基于接触区域的球头铣刀颤振稳定域预报方法研究

运用半解析法精准搭建出球头铣刀与工件接触区域边界的投影方程,对铣削系统时滞动力学方程进行全离散时域数值求解,在单齿周期内球头铣刀视为圆弧切削的基础上,通过接触区域投影和切削刃投影不同时刻的关系,确定出数值求解方程中所需要的瞬时参与切削刀刃的实际切削部位,利用Floquet定理获得了不同转速下的临界切削深度,构建出了高精度的球头铣刀颤振稳定域叶瓣图,并在三轴数控机床上进行了试验验证,试验结果与预测结果相符合,表明了该方法的正确性。同时,与传统方法相比,这里所提供的方法拥有较高的预测精度,最后分析了不同参数对颤振稳定域的影响规律,为叶瓣图指导实际加工奠定了基础。     

考虑模态耦合的球头铣刀颤振稳定域建模方法

球头铣刀广泛应用于曲面加工中,因此构造出针对球头铣刀的颤振稳定域叶瓣图意义重大。利用精细积分法对铣削系统二阶动力学方程进行时域数值求解,由切削刃与切触区域不同时刻的关系,确定出时域数值求解方程中所需要的刀刃瞬时切削部位,通过Floquet定理获得了高精度的颤振稳定域叶瓣图,并在三轴数控机床上进行了正确性试验验证。试验结果与预测结果相一致,表明所提供的方法能够为球头铣刀实现无颤振切削加工提供有力的技术支撑。     

平前刀面球头铣刀的几何角度分析

分析了平前刀面球头铣刀的几何角度,给出了该铣刀的刀刃参数方程,推导了铣刀法向前角、刃倾角和主偏角计算公式。     

凸曲面拼接模具球头铣刀的瞬时铣削力预测

在曲面模具拼接区域球头铣刀铣削过程中,刀具载荷变化大,瞬态铣削力有突变现象,影响模具拼接区域的加工精度和表面质量。为了预测拼接区域球头铣刀的瞬态铣削力,首先,建立考虑冲击振动的球头铣刀三维次摆线轨迹方程,得到瞬时未变形切屑厚度模型;然后,基于铣削微元的思想,建立凸曲面双硬度拼接模具球头铣刀的瞬态铣削力模型,该模型能够综合考虑拼接区冲击振动、硬度变化、刀具工件切触角度变化对瞬态铣削力的影响;最后,进行凸曲面拼接区域球头铣刀铣削加工实验。实验结果表明,预报的瞬态铣削力和实验测量结果在幅值上和变化趋势上具有一致性,在平稳切削时最大铣削力预测误差值基本在15%以内,验证了该模型能有效地预报凸曲面模具拼接区域球头铣刀的瞬态铣削力。     

基于UG模型分析的两刃球头铣刀开发与试验

用球头铣刀加工模具和叶片零件时,球头刃的轮廓度和切削参数决定了零件的精度。采用UG软件对整个球头铣刀的圆弧轮廓度和球头前角进行分析,并结合切削理论找出球头铣刀加工的薄弱点,开发了新结构的球头铣刀,并对模具钢NAK80和叶片材料GH4169进行了切削试验。结果表明:新结构的球头铣刀比原结构更适合模具钢、叶片材料的端铣加工,刀具轮廓精度等级和耐用度更高;在模具加工方面,给出了不同加工精度的切削参数,为模具的高效加工提供参考依据。     

自由曲面数控加工表面形貌仿真

建立了整体式螺旋刃球头立铣刀和可转位式球头立铣刀的几何刃线模型。基于自由曲面方程,由矩阵运算得出刃线运动包络面,对球头铣刀加工的表面形貌进行了建模和仿真。结果表明:加工平面时,刀轴摆角的选择对表面形貌影响较大;而加工自由曲面时,刀轴摆角的变化对表面形貌影响不大。     

机夹式球头铣刀有限元及试验模态分析

针对加工过程中机夹式球头铣刀振动控制和铣削稳定性优化等问题,基于通用有限元软件ABAQUS建立了机夹式球头铣刀的有限元模型,对其模态特性进行有限元分析,给出了前6阶固有频率和振型;同时采用锤击激振法对球头铣刀进行了模态试验,应用模态参数识别的新技术PolyMAX方法对试验结果进行了处理,获得了模态参数识别稳态图,拾取了可能的模态频率,并将所得试验结果与有限元模态分析结果作了比较,计算了仿真值与试验值之间的误差,分析了出现误差的主要原因。研究结果表明,有限元模态分析结果与模态试验结果相吻合,模态频率误差在13%以内,较好地反映了结构的物理特性,同时验证了有限元模型的合理性,分析结果为球头铣刀振动控制和铣削稳定性研究提供了依据。     

