MD1 10 Keys and Couplings NS converted Aug2024 (2).pdf

# Machine Design 1: Keys and Couplings ## 10. Keys and Couplings ### Objectives of this Chapter After completing this chapter, the student will be able to: 1. Describe several kinds of keys, their suitable materials, and dimensions in relation to a given shaft size. 2. Complete the design of key...

# Machine Design 1: Keys and Couplings ## 10. Keys and Couplings ### Objectives of this Chapter After completing this chapter, the student will be able to: 1. Describe several kinds of keys, their suitable materials, and dimensions in relation to a given shaft size. 2. Complete the design of keys by considering stresses and standard proportions. 3. Design other kinds of keys such as the Woodruff key or multiple keys like splines. 4. Familiarize with the standard couplings used for power transmission: rigid couplings and types of flexible couplings. 5. Complete the analysis of a flange bolt coupling in terms of stresses and factors of safety during transmission of power. ### Definition of Terms * **Key** - a machine member used to connect two mating parts (usually a shaft to a pulley, gear, coupling, etc.) such that relative motion is prevented between them. * **Keyway** - a groove at the mating members where the key fits. ### Types of Keys: | Type | Description | |---|---| | Flat Key | A rectangular key with the smaller dimension placed in a radial direction relative to the shaft. | | Square Key | A key with a square section. | | Gibhead Key | A square or flat tapered key with a head for ease in removal. | | Pin Key | A key of round section; sometimes used as a shear pin. | | Rollpin | A hollow round key with a slit to produce flexibility along its circumference, when inserted into the keyway. | | Saddle Key | A flat key with its bottom side having a radius of curvature slightly less than that of the shaft radius. This is a friction-dependent key and thus, its torque capacity is minimal. | | Kennedy Keys | Two square keys that are 90° apart whose diagonals coincide with the shaft circumference. Kennedy keys are also known as tangential keys. | | Woodruff Key | A key that fits into a semi-cylindrical seat at the shaft. Since it goes deeper into the shaft, it has a less tendency to tip when the load is applied. | | Feather Key | A long flat key that allows the hub to move along the shaft but prevents rotation on the shaft. | | Barth Key | A flat key with beveled bottom corners. | ### Design or Selection of a Rectangular Key **Hints:** * Key material is usually plain carbon steel (C1010, C1015 or C1020). * Factor of safety ranges from 1.5 to 4.5. (DME Faires) * Key length is generally referred to the hub length. ### Compressive stress in key $S_c = \frac{F}{tL} = \frac{1}{t}\cdot S_{sa}$ (eqn. 10.2) Where: * L = length of key * b = width * t = thickness * F = force applied * S_s = shearing stress * S_c = compressive stress or bearing stress * S_sd = shear design stress * S_a = normal design stress ### Stress Analysis for a Rectangular Key * T = torque transmitted * F = tangential force at shaft, applied force in key * D = shaft diameter $\begin{aligned} [ΣΜΟ = 0] : T = F(\frac{D}{2})\Rightarrow F = \frac{2T}{D} \end{aligned}$ ### Shearing stress in key $S_s = \frac{F}{Lb} = \frac{F}{LD} \cdot S_{sa}$ (eqn. 10.1) ### Splines * **Spline** - permanent keys made integral with the shaft. $T = FrmNt = (S_c)(A)(r_m) : T = S_c(L)(h)D_mN_t$ Where: * T = torque capacity * F = force acting on each spline * h = height of each spline * L = contact length * D = outside diameter * d = inside diameter * D_m = mean diameter * r_m = mean radius * N_t = number of splines * S_c = compressive stress on each spline; generally, this side pressure is based on 1000 psi, if axial sliding is present. ### Woodruff Key * A Woodruff key is a key that fits into a semi-cylindrical seat at the shaft. Since it goes deeper