Torsional Response of Internal Combustion Engines

Abstract

A digital simulation technique for determining the torsional response of internal combustion engines subject to constant and pulsating end item torques is described herein. A refined mathematical model of the engine and end item power shafts is utilized to determine their natural frequencies, mode shapes, torsional motions and stresses using a digital computer. The mathematical model is composed of a finite number of elements which simulate lengths of continuous, massive, elastic shaft with end attached lumped masses and springs. Forcing functions, obtained by Fourier series expansion of the engine pressure-crank angle curve, are applied at the lumped masses. The technique is applied to a small gasoline engine attached to a reciprocating compressor and to a large Diesel engine with a constant torque end item.

Dynamic instability of composite-material drive shaft subject to fluctuating torque and/or rotational speed

“…The torsional response of internal combustion engines subject to constant and varying end item torques was investigated by Eshleman (1974) by experiment using a digital simulation technique. Also, plain rotor and rotor-disk systems made of conventional homogeneous material subject to combinations of constant and fluctuating torques were examined through a series of experiments by Eshleman and Euhmks (1970) and ana!yrirally investigated by Wehrli (1963) by using beam theory.…”

Analysis of multi-branch torsional vibration for design optimization

“…where ii ω is the natural frequency of an equivalent mass spring system with acting along at station . ω ω (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) which is Dunkerley's equation.…”

“…Simplifying the above equations Substitute the values of θ 1 , θ 2 and θ 3 into equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) or (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) or (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)…”

“…In summary, this method consists of the repeated application of equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and for different trial frequencies. If the trial frequency is not a natural frequency of the system, equation (2-21) will not be satisfied.…”

“…Dawson and Davies [11] Eshleman [12] used the transfer matrix method to build up a refined mathematical model of the engine and end item power shafts. He utilized the model to determine their natural frequencies, mode shapes, torsional motions and stresses.…”