LOVE6Problem:Design a bell crank, similar to the one shown, to carry a mild shock load. The mechanical advantage ( L1 / L2 = F2 / F1 ), the force F1, the length L1, and the material are given in the accompanying table, a) Make all significant decisions including tolerances and allowances. One approach could be to compute dimensions of the yoke connections first: t should a little less than:An assumption for the shaft may be that, on occasion, the torque for F1 is transmitted through the shaft (ignoring bending for local convenience).Check all dimensions for good proportion; modify as desirable.Sketch to scale each part, showing all dimensions with tolerances necessary to manufacture.REQ: D:a.Determine all dimensions including tolerances and allowances.b.Check all dimensions for good proportionc.Sketch to scale each part.d.All dimensions with tolerances and allowances necessary to manufactureGiven Data:Problem No.LoadF1L1AISI No.as rolledMech. Advantage115600 lb20 inC10404SOLUTIONS:From given data: Mechanical advantage = ( L1/L2 = F1/F2 ) = 4L2 = 5 inF2 = 2,400 lbFrom Table AT 7 (page 576 text)For AISI C1040, as rolledSy = 50,000 psiFor Design Stresses:Ss= 0.5 Sy / NSs= 0.5 ( 50,000 ) / 3Ss= 8,333.33 psi From table 1.1 ( page 20 text )Design Factor ( Factor of Safety ), for repeated, one directionN = 3, based on ultimate strength ( Su )Solving for design stress (St):St= Sy / N = 50,000 psi 3St= 16,666.67 psiFor Compression stress (Sc):Sc= Sy / N = 50,000 psi 3Sc= 16,666.67 psiFor Shearing stress (Ss):Sys= Sys / N = 30,000 psi 3Sys= 10,000 psiA.) Tension across the circular section of F1 at joint A: ( @ Junction A )F1= SdD12 4D12= F1(4) SdD1= 0.214 in ( 1/16 between 3/16 - 7/8 )For Standard fraction: Use D1 = 1/4 in. The pin may fail by shearing stress in the rod (double shear):Solving for pin diameter (d1):Fig:For area :d1 = 0.214 in For Standard Fraction Use d1 = 1/4 in. The compressive stress between the pin and the rod: Fig: ;a1 = 0.144 inFor Standard Fraction Use a1 = 5/32 in. The compressive stress between the pin and the yoke:Projected area on one side of a yoke is ( bd ) and for two of the yoke (bd ):Fig:Where:a1 = 2 b1b1 = 0.072 inFor Standard Fraction Use b1 = 5/64 in. The rod and the yoke may fail in tension across the hole of the pin:Fig: For the Rod:m1 = 0.48 inFor Standard Fraction Use m1 = 1/2 in. For the Yoke:Fig:m1 = 0.48 inUse: 1/2 inShearing stress on the lever, solving for thickness ( t1 ):Fig:;t1 = 0.144 inFor Standard Fraction Use t1 = 5/32 in. For the margin of the hole, the pin may tear at the end of rod or yoke:Fig:F1 = Ss A ; A = 2a1 e1e1 = 0.23 inFor Standard Fraction Use e1 = 1/4 in. B.) FOR ANALYSIS OF JOINT B:Tension across circular section of F2 @ joint b: Fig:For the area:D2 = 0.428 inFor Standard fraction: use: D2 = 7/16 in The pin may fail by shearing stress in the Rod (Double Shear):Fig:for area :d2 = 0.428 in For Standard Fraction Use d2 = 7/16 in. The compressive stress between the pin and the rod:Fig: a2 = 0.329 inFor Standard fraction: 1/16 between 3/16 7/8 Use a2 = 5/16 or 3/8 in. The compressive stress between the pin and the yoke projected on the two side of the yoke ( A = 2 bd ):Fig:b2 = 0.165 inFor Standard Fraction Use b2 = 3/16 in. The rod and the yoke may fail in tension across the hole of the pin:Fig: F = S AF = St ( m - d2 ) a2For the Rod:m2 = 0.821 inFor Standard Fraction Use m2 = 13/16 in. For the Yoke:m2 = 0.821 inFor Standard Fraction Use m2 = 13/16 in. For Shearing stress on the lever, solving for thickness ( t2 ):Fig:For the area: A2A2 = m2 t2t2 = 0.354 inFor Standard Fraction Use t2 = 3/8 in. Solving for the margin of the hole, the pin may tear at the end of rod or yoke:Fig: a = 2 a2 e2F2 = Ss 2a2 e2e2 = 0.384 inFor Standard Fraction Use e1 = 3/8 in. C.) ANALYSIS AT JOINT C:The shaft is subjected to torsional stress:For the Torque: T1 = F1 x L1T1 = 600 x 20T1 = 12,000 psiSolving for shaft diameter ( Ds):Fig:From Table 9.1 ( Page 279, Text )Using minor shafts;ks = 1.0Ds = 1.943 inFor Standard Fraction Use Ds = 1 7/8 in. Solving for hub Diameter ( Dh ): page388Dh = 1.8 DsDh = 1.8 ( 1 7/8 in )Dh = 3.375 in For Standard Fraction Use Dh = 3 1/4 in. FOR THE KEY DIMENSION:From