Mechanics and dynamics of general milling cutters. Part II: inserted cutters

Inserted cutters are widely used in roughing and finishing of parts. The insert geometry and distribution of inserts on the cutter body vary significantly in industry depending on the application. This paper presents a generalized mathematical model of inserted cutters for the purpose of predicting cutting forces, vibrations, dimensional surface finish and stability lobes in milling. In this paper, the edge geometry is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using the cutter's global coordinate system. The cutting edge locations are defined mathematically, and used in predicting the chip thickness distribution along the cutting zone. Each insert may have a different geometry, such as rectangular, convex triangular or a mathematically definable edge. Each insert can be placed on the cutter body mathematically by providing the coordinates of the insert center with respect to the cutter body center. The inserts can be oriented by rotating them around the cutter body, thus each insert may be assigned to have different lead and axial rake angles. By solving the mechanics and dynamics of cutting at each edge point, and integrating them over the contact zone, it is shown that the milling process can be predicted for any inserted cutter. A sample of inserted cutter modeling and analysis examples are provided with experimental verifications.     

Mechanics and dynamics of general milling cutters.: Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cylindrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining industry. While the geometry of each cutter may be different, the mechanics and dynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills used in the industry. The end mill geometry is modeled by helical flutes wrapped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip thickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. The predicted and measured cutting forces, surface roughness and stability lobes for ball, helical tapered ball, and bull nosed end mills are provided to illustrate the viability of the proposed generalized end mill analysis.     

Identification of dynamic cutting force coefficients and chatter stability with process damping

This paper presents a cutting force model which has three dynamic cutting force coefficients related to regenerative chip thickness, velocity and acceleration terms, respectively. The dynamic cutting force coefficients are identified from controlled orthogonal cutting tests with a fast tool servo oscillated at the desired frequency to vary the phase between inner and outer modulations. It is shown that the process damping coefficient increases as the tool is worn, which increases the chatter stability limit in cutting. The chatter stability of the dynamic cutting process is solved using Nyquist law, and compared favourably against experimental results at low cutting speeds.     

Identification of cutting force characteristics based on chatter experiments

Cutting force coefficients exhibit strong nonlinearity as a function of chip loads, cutting speeds and material imperfections. This paper presents the connection between the sensitivity of the dynamics of regenerative cutting and the cutting force characteristic nonlinearity. The nonlinear milling process is mathematically modelled. The transitions of dynamic cutting process between the stable and unstable zones are considered and experimentally illustrated by applying wavelet transformations on the measurement data.     

Generalized dynamic model of metal cutting operations

This paper presents a unified mathematical model which allows the prediction of chatter stability for multiple machining operations with defined cutting edges. The normal and friction forces on the rake face are transformed to edge coordinates of the tool. The dynamic forces that contain vibrations between the tool and workpiece are transformed to machine tool coordinates with parameters that are set differently for each cutting operation and tool geometry. It is shown that the chatter stability can be predicted simultaneously for multiple cutting operations. The application of the model to single-point turning and multi-point milling is demonstrated with experimental results.     

Simulation of the main cutting force in Crankshaft turn broaching

The measurement of the cutting forces of a turn-broaching machine is very complex due to the relative movement between workpiece and tool. In this work the cutting forces were simulated through the modeling of the process kinematics and by applying the Kienzle equation. A new experimental approach was proposed to determine the cutting forces using a conventional CNC turning machine tool. Through a series of experiments, the model has been calibrated. A comparison between the numerical and experimental results showed a similar trend. The effect of maximum cutting depth, workpiece diameter, cutting edge inclination angle, and feed rate on the main cutting force has been studied.     

机床加工过程中的振动实验研究

分析了数控车床加工过程中切削颤振的产生机理,总结了目前国内外对切削颤振抑制理论和实践的研究现状.基于CJK6140数控车床利用脉冲激振法对刀架系统进行初步实验研究,并且提出了基于计算机仿真技术对加工过程进行动态仿真的方法,研究结果为提高加工效率提供了依据.     

Time domain model of plunge milling operation

Plunge milling operations are used to remove excess material rapidly in roughing operations. The cutter is fed in the direction of spindle axis which has the highest structural rigidity. This paper presents time domain modeling of mechanics and dynamics of plunge milling process. The cutter is assumed to be flexible in lateral, axial, and torsional directions. The rigid body feed motion of the cutter and structural vibrations of the tool are combined to evaluate time varying dynamic chip load distribution along the cutting edge. The cutting forces in lateral and axial directions and torque are predicted by considering the feed, radial engagement, tool geometry, spindle speed, and the regeneration of the chip load due to vibrations. The mathematical model is experimentally validated by comparing simulated forces and vibrations against measurements collected from plunge milling tests. The study shows that the lateral forces and vibrations exist only if the inserts are not symmetric, and the primary source of chatter is the torsional–axial vibrations of the plunge mill. The chatter vibrations can be reduced by increasing the torsional stiffness with strengthened flute cavities.     

