An Enhanced Force Model for Sculptured Surface Machining

Abstract

The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.     

MODELING OF 5-AXIS MILLING PROCESSES

5-axis milling operations are common in several industries such as aerospace, automotive and die/mold for machining of sculptured surfaces. In these operations, productivity, dimensional tolerance integrity and surface quality are of utmost importance. Part and tool deflections under high cutting forces may result in unacceptable part quality whereas using conservative cutting parameters results in decreased material removal rate. Process models can be used to determine the proper or optimal milling parameters for required quality with higher productivity. The majority of the existing milling models are for 3-axis operations, even the ones for ball-end mills. In this article, a complete geometry and force model are presented for 5-axis milling operations using ball-end mills. The effect of lead and tilt angles on the process geometry, cutter and workpiece engagement limits, scallop height, and milling forces are analyzed in detail. In addition, tool deflections and form errors are also formulated for 5-axis ball-end milling. The use of the model for selection of the process parameters such as lead and tilt angles that result in minimum cutting forces are also demonstrated. The model predictions for cutting forces and tool deflections are compared and verified by experimental results.     

MODELING OF 5-AXIS MILLING PROCESSES

5-axis milling operations are common in several industries such as aerospace, automotive and die/mold for machining of sculptured surfaces. In these operations, productivity, dimensional tolerance integrity and surface quality are of utmost importance. Part and tool deflections under high cutting forces may result in unacceptable part quality whereas using conservative cutting parameters results in decreased material removal rate. Process models can be used to determine the proper or optimal milling parameters for required quality with higher productivity. The majority of the existing milling models are for 3-axis operations, even the ones for ball-end mills. In this article, a complete geometry and force model are presented for 5-axis milling operations using ball-end mills. The effect of lead and tilt angles on the process geometry, cutter and workpiece engagement limits, scallop height, and milling forces are analyzed in detail. In addition, tool deflections and form errors are also formulated for 5-axis ball-end milling. The use of the model for selection of the process parameters such as lead and tilt angles that result in minimum cutting forces are also demonstrated. The model predictions for cutting forces and tool deflections are compared and verified by experimental results.     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

A cutting force model considering influence of radius of curvature for sculptured surface machining

A new cutting force model considering influence of radius of curvature is introduced in this research for sculptured surface machining with ball-end mill. In this model, first the whole cutting region near the cutter contact (CC) point on the sculptured surface is approximated by a spherical surface, and the radius of this spherical surface is used as the radius of curvature at the CC point. Then equations to estimate the cutting forces at a differential element on the cutting edge are established. By obtaining the cutter-workpiece contact areas based on geometries of the cutter and the sculptured surface, the mathematical model for estimating the total cutting forces in different directions is then developed. Experiments have also been conducted to measure the cutting forces considering different radii of curvatures on the sculptured surfaces. The analytically estimated cutting forces match well with the actual cutting forces obtained through experiments.     

曲面铣削过程加工路径对切削力和磨损的影响研究

针对不同走刀路径下的复杂曲面加工过程进行球头铣刀铣削Cr12MoV加工复杂曲面研究,分析不同走刀路径下铣削力和刀具磨损的变化趋势。试验结果表明:通过对比分析直线铣削和曲面铣削过程中的最大未变形切屑厚度,可以得出单周期内曲面铣削的力大于直线铣削过程的力,铣削相同铣削层时环形走刀测得的切削力普遍大于往复走刀测得的切削力;以最小刀具磨损为优化目标,运用方差分析法分析得出不同走刀路径的影响刀具磨损的主次因素,同时利用残差分析方法建立球头铣刀加工复杂曲面刀具磨损预测模型,并通过试验进行验证。     

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.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

Cutting force prediction for ball-end mills with non-horizontal and rotational cutting motions

Accurate cutting force prediction is essential to precision machining operations as cutting force is a process variable that directly relates to machining quality and efficiency. This paper presents an improved mechanistic cutting force model for multi-axis ball-end milling. Multi-axis ball-end milling is mainly used for sculptured surface machining where non-horizontal (upward and downward) and rotational cutting tool motions are common. Unlike the existing research studies, the present work attempts to explicitly consider the effect of the 3D cutting motions of the ball-end mill on the cutting forces. The main feature of the present work is thus the proposed generalized concept of characterizing the undeformed chip thickness for 3D cutter movements. The proposed concept evaluates the undeformed chip thickness of an engaged cutting element in the principal normal direction of its 3D trochoidal trajectory. This concept is unique and it leads to the first cutting force model that specifically applies to non-horizontal and rotational cutting tool motions. The resulting cutting force model has been validated experimentally with extensive verification test cuts consisting of horizontal, non-horizontal, and rotational cutting motions of a ball-end mill.     

