【作者】 李健；

【导师】 王勇勤；

【作者基本信息】 重庆大学 ， 机械工程， 2021， 博士

【摘要】 精度是数控机床的主要性能指标之一,决定了产品的加工精度和质量。为了提高数控机床的精度,本文以元动作和元动作链为基础,分析了数控机床中机械传动系统运动误差的形成过程,开展了元动作链运动精度分配、元动作误差建模和元动作运动精度优化分析的研究工作。提出了元动作链运动精度优化分配技术,得到元动作运动误差允许值;分析了元动作的主要功能和元动作单元的结构组成,提出了基于自由度约束概念的误差累积路径识别方法,建立了元动作单元装配误差模型;分析了元动作单元中误差源的种类,明确了元动作运动精度与各个误差源的逻辑关系,建立了元动作运动精度模型;分析了零件装配过程对生产成本的影响,建立了元动作单元综合制造成本模型,并以此为基础进行了元动作运动精度优化分析工作。具体研究内容如下:(1)提出了元动作链运动精度优化分配技术。利用FMA分解树对机械系统进行结构化分解,得到了串联的元动作和元动作链,在元动作链的基础上分析了机械传动系统的运动误差形成过程。提出了一种元动作链运动精度优化分配方法,将元动作链的运动精度进行优化分配,得到元动作运动误差允许值。为了提高分析结果的合理性和准确性,综合考虑了成本因素和灵敏度因素的影响。通过计算元动作单元的综合装配复杂度,建立了成本函数;同时对各个元动作运动精度进行了灵敏分析,建立了鲁棒性函数。然后,将成本函数和鲁棒性函数作为目标约束,建立了元动作链的运动精度优化分配数学模型。最后,得到了元动作的运动误差允许值。该方法从机械传动系统运动误差形成过程出发,实现了运动精度的优化分配,分配结果更加符合实际情况。(2)提出了元动作单元内部误差累积路径快速识别方法。分析了零件主要特征及结合面的误差模型,并用小位移旋量模型进行了建模。同时,分析了机械系统中常见的相邻并联结合面和并联支撑结构形式并进行了建模工作。在结合面误差模型的基础上,利用SDT模型的二进制矢量表示装配体中零件自由度的约束情况。然后,提出了一种基于自由度约束概念识别元动作单元内部误差累积路径的新方法。该方法计算简单,避免了繁琐的分析过程,为元动作单元装配误差建模和运动误差分析奠定了基础。(3)分析了元动作运动误差影响因素并建立了运动精度模型。根据了元动作单元的结构特点,分析了元动作运动精度的影响因素。明确了影响运动精度的各个误差源,即元动作单元的装置误差以及动力输入件和动力输出件的固有误差。分析了装置误差的组成要素以及元动作运动误差与各个误差源的逻辑关系。利用雅克比旋量模型建立了元动作单元装配误差计算模型,实现了元动作单元装置误差的分析和计算。最后,综合考虑元动作单元动力输入件和动力输出件的固有误差以及装置误差,建立了元动作运动精度模型,为元动作运动精度优化分析奠定了基础。(4)开展了元动作运动精度优化技术研究。元动作运动精度模型建立了零件几何误差与元动作运动精度的数学关系,通过优化零件特征的公差可以实现元动作运动精度的优化分析。因此,元动作的运动精度优化分析研究变成了以运动精度为约束的公差优化问题。研究了装配成本对元动作单元综合制造成本的影响,分析了影响零件装配过程的各种因素,通过求解零件装配难度系数,对传统公差-成本函数进行修正,得到元动作单元综合制造成本模型。然后,以元动作单元综合制造成本最小,同时运动精度质量损失成本最小为目标,元动作运动精度为约束条件,以单元中零件特征公差以及动力输入件和动力输出件的固有误差为优化变量,建立了元动作运动精度多目标优化模型。通过多目标优化模型求解得到了Pareto前沿解集,利用TOPSIS多准则决策方法对Pareto前沿解集中的候选解进行综合分析和排序,最终确定最优解。以最小的制造成本和运动精度的质量损失成本,保证了元动作的运动精度。更多还原

