摘要
针对现有公差建模及模型求解方法实用性不强的问题,提出了基于小位移旋量理论的圆柱度公差建模方法,以及一种蒙特卡罗模拟与响应面方法相结合的圆柱度公差模型求解方法。首先,依据小位移旋量理论对公差进行数学表示,结合公差的数学定义建立圆柱面尺寸公差与圆柱度公差综合作用的公差变动不等式及约束关系,采用蒙特卡罗方法分别对不同的旋量参数变动顺序进行仿真试验,获得公差变动要素的实际变动区间;然后,采用响应面方法,以圆柱度公差及试验获得的公差变动要素实际变动区间带宽值为样本,建立两者之间的响应面模型,并通过复相关系数法验证响应面模型的精度;最后,通过对典型工程实例的分析,验证了该方法具有较高的建模精度,可提高机床精度设计方法的实用性,降低机床的生产成本。
Aiming at the poor practicability of existing tolerance modeling and model solution method,a new cylindricity tolerance modeling method based on small displacement screw theory is proposed,and a cylindricity tolerance model solution method based on Monte Carlo Simulation（MCS）and response surface method is presented.Firstly,the tolerance is mathematically described by small displacement screw theory,and the tolerance change inequality and constraint relationship under the comprehensive effect of cylindroid dimension tolerance and cylindricity tolerance are established using the mathematic definition of tolerance.Then,the simulation test with MCS method is conducted on the changing orders of different screw parameters to get the actual variation range of the tolerance changing factor.With the samples based on the cylindricity tolerance and the bandwidth of actual variation range obtained above,the response surface model of the relation between the tolerance and bandwidth is constructed by response surface method.Finally,a typical example is analyzed,and the result indicates that the proposed method has high modeling accuracy,can improve the practicability of machine tool precision design method,and can reduce the production cost of machine tools.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2014年第7期53-59,共7页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目(51305132
51175161)
关键词
数控机床
圆柱度公差
小位移旋量法
约束不等式
蒙特卡罗模拟
响应面法
numerically-controlled machine tool
cylindricity tolerance
small displacement screw method
constraint inequality
Monte Carlo simulation
response surface method
