Cutter-workpiece Engagement Research Articles

Accurate cutting force prediction of helical milling operations considering the cutter runout effect

Helical milling is a new hole-making technique which has lower burr formations and fiber delamination compared to the conventional drilling. In the helical milling process, the cutter follows the circular and vertical movements simultaneously, leading to two cutting zones at the peripheral part and the bottom part of the cutter, respectively. In this paper, the total cutting forces generated by both the side flutes and the bottom flutes are analytically predicted in the presence of cutter runout. Based on the kinematics analysis of the helical milling process, the bottom cutter-workpiece engagements (CWEs) are found to be the whole bottom part of the cutter due to its continuous plunge cut, while the peripheral CWEs are extracted by determining the feasible contact region and the axial depth of cut at any immersion angle. Next, an analytical method is proposed to calculate the instantaneous uncut chip thickness (IUCT) with high precision considering the cutter runout effect, which is defined as the distance from the cutting point to the previous flute’s circular trajectory. Combining the calibrated cutter runout parameters and cutting force coefficients of both side and bottom flutes, the dual mechanism force model is adopted to predict cutting forces. The helical milling tests have been conducted to validate the proposed mechanical model. The results show that the predicted cutting forces using this method match the measured data more closely compared to the existing methods which do not take into account the cutter runout effect.

Dynamics and Stability Prediction of Five-Axis Flat-End Milling

The tool orientation of a flat-end cutter, determined by the lead and tilt angles of the cutter, can be optimized to increase the machining strip width. However, few studies focus on the effects of tool orientation on the five-axis milling process stability with flat-end cutters. Stability prediction starts with cutting force prediction, and the cutting force prediction is affected by the cutter-workpiece engagement (CWE). The engagement geometries occur between the flat-end cutter and the in-process workpiece (IPW) are complicated in five-axis milling, making the stability analysis for five-axis flat-end milling difficult. The robust discrete vector method (DVM) is adopted to identify the CWE for flat-end millings, and it can be extended to apply to general cutter millings. The milling system is then modeled as a two-degrees-of-freedom spring-mass-damper system with the predicted cutting forces. Thereafter, a general formulation for the dynamic milling system is developed considering the regenerative effect and the mode coupling effect simultaneously. Finally, an enhanced numerical integration method (NIM) is developed to predict the stability limits in flat-end milling with different tool orientations. Effectiveness of the strategy is validated by conducting experiments on five-axis flat-end milling.

A Semi-analytical Cutter Workpiece Engagement Model for Ball End Milling of Sculptured Surface

A Semi-analytical Cutter Workpiece Engagement Model for Ball End Milling of Sculptured Surface

Tool posture dependent chatter suppression in five-axis milling of thin-walled workpiece with ball-end cutter

In aerospace industry, five-axis ball-end milling is widely used for flexible thin-walled aerospace parts by considering the process mechanics. A new analytical method is proposed to investigate the effects of the change of tool posture, especially lead and tilt angle, on chatter stability in milling. In this method, the dynamic cutter-workpiece engagement regions, which are essential to predict dynamic cutting forces and investigate chatter stability of the thin-walled workpiece, are determined considering the dynamic machining conditions. Then, according to dynamic cutter-workpiece engagement region data, the dynamic cutting force model considering the effects of lead and tilt angle is developed in machining the thin-walled aerospace parts with ball-end cutter. Subsequently, the milling chatter stability model is established based on the dynamic cutting force model, and the milling stability limits are determined in different lead and tilt angles. Finally, the feasibility and effectiveness of the proposed method are verified by experiments with ball-end cutter in five-axis machining center. The results are shown that the predicted values well match with the experimental results.

The Effect of Tool Orientation to Cut Geometry in Five-Axis Milling Using Analytical Boundary Simulation

One of the characteristics of five-axis milling is the tool can be oriented in any direction. It makes the tool orientation could be changed continuously during a free-form machining process. Consequently, the work to predict Cutter Workpiece Engagement (CWE) become more challenging. The existence of tool inclination angle and screw angle influence the profile of cut geometry. In this paper, an improved method to define the lower engagement point (LE-point) is presented. The algorithm was developed by taken into consideration the existence of inclination angle and screw angle. The extended method to calculate grazing point in swept envelope development was utilized to define LE-point. The developed model was successfully implemented to generate CWE data with various combination of tool orientation angle. From the test it was found that inclination angle gives significant effect to the location of LE-point.