虚拟制造系统中球头铣刀的磨损预测

基于球头铣刀铣削方式及铣削参数的特点,应用微分理论基本方法提出了一种虚拟制造系统中球头铣刀磨损预测的数学模型,为提高虚拟制造系统的真实感和实时性奠定了基础;该模型预测的结果与铣削试验的测量结果基本吻合。     

两类柱状回转铣刀NC加工的难点

介绍了球头柱状和带角圆柱状铣刀的设计与NC加工中相关主干模型，集中就这两类铣刀的难点——二轴联动NC加工中的径向进给和球头顶尖问题，给出了较为理想的处理方案。     

等法向前角和等径向后角微细球头铣刀刃磨研究

微细球头铣刀因其在制造复杂的曲面和零部件方面具有很大的优势而广泛应用于微机械加工领域。目前多轴数控磨削方法仍是实现微细球头铣刀批量化制造的主要方法,但是由于微细球头铣刀尺寸小,误差敏感性大,在刃磨过程中难以保证其制造精度和质量,因此迫切需要精确高效的刃磨方法来提高微细球头铣刀制造精度,降低其刃磨制备难度。为此,基于球面等导程螺旋线切削刃曲线,提出了用于等法向前角前刀面的刃磨模型。为了实现球部和圆柱形部分的后刀面的平滑连接,提出了等径向后角后刀面的刃磨模型。基于提出的刃磨模型和6轴CNC磨床运动原理,通过Matlab编程求解等法向前角和等径向后刀面微细球头铣刀刃磨过程中机床各轴运动轨迹。最后,通过磨削仿真和实验成功制造了直径为0.5mm的硬质合金微细球头铣刀,其最大几何误差不超过5%,从而验证了磨削方法的正确性和有效性。     

基于载荷控制的拐角铣削进给优化*

针对模具型腔拐角铣削过程,提出一种考虑刀具变形及铣削力变化的基于载荷控制的进给量优化方法。根据拐角的铣削中刀具与工件接触情况的不同,将铣削过程分为五个阶段,分别分析拐角铣削时刀具切削刃真实运动轨迹,建立拐角圆弧运动轨迹下瞬时切屑厚度模型,提高切屑厚度模型在拐角加工中的预测精度。修正铣削力预测模型,使其满足拐角加工过程不同阶段的要求。选取刀具变形量为约束条件,计算不同阶段的允许最大载荷,利用二分迭代法得到该载荷下对应的进给量值。考虑到数控机床的运动加速度限制,对得到的优化进给量值进行二次优化,以满足实际加工的要求。仿真结果表明,在进给优化后的拐角铣削过程中,载荷变化趋于平稳,加工时间缩短。进行拐角加工验证试验,数值仿真计算和试验测量结果表明,建立的铣削力模型能够很好地预测拐角铣削过程。所建立的优化模型为模具型腔的高精、高效加工提供理论支持。     

Design and fabrication of a new micro ball-end mill with conical flank face

Micro ball-end milling is an efficient method for the fabrication of micro lens array molds. However, it is difficult to meet the machining quality of micro dimple molds due to the wear and breakage of the milling cutter, which presents large challenges for designing geometric structure and edge strength of micro ball-end mills. In this study, a new configuration of a micro ball-end mill for micro dimple milling is designed and named the micro conical surface ball-end mill. The cutting edge is formed by intersecting the conical surface and the inclined plane. A practical grinding method is proposed based on the kinematic principle of the six-axis computer numerical control (CNC) grinding machine for micro conical surface ball-end mills and is validated by grinding simulations and experiments. Micro dimple milling experiments are conducted on the hardened die steel H13 to investigate the cutting performance of the mill. The milling force, the micro dimple roundness error, and the tool wear morphology are observed and analyzed. The results show that the radial milling force is more stable and the wear resistance is improved for the micro conical surface ball-end mill compared to the traditional micro spiral blade ball-end mill. Therefore, a more stable roundness at the entrance hole of the micro dimple can be obtained by using this design after a number of micro dimples have been milled.     

基于机床运动学约束球头刀多轴加工刀轴矢量优化方法

针对目前航空发动机叶片进排气边加工精度和表面质量较差的问题,提出了一种基于机床运动学约束球头刀多轴加工刀轴矢量优化方法。建立刀位优化变量与刀位数据之间的关系方程,同时建立刀位数据与机床回转轴角度之间的运动变换方程,从而推导出刀位优化变量与机床回转轴角度之间的关系方程。通过求解上述方程得到球头刀多轴加工复杂曲面的刀轴矢量计算公式。在此基础上,给出球头刀多轴加工刀轴矢量优化方法和刀轨生成方法。同时,以某航空发动机叶片为例,分析了本文算法和Sturz算法对机床回转轴角度的影响。分别利用本文算法和Sturz算法生成该叶片进气边加工的刀轨,并在五轴数控机床上进行加工试验。试验结果表明,该算法能够避免加工过程中机床回转轴的大幅波动,使机床轴运动更加平稳和光滑,从而提高曲面的加工质量和加工效率,具有一定的实际应用价值。     