into the shaft, it has a less tendency to tip when the load is applied. * During assembly, the key is to be inserted first into the shaft. The pulley is next fitted, and it is usually held in place with a threaded nut into the end of the shaft. * Woodruff keys come in two shapes, semi-cylindrical key with or without a flattened bottom as shown in the figure below. ### Selected Woodruff Key Dimensions | Key No. | Shaft Size | AxB | Height of Key | Max C below center | Max D (with flat bottom) | E in. | Shearing area sq. in. | |---|---|---|---|---|---|---|---| | 204 | 5/16 x 3/4 | 1 x 1 | 0.203 | 0.194 | 3/4 | 0.030 | 0.030 | | 305 | 7/16 x 7/8 | 1-1/2 x 1-1/2 | 0.250 | 0.240 | 1 | 0.052 | 0.052 | | 405 | 1/2 x 1 | 1-1/2 x 1-1/2 | 0.250 | 0.240 | 1 | 0.072 | 0.072 | | 406 | 1/2 x 1-1/4 | 1-1/2 x 1-1/2 | 0.313 | 0.303 | 1 | 0.109 | 0.109 | | 506 | 1/2 x 1-1/2 | 1-1/2 x 1-1/2 | 0.375 | 0.365 | 1 | 0.129 | 0.129 | | 608 | 5/8 x 1-1/4 | 1-1/2 x 1-1/2 | 0.438 | 0.428 | 1 | 0.178 | 0.178 | | 807 | 5/8 x 1-1/2 | 1-1/2 x 1-1/2 | 0.375 | 0.365 | 1 | 0.198 | 0.198 | | 809 | 5/8 x 1-1/2 | 1-1/2 x 1-1/2 | 0.484 | 0.475 | 1 | 0.262 | 0.262 | | 810 | 5/8 x 1-1/2 | 1-1/2 x 1-1/2 | 0.547 | 0.537 | 1 | 0.296 | 0.296 | | 812 | 5/8 x 1-1/2 | 1-1/2 x 1-1/2 | 0.641 | 0.631 | 1 | 0.356 | 0.356 | | 1012 | 3/4 x 1-1/2 | 1-1/2 x 1-1/2 | 0.641 | 0.631 | 1 | 0.438 | 0.438 | | 1212 | 3/4 x 2 | 1-1/2 x 1-1/2 | 0.641 | 0.631 | 1 | 0.517 | 0.517 | ### Set Screws * Set screws are also used to prevent relative motion between a shaft and the hub of pulley, gear, or sprocket. * The set screw is threaded to the hub and its connection to the shaft is generally by friction. Hp rating of a standard set screw $P = \frac{DN d^{2.3}}{50}$ Where: * d = set screw diameter required, in. * P = horsepower transmitted by shaft * D = shaft diameter used, in. * N = shaft rpm ### Couplings * **Coupling** - a machine member used for connecting shafts directly by means of detachable fasteners. The shafts may be collinear or with permissible misalignments. #### Types of Coupling: 1. **Rigid Couplings** - coupling used with collinear shafts where axial, rotational and angular flexibility is not permitted. The flanged-bolt coupling is the most common example. 2. **Flexible Couplings** - couplings used if shaft misalignment (angular, axial, or rotational) is present. These couplings include the Roller Chain coupling, Morflex coupling, Flexpin coupling, Flexible disk coupling, Gear type coupling and Universal joints. Flexible couplings are usually used for more sensitive machines to avoid direct transmission of tremendous shock from the driving to the driven machines. ### Flange Coupling ### Torque capacity of coupling $\begin{aligned} [ΣΜΟ = 0] : T = F\cdot R_{bc} = F (\frac{D_{bc}}2)N_b = S_{sd} (\frac{d_b^2}{4}) (\frac{D_{bc}}2)N_b \end{aligned}$ (based on shearing of bolts) Where: * T = torque capacity of coupling * F_r = total force on bolts * R_bc = bolt circle radius <start_of_image> Schematic of a flange coupling ### A Flange Coupling Example: * A flange coupling is to connect two 57mm diameter shafts. The hubs of the coupling are each 111 mm in diameter, 92mm thick and the flange webs are 19 mm thick. Six 16 mm diameter bolts in a 165mm diameter bolt circle connect the flanges. The keyway is 6mm shorter than the hub’s thickness and the key is 14mm x 14 mm. The coupling is to transmit 45 kW at 160 rpm. For all parts, the yield point value in shear is one-half the yield point value in tension and compression which is 448 MPa. Find the following stresses and factors of safety based on yield point: (a) shear in the key; (b) bearing in the key; (c) shear in bolts; (d) bearing in the bolts; (e) shear in shaft; (f) shear in hub. * **Solution:** <start_of_image> Schematic breakdown for a flange coupling You will need to include a physical image from the document to provide a solution to the problem.