Solid subtraction model for the surface topography prediction in flank milling of thin-walled integral blade rotors (IBRs)

Current CAM and milling verification software packages are not ready to predict form and surface errors derived from non-ideal conditions such as runout tool error or tool–workpiece flexibility. As a consequence, high-end parts like integral blade rotors (IBR) suffer from this lack of estimation to achieve a sound manufacturing process preparation. This work describes the implementation of a cutting force prediction model that introduces the radial engagement reduction caused by (i) tool runout and (ii) workpiece flexibility. The model is used as the seed for a calculation module based on solid modeling to obtain the surface roughness and topography applying the cutting force–wall restitution equilibrium, making use of the power of CAM solid modelers for the final topography definition. This idea takes advantage of the good accuracy of current solid modelers in comparison with the z-map topographical approach for obtaining the cutter–workpiece engagement (CWE) at each tool path step. Several flank milling tests were carried out to validate the simulations. The results demonstrated a significant level of accuracy to predict shape errors. The model may be integrated in a CAM procedure, and it is a useful utility for reducing deformation on the manufacturing of blisks and impellers.

An Implementation of Analytical Boundary Simulation on Feedrate Scheduling during Semi-Finish Milling

In five-axis milling, determining the continuously changing Cutter Workpiece Engagement (CWE) remains a challenge. All the feedrate calculation method that have been reported need a precise information about Cutter Workpiece Engagement. In this paper, the cut geometry was calculated using an analytical method called Analytical Boundary Simulation (ABS). This method was reported accurate and less expensive in term of calculation time. The cut geometry data was then used to calculate the instantaneous cutting forces. A new mechanistic force model was developed by taken into account the variation of axial depth of cut, the feedrate, the tool orientation, and the helical angle. Analytical boundary simulation and mechanisitic cutting force model were then used to optimize a semi finish machining process using feedrate scheduling. The applicability of the proposed method was verified experimentally and the result show that the calculated cutting forces of feedrate scheduling have a good agreement with those obtained from the experimental work.

Generalized model for dynamics and stability of multi-axis milling with complex tool geometries

Multi-axis milling offers increased accessibility in milling of parts having geometrical constraints or free form surfaces, where variety of cutting tools and edge geometries are utilized to improve stability and productivity of the processes. In order to machine the desired geometries effectively, in conjunction with multi-axis orientations, special tools ranging from taper end mills to process specific form tools are utilized. For such cases, the cutter workpiece engagement boundaries (CWEB) and directional force vector definitions are very complex and cannot be defined analytically. Furthermore, irregular cutting edge geometries, such as variable helix, pitch and serrations introduce multiple time delays between successive cuts where the conventional analytical frequency domain stability solution cannot be used. Prediction of stability diagrams for such variety of tool forms and edge geometries requires both the process and the tool to be defined in a generalized manner. In this paper, a numerical frequency domain milling stability solution method is proposed. The CWEB for complex multi-axis cases are calculated by the general projective geometry approach, where the cutting tool envelope and the cutting edges are represented as organized point clouds. Zeroth-Order approximation (ZOA) frequency domain method is adapted by introducing a speed average time delay term to encompass regular and irregular tool geometries. The stability limits are predicted by iterative solution of the eigenvalue problem using the ZOA frequency domain with the proposed revision. The effect of the process damping is also introduced into the generalized stability solution in order to predict the increase in the stability limits at low cutting speeds. A previously proposed approach is used to calculate the average process damping coefficients, which are introduced as modifiers to the modal parameters. The proposed generalized methodology is applied on several cases and it is shown that stability limits can be predicted within a reasonable accuracy for wide variety of cutting tools and milling operations.