A novel CNC grinding method for the rake face of a taper ball-end mill with a CBN spherical grinding wheel

A novel method using a CBN spherical grinding wheel to grind the rake face of a taper ball-end mill and the configuration of corresponding CNC tool grinder are presented. This method utilizes the self-adaptation characteristics of a sphere to decrease the number of simultaneous cooperative axes of a CNC tool grinder and to smooth the rake face on the transition area between the taper and the ball-end of the mill. In order to obtain an accurate normal rake angle, which is one of the key factors affecting tool cutting performance, a moving coordinate system based on the required normal rake angle and the cutting edge was established. Then, by the proposed moving coordinate system, an algorithm to determine the position and orientation of a spherical grinding wheel, the basis of CNC code generation, is proposed and the relevant formulations are deduced. The 3D simulation of rake face grinding for a taper ball-end mill with constant helical angle indicates that the number of simultaneous cooperative axes of the CNC tool grinder is decreased from five to four and the smooth transition of the rake face is realized by the proposed method herein.     

高速铣削半圆弧工件表面形貌的仿真

在高速铣削情况下,利用平面刃球头铣刀沿半圆弧路线进行加工,对加工后的表面形貌进行理论建模与仿真。给出在空间三维切削时刀具切削刃的运动轨迹数学模型,并借助该模型给出球头刀切削半圆弧工件表面形貌的仿真算法。     

自由曲面等高加工铣削载荷预报

实际生产过程中球头铣刀主要用于曲面加工,但是关于球头铣刀曲面加工切削力的研究很少.本文针对曲面铣削加工中球头铣刀切削力预报的问题,通过离散近似将动态的切削过程分解为一系列进给方向和刀具与工件接触区不断变化的微小瞬态阶段,将剪切和犁切双重作用的静态球头铣刀切削力模型引入到自由曲面铣削载荷预报中,并选取一自由曲面工件进行铣...     

A Mathematical Model for Manufacturing Ball-End Cutters Using a Two-Axis NC Machine

The paper presents a mathematical model for producing a ball-end cutter by first defining the helical angle as the angle between the cutting edge and the centre-line axis. The velocities of the cutter in the radial and axial directions are then derived based on a given rotating speed. The radial feed speed of the grinding wheel is calculated according to the groove cross-section passing through the centre of the ball-end cutter. A ball-end cutter of constant helical angle is designed and produced by using a two-axis NC machine. To enhance the dimensional accuracy of the mathematical model, a compensatory grinding operation is also proposed and applied to the ball-end cutter. A ball-end milling cutter is selected for design and manufacture to illustrate the effectiveness of the proposed design and numerically controlled (NC) manufacturing procedure. The result of data verification indicates that the proposed procedure is systematic, straightforward and reliable. The ball-end cutter that is designed, refined and produced by using a simple two-axis NC machine is accurate enough to meet the specified tolerance.     

THE GEOMETRY, SPECIFICATION AND PREDICTIVE FORCE MODELS FOR PLANE FACED BALL-END MILLING CUTTERS AND OPERATIONS

In this paper the geometry and specification of ball-end milling cutters are studied and discussed followed by an outline of the development of computer-aided predictive models for the three force components, torque and power in plane faced ball-end milling operations, based on the 'Unified-Generalised Mechanics of Cutting Approach'. The models allow for six milling modes, namely; slotting, 'on-centre' end-milling and 'off-centre' end-milling, each machining at the cutter ball-end cutting edge only or at the cutter ball-end and cylindrical periphery cutting edges for two or more flute cutters. The models include all the tool and cut geometrical variables and the cutting speed as well as the tool-workpiece material combination (via the database of basic cutting quantities). The models are verified through extensive numerical simulation studies and a comprehensive experimental testing programme. Good qualitative and quantitative correlation has been found between predicted and measured fluctuating and average force components and torque.     

Dynamic Force Modelling for a Ball-End Milling Cutter Based on the Merchant Oblique Cutting Theory

A new dynamic force model for a ball-end milling cutter is presented in this paper. Based on the principle of the power remaining constant in cuts, the Merchant oblique cutting theory has been successfully used for the differential cutting edge segment of a ball-end milling cutter. A concise method for characterising the relationship of the complex geometry of a ball-end milling cutter and the milling process variables is determined, so that the force coefficients can be decomposed. The geometric property of a ball-end milling cutter and the dynamics of the milling process are integrated into the general model to eliminate the need for the experimental calibration of each cutter geometry and milling process variable. The milling experiments prove that this model can predict accurately the cutting forces in three Cartesian directions.