Such a 720°-periodic function can be created in AxSTREAM RotorDynamics™, which provides a transient approach to determine the response torque in the shaft after a respective torque excitation. In this example, a rotor speed of 3000 rpm is considered. With this information, the total time for two crankshaft-revolutions (720°) reads:
By multiplying the tangential force in Figure 1 with the length of the connecting rod of 0.1 m, the stepwise function can be defined.
A single piston engine is considered in this example, for which reason only one firing cycle is present during the two revolutions. The rotor model consists of a massless shaft with applied torsional stiffness and mass inertia elements, representing the piston as well as inertia effects of the remaining shaft sections, (see Figure 2). Please refer to Blog 1: Torsional Analysis of a Four-Stroke Engine for further information about modeling the piston’s geometry.
The transient response in each shaft section can be calculated by using the system’s natural frequencies and shapes. A superposition of a finite number of torsional modes is used in this example to evaluate the vibration behavior of the crankshaft. To describe the complex interrelations, 1000 time steps between 0 and 0.04s were chosen.
The torque function in Figure 3 corresponds to a particular Finite Element-node of the rotor. The influence of the firing process can clearly be seen after approximately 0.02s, which leads to higher torque amplitudes. However, due to the system’s damping (modal damping of ξ = 0.02 for each mode respectively) the torque tends to zero. Notable angular deflections can also be seen after 0.02s.
Effects of varying speeds of the crankshaft also need to be investigated to find optimal speed ranges or identify possible collision of torsional natural frequencies and operating speeds. Therefore, the speed range was varied from 3000-9000rpm, which is a common speed range of internal combustion engines. As it can be seen in Figure 4, the maximum shaft torque occurs at 5500rpm, whereas the minimal value is stated at 7000rpm. Either the operating speed or the geometry and components can be changed/added (e.g. torsional vibration dampers) in order to achieve satisfactory results.[:]