Mechanistic Modeling of Five-Axis Machining With a Flat End Mill Considering Bottom Edge Cutting Effect

In five-axis milling, the bottom edge of a flat end mill is probably involved in cutting when the lead angle of tool axis changes to negative. The mechanistic model will lose accuracy if the bottom edge cutting effect is neglected. In this paper, an improved mechanistic model of five-axis machining with a flat end mill is presented to accurately predict cutting forces by combining the cutting effects of both side and bottom edges. Based on the kinematic analysis of the radial line located at the tool bottom part, the feasible contact radial line (FCRL) is analytically extracted. Then, boundaries of the bottom cutter-workpiece engagements (CWEs) are obtained by intersecting the FCRL with workpiece surfaces and identifying the inclusion relation of its endpoints with the workpiece volume. Next, an analytical method is proposed to calculate the cutting width and the chip area by considering five-axis motions of the tool. Finally, the method of calibrating bottom-cutting force coefficients by conducting a series of plunge milling tests at various feedrates is proposed, and the improved mechanistic model is then applied to predict cutting forces. The five-axis milling with a negative lead angle and the rough machining of an aircraft engine blisk are carried out to test the effectiveness and practicability of the proposed model. The results indicate that it is essential to take into account the bottom edge cutting effect for accurate prediction of cutting forces at tool path zones where the tool bottom part engages with the workpiece.

Chatter free tool orientations in 5-axis ball-end milling

Dies, molds and parts with complex free form surfaces are usually machined with ball end mills on 5-axis CNC machining centers. This paper presents automatic adjustment of tool axis orientations to avoid chatter along the tool path. The process mechanics and dynamics of ball end milling are modeled in cutter-workpiece engagement coordinate system. The structural dynamics of tool and workpiece are transformed to cutter-workpiece engagement coordinates by considering the tool path and the kinematics of the machine tool. The stability of the 5-axis ball end milling is modeled at each tool path location, and the chatter free tool axis orientations are searched iteratively using Nyquist criterion while avoiding gouging limits. The tool path, i.e. cutter location (CL) file, is updated to generate chatter free, 5-axis ball end milling of the parts. The proposed algorithm has been experimentally proven in 5-axis ball end milling tests.

Chip geometry and cutting forces in gear shaping

Abstract Shaping is a versatile process for machining gear teeth on complex monolithic components, which cannot otherwise be produced using other methods (like hobbing) due to geometric constraints. This paper presents a new model to accurately predict the chip geometry and cutting forces in shaping. Kinematics of gear shaping is modeled and verified. Cutter–workpiece engagement is predicted using a dexel-based geometric modeler, and refined by alpha-shape reconstruction. Varying rake and oblique angles are resolved along the cutting edges and used in three-dimensional force predictions. Simulated forces are shown to agree closely with those measured on a gear shaping machine.

Cutting Force Prediction in Four-axis Milling of Curved Surfaces with Bull-nose End Mill

This paper presents a mechanistic model for prediction cutting forces in bull-nose end milling of curved surfaces. Firstly, a mechanistic cutting force model for bull-nose end mill is established. Secondly, the machining process characteristics for four-axis milling of ring-shaped casings are discussed. A slice-based method is proposed for prediction the cutter-workpiece engagements. Then, the cutting forces with three different lead angles are predicted and compared with the corresponding experimental values. The results show the feasibility and effectiveness of the presented prediction approach.

Numerical Simulation of Chip Ploughing Volume and Forces in 5-axis CNC Micro-milling Using Flat-end Mills

It is a challenging task to avoid ploughing effects in micro-milling. When one tooth of the cutting tool crosses the minimum chip thickness boundary, the tool would enter into the ploughing zone with no chip formation. Therefore, it is significant to predict the ploughing volume and forces in micro-milling. In this work, the ploughing mechanism for micro-milling is proposed by considering the minimum chip thickness effects. A 3D chip geometry is developed to calculate chip thickness, ploughing volume and ploughing forces in micro 5-axis flat-end milling with a flat-end mill. The local parallel sliced tool based method is then applied to get cutter-workpiece engagement domain where the cutting flutes entry and exit the workpiece, minimum chip thickness and depth of cut are required to predict ploughing forces. Local parallel sliced method divides the cutting tool into several slices that are perpendicular to the tool axis along the local coordinate system. On each layer, the removal chip area is dividing into ploughing zone and shearing zone by the minimum chip thickness. Ploughing zone is the area as chip thickness is less than the minimum chip thickness. In the shearing zone, chip thickness is larger than the minimum chip thickness. The total chip ploughing volume is obtained by adding all ploughing area along axial direction.

