Threaded fastener problems

1. A 30 mm single start Acme power screw, of 6 mm pitch, has a thrust bearing of 40 mm mean diameter. Thread and bearing coefficients of kinetic friction are 0.15 and 0.1 respectively.
   1. Estimate the torque necessary to raise a load of 100kN.   [ 501 Nm]
   2. If the screw rotates at 1 Hz ascertain the power input to the screw, and the combined efficiency of screw and thrust bearing.   [ 3.15 kW 19%]
   3. If bearing friction is eliminated by a rolling thrust element, show that the screw is self-locking and determine the torque necessary to lower the load.   [ 106 Nm]
   4. The thread is further lubricated to halve the friction coefficient. Does this result in overhauling behaviour? What is the effect of lubrication on performance here?
   
   
2. The two arrangements are identical except for the spring washer's position. The washer is the only element of the assembly having appreciable compliance - the bolt and joint components are essentially rigid. The bolt is initially tightened to F_i , then the external load P is applied.
   If F_w is the washer load, F_b is the bolt load, and F_j is the load transferred between the joint components 1 and 2 prior to separation, plot for each arrangement F_b and F_j versus the external load, P. Identify the separation load P*.   Hint : note that prior to separation F_w must be constant at F_i , so equilibrium alone gives the information required.
   Evaluate the bolt load when P is 2 kN and F_i is 10 kN.   [ 12 kN and 10 kN]
    
3. The cover of a pressurised cylinder is secured by ten bolts whose aggregate stiffness is a quarter of the total joint stiffness. Each bolt is tightened initially to 5 kN, then a constant external load of 20 kN is applied to the cover by the pressurised contents of the cylinder.
   Plot the variation of bolt and joint loads against external load, and evaluate the maximum load on each bolt, the minimum total joint load, and the separation load.   [ 5.4, 34, 62.5 kN]
    
4. The steel bracket is bolted to steel ceiling joists by two bolts of class 8.8 and 48 mm grip length. What tightening torque should be used, and what is the corresponding load in each bolt when the 40 kN external load is subsequently applied?   [ 480 Nm; 125 kN]
    
5. The cover of a pressurised cylinder is attached by a self-energising seal and a number of identical bolts. The fluid pressure is essentially constant at 6 MPa. Select suitable class 8.8 bolts for this duty given that the ratio of bolt spacing ( around the ¿180 mm pitch circle ) to bolt size should not exceed 10 to minimise flange bending, and should not be less than 5 in order to allow spanner access. A safety factor of three is applicable to the external load on the assembly.
    
6. An electric motor weighing 20 kN is provided with a steel eye bolt for lifting. Determine a suitable size of class 8.8 bolt, explaining your choice of safety factor.   [ M30x3.5]
   If the strength of the motor housing ( into which the bolt is screwed ) is only half that of the bolt, what minimum number of threads should be engaged?   Hint : consider cylindrical area in nut (housing) such that shear failure here is equally likely as tensile failure in way of the exposed threads.   [ 7 threads]
    
7. The big-end cap of a steel connecting rod is secured by two class 8.8 M12x1.25 (fine pitch) steel bolts. A reversing load of 20 kN amplitude is transmitted between the connecting rod and the crankshaft journal via the big-end bearing. The portion of the connecting rod which surrounds each bolt and which is elastically compressed may be assumed to be a cylinder of annular area 300 mm².
   Determine the safety factor appropriate to the reversing load, with
   1. zero initial bolt load,   [ 2.0]
   2. initial bolt load just sufficient to prevent separation,   [ 6.8]
   3. bolts tightened initially to 70% proof.   [ 3.6]
   Estimate the tightening torque necessary for ( c).   [ 91 Nm]
    
8. A connecting link consists of two circular sections of forged aluminium alloy ( E = 71 GPa ) spigotted and joined by six equally spaced steel studs, M8x1.25 class 10.9, having shanks of reduced diameter with transition radii of 20 mm and polished surfaces.
   1. Explain briefly but clearly why the studs are provided with reduced shank sections.
   2. To what minimum diameter can the shanks be reduced without compromising the fatigue strength of standard studs with unreduced shanks?   [ 5 mm]
   3. Studs with 6 mm diameter shanks are used, tightened to half their yield strength   ( caution : occurring where? ). What is the factor of safety when an alternating axial load of 60 kN amplitude is applied?   ( caution : evaluation of the bolt load needs care )   [ 0.92]
   
   
9. The components of an hydraulic actuator are of steel - the cylinder is of bore D = 100 mm, wall thickness t = 10 and length L = 300 mm. The thickness of the end brackets is w = 20 mm, and they are connected together by five M12x 1.75 grade 5.8 bolts, tightened to 75% proof. In operation the cylinder is pressurised between 0 and 4 MPa.
   1. Determine the stiffnesses of the bolts and of the joint assuming that the cylinder is compressed uniformly and that the end brackets are rigid.   [ 344, 2240 kN/mm]
   2. Find the mean and alternating stresses in the bolts.   [ 289, 4.7 MPa]
   3. Estimate the endurance limit of the bolts based upon 50% reliability.   [ 115 MPa]
   4. What factors of safety guard against fatigue failure and against static failure?   [ 8.3, 9.8]
   
   
10. A pipe joint incorporates flanges of width w = 12 mm together with a full face gasket of bore D_i = 150, outside diameter D_o = 250 and thickness t = 2 mm. The gasket material has a stiffness of 100 MPa/mm with   m= 1.5 and   y= 2 MPa.
    Neglecting rotation, assess the joint's suitability to withstand fluid pressure fluctuating between 0 and 1 MPa, if six M10x1.5 class 5.8 steel bolts are used.
     
11. Transform equation ( 6b) into the form suitable for initial design :

    	As   =   β n C P / Se       where
    		n is the safety factor corresponding to the external load P,
    		As is the bolting stress area required to support P, and
    		β = 1/2 ( 1 + Se /Su ) / ( 1 - σi /Su )   and lies generally in the range 1.3 ≤ β ≤ 2.1 for rolled threads, steel classes 5.8 through 12.9, and an initial load of between 75 and 90% proof.

    Select a suitable size and number of class 9.8 bolts for a narrow face flanged joint to contain fluid whose pressure fluctuates continuously between 0 and 150 kPa. The metal jacketed asbestos filled gasket has y = 50 MPa, m = 3.5 and stiffness 1.5 GPa/mm, with diameters 1840 and 1865 mm, and thickness 3 mm. Bolt spacing between 5 and 10 diameters, and a design factor of 5 on the fluid pressure load are appropriate. Assume a flange thickness of around 50 mm is sufficient to prevent appreciable rotation.