Keys ·        Keys connect functional parts of mechanisms and machines, allowing moving parts to transmit power or to locate parts relative to each other. OBJECTIVES OF THIS CHAPTER 1. Describe several kinds of keys and their complete geometries. 2. Specify a suitable size key for a given size shaft. 3. Specify suitable materials for keys. 4. Describe splines and determine their torque capacity. 5. Describe several alternate methods of fastening machine elements to shafts.

Types of keys Round Kennedy Square Flat Tapered pin Woodruff Cross Section Gib-head key of Roll Pin

Involute 10 spline Standard straight 8 spline

Key and keyseat applied to a gear and shaft Parallel keys. Key and keyseat applied to a gear and shaft Radiused Chamfered Square key, Rectangular key

Radiused keyseats and chamfered keys is used to reduce the stress concentrations. The use of parallel keys, taper keys, gib head keys, pin keys, and Woodruff keys are used to provide special features of installation or operation. Keyseats in shafts are machined with either an end mill or a circular milling cutter, producing the profile or sled runner keyseat.

Dimensions for parallel keyseats T=D-Y+(H/2)+C Depth of shaft keyseat Depth of hub keyseat Chordal height C = Allowance: + 0.12mm clearance for parallel keys - 0.05mm interference for taper keys D = Nominal shaft or bore diameter. H = Nominal key height, W = Nominal key width, Y = Chordal height

Cylindrical and Taper Keys Cylindrical and Taper keys are designed to be inserted from the end of the shaft after the hub is in position rather than installing the key first. The taper extends over at least the length of the hub, and the height, H, measured at the end of the hub. This design gives a smaller bearing area on the sides of the key.

Gib head key Gib head key has a tapered geometry inside the hub that is the same as that of the plain taper key. The extended head provides the means of extracting the key from the same end at which it was installed. This is very desirable if the opposite end is not accessible to drive the key out. Key types. (a) Plain taper key (b) Alternate plain taper key (c) Gib head taper key

Pin Keys The pin key is a cylindrical pin placed in a cylindrical groove in the shaft and hub. Lower stress concentration factors result from this design as compared with parallel or taper keys. A close fit between the pin and the groove is required to ensure that the pin does not move and that the bearing is uniform along the length of the pin.

Woodruff Keys Where light loading and relatively easy assembly and disassembly are desired, the Woodruff key should be considered. The circular groove in the shaft holds the key in position while the mating part is slid over the key.

Selection and Installation of Keys and Keyseats The key and the keyseat for a particular application are designed after the shaft diameter is specified . With the shaft diameter, the size of the key is selected from Table 1. The key material are specified, and the requirements then be computed. The length of a key is specified to be a substantial portion of the hub length of the element in which it is installed to provide for good alignment and stable operation. Square cut keys are used with the sled-runner-type keyseat. The key is sometimes held in position with a set screw in the hub over the key. Axial location of the assembly provided by shoulders, retaining rings, or spacers.  

MATERIALS FOR KEYS Keys are most often made from low-carbon, higher-carbon steel, cold-drawn steel, heat-treated steels that having an ultimate tensile strength of 420 MPa , a yield strength of 352 MPa , and a 15% elongation. The actual material, guaranteed strength of key stock and good ductility used in critical applications

STRESS ANALYSIS TO DETERMINE KEY LENGTH There are two modes of potential failure for keys transmitting power: (1) shear across the shaft/hub interface and (2) compression failure due to the bearing action between the sides of the key and the shaft or hub material.

The reaction force of the hub back on the key then produces a set of opposing forces that place the key in direct shear over its cross section, WL. The magnitude of the shearing force is F = T/(D/2) The shearing stress is In design, the shearing stress equal to a design stress in shear for the maximum shear stress theory of failure: (N - design factor, sy – yield strength ) The required length of the key is

The failure in bearing is related to the compressive stress on the side of the key, the side of the shaft keyseat, or the side of the hub keyseat. The area in compression is A = L* (H/2). The failure occurs on the surface with the lowest compressive yield strength. A design stress for compression as σd = sy/N The compressive stress is The required length of the key for this mode of failure: In typical industrial applications, N = 3 (design factor)

Design Procedure for Parallel Keys. 1. Specify the actual diameter at the location of the keyseat. 2. Select the size and type of the key from standard table. 3. Specify the material for the key. 4. Determine the yield strength of the materials for the key, the shaft, and the hub. 5. Compute the minimum required length of the key based on shear and bearing stress. The larger of the two computed lengths governs the design. The computed length must be less than the hub length. 6. The key should extend over all or a substantial part of the length of the hub. The keyseat should not run into other stress raisers such as shoulders or grooves. 8. Complete the design of the keyseat in the shaft and the keyway in the hub. Standard should be consulted for standard tolerances on dimensions for the key and the keyseats.