A general approach to simulating workpiece vibrations during five-axis milling of turbine blades

Workpiece vibrations have a significant influence on the machining process and on the quality of the resulting workpiece surface, particularly when milling thin-walled components. In this paper a simulation system, consisting of an FE model of the workpiece coupled with a geometric milling simulation for computing regenerative workpiece vibrations during the five-axis milling process, is presented. Additionally, a modeling method for visualizing the resulting surface is described. In order to validate the simulation model, turbine blades were machined and the experimental results were compared to the simulation results.     

An example of selection of the cutting conditions in broaching of heat-resistant alloys based on cutting forces, surface roughness and tool wear

Despite the fact that broaching has been used for long a time as a machining process for manufacturing highly accurate, complex profiles, little work has been published on the selection of cutting conditions to maximise tool life while achieving the required surface quality and level of cutting forces. This is even more important when notorious difficult-to-cut materials, such as Ni and Ti alloys, used in the aero-engine/power generation industry where high geometrical accuracy, along with restricted surface quality are required. The paper describes a multi-step methodology to select the cutting conditions for the broaching of Ni and Ti alloys used in the manufacture of aero-engines and power generators. Based on the application of the Taguchi technique, the cutting conditions (cutting speed, rise per tooth, rake angle, coolant type) were selected in order to obtain fine surface quality along with reasonably low levels of main cutting force (Fz) and perpendicular cutting force (Fy). This was followed by a reduced number of tool life tests which were carried out in order to select the final cutting conditions. Scanning electron microscopy (SEM) and chemical composition analysis on the flank and rake faces of the tools were employed to characterise the worn tools. It was found that when broaching forces, surface roughness and tool life are considered as process output measures, and taking into consideration generic process constraints on process productivity, machine tool stability, and tool stiffness, only a “pseudo-optimal” solution for the cutting conditions could be specified.     

A simplified methodology to determine the cutting stiffness and the contact stiffness in the plunge grinding process

This paper presents a simplified experimental technique to determine approximately the cutting stiffness and the contact stiffness in the plunge grinding process. The experimental methodology consists of a machine static stiffness test and several grinding processes. The cutting stiffness is obtained from the workpiece headstock static stiffness and from its displacement during the grinding processes, measured by a LVDT transducer. The contact stiffness is resolved from the expression that relates it with the grinding process time constant and other grinding parameters. The time constant is obtained from the exponential that characterises the machine deformation during the spark-out, measured as well by the LVDT transducer placed on the workpiece headstock. The variation of the obtained values of the contact stiffness with some of the grinding parameters is also shown.     

薄壁件铣削加工稳定性分析及试验验证

薄壁件由于刚性差,在铣削过程中难免会出现各种扰动,从而容易发生颤振,严重影响了零件的精度和表面质量。在分析薄壁件铣削过程中的动态位移和动态切削力的前提下,建立了薄壁件侧铣工艺系统的动力学模型和薄壁件再生颤振系统的传递函数。在此基础上应用有限元分析技术对铣削工艺系统进行了模态分析并绘制了工艺系统的稳定性叶瓣图,为稳定的切削参数的确定提供了参考。切削实验验证了所构建的模型和方法对于防止切削颤振是正确和可行的。     

On the chatter frequencies of milling processes with runout

The detection of undesirable vibrations in milling operations is an important task for the manufacturing engineer. While monitoring the frequency spectra is usually an efficient approach for chatter detection, since these spectra typically have a clear and systematic structure, we show in this paper that the stability of the cutting process cannot always be determined from solely viewing the frequency spectra. Specifically, the disturbing effect of the tool runout can sometimes prevent the proper determination of stability. In this paper, we show these cases can be classified by alternative analysis of the vibration signal and the corresponding Poincaré section. Floquet theory for periodic systems is used to explore the influence of runout on the structure of milling chatter frequencies. Finally, the results from theoretical analysis are confirmed by a series of experimental cutting tests.     

磨削振动控制系统设计与开发

磨削常做为工件加工的最后一道工序,其几何误差和表面完整性等加工质量要求很高,磨削振动是影响加工质量的重要因素,众多研究者对探测和避免此动态过程进行了研究以消除砂轮磨损和提高工件加工质量,运用砂轮与工件间周期性的分离或者跟随工件速度周期性的振动来实现磨削振动控制的可行方法尚未可见。本文作者对磨削振动进行了研究,基于对磨削低碳钢和硬化钢的磨削力进行实验检测,设计了一套闭环控制器,实现对工件振动的控制。并通过普通磨削过程进行验证,结果显示,此控制器对磨削振动有较好的改善作用。     

一种快速的变螺旋铣刀铣削稳定性预测方法

变螺旋铣刀铣削作为一种有效的颤振控制策略,已经受到了广泛关注。由于在建立的变螺旋铣刀铣削动力学方程中,出现了由铣刀变螺旋特性引发的系统变时滞相,而现有方法无法求解该问题。针对该问题,提出了对刀具进行轴向离散,而后将每个离散后的变螺旋刀具单元,近似模拟成变齿距刀具,从而完成变时滞微分方程向多时滞微分方程的转化。通过与前人研究工作作比较以及模型验证与分析可知,所提出的方法具有良好的预测变螺旋铣刀铣削稳定性的能力,更高的计算精度、收敛效率和计算效率。     