Table AT 19, ( Page 594, Text )Ds = 1 7/8 inRange:1 13/16 - 2 1/4 ;b = 1/2 t = 3/8 Tolerance on b = - 0.0025 inFor the size of the Key ( L ):L = 3.07L = 4.096 in for compressionTherefore: use L = 4.096 in, with 1/2 x 3/8 in cross sectionFor the Length of the hub (Lh):From Chapter 10, of the Text on page 283 (Typical hub length fail between 1.25 to 2.4 Ds, where D is the shaft diameter:Lh = 2.4 DsLh = 2.4 ( 1.875 )Lh = 4.5 inTOLERANCE AND ALLOWANCES:For the Yoke at section A & B connection use loose running fit (Rc-9)At Yoke C:Ds = 1 7/8 in = 1.875 inFrom table 3.1, page 83 (Tolerance and allowances)Nominal size:HoleShaft1.19 - 1.97+ 6.0- 8.0 x 10 -3- 12.0Hole tolerance: 0.006 - 0.0000 = 0.006 inShaft tolerance: - 0.008 - (- 0.012) = 0.004 inAllowance: 0.000 - (- 0.008) = 0.008 inFOR THE HOLE:Hole = Nominal size + Hole tolerance - 0.0000Hole = 1.875 + 0.006 - 0.000FOR THE SHAFT:Shaft = ( 1.875 - 0.008 ) + 0.0000 - 0.004Shaft = 1.867 + 0.000 - 0.004For the yoke at Joint B: d2 = 7/16 in = 0.4375 inFrom Table 3.1 ( Tolerance and Allowances ) Class Rc 9Nominal size:HoleShaft 0.40 - 0.71+ 4.0- 6.0 0 - 8.8Hole Tolerance: = 0.004 inShaft Tolerance: - 0.0060 - ( -0.0088 ) = 0.0028 inAllowance: 0.000 - ( -0.006 ) = 0.006 inFOR DIMENSIONING: FOR THE HOLE:Hole = 0.4375 + 0.0040 in - 0.000FOR THE PIN AND SHAFT:Shaft = 0.4315 - 0.0028 + 0.000AT YOKE A:d1 = 1/4 in = 0.25 inNominal size range = 0.24 - 0.40 From Table 3.1 ( Tolerance and Allowances ) Class Rc 6Nominal size:HoleShaft 0.24 - 0.40+ 3.5- 5.0 0 - 7.2Hole Tolerance: = 0.0035 inShaft Tolerance: = 0.0022 inAllowances: = 0.005 inDIMENSIONING:FOR THE HOLE:Hole: 0.25 + 0.0035 - 0.000FOR THE SHAFT:Shaft: 0.245 + 0.000 - 0.0022 SUMMARY OF COMPUTED AND ADJUSTED VALUESPartsComputed values( inches )Computed values( mm )Adjusted values( mm )L120508508D11/46.357d11/46.357a15/323.9694b15/641.9842m11/212.713t11/83.1754e11/46.357L25127127D27/1611.1112d27/1611.1112a23/89.52510b23/164.7635m213/1620.63821t23/89.52510e23/89.52510Ds1 7/847.62548Dh3 1/482.5583GLOSSARYAllowance - it is the difference in size, which in running fits is the maximum specified difference between the dimensions of the pin and the hole.Allowable Stress - the stress used in design for a safe one to use for computations if failure is not occur.Compress - flattened from side to side.Cotter - A key of wedge, used to fasten parts of machinery together, as a wheel on its shaft.Design Factor - is a number that is divided into a criterion of strength in order to obtain a design criteria.Ductility - is that property that permits permanent deformation before fracture on tension.Design stress (Working stress) - it is a design, used in such a way all criteria of strength are modified. Machine design - which involve the calculation of the forces acting on different part of the machines.Stress - the state of an elastic body under conditions of strain expressed quantity as force applied per unit area.Shear - a deformation within a body on which two adjacent planes tend to move in a parallel direction relative to one another while remaining parallel.Tension - a force tending to cause extension of a body, or the shape of an extended elastic object.Tolerance - it is the stated permissible variation of the size of a dimension.Strength of material - it is the capacity to resist the action or applied forces.Ultimate strength or tensile strength - the highest point on the stress strain curves, is the maximum load divided by the original before straining occurs.Yield strength - is the stress for a specified deviation from the straight part of the stress - strain curve.B I B L I O G R A P H YDoughtie,Venton Levy, Design of Machine Members, 4th Edition, New York: Mcgraw-Hill Book Company, Inc. 1964.Faires,Virgil Moring, Design of machine Elements, 4th Edition, New York: Mcmillan Publishing Company, Inc. 1965.Clark, Donalds, Engineering Materials and Processes , 3rd Edition, International Textbook Company, Pennsy Lvania, C 1967. Parker, Sybil P., McGraw-Hill Dictionary of Engineering , 3rd Edition, McGraw-Hill Book Company, New York, C 1984. Faires, Virgil Moring, Design of Machine Elements , 4th Edition, The Macmillan Company, New York, C 1969.