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This paper approach the issue of side mill profiling, for generation of helical surfaces – the sealing worms from the construction of the helical pumps with cycloid worms. The issue of side mill profiling is based on the complementary theorem of the “substitutive circles family”. This method will be applied as so as for profiling the crossing section of the worm, in order to generate the helical flute and for profiling the revolution surface that constitutes the primary peripheral surface of the side mill. They are discussed some aspects related to singular points onto profiles and problems related to discontinuities onto the tool’s profile. For a certain case, are presented profiles determined in numerical form, which may serve for design of templates for side mill check and, obviously, for design of relieving tools.

In this paper, we present, comparatively, two analytical methods for profiling the tools delimited by revolution surfaces, used to generate helical surfaces with constant pitch. The first method lays on a complementary theorem used for tools profiling, namely the Minimum distance theorem. A specific algorithm for applying it has been developed, in order to profile the tools delimited by revolution surfaces, which generates helical surfaces with constant pitch by enwrapping. The methodic is referring, here, to a tool whose symmetry axis is incident and, at the same time, normal to the helical surface axis – the end mill cutter. The other analytical method here applied grounds on Nikolaev classical theorem. We also present an example of application for both methods, in the case of profiling the end mill cutter used to generate a helicoid with circular frontal generatrix. The tool axial sections are determined and compared in a numerical representation.

The generation of the ordinate surfaces whirl attached to a centrode (e.g. cylindrical or helical gears teeth generation) with a hob mill is an efficient method, also recommended in machining the teeth of slitting saw cutter with high dimensions. Profiling the hob mill conjugated to the disc-tool (slitting saw cutter) teeth, depending on its tooth profile, is a specific problem. There are known both analytical methods to profile the hob mill – e.g. the Gohman method (which uses an intermediary surface – the reference rack-gear), and graphical methods (developed in AutoCAD). A profiling method, which uses the CATIA environment facilities in graphical design, laying on the principle of helical motion de-composition (Nikolaev theorem) has been recently suggested. In this paper, we present a method for hob mill profiling, in graphical form, based on a complementary theorem (the Minimum distance method). The reference rack-gear, conjugated to the disc-tool teeth, is firstly profiled and then, by starting from it, the peripheral surface of the hob mill for machining the slitting saw cutter teeth is determined.

The issue of enwrapping surfaces study can be solved using the basic theorem Olivier or Gohman. Also, are known and used some specific theorems for the study of the enveloping of the helical surfaces. More, they were developed and applied complementary theorems as: “the minimum distance” method or “the inplane generating trajectories family”. The development of the graphical design environment allows the approach of the issue of surface enwrapping using the capabilities of this software. In this paper it is proposed a methodology for application of the “minimum distance method” for generation of the surface associated with a pair of rolling centrodes using various tools: rackgear tool and gear shaped tool. They are presented applications of this graphical method and the results. This proves the quality of the proposed method. The graphical methods have the advantages that are fast, rigorous and intuitive.

The Family of Substituting Circles method is one among the methods used to study the reciprocal enwrapped surfaces. It is a complementary method, to whom a graphical application, designed in a dedicated environment (AutoCAD, CATIA etc.) can be associated. Diverse graphical solutions, for solving tools profiling problems, have been already conceived, associated to the Family of Substituting Circles method. In this paper, we suggest a new graphical application, developed in CATIA, for profiling the ring-tool reciprocal enwrapped to a cylindrical helical surface. An example of the new profiling method application is enclosed. The quality of the results obtained by using the new profiling method is assessed by comparison to the solution of the same problem found through an analytical method.

In this paper, we present a graphical method, developed in CATIA environment, based on the method of substituting circles family and dedicated to profile pinion cutters for generating interior surfaces. Hereby, the family of substituting circles associated to the worked piece (the profile to be generated) is determined at the same time to the curve transposed, in the rolling motion, to the tool centrod. After finding the position of the contact points between the generated profile and the family circles, we can determine, in the transposed family, the locus of the points from the reciprocal enwrapping profile the pinion cutter profile. The paper also includes a method application for generating a hole with square transversal section, and a comparison between the profiling results when using the graphical method, versus an analytical method. The results prove the coincidence between the two profiles determined as above, on one hand, and both rapidity and precision of the graphical method, on the other hand.

The compressor rotors usually are helical surfaces with constant pitch and are composed crossing profiles. Frequently, for repair operations occurs the reconstruction necessity for one or both of the worms, drive and driven, from the helical compressors gear. The helical composed surface of rotor flank is generated usually with side mill. The knowledge of worm shape can not be made from geometrical conditions. In these conditions it is necessary to determine the flank form by actual measuring the crossing profiles of these parts. So, the theoretical helical surface of the worm is being substituted by an assembly of helical lines which together with crossing profiles forms points cloud resulted from measuring leads to a polyhedral expression of the flank rotor. Numerically, this surface type is expressed by a coordinate array which shows its discrete image. The profiling of cutting tool bounded by a revolution surface reciprocally enveloping with the substitutive surface of the helical one represents a special problem. In this paper is proposed an algorithm for polyhedral expression of the helical surface previously determined by reverse engineering methods and an algorithm for the determination of the specific enveloping condition at contact with a discrete surface.It is presented an example for a compressor rotor measured on a 3D measuring machine, the algorithm for the transformation of the gathered points cloud in a surface with polyhedral expression. Given these conditions there were determined the enveloping condition and the axial section of the side mill.

In this paper, it is analyzed, in a comparative way, two methods for profiling disc tools (mills or grinding wheels) for generation of specific threads used in the construction of the prosthetic screw for dental implants. It is proposed an analytical method, based on the fundamental theorem of the surfaces enveloping versus a graphical method, developed in CATIA. They are presented numerical examples for the both methods.

The machining of ordered curl of surfaces, associated to a centrode, is completed in very good yield and precision conditions with hob mill tool. In this case, the issue is to determine the enwrapping worm of the ordered curl of profiles, as a fundament for hob mill tool's construction. Based on the "generating trajectories" method, an algorithm for profiling the generating hob mill for machining the trilobed rotor of a peristaltic pump is presented. A graphical example, developed in CATIA design environment, shows the profiling technique.