Study On The Design, Generation And Quality Evaluation Of Spatial Indexing Cam Profiles Based On NURBS Method

Spatial indexing cam mechanisms are widely used in various automatic machines, production lines and machining centres as the key component to realize the function from continuous input to intermittent output. The Spatial cam, which is the core part of the cam mechanism, determines the kinematic and dynamic performances of the whole mechanism. So it is of importance to study the technology to design and machine spatial cam surfaces with high accuracy and high performance. Under actual engineering conditions, around the generation technology of spatial cam surfaces, the main research work done in the paper is as follows:Firstly, the concept of flexible NURBS cam curve is put forward in the paper to meet various requests on cam mechanisms in the engineering practice. Then the realization and multi-objective optimization of flexible NURBS cam curves are investigated. Many dimensionless motion curves such as displacement, velocity, acceleration, jerk etc, can be all described with NURBS, regarding the dimensionless cam rotation angle as the node variable. The dynamics model of cam mechanisms with single freedom is studied. The residual vibration of the output motion is analyzed. The multi-objective optimization model is established, in which it is the leading dynamic optimization objective to minimize the amplitude of residual vibration. Optimization on NURBS cam curves can be transformed into the optimization on the control points and the corresponding weight factors.A new kind of improved multi-objective genetic algorithm-----INSGAalgorithm is presented to solve the multi-objective optimization model of NURBS cam curves, combining the multi-objective genetic algorithm with the traditional multi-objective optimization method. The INSGA algorithm integrates the reverse calculation method of control points to initialize the population, the new treatment method about constraint conditions and the object approach method to adapt the individualization design of flexible NURBS cam curves. The fast convergence of this algorithm is proved by kinematic and dynamic optimization examples.Secondly, according to the envelope movement between the spatial cam and rollers, the shaping movement while machining the spatial cam with the NC machine is analyzed. It is indicated that the generation movement between the cutter and the workpiece must be topological isomorphism with the conjugating movement between the cam surface and the rollers. So only NC machines with appropriate coordinate motions can be chosen out to realize the generation motions. Based on the movement of cam mechanism, the topological structure of NC machines to manufacture different kinds of spatial cam is researched and the motion coordinates are calculated. Then the kinematic spectrum of every NC machine to machine the spatial cam surfaces is summarized in the paper.According to the differential geometrical structure of theoretical surface of tool axis trajectory, the machinability of the contact line between the spatial cam and the rollers is analyzed. It is pointed out that the cam surfaces can not be reconstructed with the nonequivalent machining method and the errors caused by the different directions of normal vector along the contact line are unavoidable. A new method to calculate the normal error of machined spatial cam surfaces is introduced based on the traditional tool location compensation method. Simultaneously, the relation between the maximum normal error and the position of compensation point along with the compensation size is discussed. It is concluded that the best compensation value is the radius difference between the roller and the tool, while the best compensation position is not fixed. Therefore, a new adaptive and flexible compensation method of tool location is brought forward to overcome the limitation of compensation method, which is often discussed in many papers. It is the objective function to minimize the maximum normal error of generated surface and the position of the compensation point is looked on as the optimized variable. In this way, the best tool location can be derived by the proposed method. Then, the approximate side milling method is put forward, which inducts the approximation theory into the tool path planning. Cutter positioning methods in five-axis side milling generation are investigated including single point offset algorithm, double points offset algorithm and three points offset algorithm. Based on the traditional tool location compensation method, a kind of single point offset method, the double points offset method to mill spatial cam surfacesis researched. On this basis, a kind of multi-point free offset method-----approximation offset method is brought forward. In this method, the theoretical surface of tool axis trajectory can be reconstructed by NURBS ruled surface. The reverse calculation method and the least squares approximation method are deeply studied to confirm control points of the NURBS ruled surfaces. A numerical calculation and simulation example is described based on the least squares approximation offset method. The results show the effectiveness and validity of this algorithm.Thirdly, the quality evaluation method on cam surface is introduced and the quality evaluation system is constructed in the paper. The spatial cam surface is measured as a free surface with the coordinate measuring machine (CMM) by scanning an equal-diameter helical line. The iterative algorithm to match the cam coordinate system and the measuring coordinate system is discussed. The profile error of spatial cam surface reflects its quality. Based on the match result of the coordinate systems, a certain equal-parameter helical line on the cam surface is measured and fitted with NURBS. Then the real output angle can be achieved based on the rotation transform of coordinate systems and the theory of conjugate surface. In this way, the transmission quality of cam surface can be evaluated.At last, a nonequivalent machining experiment is performed based on the traditional compensation method and the proposed least squares approximation offset method, taking a cylindrical spatial cam with oscillating rollers as an example. The experiment results can verify the validity and feasibility of this new proposed tool path planning method. The manufactured cylindrical cam surfaces are measured with the CMM. Based on the measured data, the quality evaluations on spatial cam surfaces are finished and the results show that the approximation offset method, which excels the tool path compensation method, can decrease the machining error and satisfy the needs in engineering practice.As stated above, several key factors related to the motion accuracy of the spatial cam mechanism such as the multi-objective optimization of cam curves, tool path planning method to generate the cam surface, quality evaluation on the cam surface, are studied deeply based NURBS method in the paper, which is helpful to upgrade the process quality of spatial cam indexers and can basically solve the practical problems on the poor product accuracy and poor performance of precisely spatial cam indexers with high speed in our country.