Development of a technique for the geometrical modeling of conjugated surfaces when determining the geometrical parameters of an engagement surface contact in kinematic pairs

Abstract

This paper reports a technique for constructing a geometric shape of the surface of contact between the interacting conjugated machine elements using computer technology. A subprogram has been developed in the MATLAB software package. The comprehensive solution to such problems is a certain scientific challenge and is of great importance when designing the kinematic pairs in mechanical engineering. The main systemic drawback in the construction of complex mechanisms is that the design process does not take into consideration the geometric characteristics of the contact spatial engagement surface in the screw kinematic pairs. As a result, during the manufacture of a kinematic pair, conventionally designed structural elements demonstrate defects that shorten their lifespan. Solving the set task could reduce the time to design toothing, cutting tools, would ensure the required estimation and graphic accuracy, as well as improve the efficiency of the manufacture of parts. The study of existing procedures for designing screw conjugated surfaces has made it possible to note their unsatisfactory compliance with modern design requirements. Therefore, the manufacture of a kinematic pair that provides for technological accuracy implies the assignment of the curvilinear shapes for a contact spatial engagement surface under the predefined conditions. The proposed geometric technique for determining the shape of a contact spatial surface of the kinematic pairs of toothing and cutting tools could make it possible to design and manufacture components and mechanisms with the required accuracy

Formation of conjugate curved surfaces that exclude interference

“…From the coordinate arrays of the original and resulting curved surfaces, the coordinates of the intersection line are determined. The intersection line arrays will contain those values that are equal for the original and curved surfaces [9].…”

“…The work [9] proposed a geometric method for determining interference based on the shape of the contact spatial surface of kinematic pairs and a cutting tool. The disadvantage is the following: for each intersection line it is necessary to calculate the coordinates using formulas specific to them; it is necessary to create an additional algorithm to determine which formula to use when determining the intersection line.…”

Modeling mated surfaces with the required parameters

“…A noteworthy study reported in [12] considered the contact surface of kinematic pairs. The noted techniques of constructing mated surfaces most often focus on a certain range of tasks that are successfully resolved under certain limitations.…”

“…1-3). Given the confirmation from the system of equations (5) [12], and assuming that the curvilinear surface can be set by any other parametric equation, we modify the method of circular conversion in the following way. Ypr(i,j) = (Xp(i,j)-x0)*sin(Angle)+ +(Yp(i,j)-y0)*cos(Angle)+y0; end end…”

Моделювання Спряжених Криволінійних Поверхонь Ріжучого Інструменту.

“…Поставлену задачу вирішимо геометричним моделюванням конволютних гелікоїдів для практичного використання при проектуванні ріжучого інструменту і зубчастого зачеплення довільного профілю кінематичних пар. За допомогою комп'ютерних технологій розробимо геометричне моделювання криволінійної поверхні ріжучого інструменту на базі параметричного кінематичної гвинта [4,5].…”