Details for proposed design of key and keyseats Hub section at keyseat

Shear and Bearing Areas for Woodruff Keys B = nominal diameter of the cylinder of which the key is a part W = width (thickness) of the key C = full height of the key ds = depth of the keyseat in the shaft Shear area = Bearing Area Ac shaft = 0.5 { G(B/2) - L[(B/2) -ds } Ac hub = 0.5 {J(B/2) - F[(B/2) - C] } -Ac shaft G = (π/180)B cos-1 {2[(B/2) - ds]/B} J= (π/180)B cos-1{2[(B/2) – C]/B}

SPLINES A spline is a series of axial keys machined into a shaft, with corresponding grooves machined into the bore of the mating part (gear, sheave, sprocket, and so on). The splines perform the same function as a key in transmitting torque from the shaft to the mating element. The advantages of splines over keys are: A more uniform transfer of the torque and a lower loading on a given part of the shaft/hub interface result. Splines are accurately machined to provide a controlled fit between the mating internal and external splines. The surface of the spline is often hardened to resist wear and to facilitate its use in applications in which axial motion of the mating element is desired. Splines can be either straight-sided or involute. The involute form is preferred because it provides for self-centering of the mating element and because it can be machined with standard hobs used to cut gear teeth.  

Straight-Sided Splines Straight splines are made according to the specifications of the Standard and contain 4, 6, 10, or 16 splines version, D - major diameter, d -minor diameter, W - spline width, and h - spline depth. There are standard tables The permanent fit, A, is used when the mating part is not to be moved after installation. The B fit is used if the mating part will be moved along the shaft without a torque load. When the mating part must be moved under load, the C fit is used.

The torque capacity for SAE splines is based on the limit of 6895 kPa bearing stress on the sides of the splines, from which the following formula is derived: T=25400NRh (SI) where N = number of splines R = mean radius of the splines (mm) h = depth of the splines (mm)

INVOLUTE SPLINES Side-fit spline (b) Major diameter fit spline: Note chamfer on tips of external spline teeth Involute splines are typically made with pressure angles of 30°, 37.5°, or 45°. The major diameter fit produces accurate concentricity between the shaft and the mating element. In the side fit, contact occurs only on the sides of the teeth, but the involute form tends to center the shaft in the mating splined hub.

Length of Splines. Common designs use spline lengths from 0. 75D to 1 Length of Splines. Common designs use spline lengths from 0.75D to 1.25D, (D is the pitch diameter of the spline). If these standards are used, the shear strength of the splines will exceed that of the shaft on which they are machined.   Metric Module Splines. The dimensions of splines made to metric standards are related to the module, m, where m=D/Z (mm) Z is the number of teeth in standards describing metric splines. Pitch diameter D = mZ, Circular pitch p= πm, Basic tooth thickness t= πm/2 Standard Modules. There are 15 standard modules: 0.25; 0.50; 0.75; 1.00; 1.25; 1.50; 1.75; 2.00; 2.50; 3; 4; 5; 6; 8; 10.

METHODS OF FASTENING ELEMENTS TO SHAFTS Pinning (a) Cylindrical pin (b) Taper pin (c) Spring pin The shear stress in the pin is T = 2F(D/2) = FmZ, or F = T/D. d is the pin diameter.

Locking assembly applied to a gear Keyless Hub to Shaft Connections Locking assembly applied to a gear

Polygon Hub to Shaft Connection Three-sided P3 external profile Four-sided PC4 external profile

Set Screws A set screw is a threaded fastener driven radially through a hub to bear on the outer surface of a shaft. The point of the set screw is flat, oval, cone-shaped, cupped Taper and Screw

Press Fit Making the diameter of the shaft greater than the bore diameter of mating element results in an interference tit. The resulting pressure between the shaft and the hub permits the transmission of torque at fairly high levels, depending the on the degree of interference. Molding Plastic and die cast gears can be molded directly to their shafts. Often the gear is applied to a location that is knurled to improve the ability to transmit torque. A modification of this procedure is to take a separate gear blank with a prepared hub, locate it over the proper position on a shaft, and then cast zinc into the space between the shaft and the hub to lock them together.