Answer:
Ultimate tensile strength = 700MPa
Yield strength = 450
Periphery of the disk= 250 mm
Friction torque= 15 Nm (during polishing)
Friction torque= 12 Nm (during sanding)
The worst loading condition:
When the object is sanded or polished near the periphery
Loading condition:
The coefficient of friction between the object and the disk = 0.3 (during polishing)
The coefficient of friction between the object and the disk = 3 (during sanding)
The worst case temperature = 100
The minimum number of hours of operation for the 99.99% is given below-
For polishing operation:
The polishing work time taken for the operation using the Preston theory is as –
Where –
For polishing pressure applied will be equal to Ultimate tensile strength i.e. 700MPa
The relative velocity of the disc can be calculated by
= 314 m/sec
Circumferential area of the disk (A) =
For sanding operation:
The polishing work time taken for the operation using the Preston theory is as –
Where –
For polishing pressure applied will be equal to yield strength i.e. 450MPa
The relative velocity of the disc can be calculated by
= 314 m/sec
Circumferential area of the disk (A) =
By this total operation time can be calculated as
= Time taken in polishing operation + Time taken in sanding operation
By this way total operation time can be calculated for the disc machine.
For plotting the modified Goodman diagram, the basic assumption need to be taken is given below-
Assumption:
For the polishing operation the variation of the cyclic load should be in between
Considering the Stress concentration factor for the rotating disc = 3
Here the assumption as per the standard of BS 6104.
Rotates of the disk shaft=
Ultimate tensile strength UTS = 700MPa
Fatigue endurance strength will be half of UTS = = 350
Yield strength = 450
Periphery of the disk= 250 mm
Friction torque= 15 Nm (during polishing)
Friction torque= 12 Nm (during sanding)
Circumferential area of the disk (A) =
The mean stress for the machine used for both polishing and the sanding operation
When the above stress concentration is plotting on the modified Goodman diagram, then the point A falls above and to the right to the line something outside to the safe zone. This indicates that the design is unsafe and the FOS is not as per the limit. In the modified Goodman diagram, the yield strength is plotted.
For the calculation of the FOS of the machine we have,
= 2.73
The minimum force ( to prevent loss of compression
For the polishing operation the machine should be having the equal length and the equal moduli.
In this condition the sanding and the polishing constant are proportional to the circumferential area of the machine disc can be calculated by
= 999.75 N
= 100.19
= 100.00
Now plotting this on the modified Goodman diagram, it shows the point C which is inside the safe zone.
The machine now has the FOS greater than 1. Now it can be shown graphically by the ration of length OD/OC which is approximately equal to the 1.07
= 1.079
References
Harlow, D.G., Cao, H. and Schmidt, P., 2016. Statistical Modeling of High Cycle Fatigue with Censored Data. Materials Performance and Characterization, 5(3), pp.364-372.
Kwak, H. and Kim, C., 2016. Structure integrity of rack module for compressed natural gas (CNG) pressure vessel-under automotive collision and vibration. Journal of Mechanical Science and Technology, 30(11), pp.5073-5081.
Wu, Q., Luo, S., Qu, T. and Yang, X., 2017. Comparisons of draft gear damping mechanisms. Vehicle System Dynamics, 55(4), pp.501-516.
Knapp, K., Scott-Emuakpor, O.E., George, T., Holycross, C. and Palazotto, A.N., 2016. Improved Pre-Strain Method for Generating Goodman Data with Vibration-Based Fatigue Testing. In 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (p. 0925).