【Abstract】 Precision is one of the main performance indexes of CNC machine tools,which determines the machining precision and quality of products.In order to improve the precision of CNC machine tools,the forming process of motion error of mechanical transmission system was analyzed based on Meta-action and Meta-action chain.The research work of optimal distribution of motion precision of the Meta-action chain,error modeling and motion precision optimization analysis of the Meta-action was carried out.The optimal distribution technology of motion precision of Meta-action chain was proposed and the allowable value of motion error of Meta-action was obtained.The main function of Meta-action and the structure of Meta-action unit were analyzed.An error accumulation path identification method based on the concept of degree of freedom constraint is proposed,and the assembly error model of Meta-action unit is established.The types of error sources in the Meta-action unit were analyzed,and the logical relationship between the motion precision of Meta-action and the error source is clarified,then the motion precision model of Meta-action was established.The influence of part assembly process on production cost was analyzed,and the comprehensive manufacturing cost model of Meta-action unit was established.Then,the optimization analysis of Meta-action motion precision was carried out.The specific research contents of this research were as follows:(1)The optimal distribution technology of motion precision of Meta-action chain was proposed.The mechanical system was structurally decomposed by FMA decomposition tree,and the series Meta-actions and Meta-action chain were obtained.Based on the Meta-action chain,the forming process of motion error of mechanical transmission system was analyzed.An optimal distribution method of motion precision of Meta-action chain was proposed.The motion precision of Meta-action chain was distributed and the allowable value of motion error of Meta-action was obtained.In order to improve the rationality and accuracy of the analysis results,the effects of cost factors and sensitivity factors were comprehensively considered.The cost function was established by calculating the comprehensive assembly complexity of the Meta-action unit.At the same time,the sensitivity analysis of motion precision of each Meta-action was carried out,and the robustness function was established.Then,the mathematical model of motion precision optimal distribution of Meta-action chain was established by taking the cost function and robustness function as objective constraints.Finally,the allowable motion error of Meta-action was obtained.Based on the forming process of motion error of mechanical transmission system,the proposed method realizes the optimal distribution of motion precision,and the distribution result was more in line with the actual situation.(2)A fast identification method of internal error accumulation path of Meta-action unit was proposed.The main characteristics of the parts and the error model of the joint surface were analyzed,and the small displacement torsor model was used for modeling.At the same time,the common forms of adjacent parallel joint surface and parallel support structure in mechanical system were analyzed and modeled.Based on the joint surface error model,the binary vector of the small displacement torsor model was used to represent the constraints of part degrees of freedom in assembly.Then,a new method for identifying the error accumulation path of Meta-action unit based on the concept of degree of freedom constraints was proposed.The proposed method avoids the tedious analysis process,and lays a foundation for the assembly error modeling and motion precision analysis of Meta-action.(3)The influencing factors of motion error of Meta-action were analyzed,and the motion precision model was established.According to the structural characteristics of Meta-action unit,the influencing factors of motion precision were analyzed.The error sources that affect the motion precision,namely the device error of the Meta-action unit,the inherent error of the power input part and the power output part were defined.The constituent elements of device error and the logical relationship between the motion error of the Meta-action and each error source were analyzed.The assembly error calculation model of Meta-action unit was established by using Jacobian torsor model,and the analysis and calculation of Meta-action unit device error were realized.Finally,considering the device error,the inherent error of the power input part and power output part of the Meta-action unit,the motion precision model of the Meta-action is established,which lays a foundation for the optimization analysis of the motion precision of the Meta-action.(4)The optimization technology of motion precision of Meta-action was studied.The motion precision model of Meta-action showed the mathematical relationship between part geometric error and motion precision.The optimization analysis of motion precision can be realized by optimizing the tolerance of part features.Therefore,the motion precision optimization analysis of Meta-action becomes a tolerance optimization problem constrained by motion precision.The influence of part assembly cost on the comprehensive manufacturing cost of Meta-action unit was studied.Various factors affecting the part assembly process were analyzed.And the comprehensive manufacturing cost model of Meta-action unit was obtained by solving the part assembly difficulty coefficient and modifying the traditional tolerance-cost model.Then,taking the minimum comprehensive manufacturing cost and the minimum quality loss cost of motion precision of the Meta-action unit as the goal,the Meta-action motion precision as the constraint condition,the part feature tolerance and the inherent error of power input part and power output part as the optimization variables,a multi-objective optimization model of motion precision of Meta-action was established.The Pareto frontier solution set was obtained by solving multi-objective optimization model.Finally,the candidate solutions in the Pareto frontier solution set were analyzed and sorted by using TOPSIS multi criteria decision-making method,and the optimal solution was determined.The motion precision of the Meta-action was guaranteed under the minimum manufacturing cost and mass loss of motion precision.更多还原