Time domain simulation of torsional–axial vibrations in drilling

A time domain model of the torsional–axial chatter vibrations in drilling is presented. The model considers the exact kinematics of rigid body, and coupled torsional and axial vibrations of the drill. The tool is modeled as a pretwisted beam that exhibits axial and torsional deflections due to torque and thrust loading. A mechanistic cutting force model is used to accurately predict the cutting torque and thrust as a function of feedrate, radial depth of cut, and drill geometry. The drill rotates and feeds axially into the workpiece while the structural vibrations are excited by the cutting torque and thrust. The location of the drill edge is predicted using the kinematics model, and the generated surface is digitized at discrete time intervals. The distribution of chip thickness, which is affected by both rigid body motion and structural vibrations, is evaluated by subtracting the presently generated surface from the previous one. The model considers nonlinearities in cutting coefficients, tool jumping out of cut and overlapping of multiple regeneration waves. Force, torque, power and dimensional form errors left on the surface are predicted using the dynamic chip thickness obtained from the exact kinematics model. The stability of the drilling process is also evaluated using the time domain simulation model, and compared with extensive experiments. This paper provides details of the mathematical model, experimental verification and simulation capabilities. Although the surface finish from unstable cutting can be predicted realistically, the actual drilling stability cannot be determined without including process damping.     

An innovative experimental study of corner radius effect on cutting forces

The cutting forces are often modelled using edge discretisation methodology. In finish turning, due to the smaller corner radii, the use of a local cutting force model identified from orthogonal cutting tests poses a significant challenge. In this paper, the local effect of the corner radius r_? on the forces is investigated using a new experimental configuration: corner cutting tests involving the tool nose. The results are compared with inverse identifications based on cylindrical turning tests and elementary cutting tests on tubes. The results obtained from these methods consistently show the significant influence of the corner radius r_? on the cutting forces.     

Approach into the use of probabilistic neural networks for automated classification of tool malfunctions in broaching

The condition of broaching tools has crucial importance for the surface quality of the machined components. If undetected, tool malfunctions such as wear, chipping and breakage of cutting teeth can result in severe damage or even scrapping expensive components, with direct implications on increasing the overall manufacturing costs. In contrast with other machining operations, broaching is characterised by non-symmetric distributions of cutting forces vs. time, making more difficult the task of recognising tool malfunctions. The paper reports on a methodology to automatically detect and classify tool malfunctions in broaching. The method was demonstrated through the use of time domain distribution of the push-off cutting force as a key sensory signal to monitor broaching tool condition when machining a nickel-based aerospace alloy. The characteristic features of the sensory signals have been extracted using in-house-developed programs and, afterwards, used to train and test a probabilistic neural network that enables automated classification of tools with fresh, worn, chipped and broken teeth. Inputting new pattern characteristics to the main categories of tool malfunctions, the system successfully classified them even when variations of signal amplitude and ranking of malfunctioned teeth occurred.     

Measurement of milling tool vibrations during cutting using laser vibrometry

Spindle and tool vibration measurements are of great importance in both the development and monitoring of high-speed milling. Measurements of cutting forces and vibrations on the stationary spindle head is the most used technique today. But since the milling results depend on the relative movement between the workpiece and the tool, it is desirable to measure on the rotating tool as close to the cutters as possible. In this paper the use of laser vibrometry (LDV) for milling tool vibration measurements during cutting is demonstrated. However, laser vibrometry measurements on rotating surfaces are not in general straight forward. Crosstalk between vibration velocity components and harmonic speckle noise generated from the repeating revolution of the surface topography are problems that must be considered. In order to overcome the mentioned issues, a cylindrical casing with a highly optically smooth surface was manufactured and mounted on the tool to be measured. The spindle vibrations, radial tool misalignment, and out-of-roundness of the measured surface were filtered out from the signal; hence, the vibrations of the cutting tool were resolved. Simultaneous measurements of cutting forces and spindle head vibrations were performed and comparisons between the signals were conducted. The results showed that vibration velocities or displacements of the tool can be obtained with high temporal resolution during cutting load and therefore the approach is proven to be feasible for analysing high-frequency milling tool vibrations.     

多机架连轧振动耦合的建模仿真分析

主要研究连轧机振动耦合.通过对轧机振动产生的原因分析,建立了一种轧制过程模型和轧机结构模型耦合的单机架颤振系统,并构建了连轧振动系统.对两个模型进行仿真,比较分析得出引起轧机振动耦合的主要原因是轧辊的振动导致出口板带缺陷和机架间张力的变化,通过现场轧制实验验证了模型和仿真结果的正确性.此外,轧制速度及合理布置轧机问的距离对整个连轧系统的稳定性有着重要的影响.