Mathematical model for parametric tooth profile of spur gear using line of action

Kinematic flowrate characteristics of external spur gear pumps using an exact closed solution

In this paper a method for generating new conjugate kinematic pairs is developed. This method, called the “Deviation-Function ” method, is to use deviation functions to reshape the original pitch pairs so that the desired profiles of generated pairs can be obtained. A deviation function is defined as the distance between contacts and their corresponding instant centers of two conjugate pairs. In other words, a deviation function measures the amount of deviation of a point on the generated profile from its corresponding point on the original pitch profile. As demonstrated, this new method is applicable to any type of pitch pairs including circular or noncircular and identical or nonidentical. In addition, by using this method, it is relatively easier to realize desired geometrical and mechanical properties into the design.

Deviation-Function Based Pitch Curve Modification for Conjugate Pair Design

The specific flowrate of deviation function based lobe pumps––derivation and analysis☆

In this paper we present a complete synthesis procedure for lobe pumps with required flow rate functions. A dimensionless flow rate expression, called the specific flow rate, is is used for our pump synthesis. This specific flow rate depends only on the pitch and deviation functions of the pump rotor, and it is independent of the individual pump size, neither pumping frequency. Another important design parameter used is the lobe noncircularity, which is defined as the ratio of the lobe length to the rotor center distance. It is found that the lobe noncircularity is linearly dependent on the ratio of maximum to minimum flow rate regardless of the type of flow rate function. As a result, our synthesis procedure can be simplified as (1) select a type ofdesirable flow rate function, (2) from the flow rate function derive the corresponding deviation function, (3) based on the deviation function generate the desired rotor profile, and (4) calculate the real pump size. Another advantage is that by using this method wide classes of lobe pumps can be designed. A detailed design example is presented for illustration. In addition, new lobe profiles are invented based on some typical flow rate functions.

Th-H. Costopoulos

Papers

Reduction of delivery fluctuation and optimum tooth profile of spur gear rotary pumps