Lecture11-4.ppt

11.4 Periodic Speed Fluctuation Therefore the conditions for the constant speed working state should be: The periodic steady working state means Table 11-1 Allowable Coefficients of Speed Fluctuation [?] Example: A machine runs at a periodic fluctuated speed with a angular period of ?T. A crank is chosen as an equivalent link. The curves of equivalent driving moment of force Md and the equivalent resistant moment of force Mr are shown in the figure. The machine has a constant equivalent moment of inertia J. What is the net work between points b and c? Calculate the maximum increment of work ?Wmax. When will the crank run at the maximum speed? When will the crank run at the minimum speed? Solution: (1000+1200)=-(-1500-300-400) The net work between points b and c is:-400 Draw curve of kinetic energy: E~? . Draw curve of kinetic energy: E~? . Draw curve of kinetic energy: E~? . Draw curve of kinetic energy: E~? . Draw curve of kinetic energy: E~? . Draw curve of kinetic energy: E~? . Emax=E0+300, Emin=E0-1500 ?Wmax=Emax-Emin =(E0+300)-(E0-1500)=1800 Note: The maximum increment of work is not equal to the area of the biggest block. The crank run at the maximum speed at point d.The crank run at the minimum speed at point a. Example: A machine runs at a periodic fluctuated speed with a angular period of ?T=2?. The resistant moment of force Mr on the equivalent link is a given function of the rotating angle ? as shown in the figure. The equivalent driving moment Md is constant. What is the value of the equivalent driving moment? Calculate the maximum increment of work ?Wmax. When will the machine have the maximum kinetic energy? When will the machine have the minimum kinetic energy? Solution: The maximum increment of work:  ?Wmax=Emax-Emin =(E0+600? /16)-(E0-600? /16) =12