Cutter-workpiece engagement determination for general milling using triangle mesh modeling

Abstract Cutter-workpiece engagement (CWE) is the instantaneous contact geometry between the cutter and the in-process workpiece during machining. It plays an important role in machining process simulation and directly affects the calculation of the predicted cutting forces and torques. The difficulty and challenge of CWE determination come from the complexity due to the changing geometry of in-process workpiece and the curved tool path of cutter movement, especially for multi-axis milling. This paper presents a new method to determine the CWE for general milling processes. To fulfill the requirement of generality, which means for any cutter type, any in-process workpiece shape, and any tool path even with self-intersections, all the associated geometries are to be modeled as triangle meshes. The involved triangle-to-triangle intersection calculations are carried out by an effective method in order to realize the multiple subtraction Boolean operations between the tool and the workpiece mesh models and to determine the CWE. The presented method has been validated by a series of case studies of increasing machining complexity to demonstrate its applicability to general milling processes. Highlights A new method to determine cutter-workpiece engagement geometry in milling. Applicable to general milling processes: all cutter types, in-process workpiece shapes and tool paths containing even self-intersections. Results validated by a series of case studies of increasing machining complexity.

Arc–surface intersection method to calculate cutter–workpiece engagements for generic cutter in five-axis milling

Calculating cutter–workpiece engagements (CWEs) is essential to the physical simulation of milling process that starts with the prediction of cutting forces. As for five-axis milling of free form surfaces, the calculation of CWEs remains a challenge due to the complicated and varying engagement geometries that occur between the cutter and the in-process workpiece. In this paper, a new arc–surface intersection method (ASIM) is proposed to obtain CWEs for generic cutter in five-axis milling. The cutter rotary surface is first represented by the family of section circles which are generated by slicing the cutter with planes perpendicular to the tool axis. Based on the envelope condition, two grazing points on each section circle are analytically derived, which divide the circle into two arcs. The feasible contact arc (FCA) is then extracted to intersect with workpiece surfaces. Using arc/surface intersection and distance fields based approach, the boundary of the closed CWEs is accurately and efficiently calculated. Compared with the solid modeler based method and the discrete method, the ASIM has higher computational efficiency and accuracy. Moreover, an analytical solution for calculating CWEs can be obtained with this method in five-axis milling of the workpiece merely comprising of flat and quadric surfaces. Finally, two case tests are implemented to confirm the validity of the ASIM and comparisons have been made with a Vericut based system which utilizes the Z-buffer method. The results indicate that the ASIM is computationally efficient, accurate and robust.

Parametric chip thickness model based cutting forces estimation considering cutter runout of five-axis general end milling

In the process of sculpture surfaces machining, due to the changes of the cutter orientation and the inevitable eccentricity between tool and spindle, machining parameters optimization based on five-axis cutting force is quite a challenge. To solve this problem, this study proposes a new method, cutting edge element moving(CEEM) method, to calculate instantaneous undeformed chip thickness(IUCT), to distinguish cutter/workpiece engagement(CWE) area and to simulate five-axis machining cutting force considering runout for general end mills. On the basis of upper work, the parameter representation of IUCT is deduced by the parametric expression of coordinate transformation matrix and feed vector, and resolved to three sub models about tool orientation, tool orientation change and cutter runout. At last, cutting force coefficients and cutter runout parameters are calibrated by cutting test and dial gauge testing. And inclined axis cutting test for bull nose mill, cylinder face-milling test for ball end mill and conical surface flank milling test for flat end mill are carried out to verify the effectiveness of the proposed model and related decomposition model. Combined with the specific test, some analysis about peak values, mean values and peak to peak difference values of cutting forces in various tool orientations are conducted, and the effect to cutting force from the changes of lead and tilt angles are evaluated. Some conclusions obtained and the methods utilized can be used to optimize tool orientation and feed rate etc.

Mechanistic modeling of five-axis machining with a general end mill considering cutter runout

The accurate and fast prediction of cutting forces in five-axis milling of free-form surfaces remains a challenge due to difficulties in determining the varying cutter-workpiece engagement (CWE) boundaries and the instantaneous uncut chip thickness (IUCT) along the tool path. This paper proposes an approach to predict the cutting forces in five-axis milling process with a general end mill considering the cutter runout effect that is inevitable in the practical machining operations. Based on the analytical model of cutting edge combined with runout parameters, the expression of the rotary surface formed by each cutting edge undergoing general spatial motion is firstly derived. Then by extracting the feasible contact arc along the tool axis, a new arc-surface intersection method is developed to determine the CWE boundaries fast and precisely. Next, the circular tooth trajectory (CTT) model is developed for the calculation of the IUCT with a slight sacrifice of accuracy. In comparison with the true IUCT calculated by the trochoidal tooth trajectory model, the approximation error introduced by the circular assumption is negligible while the computational efficiency improves a lot. Finally, combining with the calibrated cutting coefficients and runout parameters, comprehensive formulation of the cutting force system is set up. Simulations and experimental validations of a five-axis flank milling process show that the novel CTT model possesses obvious advantages in computing efficiency and accuracy over the existing approaches. Rough machining of a turbo impeller is further carried out to test the practicability and effectiveness of the proposed mechanistic model.

