For instance, a gear mounted on a shaft might use a male spline on the shaft that matches the female spline on the gear. Adjacent images in the section below show a transmission input shaft with male splines and a clutch plate with mating female splines in the center hub, where the smooth tip of the axle would be supported in a pilot bearing in the flywheel (not pictured). An alternative to splines is a keyway and key, though splines provide a longer fatigue life, and can carry significantly greater torques for the size. [2] Types [ edit ] These might be in the form of parallel or involute teeth. The lead and helix angles of the helical spline are specified. These splines have a variety of applications.

This type of spline features a non-involute tooth shape. The male teeth are shaped like an included angle, while the female serration has gaps with the same included angle. The sides of the evenly spaced grooves are involute, but not as tall as an involute gear. By reducing tensile stress, the curves boost strength. A Hirth joint is similar to a spline joint but with the teeth on the end of the shaft instead of on the surface.

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Improperly machined keyways that had cutter deflection or drifting occur, may not be strong enough for the required application. [12] See also [ edit ] Drive shafts on vehicles and power take-offs use splines to transmit torque and rotation and allow for changes in length. Splines are ubiquitous in aerospace, due to the spline's higher reliability and fatigue life compared to keyed shafts. Rotational ball splines integrate linear and rotary motion in one device, whereas standard ball splines provide both linear and torque transmission. The given k + 1 points t i are called knots. The vector t = ( t 0, …, t k) is called a knot vector for the spline. A rolling assist spline bearing is the Ball Spline. This is a novel product that uses a ball rolling on a groove attached to the shaft to achieve higher permissible loads than a linear bushing and allows torque transmission while moving linearly.

A shear key is a feature intended to fail and avoid further damage should the machinery be accidentally operated in excess of its design limits. Shear keys may be any of the designs described above, but are made from a weaker material than the shaft. The shear key is easily and inexpensively replaced, and avoids more serious damage to the mechanism that would be costly or difficult to repair. For example, a steel shaft and pulley may employ a brass key. When excessive torque is applied to the joint, the steel edges shear the brass key into two pieces, leaving the pulley spinning loosely on the shaft and relieving the rest of the machine from possible damage. Shigley, Joseph; Mischke, Charles (1989), Mechanical Engineering Design (5ed.), McGraw-Hill, ISBN 0-07-331657-1. Parallel, tapered, and Woodruff keyways can be produced on a milling machine. End mills or slotting cutters are used for parallel and tapered keyways, while a Woodruff cutter is used for Woodruff keyways. [10] There are several types of splines: [2] Parallel key spline where the sides of the equally spaced grooves are parallel in both directions, radial and axial. Involute spline where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The curves increase strength by decreasing stress concentrations. Crowned splines where the sides of the equally spaced grooves are usually involute, but the male teeth are modified to allow for misalignment. Serrations where the sides of the equally spaced grooves form a "V". These are used on small-diameter shafts. Helical splines where the equally spaced grooves form a helix about the shaft. The sides may be parallel or involute. This can either minimize stress concentrations for a stationary joint under high load, or allow for rotary and linear motion between the parts. Ball splines where the grooves of the inner and outer parts are formed as linear races filled with ball bearings to allow for free linear motion even under high torque. To allow longer travel the outer spline can incorporate channels to re-circulate the balls, in this way torque can be transferred from a long shaft while travelling up or down the length.

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a b c d Keys and Keyways (PDF), archived from the original (PDF) on 2011-06-14 , retrieved 2010-03-19. Kibbe, R. R. (1995). Machine tool practices. (5th ed. ed., p.572). Englewood Cliffs, New Jersey: Prentice-Hall, Inc. P i − 1 ( 0 ) ( t i ) = P i ( 0 ) ( t i ) , P i − 1 ( 1 ) ( t i ) = P i ( 1 ) ( t i ) , ⋮ P i − 1 ( r i ) ( t i ) = P i ( r i ) ( t i ) . {\displaystyle {\begin{aligned}P_{i-1} In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. Wire-cut electrical-discharge machining (EDM) is primarily used for small production lot sizes where either extreme precision is required or other cutting technologies are not readily available. Wire-cut EDM cuts keyways by eroding material away from the workpiece through a series of rapid electric current discharges between a spooling wire and the workpiece through a dielectric liquid. Computer numerical control (CNC) wire-cut EDM machines allow for a wide variety selection of keyways to be cut, inclusive of multiple keyways on the same hub. The main limitations of CNC wire-cut EDM is the time it takes to cut a keyway as well as the size of parts a given wire-cut EDM machine can accommodate. [9] Shaping or slotting [ edit ]

