Involute Spline Maximum Effective Length. Le

[kurtmcm]

I am Looking for some Help with determining the Effective length of a spline but can not find a calculation anywhere. I have the Machinist Hand book Spline section and it has a chart but I seems like there should be a calculation for this.

This is considered a Flexible Spline in the machinist handbook.

Ultimately I am trying to calculate the torque capacity of this spline shaft.

This is the data on the Spline:
Internal Involute Spline Data:
Flat Root Side Fit:
Number of Teeth: 16
Module: 2
Pressure Angle: 30°
Base Diameter: 27.7128mm
Pitch Diameter: 32.00mm
Major Diameter: 35.2800mm
Form Diameter: 34.40mm
Minor Diameter: 30.29mm
Circular Space Width:
Max Actual: 3.142mm
Min Effective: 3.183mm
Tolerance Class: 4H
Spline Callout: INT 16Z x 2m x 30P x 4H ANSI B92.2M-1980

External Involute Spline Data:
Flat Root Side Fit:
Number of Teeth: 16
Module: 2
Pressure Angle: 30°
Base Diameter: 27.7128mm
Pitch Diameter: 32.00mm
Major Diameter: 34.0000mm
Form Diameter: 29.89mm
Minor Diameter: 28.72mm
Circular Tooth Thickness:
Max Effective: 3.142mm
Min Actual: 3.076mm
Tolerance Class: 5h
Spline Callout: EXT 16Z x 2m x 30P x 5h ANSI B92.2M-1980

Shear Stress under roots of External Teeth:
Allowable Shear Stress (Table 11): SS: 40,000PSI
Spline Application Factor (Table 7):Ka: [/indent]1.2
Fatigue-Life Factors (Table 9): Kf: 0.5
Minor diameter, external spline root: Dre: 1.1925 in =30.29mm
Solid Shaft Stress: Ss: 10,511 PSI 3.81 Service Factor
Shaft stress with Fatigue and Life Factors: 25,226PSI = 1.59 Service Factor
Max Transmitable torque: T: 5,550 in-lbs = 1.59 Service Factor

Shear Stress at Pitch Diameter of teeth:
Allowable Shear Stress (Table 11): SS: 40,000 PSI
Spline Application Factor (Table 7): Ka: 1.2
Fatigue-Life Factors (Table 9): Kf: 0.5
Load Distribution factor (Table 8): Km: 2.5
Maximum effective Length (Fig. 4): Le:1.200 This is what I would like to calculate.
Pitch Diameter: D: 1.2598 in = 32.00mm
Number of Teeth: N: 16
Circular Tooth Thickness: Max Effective: t: 3.142
Actual Transmitted torque: T: 3,500 in-lbs
Calculated Shear Stress: 1,105 PSI = 36.19 Service Factor:

Compressive Stresses on the Sides of the Spline Teeth:
Allowable Compressive Stress (Table 11): SS: 3,000 PSI
Spline Application Factor (Table 7): Ka: 1.2
Fatigue-Life Factors (Table 9): Kf: 0.5
Load Distribution factor (Table 8): Km: 2.5
Maximum effective Length (Fig. 4): Le: 1.2
Pitch Diameter: D: 1.2598 in = 32.00mm
Number of Teeth: N: 16
Circular Tooth Thickness: Max Effective: t: 3.142
Actual Transmitted torque: T: 3,500 in-lbs
Wear-Life Factors (Table 10): Kw: 0.7
Circular Pitch: P: 12.7
Depth of engagement of teeth: h: 0.070866142
Compressive stress: Sc: 17,501 PSI = 0.17 Service Factor This is low and want to confirm the length.


Thanks in advance

 

[kurtmcm]

Also I am using the Standard calcs from D.W.Dudley but I have Metric splines. Does anyone have a metric version of these calcs?

 

[tbuelna]

If you determine your spline to be flexible, the Le=1.2 for a 1.26"PD spline is about right. The low compressive stress limit you calculated is due to the large knock-down factors used to account for misalignment in a flexible spline.

The simplified analysis approach you used naturally gives a very conservative result. If you want a more precise result you can always make an FEA of the spline connection.

 

[kurtmcm]

How did you determine the Le=1.2in was about right? Do you have a chart or calculation?

 

[tbuelna]

I used the chart in Machinery's Handbook (22nd edition, fig.2, page 923).

If you read thru the Dudley reference and Machinery's Handbook they both tell you that with "flexible" spline joints there is no benefit to having a L/D ratio much greater than about 1.0 with your particular spline. The reasons for this are that the misalignment between mating halves of a "flexible" spline connection typically means that the spline capacity is limited by contact sliding rather than shear strength of the teeth. And due to factors like accumulated geometry errors, as the spline diameter gets larger the recommended L/D limit gets smaller. So there is no benefit to using a L/D ratio greater than recommended with a flexible spline. This recommendation is based on accumulated industry experience, and there are not any simplified formulas for calculating Le values for flexible splines.

As I noted in my previous post, if you require a more precise analysis result for your spline you can always do an FEA of the connection. But building a FEM that accurately reflects the spline contact, including factors like geometry and tolerance errors, can also be quite complicated.

The other option with a spline connection subject to misalignment is to crown the external spline teeth. Both the Machinery's Handbook and Dudley references give equations for calculating the torque capacity of crowned splines.

Good luck to you.
Terry

 

[kurtmcm]

Thanks for the explanation.

One more thing. Can you tell me how to determine the Min thickness of the female spline hub. Or Min Outer Diameter. I want to make the spline as large as possible but I am limited but the OD of the female half of the spline.

Kurt

 

[kurtmcm]

I did find the calc for the Min OD. it was further down in the Machinery Handbook under "Bursting Stresses on Splines".