-1


22

When the model is solved we get a message that the specified crown is not enough, but that it should be greater than .032 mm. Change the crown to 0.035 mm and solve again. The completed data input form is shown in Figure 3-2, the solved model in Report 3-2. Fig. 3-2


23

Report 3-2

Model Title : Program 60-740 Unit System: Metric GEOMETRY

Number of Teeth 10




Pitch Diameter 20.000 mm

Radial Contact Height 1.350 mm

Face Width 12.000 mm

Effective Face Width 12.000 mm

Type of Spline Connection Crowned

Misalignment 0.0050 mm/mm

Internal Spline

Outside Dia of Hub 27.000 mm

Major Diameter 22.560 mm

Effective_Minor (Inside) Diameter 18.600 mm

Wall Thickness 2.220 mm

Tooth Thickness @ PD 3.103 mm

Space Width @ PD 3.180 mm

External Spline

Effective_Major (Outside) Diameter 21.300 mm

Minor (Root) Diameter 17.380 mm


24

Model Title : Program 60-740 Unit System: Metric Inside (Bore) Diameter of Shaft 0.000 mm

Wall Thickness 8.690 mm

Tooth Thickness @ PD 3.038 mm

Height of Crown on Tooth 0.035 mm

Crown Radius 514.290 mm

Axial Plane Generating Radius 514.290 mm

LOAD

Power 10.00 kW

Torque 19.10 N-m

Unidirectional / Fully-reversed r




Material # 4.0000

Allowable_Shear Stress 275790.2917 kPa

Allowable_Compressive Stress 110316.1167 kPa

Max Allowable Tensile Stress 310264.0782 kPa STRESS/LIFE

Tooth_Shear Stress 15448 kPa

Life_Factor 0.06


Tooth_Compressive Stress 99729 kPa



25

Model Title : Program 60-740 Unit System: Metric Compressive On-Off Torque Cycles



Wear Life 696.3 hr

Hub_Shear Stress (Torsion) 9641 kPa

Life_Factor 0.03


Bursting Stress (Tensile) 24991 kPa STRESS/LIFE EXTERNAL

Material # 4.0000

Allowable_Shear Stress 275790.2917 kPa

Allowable_Compressive Stress 110316.1167 kPa STRESS/LIFE

Tooth_Shear Stress 15777 kPa

Life_Factor 0.06


Tooth_Compressive Stress 99729 kPa





Wear Life 696.3 hr

Shaft_Shear Stress (Torsion) 18528 kPa

Life_Factor 0.07



26

We now have enough crown to accommodate a misalignment of 0.005 mm/mm. The wear life is about 700 hours. References: 1. Darle W. Dudly, How to Design Involute Splines. 2. Darle W. Dudly, “When Splines Need Stress Control”, in N.P. Chironis, editor, Gear Design and Application. McGraw-Hill Book Co., New York, 1967.

Program 60-740—Steel Involute Spur Spline Load and Stress Analysis Introduction€¦ · ·...

Documents

Transcript of Program 60-740—Steel Involute Spur Spline Load and Stress Analysis Introduction€¦ · ·...