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.     

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.     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

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.     

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...     

Determination of Cutting-Condition-Independent Coefficients and Runout Parameters in Ball-End Milling

This paper presents a systematic and practical method for determining cutting-condition-independent coefficients in ball-end milling. An approach for estimating the runout offset and its location angle is also described based on a single cutting force measurement. An in-depth analysis of the characteristics of these cutting coefficients, which can be determined from only a few test cuts, is provided. The size effect is also modelled, including the characteristics of the ball-end mill geometry, and incorporated into the cutting force model. This method of estimating the 3D ball-end milling force coefficients was tested experimentally for various cutting conditions and gave excellent cutting force predictions. Also, the estimated values of the runout offset agreed well with the measurements.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

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.     

一种新的螺旋刃球头铣刀铣削力模型

为提高铣削加工的安全性和生产效率，有必要在加工实际进行之前准确地预测切削过程的物理信息，如铣削力、刀具振动等。给出了球头铣刀丸线几何模型，采用理论削力分析与实验--系数识别相结合的方法建立了新的螺旋刃球头铣刀的铣削力模型。对不同切削条件下的铣削力进行了仿真，与实验测量数据吻合良好，证明离线仿真可以对铣削力做出较准确的预测。     

一种螺旋刃球头铣刀的动态铣削力模型

针对高速铣削中广泛应用的螺旋刃球头铣刀建立刀具微元的铣削力模型,给出了瞬时切削厚度的计算方法,通过积分得出了一种新的整体铣削力模型。该模型考虑了动态铣削时刀杆振动对铣削力的影响,实验数据与仿真结果吻合较好,验证了该模型的正确性。     

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。     

Improved Dynamic Cutting Force Model in Peripheral Milling. Part I: Theoretical Model and Simulation

The accurate prediction of cutting forces is important in controlling the tool deflection and the machining accuracy. In this paper, the authors present an improved theoretical dynamic cutting-force model for peripheral milling with helical end-mills. The theoretical model is based on the oblique cutting principle and includes the size effect of undeformed chip thickness and the influence of the effective rake angle. A set of closed-form analytical expressions is presented. Using the cutting forces measured by Yucesan [1] in tests on a titanium alloy, the cutting-force coefficients are estimated and the cutting- force model verified by simulation. The simulation results indicate that the improved dynamic cutting-force model does predict the cutting forces in peripheral milling accurately. Simulation results for a number of particular examples are presented. ID="A1" Correspondence and offprint requests to: Prof K. Cheng, School of Engineering, Leeds Metropolitan University, City Campus, Calverley Street, Leeds LS1 3HE, UK. E-mail: k.cheng@lmu.ac.uk     

螺旋棒铣刀铣削力建模与仿真

在对螺旋棒铣刀铣削力建模中考虑了切削厚度变化对铣削力影响的指数关系、铣刀偏心对实际切削厚度、切入与切出角、铣削力波动的影响,并提出采用实测各刀齿铣削最大值比求解铣刀偏心和识别铣削力系数的方法。在考虑铣刀偏心因素的情况下仿真与实测的铣削力达到非常好的一致性。提出的铣削力仿真方法充分反映了铣削力的实际状态,提高了铣削力仿真精度。     

CALCULATION OF THE SPECIFIC CUTTING COEFFICIENTS AND GEOMETRICAL ASPECTS IN SCULPTURED SURFACE MACHINING

This article presents a method for obtaining the shear and ploughing specific cutting coefficients for a ball-end milling cutting force model. Thus, by using the proposed calculation method, the need for introducing variable shear cutting coefficients has been identified. This fact is due to the dependency among the specific cutting coefficients and the cutting edge inclination angle, which is variable in ball-end mills. Linear, quadratic and cubic polynomial shear cutting coefficients have been calculated, and the degree of adjustment obtained in each approach has been analyzed. At the same time, the expressions of the ploughing specific coefficients have been analyzed. The proposed calculation method has been applied to the following materials: a 7075-T6 aluminum alloy and a 52HRC AISI H13 tool steel. The results obtained from the validation demonstrate how the obtained coefficients are capable of predicting cutting forces over a wide range of cutting conditions. Finally, the results from applying the coefficients calculated in horizontal slot milling tests have been introduced in a model capable of calculating cutting forces in slope milling cases, which validates the calculation method proposed as a generic method for estimation of cutting coefficients.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

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.     

基于切削层形状的动态铣削力试验研究及建模

选取轴向切深、每齿进给量、径向切深和主轴转速为试验因素,采用YDX-Ⅲ9702型压电式铣削测力仪,进行了动态铣削力正交实验。针对立铣刀侧铣加工,研究了单刃铣削的临界条件,为设计试验方案提供了理论依据。结合铣削过程,采用角度积分方法求解铣削力模型,避免了轴向积分的繁琐计算。精确地建立了简捷且适应性强的基于切削层形状的动态铣削力预测模型,模型的仿真结果和试验数据相吻合。     

Cutting force prediction in ball-end milling with inclined feed by means of geometrical analysis

A geometrical model for the analysis of cutting forces in ball-end milling has been presented in a previous work (Tsai CL, Liao YS, J Mater Process Technol 205:24–33, 10), which can be used to analyze cutting forces in vertical or horizontal feed. In this paper, the three-dimensional geometrical analysis is depicted with different interacting relations among cutting edge, undeformed chip and shear zone along nonhorizontal cutting direction, and a general geometrical model of inclined feed in ball-end milling is presented. According to the geometrical analysis, the cutting directions of horizontal, vertical, inclined downward, and inclined upward feed are defined with a feed angle. A general force model is derived, and the three-dimensional cutting forces are predicted. Experiments are conducted to verify the geometric force model. The influences of different feed angle and helix angle on cutting forces in inclined downward and inclined upward feed are discussed and simulated.