The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data may be either one-dimensional or multi-dimensional. Spline functions for interpolation are normally determined as the minimizers of suitable measures of roughness (for example integral squared curvature) subject to the interpolation constraints. Smoothing splines may be viewed as generalizations of interpolation splines where the functions are determined to minimize a weighted combination of the average squared approximation error over observed data and the roughness measure. For a number of meaningful definitions of the roughness measure, the spline functions are found to be finite dimensional in nature, which is the primary reason for their utility in computations and representation. For the rest of this section, we focus entirely on one-dimensional, polynomial splines and use the term "spline" in this restricted sense. This concludes the Splines key segment for the time being. I hope this has helped you in some way or provided you with some value in return. If so, consider sharing with those in need and bookmarking Engineers Rail for future reference.Read More- Involute Splines- Definition, Types, Materials Selection and Applications Crowned Splines- There are two complementary types of spline, internal and external. External splines may be broached, shaped (for example on a gear shaping machine), milled, hobbed, rolled, ground or extruded. There are fewer methods available for manufacturing internal splines due to accessibility restrictions. Methods include those listed above with the exception of hobbing (no access). Often, with internal splines, the splined portion of the part may not have a through-hole, which precludes use of a pull / push broach or extrusion-type method. Also, if the part is small it may be difficult to fit a milling or grinding tool into the area where the splines are machined. on a drive shaft that matches with groove in a mating piece and transfer torque to it, maintaining the angular correspondence between them. a b Cutting Keyways - Broaching, Keyseating, Wire-Cut EDM, Shaping, & Milling , retrieved 2014-12-03. For the drafting tool, see Flat spline. Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C 2 parametric continuity. Triple knots at both ends of the interval ensure that the curve interpolates the end points

The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Tangent keys are used in high-torque heavy-duty applications. What would have been the side of each keyway forms heels against which the key sits, and transfers force compressively. This latter point means that for reversible motion of the shaft, another key along a tangent outwards in the opposing direction is needed. Typically this will be offset by 90° or 180° on the shaft. The key may be wedge, rectangular, or square shaped, but particularly rectangular double-taper keys are used. Broaching is primarily used to cut square cornered internal keyways. The specific broach, bushing and guide are used for each given keyway cross-section, which makes this process more expensive than most of the alternatives. However, it can produce the most accurate keyway out of all the processes. There are three main steps in broaching a keyway: First, the workpiece is set on the arbor press and the bushing is placed in the opening of the workpiece. Next, the broach is inserted and pushed through, cutting the keyway. Finally, shims are placed between the bushing and the broach to achieve the correct depth necessary for the key. [6] Keyseater [ edit ] A keyseater and a sample of various shapes that can be cut Modern keyseating machine A Scotch key or Dutch key features a circular keyway hole (instead of rectangular), produced by drilling axially into the assembled hub and shaft, with a metal dowel pin serving as the key. If the hole and key are tapered, the key is referred to as a Dutch pin, which is driven in and optionally finished by cutting or grinding flush with the end of the shaft. If a straight Dutch keyway hole is optionally tapped with a thread, then an ordinary screw serves as the threaded Dutch key.Shaping or slotting is largely used for cutting keyways that do not extend through the full length of the part. Like keyseating, shaping uses a single-point cutting tool for cutting, however, shapers are not guided through the cut on a fixed post. As such, shaper cuts are generally more susceptible to deflection than keyseater cuts. [9] Milling [ edit ] In the computer science subfields of computer-aided design and computer graphics, the term spline more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design.