In a typical computer simulation of positive displacement compressors, the mathematical equations that model the compressor process are integrated in the time domain starting from a set of assumed initial conditions. The simulation has to be continued for enough iterations for the results to converge. The pulsation pressures in the suction and discharge cavities, which are assumed constant in the beginning, are calculated at the end of each iteration and used for the calculation in the next iteration. However, when this scheme is actually applied to fractional horsepower reciprocating compressors, it is found that the suction cavity pressure does not converge well, while all other parts of the results converge relatively quickly. The cause of this problem is explained qualitatively by the characteristics of the simulation method. A unique iteration scheme for the simulation was developed in this work to overcome this problem. In the new scheme, the updating rate of the pulsation pressures is adjusted based on the convergence trend of the previous iterations. A practical example is used to demonstrate the convergence of the simulation results and practicality of the simulation program.

The compression mechanism in a twin screw compressor consists of two helical rotors. In this work, a method is presented for computing the forces and moments induced on each rotor due to gas compression. These are defined as the compression loads. The helical rotor surfaces are defined by the end profiles, wrap angle and rotor length. The 3D surface of each rotor is mapped to 2D integration regions. These regions correspond to the surfaces associated with individual compression chambers. The compression loads are computed by integrating the chamber pressure over the rotor surfaces. The integrals are evaluated at incremental values of the rotor angular position. The method is presented and implemented for a specific compressor configuration. The compression loads are resolved to forces at the bearing locations. These bearing forces are presented for operating pressures which represent an under-pressure condition. A frequency analysis demonstrates the rich frequency content of the bearing forces due to the sharpness of the compression loads as a function of the rotor angular position. In addition, it is demonstrated that the moment load about the axis of rotation induced on the female is approximately 12 percent of that induced on the male. Therefore, the female rotor motion approaches that of an idler gear.

The planar rotary mechanisms, by virtue of its volume changing ability can be used as a pump, engine, or compressor. Most of the types of rotary mechanisms used today, from the Wankel rotary engine to the gerotor pump, are based on epitrochoidal generation and its conjugate shape. This paper presents a very general mathematical relationship for a generating arc traveling on a hypotrochoidal path and also compares the flow rate, pocket displacement, and compression ratios of the hypotrochoidal and epitrochoidal generated profiles.

If an acoustic system has one or more large dimensions compared to the shortest wave length of interest, the pressure responses which are necessary to formulate four pole parameters have to be obtained by solving the continuous wave equation of the system. In this paper, a general procedure is established to derive four pole parameters from the pressure response solutions utilizing modal series expansion. As an example, four pole parameters of a cylindrically annular cavity are obtained. The validity of the procedure is proven by applying it also to a one-dimensional pipe whose four pole parameters are available by direct method. The comparison is made in terms of four pole parameters and pressure profiles along the pipe. The comparison allows interesting observations with regard to the equivalence of the two approaches. The theory was further generalized to be applied to more complex acoustic systems, namely multiply connected systems. A cylindrically annular cavity connected by two pipes to a small lumped parameter cavity is taken as an example of the application. Noise control by either mode cancellation or wave cancellation is explored.

A mathematical model is developed for the nonlinear vibrations of automatic reed valves in high-speed refrigeration compressors. Specifically considered are a general class of values which wrap about curved backer plates. Two simple experiments are described which allow the nonlinearities of the valve system to be defined by a single nonlinear second order differential equation. Valve oscillation frequencies inside an operating compressor are predicted through a linearization of the valve equation. Comparisons with experiment are included.