Involute Spline Applications
Involute Spline Applications
When the application is properly selected, an involute spline is reliable and robust elements of power drive systems. Let’s take a deeper look into the involute spline and the preliminary aspects of designing a spline driven gearbox.
What is an involute spline?
An involute spline is an external spur gear with stubbed teeth. This is why the word “involute” is applied to the title. Involute splines are formed in the same manner as an involute spur gear or helical gear. As with gears, an involute curve is formed on each side of the tooth to allow for conjugate action. Although splines are different from gears in many other ways, they do benefit from a conjugate rolling motion.
How are involute splines made?
Involute splines are manufactured using the same standard methods of cutting straight tooth and helical gears. For external splines the common cutting methods are hobbing, shaping, rolling, grinding, wire EDM and skiving. Internal spline can also be manufactured by shaping, wire EDM and skiving, but additionally broaching can be a forming method as well. The method of cutting will be determined by the splines tolerancing by working with a qualified gear manufacturing facility.
What is the difference between straight tooth splines and involute splines?
Both straight tooth splines and involute splines are similar in nature but have significant differences when it comes to application. Hence the name “straight tooth” not having an involute profile makes load sharing and contact stresses difficult to control, in comparison to an involute spline. Straight tooth splines should closely be evaluated when torsional load will be applied to the joint. Figure 1: Involute External Spline and Figure 2: Straight Tooth Spline show the differences between the types of spline teeth.
Figure 1: Involute External Spline
Figure 2: Straight Tooth Spline
Straight spline advantages
- Ideal for applications requiring axial motion of the splined interface
- Cost effective when it comes to manufacturing
- Easier methods for designing spline teeth
- Ideal for low torsional loaded joints
Straight spline disadvantages
- Low torsional load carry capability
- Poor tooth load sharing
- Small root fillets – high stress region
- Poor contact pattern – high end loading or tooth tip loading
- High tooth to tooth error
Involute spline advantages
- High torsional load carrying capability
- Controllable root fillet stresses
- Self-centering capability
- Excellent contact pattern
- High tolerance capability
Involute spline disadvantages
- Higher cost to manufacture
- Not ideal for axial motioned joints
Involute Spline Design Considerations
When beginning the process to incorporate a splined shaft element into a machine; the first step is to consider the type of involute spline required. Understanding the type of involute spline needed will be based on aspects like using a flexible spline, or a spline with a lead crown. These are some examples to consider when evaluating the application.
Flexible vs Fixed Spline
This may be the most important concept to consider when beginning the design process. Fixed splines also known as piloted spline or non-working spline and a flexible spline known as working spline or un-piloted spline. Two key aspects to consider for the selection between a flexible or fixed spline, are the allowance for axial play and estimated shaft to shaft misalignment.
Starting off with shaft misalignment, flexible splines are the best choice when shaft misalignment is anticipated to be greater than 0.002”. Flexible splines are ideal because of their ability to self-center. The terms flexible/working come from the splines ability to move axially and provide a rocking motion in the radial direction. This radial rocking motion is the key player in allowing the two splined elements to self-center when misalignment is present. This does of course come with the disadvantage of higher rates of spline tooth wear. Fixed splines restrict any axial motion and radial rocking, as a result the spline connection only experiences pure torsional loading. Flexible splines have an opposite effect with the combination of torsional loading and surface loading under axial sliding conditions. These sliding load conditions must be considered when evaluating the allowable contact stress. The contact stress of a flexible spline includes a wear factor, as shown in Table 1: Life Factor for Splines below which is based on the amount of load cycles under evaluation.
Table 1: Life Factor for Splines
Number of Revolutions | Wear Factor Lw |
10,000 | 4.0 |
100,000 | 2.8 |
1,000,000 | 2.0 |
10,000,000 | 1.4 |
100,000,000 | 1.0 |
1,000,000,000 | 0.7 |
10,000,000,000 | 0.5 |
In opposition to what was discussed about a flexible spline, a fixed spline offers its own advantages and disadvantages. As mentioned earlier fixed splines are an excellent design selection because they transmit pure torsion. Within a fixed spline connection, no rocking or axial motion exists. The absence of the additional motions prevents rubbing within the spline mesh and eliminating the wear factor as listed within Table 1: Life Factor for Splines. This rigid connection is possible because of the splined shaft having piloted surfaces on one or both ends of the spline as shown in Figure 3: Double piloted Shaft (Fixed Spline). These piloted surfaces are either transitional fits or interference fits. The fit type should be determined by the application’s operating conditions, this will ensure the fit stays consistent throughout the life of its use. This tightly controlled fit allows the spline teeth to remain centered and in the case of an interference fit, prevents the piloted shaft from sliding axially. For the fixed spline, fatigue is the main factor to consider as shown in Table 2: Fatigue Life Factors for Splines.
