Giovanni Mimmi

Non Undercutting Conditions in Internal Gears

Many contributions regarding internal gear theory exist in literature. They mainly consider the problem of undercutting by means of analytical methods applied to specific and limited cases. The present paper deals with a general method showing the analytical condition for avoiding undercutting by the use of the concept of the limit curve. In particular the analytical determination of the limit curve allows the designer to obtain significant graphical representations of the design limits.

Analytical Model of a Particular Type of Positive Displacement Blower

Abstract Many papers exist in the literature that deal with the twin-screw compressor. This usually has two different rotors, a male and a female, and is commonly used to produce compressed gas for industrial uses. However, a different type of positive displacement rotary compressor with two screws is sometimes used, one of its typical applications being in car engine supercharging. The present paper deals with the latter type, which is defined as a two-screw blower. This blower has two identical helical rotors, each with three lobes. The kinematics and the geometry of the rotors are analysed here, and a complete mathematical model for the rotor is defined. Moreover, different possible shapes of the rotors, depending on the design parameters, are analysed and the limitations in the choice of the design parameters are presented. Finally, an analysis of the theoretical specific slipping of the rotors is presented, showing which zones of the profile are the most stressed. This model will be useful for further studies on rotor pressure loads and blower dynamics.

Pre-Shaping Motion Input for a Rotating Flexible Link

The interest in the design of manipulators for space operations with a light structure has grown meaningfully in comparison with rigid manipulators, even if these flexible manipulators are unavoidably characterized by a nonnegligible structural flexibility. This paper deals with the first phase of a project financed by a grant from the Italian Space Agency, which is concerned with the setting up of an open-loop control for a planar manipulator with flexible linkages. In this phase, the project is subdivided into two parts: on the one hand, different command inputs have been proposed for point-to-point operations; on the other hand, dynamic simulations have been carried out by using a multibody model with flexible parts, in order to evaluate the residual vibrations due to the selected command input at the end of the motion. These command inputs will be applied to the actual manipulator, which is already available, in a future phase of the project. The command inputs, which are described here, are based on both the convolution of special impulse inputs suitably chosen on the basis of the system natural frequencies and the reduction of impulsive inertia forces by means of a suitable algorithm proposed here and derived from cam design. The simulations are carried out by commercial software for the study of multibody systems and custom programs for the command input implementation. The results obtained for the residual vibrations are compared to those obtained by conventional command inputs in the simulations on the same model.

Involute Gear Pumps Versus Lobe Pumps: A Comparison

In previous studies we have considered several types of positive displacement rotary pumps and deeply analyzed the generation of the flow rate and the design limits. This has been done in order to evaluate the main performance indexes; one of which, the flow rate irregularity, is related to the possibility that the pump becomes a source of vibration and noise. A second index is the specific flow rate, related to the delivery capacity of the pump. In this paper, following our previous researches, we analyzed internal involute gear pumps and internal lobe pumps, that have similar operations but different performances. The design parameters and the way to optimize the performances are proposed for both cases. Finally a comparison is made between the two types of pumps with optimum design parameters.

Determination of Tool Profile for the Milling of Three-Screw Pump Rotor

The rotors of three screw pumps are commonly machined using shape milling cutters. The determination of the exact shape of the cutter is very important, since a high precision in the machining is required to obtain a high volumetric efficiency of the pump. This paper describes a method to determine the theoretical shape of the cutter, starting from the characteristic parameters of the pump. The rotors are modeled in space by helicoids. The contact line between the tool and the workpiece is then determined and this allows us to define the exact cutter profile, with a suitable reference system transformation.

Theoretical analysis of internal epitrochoidal and hypotrochoidal machines

Abstract In this article, a complete and original method to analyse both the epitrochoidal and the hypotrochoidal rotary machines is presented. The internal trochoidal machines consist of two rotors: the first rotor is an envelope of a trochoid, the second rotor is its conjugate. In particular, in this article, the profiles of the trochoidal rotor and its conjugate are expressed by original and particularly synthetic equations using a method based on the theory of gearing. Then the geometry of these machines is completely defined by the choice of four non-dimensional parameters. Once these parameters are selected, the geometric and kinematic characteristics of the rotor profiles are obtained in an original analytic form; hence, the main theoretical performance indexes are computed by a proper method. The results of the analysis allow us to choose the best geometric configuration for a specific application.

Compression Load Dynamics in a Special Helical Blower: A Modeling Improvement

The instantaneous variation of pressure loads acting on the rotors of positive displacement rotary blowers may produce vibrations and noise that in some case produce the failure of the machine and of the piping. In a previous paper the authors determined the pressure loads acting on the rotors, starting from the geometry of the chambers that are formed during the rotor meshing and the thermodynamic transformation of the working fluid. The calculation of the loads has been made in a quasi-static manner. In this paper the model has been improved by taking into account the effects due to a closed volume chamber at the discharge. This assumption better reproduces the real cases and allows the researchers to perform more efficient calculations and more reliable predictions.

Dynamic Effects of Pressure Loads in Three Screw Pump Rotors

In a previous paper the authors have dealt with the calculation of the pressure loads on the rotors of a three screw pump. The pressure loads can be modelled as a force and a moment. In particular, starting from the knowledge of rotor geometry, the loads can be calculated and subdivided into their components along the screw axes. In this paper the simulation results obtained by using the proposed model are presented. The results show that the satellite screws are thrust towards the case in a specified direction. This fact can be verified in practice, since the cases actually present a wear zone in a particular position.

Dynamic Loads in the Three-Lobe Supercharger

In previous papers the authors have analyzed the functioning of the three lobe supercharger. This analysis was made possible by a complete analytical model of the rotors. The dynamic transformation of the chambers occupied by the fluid allows us to point out specific problems regarding trapped volumes and to design special devices to avoid these problems. As a result it is possible to simulate the performance of the compressor and to propose an analytical model in order to determine the dynamic loads on the rotors. The topic of this paper is the comparison between the performances achieved by helical and spur rotors, with particular attention to the loads, force and moment, acting on the rotors.

Theoretical Analysis of an Original Rotary Machine

In this study an original analysis of the geometric design of a particular internal rotary machine and an investigation on its theoretical performances are presented. The first part of the work is focused on the geometry of the machine, characterized by more complex rotor profiles compared with the classical epitrochoidal pumps. Suitable parameters are pointed out to completely define the geometry of the machine. In the second part of the study, proper indices are set and evaluated as functions of the design parameters, in order to evaluate the performance of the machine. Finally a specific configuration of the considered pump is compared with the conventional trochoidal pumps in terms of flow-rate indices. The analysis performed allows one to highlight the basic advantages and drawbacks of this original design in comparison with the classical trochoidal profiles and can be used as a basis for CAD/CAE (Computer-Aided Design and Engineering) or experimental studies.