Bachelor International 3rd – Machine elements
2018-2019
Exercise Bolt and washer
Cable car
The loading cable of the cable car « Vanoise Express » is secured by a 6 jaws. The tightening of a jaw is obtained by 10 bolts / jaw. Also, 6 Belleville washers are located between the screw head and the jaw, for each bolt.
The goal of the exercise is to design the bolt and the washer in order to ensure a correct tightening of the cable.
Figure 1 : Cable system
Figure 2 : Jaws close-up and cable car
Figure 3 : Perspective and cross-section of a jaw.
1 Câble
Security by jaw
Bachelor international 3rd 2018-2019
Data :
The tension on the cable is 220 tonnes. The cable diameter is 50mm, in steel, as jaws. The friction coefficient between cable and jaw is f=0.18. The length of a jaw is L=400mm (Figure 3).
1) Compute the minimal tightening load that the system « bolt + washer » must apply on the jaw to prevent cable sliding. Two half cylinders contact is assumed between cable and jaws (the sapce between jaws is neglected). This force is then majored of 50% to have a safety margin for overload during transport and meteorology.
2) Compute the minimum diameter d for bolt, and choose a normalised value in Tab 1. Give head screw and bolt dimensions.
Data : Kt=2.2, secu=1.4, E=900 MPa, E=210 000 MPa
3) Show that among washers given in Tab 2, only PVD060031350XD can be used. To simplify the analysis, friction is neglected. We remind that when several washers are used, the maximal deflection should not reach more than 0.75h.
4) Determine the total deflection of the 6 washers under load. The curve below provides the relationship force – deflection for the PVD060031350XD washer.
Figure 3 : Force – deflection curve for the PVD060031350XD washer
5) Once the cable is functioning, its diameter is reduced of 0.08mm.
a) Compute the rigidity of the bolt Kb,
b) Compute the rigidity KR or the 6 washers using Figure 3. (Consider linear rigidity from the functioning point determined Question 3)
c) Compute the equivalent rigidity KBR of the assembly (bolt + 6 washers),
d) Determine the force variation due to cable diameter reduction (jaws are assumed rigid). Is the cable still tightened?
6) Compute the force variation due to cable diameter reduction, without washers (you need to compute the rigidity of the bolt again, with a shorter length). Explain the interest of using washers.
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Bachelor international 3rd 2018-2019
Annexe
Table 1 : Normalized dimensions of screws and nuts
Table 2 : Belleville washers (cup springs) characteristics
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