ME6760 Keys and Couplings Ratna Kumar Annabattula Department of Mechanical Engineering IIT Madras Key Design ❖ Key is used to connect a transmission shaft to a rotating machine element such as a gear, hub, pulley, etc.. ❖ Primary function is to transmit torque from shaft to the hub of mating element ❖ Secondary function is to prevent relative rotation between the joining machine elements ❖ Types of Keys ❖ Saddle key ❖ Fits in the keyway of hub only; no keyway on the shaft ❖ Torque is transmitted only through friction between key, shaft and hub only ❖ Used for light duty application ❖ Sunk key ❖ Fits half in the keyway of hub and remaining half in the keyway of shaft ❖ Torque transmission is through shear resistance of the key ❖ Suitable for heavy duty application ❖ Positive drive ❖ Flat and Rectangular keys (more stable) Source: V. B. Bhandari, Design of Machine Elements Example Problem ❖ It is required to design a square key for fixing a gear on a shaft of 25 mm diameter. 15 kW power at 720 r.p.m. is transmitted from the shaft to the gear. The key is made of steel 50C4 (Syt = 460 MPa) and the factor of safety is 3. The yield strength in compression can be assumed to be equal to the yield strength in tension. Determine the dimensions of the key. Example Problem ❖ The standard cross section for a flat key, which is fitted on a 50 mm diameter shaft, is 16 x 10 mm. The key is transmitting 475 N-m torque from the shaft to the hub and is made of commercial steel (Syt=Syc=230 MPa). Determine the length of the key, if the factor of safety is 3. Rigid Couplings ❖ Box or Muff or Sleeve Coupling ❖ Clamped Coupling ❖ Rigid Flange Coupling Box or Muff Coupling ❖ Coupling are checked for shear of the pins and crushing of sleeves and shaft by pin ❖ For shaft: Mt/J = s/r ❖ s =Mtr/J = 16 Mt/ d 3 ❖ sleeve = Tr/J; J = (D 4 -d 4 )/32; r = D/2 ❖ The key/pin must have equal depth in shaft and muff to avoid bending ❖ muff - made of cast iron and key - plain carbon steel ❖ Outer diameter of the muff d 0 = 2d+13 mm ❖ Length of the muff l = 3.5 d ❖ Width of key b=d/4 ❖ Thickness of key h = d/4 ❖ Mean diameter of the pin d p = 0.2 - 0.3 d ❖ Taper of the pin = 1:20 to 1:30 ❖ Edge distance e = 0.75 d Design Procedure for Muff Coupling ❖ Calculate the diameter of each shaft by following equations Mt = 60× 106(kW ) 2πn and τ = 16Mt πd3 ❖ Calculate the dimensions of the sleeve by following empirical equations D = (2d+ 13) mm and L = 3.5d Also check the torsional shear stress induced in the sleeve by the following equation τ = Mtr J , J = π(D4 − d4) 32 , r = D 2 ❖ Determine the standard cross section of the flat sunk key. The length of the key in each shaft is half of the sleeve length. Therefore l=L/2 τ = 2Mt dbl , σc = 4Mt dhl Exercise ❖ Design a muff coupling for the following data ❖ The yield strength of plain carbon steel is 400 MPa ❖ Ultimate tensile strength of cast iron is 200 MPa ❖ Power to be transmitted is 25 kW ❖ Shafts rotates at 360 rpm ❖ Factor of safety for key and shaft material is 4 ❖ Factor of safety for muff is 6 Clamp Coupling ❖ For sleeve halves: ❖ D = 2.5d ❖ L = 3.5 d ❖ For clamping bolts: ❖ d1 = 0.20d+10 mm for d < 55mm ❖ d1 = 0.15d+15 mm for d > 55 mm Clamp or Split Muff Coupling ❖ In Clamp Coupling, torque is transmitted by means of friction between sleeve halves and shaft surface and partly by shear resistance of keys ❖ Not suitable for shock loads Exercise ❖ Design a clamp coupling for the following data ❖ The yield strength of plain carbon steel in tension is 400 MPa and in compression it is 150% of tensile strength ❖ Ultimate tensile strength of cast iron is 200 MPa ❖ Power to be transmitted is 50 kW ❖ Shafts rotates at 120 rpm ❖ Factor of safety for key, bolts and shaft material is 5 ❖ Number of bolts is 8 ❖ Coefficient of friction between sleeve and shaft is 0.3 Flange Coupling Unprotected Flange Coupling Protected Flange Coupling Proportions • dh = Outer diameter of hub = 2d • lh = Length of hub (key) = 1.5 d • D = PCD of bolts = 3d • t = Thickness of flange = 0.5d • t1 = Thickness of protecting rim = 0.25d • dr = Dia of spigot and recess = 1.5d • D0 = OD of flange = (4d+2t1) • N = (3,4,6) for (d Flange Coupling ❖ Consists of two flanges - one keyed to the driving shaft and other to the driven shaft ❖ Two flanges are connected together by means of four or six bolts ❖ Power is transmitted ❖ from the driving shaft to the left flange through key ❖ left flange to right flange through bolts ❖ right flange to right shaft through key ❖ Provision for spigot (on left flange) and recess (on right flange) for easy alignment ❖ Two type - protected and unprotected Design Procedure for Flange Coupling ❖ Calculate shaft diameter by usual method adopted in muff and clamp coupling (We have Mt and d now) ❖ Dimensions of flange (from standard proportions). Torsional shear stress in the hub can be calculated by assuming it to be a hollow shaft subjected to torsional moment Mt, τ = Mtr/J, where J = π(dh 4 -d 4 )/32 and r = dh/2 ❖ Flange at the junction of hub is under shear while transmitting moment Mt ❖ area under shear = (πdh)t; Shear force = (πdht) τ ❖ Resisting torque Mt = (πdht τ)(dh/2) ❖ Diameter of bolts ❖ Number of bolts N = 3 for d < 40 mm; N = 4 for 40 < d < 100 mm; and N = 6 for 100 < d