Key and Spline Design Factors

This page provides the design factors used by the RoyMech Key and Spline Strength Calculations. The factors allow preliminary key and spline calculations to take account of the type of connection, applied loading, spline misalignment, fatigue life and sliding wear.

The spline-factor method is based on the established spline design approach associated with Darle W. Dudley's work on spline stress control and subsequently published in engineering references including Machinery's Handbook. RoyMech uses these factors within its own simplified key and spline strength calculation method.

Design Factor K_d

RoyMech uses the design factor K_d to distinguish between fixed connections and connections in which relative axial movement can occur. The factor increases as the operating condition becomes more severe.

This is part of the RoyMech implementation of the calculation method. Other spline design methods may distinguish fixed and flexible connections through separate equations rather than through this factor, so factors from different methods should not be mixed.

Spline Application Factor K_a

The application factor K_a allows for the combined effect of the power source and the character of the driven load. A smooth power source driving a uniform load requires a lower factor than a shock-producing power source driving machinery subject to severe shock loading.

Spline Load Distribution Factor K_m

The load distribution factor K_m allows for the reduction in effective spline capacity caused by misalignment. Misalignment can cause the load to be distributed unevenly along the spline face width rather than being carried uniformly by the full engagement.

The effect becomes increasingly important as spline face width and misalignment increase.

Spline Fatigue Life Factor K_f

The fatigue life factor K_f relates the allowable spline stress used by this calculation method to the required number of torque cycles. Separate values are given for unidirectional and fully reversed torque.

For this table, a torque cycle is associated with the application and removal or reversal of transmitted torque rather than simply one revolution of the shaft.

Spline Wear Life Factor K_w

The wear life factor K_w is used for spline connections where relative movement between the mating spline surfaces makes wear an important design consideration.

It relates the design calculation to the required number of spline revolutions. Increasing the required wear life reduces the factor used in the RoyMech calculation.

Using the Factors in the RoyMech Calculations

The factors are combined differently according to the type of component and the operating condition being considered.

Shaft

For the shaft calculation used by RoyMech:

K_s = K_a / K_f

Fixed or Close-Fit Key

K_s = K_a . K_d / K_f

Sliding Key

K_s = K_a . K_d / K_w

Fixed or Guided Straight-Sided Spline

K_s = K_a . K_d / K_f

Flexible or Sliding Straight-Sided Spline

K_s = K_a . K_m . K_d / K_w

The applicable expression depends on the connection and the failure mode being assessed. These expressions should be used with the equations and definitions on the Key and Spline Strength Calculations page.

Indicative Material Design Strengths

The following values are the generic material design strengths used by the original RoyMech key and spline calculation method.

Worked Example

The companion Key and Spline Strength Calculations page demonstrates how these factors are used in practice.

Its worked example considers a 10 kW drive at 1500 rev/min and compares a keyed connection, a straight-sided spline and an involute spline. The example uses:

• K_d = 1,0
• K_a = 1,0
• K_m = 1,0
• K_f = 0,5
• K_w = 0,7

The resulting service factors are then applied to the shaft, key and spline stress equations before the calculated stresses are compared with the design strengths used in the example.

Basis and Provenance of the Factors

The spline application, load-distribution, fatigue-life and wear-life factors used by RoyMech are based on the established spline stress-control methodology associated with the work of Darle W. Dudley.

Dudley's spline design approach has subsequently been reproduced in established mechanical engineering references, including Machinery's Handbook. The method considers the effects of application loading, tooth load distribution, fatigue life and wear when assessing spline capacity.

RoyMech incorporates these principles into a simplified calculation method for keys and splines. In particular, RoyMech uses the design factor K_d shown on this page to represent the severity of fixed and sliding connection arrangements. Other presentations of the Dudley method may instead distinguish these conditions through separate calculation equations.

For this reason, individual factors should not be taken from this page and combined indiscriminately with equations from another spline design method. A calculation method and its associated factors should be used consistently.

References and Further Engineering Resources

• Darle W. Dudley, When Splines Need Stress Control – original engineering work forming the basis of the spline stress-control method represented on this page.
• Machinery's Handbook – engineering reference containing spline design methods and associated application, load-distribution, fatigue and wear considerations.
• MITCalc – Shaft Connections – engineering calculation software for shaft connections.
• Zakgear – Spline Stress Calculation – spline calculation equations and supporting tables.
• Tasman Industries – key and shaft-connection products.
• Bonut Engineering – key manufacturing information.
• Technifast Ltd – fastener and key information.

Related Key and Spline Information

• Key and Spline Strength Calculations
• Parallel Keys
• Taper Keys
• Woodruff Keys
• Straight-Sided ISO Splines
• Involute Splines