虚拟制造中基于刀具变形的复杂曲面加工误差预报

复杂曲面加工过程中刀具的弹性变形是产生曲面加工误差的重要原始误差。着重研究了虚拟制造环境下基于球面铣刀弹性变形的曲面加工误差预报模型。研究并建立了球面铣刀加工复杂曲面的切削力模型和刀具弹性变形模型,在此基础上,分析了曲面生成机理,提出了利用曲面变形敏感系数建立刀具弹性变形对法向加工误差的影响关系。利用该模型可以在实际切削加工前对曲面加工误差进行预报,用以进行误差补偿或切削参数优化。最后,以二维半圆形拉伸曲面为例通过切削实验对本文提出的模型进行了验证。     

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。     

球头铣刀曲面加工的刀具切触区域解析建模

针对球头铣刀三维曲面加工,提出一种刀具切触区域仿真的通用解析模型。采用微分方法,将曲面加工过程离散为一系列连续的微小斜平面稳态加工。以每一小斜面切削过程为研究对象,建立描述刀具进给方向变化的数学模型,针对不同的进给方向并基于空间坐标系旋转变换,提出一组确定刀具切触边界曲线及各边界交点的解析公式,以精确界定刀具切触区域的封闭几何。通过与Z-Map模型的切触区域仿真对比,验证了本文模型的有效性及其精确高效的特点。     

A novel mathematical model for grinding ball-end milling cutter with equal rake and clearance angle

In this paper, new mathematical models and grinding methods of ball-end milling cutter were proposed based on the orthogonal spiral cutting edge curve. In order to avoid interference, a conical wheel was also designed and employed to grind the rake and rear faces of ball-end milling cutter on a five-axis grinder. Mathematical models of both rake face with equal rake angle and rear face with equal clearance angle were established to improve the machining characteristics of ball-end milling cutter. The design and simulation software of ball-end milling cutter was developed to design and optimize different shapes of both rake face and rear face. Furthermore, grinding experiment of the new ball-end milling cutter was carried out to confirm the validation of the mathematical models.     

基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础,然而,球头铣刀的刀齿形状复杂,加工过程中姿态多变,瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下,通过齐次坐标变换建立了刀齿的运动轨迹,提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法,通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度,并采用非线性回归的方法辨识了切削力系数,在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性,分别进行了垂直加工和倾斜加工试验,试验和仿真结果具有较高的一致性,表明该建模仿真方法是有效的,可以为实际加工中参数的选择和优化提供理论依据。     

变密度微织构球头铣刀切削性能多目标优化

为深入研究微织构排列形式对微织构理刀具的抗磨减摩机理的影响,分别从理论、仿真及试验等方面对最优的微织构排布形式进行研究。首先,建立微织构在刀具前刀面的数学模型及仿真模型。其次,通过试验验证仿真结果的准确性。仿真及试验研究均发现,变密度微织构球头铣刀的铣削性能优于均匀分布密度的微织构球头铣刀。最后,运用模糊评价法优选最优的铣削性能的微织构球头铣刀,优化结果表明,两排织构间距先为200 μm,再为150 μm,最后为175 μm的微织构球头铣刀的铣削性能最好。该项研究使刀具具有良好的抗磨减磨性,提高加工效率及被加工工件的表面质量。     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting conditions.     

虚拟制造中基于刀具磨损的复杂曲面加工误差补偿

基于数控铣削加工仿真系统,研究了在虚拟制造环境下对球头铣刀磨损引起的曲面加工误差的预测与补偿。建立了与加工参数相关的球头铣刀磨损模型,用于预测球头铣刀切削刃的磨损量,提出了球头铣刀铣削加工误差的补偿方法,并通过实验验证了该方法的有效性。     

Extraction of 5-axis milling conditions from CAM data for process simulation

5-axis milling is widely used in machining of parts with free-form surfaces and complex geometries. Although in general 5-axis milling increases the process capability, it also brings additional challenges due to complex process geometry and mechanics. In milling, cutting forces, tool deflections, and chatter vibrations may reduce part quality and productivity. By use of process simulations, the undesired results can be identified and overcome, and part quality and productivity can be increased. However, machining conditions and geometry, especially the tool–work engagement limits, are needed in process models which are used in these simulations. Due to the complexity of the process geometry and continuous variation of tool–work engagement, this information is not readily available for a complete 5-axis milling cycle. In this study, an analytical method is presented for the identification of these parameters from computer-aided manufacturing data. In this procedure, depths of cut, lead, and tilt angles, which determine the tool–workpiece engagement boundaries, are directly obtained the cutter location file analytically in a very fast manner. The proposed simulation approach is demonstrated on machining of parts with relatively complex geometries.     

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.     

Development of an automatic arc welding system using SMAW process

In end milling of pockets, variable radial depth of cut is generally encountered as the end mill enters and exits the corner, which has a significant influence on the cutting forces and further affects the contour accuracy of the milled pockets. This paper proposes an approach for predicting the cutting forces in end milling of pockets. A mathematical model is presented to describe the geometric relationship between an end mill and the corner profile. The milling process of corners is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. For the cutting force prediction, an analytical model of cutting forces for the steady-state machining conditions is introduced for each segmented process with given radial depth of cut. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpiece material properties, as well as the relative position of the tool to workpiece. Experiments of pocket milling are conducted for the verification of the proposed method.