Figure 3: Double piloted Shaft (Fixed Spline)
Table 2: Fatigue Life Factors for Splines
Life Factor Lf | ||
Number of Torque Cycle | Unidirectional | Fully Reversed |
1,000 | 1.8 | 1.8 |
10,000 | 1.0 | 1.0 |
100,000 | 0.5 | 0.4 |
1,000,000 | 0.4 | 0.3 |
10,000,000 | 0.3 | 0.2 |
Crowned vs uncrowned spline
Now that fixed splines and flexible splines have been explained, let’s turn the topic to the fundamentals of crowning a spline tooth. The first criteria to be determined is if the spline requires a lead crown. Determining the need for a lead crown requires the use of a tooth contact pattern analysis FEA tool. Each design must be evaluated on a case-by-case basis to understand the need for a crown and the amount of crowning required. Lead crowning is typically applied based on shaft/hub wind up. As load is driven through the splined connection both external and internal splined components will experience an amount of wind-up per their respective materials. Wind-up is always to be expected but it becomes problematic when one component like the hub has a larger amount than the shaft. When this occurs the spline connection runs the risk of tooth end loading as shown in Figure 4: Spline End Loading below. End loading a spline can cause HCF and LCF failure within the root fillet or even the mid-section (pitch point) of the tooth.
Figure 4: Spline End Loading
Figure 5: Spline End Loading Failure
In the right case, applying a lead crown will help to eliminate the end loading and recenter the contact along the tooths face. But this is where applying the correct amount is critical because too much crowning can increase the contact stress because load is being concentrated on a percentage of the tooth, rather than 100% of the tooth carry the load. In some cases, lead crowning can be avoided completely by adding only a helix angle to the tooth.
Figure 6: Lead Crown
The next factor to determine is if the spline transmits load uni-directionally or if the spline will be fully reversed under loaded conditions. The answer to this question will help determine if crowning must be applied to both sides of the spline tooth or just one side. Applying lead crown to a spline will automatically require grinding to form the final tooths geometry. This will of course increase the cost to manufacture the part and inspect. Applying lead to one face of the spline will help with reducing the overall processing time and cost.
Hollow spline shaft vs solid spline shaft
The demands for light weight systems forces solutions on how to cut individual part weight. When thinking in terms of splined shafts, this creates the question of using a hollow shaft versus a solid shaft. Designing a hollow involute splined shaft is very feasible but requires extras steps of analysis to ensure a robust design is produced. As discussed in the last section on crowning, shaft wind-up is one of the first criteria to be evaluated. By hollowing the shaft, wind-up will increase due to the applied load. This may drive more of a need to crown the spline in use to maintain centered contact. But if thickness can always be added back to the rim thickness to counter act this affect.
Figure 7: Hollow Splined Shaft
By utilizing a hollow splined shaft, rim hoop stress must be assessed as well. The two primary stress criteria evaluated with a spline are contact stress and shear stress. With the tooth being stubbed, bending stress of the tooth is much lower in magnitude and not of high concern. When a solid spline shaft is being applied to the design the rim thickness is not relevant, so tooth bending stress becomes less of a concern. A hollow shaft is quite the opposite because rim fractures are a common fatigue failure. When the tooth is under load, the bending effect on the tooth will create a tensile stress along the surface of the root fillet. That tensile stress is then combined with centrifugal effects and radially loading, which will make the root fillet want to fracture through the rim.
In Closing
Involute splines are still a leading method to drive power within a machine, gearbox and many other mechanical systems. Industry experience with splines have created affordable solutions to manufacture the components. The high reliability of involute splines make their application a no brainer, but understanding how to select the correct spline for the application is key. Here at Covalo Industries we enjoy solving gear application problems and sharing our knowledge to support your project. Our experience and internal engineering standard work make our design process very efficient to help bring your product to market. Feel free to reach out to us today if you have any questions regarding this article or our capabilities.
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