摘要
空间分度凸轮机构作为实现“连续输入—间歇输出”功能的关键组件,广泛应用于各种自动机械、生产线和加工中心中,而空间凸轮作为机构的核心零件,决定了整个机构的运动学和动力学性能。因此,对空间凸轮廓面的高精度和高性能设计与制造技术的研究至关重要。本文从工程实际出发,围绕空间凸轮廓面的创成技术,主要开展了如下研究工作:
首先,为了适应工程实践中对凸轮机构的各种性能要求,本文提出了NURBS柔性凸轮曲线的概念,并研究了它的实现和多目标优化问题。将凸轮转角无因次化作为节点变量,以NURBS形式描述了凸轮机构的无因次位移、速度、加速度和跃度等运动曲线。基于凸轮机构单自由度动力学模型,分析了输出运动的残余振动,并以NURBS凸轮曲线的控制顶点和对应权因子值为优化变量,以残余振动特性为主要动力学优化目标函数,建立了NURBS柔性凸轮曲线的多目标优化模型。
将多目标遗传算法与传统的多目标优化方法相结合,提出了一种适合NURBS柔性凸轮曲线个性化设计的改进多目标遗传算法——INSGA算法,用于求解凸轮曲线的多目标优化模型。在该算法中,集成了初始化种群的反算方法、约束条件处理新方法和目标达到选择策略等保证算法快速收敛的一些关键技术。
其次,根据啮合理论,分析了数控加工空间凸轮时的成形运动,指出数控加工时刀具与工件的创成运动必须与凸轮与滚子的共轭运动拓扑同构。对于不同类型的空间凸轮,根据凸轮机构运动形式,研究了用于加工凸轮的数控机床的拓扑结构,计算了机床运动坐标,并归纳构建了实现空间凸轮加工的数控机床的运动学图谱。
根据微分几何理论,对空间凸轮与滚子接触线可制造性进行分析,指出非等价加工不能实现凸轮廓面的重构,不可避免的存在法矢异向误差。基于传统的刀位补偿加工法,给出了计算廓面法向误差的新方法,并研究了最大法向误差与补偿点位置和补偿量的关系,得出了滚子和刀具的半径差是最佳补偿量,而最佳补偿点位置并不固定的结论。为此,提出了自适应的柔性刀位补偿方法,以实际廓面的最大法向误差为目标函数,通过优化任意时刻的补偿点位置参数,得到加工误差趋于最小的优化刀位路径。
然后,基于逼近理论阐述了曲面的逼近侧铣创成原理,分析了五坐标侧铣创成的单点偏置、双点偏置和三点偏置刀位计算方法。基于刀位补偿单点偏置法,研究了侧铣空间凸轮廓面的双点偏置法,并在此基础上提出了侧铣空间凸轮廓面的多点自由偏置法——逼近偏置法,即以NURBS直纹面逼近空间凸轮廓面的理论刀轴迹面,并具体研究了插值曲面反算和最小二乘逼近两种确定NURBS直纹面控制顶点的方法。以最小二乘逼近偏置法侧铣弧面凸轮廓面为例,进行了刀具位姿的实例计算和廓面的创成加工仿真,验证了算法的正确性和实用性。
再次,研究了空间凸轮廓面的品质评价方法,构建了廓面品质评价体系。把空间凸轮廓面看作自由曲面,基于三坐标测量机,以等径扫描方式实现凸轮廓面的测量。提出了实现凸轮坐标系和测量坐标系匹配的迭代算法,通过对空间凸轮廓面轮廓度误差的评定来评价廓面自身品质。基于坐标匹配结果,测量凸轮廓面上某一条等参数螺旋线,利用NURBS曲线重构被测节点,然后根据坐标旋转变换和共轭曲面原理,反求出实际输出转角,实现了廓面传动品质的评价。
最后,以圆柱凸轮工作廓面的创成加工为例,基于刀位补偿和最小二乘逼近偏置刀位规划方法,进行了数控加工圆柱凸轮的仿真校验和创成实践。实验结果充分说明了逼近偏置法在生产实际中的可行性和实用性。基于三坐标测量机,对加工后圆柱凸轮廓面进行了测量,实现了廓面自身品质和传动品质评价。评价结果表明逼近偏置法的加工误差要小于刀位补偿法。
综上所述,本文基于NURBS方法研究了凸轮曲线的多目标优化、侧铣创成空间凸轮廓面的刀位规划以及廓面品质评价等影响空间凸轮机构综合性能的关键因素,有助于提升空间凸轮分度器的制程能力,从根本上解决目前我国高速高精空间凸轮分度器产品精度和性能差的实际问题。
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.
引文
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