![]() ![]() A definition of, and calculations for, the effective pressure angle of a straight-sided spline is provided, and backlash effects are discussed to enable effective design and analysis of these splines. ISO 14 defines geometry but does not describe how to determine the radial loads associated with transmitting torque. Square and hex drives can even be considered and analyzed as splines. Straight-sided splines come in many varieties, from parallel straight-sided splines defined by ISO14 to non-parallel straight-sided splines that are not defined by an industry standard. Tip-to-root clearances are larger than the backlash and form-clearance is large enough to prevent tip-to-root fillet contact. The results provide insight into how splines behave in non-dynamic conditions.Īll splines described in this paper have a side fit with positive backlash and consist of a shaft and a hub as the interfacing parts. This paper presents some practical approaches to some details of spline design that are not covered in widely used spline-design guidelines or are not clearly covered in standards. ![]() The friction force calculation method is a correction to widely published (Maag, and others) formulae that do not include the cam effect of normal force. The misalignment factors are an update to the published table (Dudley) that covers a very limited - and undefined - spline size range. The centering force analysis is supported by results from prior published measurement data (Medina, Olver) and new measurements. The effective pressure angle calculation method is based on the tooth thickness and profile angle and can be included in future standards and guidelines. Results from analytical studies of centering forces and misalignment factors are provided, and an experimental study of centering force is discussed. These include: how to calculate the effective pressure angle of straight-sided splines that is needed to accurately determine normal and radial loads how to calculate the effective centering force of a spline pair an update to the Dudley misalignment factors that can be applied to splines of any size and an update to the calculation of the maximum axial force that a spline can transmit via friction. This paper presents information that is not found - or is not satisfactorily covered - in current standards and existing papers. Additionally, for some characteristics, small-diameter spline interfaces behave very differently from larger diameter splines. Even armed with all these documents, the engineer is not provided with adequate guidance regarding several factors that influence how a splined interface functions. Many recent studies of load distribution have been published, but a general approach is not defined. Other widely used published documents, such as those written by Dudley, and Cedoz & Chaplin, provide information about stresses, including some axial effects such as misalignment. I nternational spline standards such as ISO 4156, ISO 14, ANSI B92.2, and SAE J499a have detailed definition of two-dimensional spline geometry but cover only the most basic axial effects such as helix error. Editor’s note: At the author’s request, some statements have been removed for clarity since the article was originally published in October, 2019. ![]()
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