A comparison of solid model and three-orthogonal dexelfield methods for cutter-workpiece engagement calculations in three- and five-axis virtual milling

Virtual simulation of three- and five-axis milling processes has started to become more important in recent years in various industries such as aerospace, die-mold, and biomedical industries in order to improve productivity. In order to obtain desired surface quality and productivity, process parameters such as feedrate, spindle speed, and axial and radial depths of cut have to be selected appropriately by using an accurate process model of milling. Accurate process modeling requires instantaneous calculation of cutter-workpiece engagement (CWE) geometry. Cutter-workpiece engagement basically maps the cutting flute entry/exit locations as a function of height, and it is one of the most important requirements for prediction of cutting forces. The CWE calculation is a challenging and hard problem when the geometry of the workpiece is changing arbitrarily in the case of five-axis milling. In this study, two different methods of obtaining CWE maps for three- and five-axis flat and ball-end milling are developed. The first method is a discrete model which uses three-orthogonal dexelfield, and the second method is a solid modeler-based model using Parasolid boundary representation kernel. Both CWE calculation methods are compared in terms of speed, accuracy, and performance for three- and five-axis milling of ball-end and flat-end mill tools. It is shown that the solid modeling-based method is faster and more accurate. The proposed methods are experimentally and computationally verified in simulating milling of complex three-axis and five-axis examples as well as predicting cutting forces.

A hybrid analytical- and discrete-based methodology for determining cutter-workpiece engagement in five-axis milling

This paper presents a new method to determine the cutter-workpiece engagement (CWE) for a toroidal cutter during free-form surface machining in five-axis milling. A hybrid method, which is a combination of a discrete model and an analytical approach, was developed. Although the workpiece surface was discretized by a number of normal vectors, there was no calculation to determine the intersection between the normal vector and the cutting tool. The normal vectors were used to define the workpiece surface mathematically; next, the engagement point was calculated using a combination of the workpiece surface equation, the parametric equation of the cutting tool, and the tool orientation data. Three model parts with different surface profiles were tested to verify the validity of the proposed method; the results indicated that the method was accurate. The method also eliminated the need for a large number of discrete vectors to define the workpiece surface. A comparison showed that the proposed method was computationally more efficient. The CWE model was subsequently applied to support the cutting force prediction model. A validation test demonstrated that in terms of trends and amplitudes, the predicted cutting forces exhibit good agreement with the cutting force generated experimentally.

A solid-analytical-based method for extracting cutter-workpiece engagement in sculptured surface milling

Five-axis milling is used extensively to machine the complex parts with sculptured surfaces in die and mold, automotive, aerospace industries, and so on. Cutting force, a key input in simulating the vibration of cutting tools prior to implementing the real machining process, is mainly determined by the feed rate, spindle speed, cutting depth, and cutter-workpiece engagements (CWE). However, identifying the CWE efficiently and accurately is one of the most challenging problems in milling workpiece with complex geometry. This paper presents a novel and integrated solid-analytical-based approach to extract the CWE data in five-axis milling complex parts with sculptured surfaces. In this method, cutting tool and workpiece are modeled exactly. By performing “Boolean Subtraction” operations between cutting tool and workpiece at any cutting location (CL), the possible CWE is obtained firstly. For first cut and slotting cases, the exact CWE can be extracted easily according to the relationship between feed direction and surface normal direction of cutting tool. For following cut cases, the extra steps are needed because the CWE in these cases is associated with the previous cut. The critical line swept surface is constructed analytically at three continuous cutting locations in a previous cut. After trimming the possible CWE using the critical line swept surface, the exact CWE can be identified finally. The advantages of the proposed method are its robustness and flexibility to cancel the complex steps for constructing tool swept volume and updating in-process workpiece. Validation tests show that the developed method has higher efficiency and accuracy.