Spherical Cam Research Articles

Theoretical and Experimental Research of Spherical Roller Transmissions

Передачи с промежуточными телами качения в настоящее время используются для решения специальных инженерных задач. Они имеют низкую материалоемкость и высокую нагрузочную способность, так как передача мощности осуществляется по нескольким параллельным потокам, число которых равно числу тел качения. К недостаткам многих конструкций, препятствующих широкому использованию в промышленности, относят низкий КПД и недостаточную надежность. В статье рассмотрены вопросы расчета и проектирования передач, у которых траектории центров масс тел качения расположены на сферических поверхностях. Ролики взаимодействуют со сферическими кулачками, образующими пространственные замкнутые периодические беговые дорожки. Преимуществами являются небольшие осевые и радиальные габариты, возможность объединения в конструкции одного механизма редукторного узла и угловой муфты. Рассмотрены конструкции сферических роликовых передач, проведен сравнительный анализ двух- и трехзвенных механизмов, представлены результаты силового анализа и произведена теоретическая оценка потерь мощности. Приведены результаты экспериментальных исследований КПД и шумовых характеристик разработанных редукторов. Обосновывается вывод о конкурентоспособности сферических роликовых передач как передач общемашиностроительного назначения в диапазонах передаточных отношений 3…15, частот вращения валов не более 3000 мин-1.

DESIGN OF A PITCH-ROLL JOYSTICK BASED ON A THREE-LOBE SPHERICAL CAM MECHANISM

A pitch-roll joystick based on a spherical cam mechanism is proposed that can be implemented as a haptics device. Spherical cams can replace the bevel gears that are conventionally used in transmission mechanisms involving shafts with intersecting axes to achieve lower backlash, lower frictional losses and higher stiffness. Such a spherical cam mechanism is essentially composed of multi-lobe-cams and conical rollers. Undercutting is a deterrent to the generation of smooth cam surfaces, which calls for the synthesis of a singularity-free spherical cam profile. The issues of high pressure angle and high contact ratio are addressed by means of a multilobe cam. The design of the cam profile and the assembly of the joystick are described. The criteria for the selection of the numbers of lobes and rollers are also explained.

DESIGN OF A SPHERICAL CAM-ROLLER MECHANISM FOR AN AUTOMOTIVE DIFFERENTIAL

Spherical cam-follower mechanisms are attractive alternatives to bevel gears, as they provide low backlash and low friction losses. The design of such a mechanism is reported here, to be incorporated in an automotive differential, whose bevel pinions and side gears are substituted by spherical cams and rollercarriers, respectively. Critical to the design of cam mechanisms is the generation of the cam-profile, free of undercutting. The profile, generated using computer algebra, is analyzed for singularities, including cusps and double points. The pressure angle, an important factor that governs the effective force transmission of cam mechanisms, is duly kept within acceptable limits. Conclusions are drawn on the suitability of cam mechanism developed for automotive applications.

Study on Engagement Features for a Novel Spherical Engine

Based on engagement theory, this paper presents the principle and the process of modeling and simulation of a novel spherical engine. When considering the operate device of the spherical engine as a spherical cam, we use the theory of conjugated surfaces to analyze the engagement surfaces between the cam and the follower, the equations of the engagement surfaces as well as the expression of pressure angle are built. Finally, we use the mathematical tools to describe the trace of the engagement surfaces.

The design of spherical multilobe-cam mechanisms

Cam—roller mechanisms can be used in transmissions and robotic devices as an alternative to their bevel-gear counterparts. As bevel gears are used to couple shafts of intersecting axes, their cam-mechanism replacements are bound to have intersecting axes as well. This means that the contact surface of the cam must be conical, which leads to spherical cam mechanisms. Compared with gear transmissions, cam—roller mechanisms feature low friction, low backlash, and high strength. However, cam mechanisms may end up with a high pressure angle if negative action, a motion in which the cam is driven by mechanism rollers, occurs. This article reports the design of transmissions with spherical multilobe cams (MLCs), as a means to reduce the pressure angle. The kinematics of MLC, including profile generation, undercutting-avoidance, and transmission-quality evaluation, is studied here. A case study has been included, in which the synthesis of a spherical MLC transmission is undertaken as a means to improve the transmission quality of a spherical epicyclic gear train. This train was introduced with the purpose of producing a singularity-free, unlimited-workspace pitch—roll wrist.

Determination of spherical cam profiles by envelope theory

Based on envelope theory and differential geometry, this paper presents a general expression for the surface geometry of spherical cams with a meshing follower. One of the significant advantages of using the concept of a cam formed as the envelope of the parameter family of the follower surfaces is that an expression can be derived which describes the cam surface. According to the transformation of the coordinates of the contact point, the meshing condition can be obtained without knowing the relative velocity between the cam and the follower. The surface analysis including the instantaneous contact lines, induced normal curvatures, comprehensive curvatures, and a limit curve of the second kind are shown for the manufacture and design of spherical cams. Moreover, the weight of the follower can be decreased by a limit curve of the second kind. A numerical example is given to illustrate the application of this method.

APPLYING TWO-PARAMETER ENVELOPE THEORY TO DETERMINING SPHERICAL CAM PROFILE WITH CYLINDERICAL FOLLOWERS

Using the envelope theory of two-parameter family of ball surfaces, two geometric models of spherical cam can be easily obtained when the follower-motion program has been given. The results of the envelope theory are used to determine an optimal spherical cam profile with an oscillating cylindrical follower. Some investigations of geometric characteristic, such as pressure angle and cutting path, are determined using the obtained geometric model. The principle curvatures are analyzed to avoid undercutting. Finally, a numerical example is given to illustrate the application of the procedure.

Machine tool setting for the manufacturing of spherical cams

This paper employs the theory of conjugate surfaces and the notion of Denavit–Hartenberg (D–H) transformation to investigate the manufacturing requirements for generating the CNC machine setting for spherical cams. The general design model is first derived and presented to determine the equations for a spherical cam and to generate the associated NC data for a five-axis CNC machine system to produce the spherical cam-oscillating roller-follower system (SCORF) mechanism. A D–H transformation is employed to derive the ability-function matrix of the machine tool and to determine the desired cutter motion trajectory. The NC program data equation is obtained by equating the ability function of the production machine and the path planning matrices. The method presented here is general and systematic. It combines the functions of design and manufacture for general cam production. The resultant cutting velocity and material removal rate are also studied to allow the efficiency of the manufacturing process be properly controlled. A SCORF is employed to illustrate the effectiveness of the proposed approach. The direct measurement data for the final product indicates that the result is satisfactory. This result, in turns, indicates that the proposed theory and the systematic modeling procedure presented in this paper are both valid and effective.