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Homework answers / question archive / The figure below shows an off-loading station at the end of a paper rolling machine

The figure below shows an off-loading station at the end of a paper rolling machine

Mechanical Engineering

The figure below shows an off-loading station at the end of a paper rolling machine.  The finished paper rolls are 0.90-m OD by 0.25-m ID by 2.8-m length, and have a density of 850 kg/m3 (use g = 9.81m/s2). The rolls are transferred from the machine conveyor to the forklift truck by the V-linkage of the off-loading station.  There are two pairs of V-links, each of 8-cm width and 4-cm thickness, arranged at the 3/10 and 7/10 locations along the roll’s length, and welded to steel tubes with a 3.5-cm thickness.  The tubes are coupled with a shaft using a square key.  The shaft is rotated by an air cylinder through a crank arm.  The shaft has the same length as the paper roll, and rotates very slowly.

                Design the shaft with a fatigue safety factor at least 1.5, and assess the maximum angle of twist of the shaft.

                Design the key with the least safety factor at most 1.3.

3.            Design the two bearings to support the shaft at the two ends.

Assume infinite life, machined surface, 90% reliability, and room temperature.  For the shaft, use SAE 1045 cold rolled carbon steel with Sut = 627 MPa = 91 kpsi, Sy = 531 MPa, E = 206.8 GPa, G = 80.8 GPa.  For the kay, use SAE 1030 hot rolled carbon steel with Sut = 469 MPa = 68 kpsi, Sy = 259 MPa. Note that stress concentration needs to be considered at the keyway location of the shaft with an assumption of r/d = 0.021, Kt = 2.2, and Kts = 3.0 (see Figure 10-16, also attached here on page 3).

It is required to write a complete report for each group and submit the report (printed copy) by the due date.  Electronic submission is not accepted.

The report should include at least the sections of Problem Statement (Introduction), Analysis, Results, Conclusion, Appendices (computer programs, printed data, etc.).  Below are some requirements:

1.            Keep the SI (metric) unit system.  Do not convert into other unit systems.

2.            Do not put data and numbers in the Analysis section.  Instead, use variables for all quantities and equations.

                All necessary free-body diagrams, equations, formulas used in programs should be integrated orderly and logically in the text of Analysis section.

                All important data (given data, result data, diagrams) should be listed in the Results section.

5.            You are required to write Matlab programs to carry out numerical calculations. The programs should be given in Appendices.

6.            All result data including diagrams should be generated and printed from the program, and presented in the Appendices.

 

The following data are required to be listed in Results section, and to be printed out from the program and put in Appendices section:

 

                Weight of the paper roll.

                For shaft design,

shaft diameter, area moment of inertia, polar moment of inertia,

diagrams for shear force, bending moment, and torque when the V-links are just lifted,

notch sensitivity and fatigue stress concentration factors for bending,

notch sensitivity and fatigue stress concentration factor(s) for torsion,

maximum and minimum bending moments,

maximum and minimum nominal normal stresses at critical point,

maximum and minimum torques,

maximum and minimum nominal shear stresses at critical point,

mean and alternating von Mises effective stresses at critical point,

all correction factors, uncorrected and corrected endurance limits,

fatigue safety factor, maximum angle of twist (in degree). 

                For key design,

key width and length,

maximum and minimum shear forces,

mean and alternative shear stresses,

mean and alternative von Mises effective stresses,

fatigue safety factor against shearing failure,

maximum bearing stress,

safety factor against bearing

                For bearing design,

Bearing type, number, and bore diameter,

Load P, design life L10, and fatigue life LP.

 

 

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