Abstract
The TwinControl product takes a holistic approach to modelling and simulation of machining processes, incorporating machine controller, machine structure, part program, part geometry, and process forces and dynamics into a single system. The focus of this chapter is on the process models used to simulate cutting forces, torques, form error, and tool dynamics throughout a part program. These predictions provide process planners with valuable information about an operation before it is executed on machine, allowing for potential issues to be identified and reduced or eliminated before the first part is produced.
Keywords
Machining dynamics 5axis milling Cutting force Chatter Surface location error4.1 Introduction
Interactions between cutting tool and workpiece are critical in any machining operation. As the tool moves through a workpiece, cutting process induces forces on both the tool and the workpiece. These forces in turn have an effect on the process and can have a detrimental effect on the machine, tool and resulting part under certain conditions. It is critical then to understand these interactions before a part is machined to avoid scrapped parts or damage to the tool or machine. This chapter first covers the development of process models used to predict cutting forces for specific part programs. The cutting force model is then used for dynamic analysis to determine the effects of tool vibration on the final part outcome.
4.2 Discrete Cutting Force Model
The 5axis machining operations bring new challenges for predicting cutting forces, where complex toolworkpiece engagements and tool orientations make it difficult to adapt 3axis process models for 5axis operations. A model is developed here to predict cutting forces with arbitrary tool/workpiece engagement and tool feed direction. A discrete force model is used, in which the tool is composed of multiple cutting elements. Each element is processed to determine its effect on cutting forces, and global forces are determined by combining the effects of multiple engaged elements. The cutting force model is combined with ModuleWorks software which predicts toolworkpiece engagement regions (TWE) based on tool motion through the workpiece geometry. Cutting forces are predicted throughout complex operations by applying TWE data to the elements of the force model. The force model is validated through cutting trials in which the measured forces are compared with predicted forces during 5axis milling.
4.2.1 Introduction
Cutting forces depend on the tool and workpiece material, cutting tool geometry and cutting conditions. In 5axis milling, cutting conditions can vary considerably in process, and the varying cutting conditions can result in complex toolworkpiece engagements (TWE). Ozturk and Budak calculated TWE analytically for 5axis ball end milling [1] and simulated cutting forces throughout a toolpath after calculating the cutting parameters at discrete intervals [2]. Although this method gives accurate results for smooth machining operations, the analytical engagement model loses accuracy when the uncut surface is more complex.
More detailed engagement calculation methods have been developed to better simulate more complex machining operations. These models operate by creating a virtual workpiece and removing any material that interferes with the geometry of a tool moved along a path. For each tool motion, the surface patches of the tool that remove material are the TWE region. In the solid modelbased material removal simulation, the engagement area is derived from finding intersections between the solid models of both the tool and the workpiece [3, 4, 5]. Taner et al. used a planar projection strategy to determine TWE for constant feed and constant lead and tilt operations [6]. Others have represented the workpiece as a Zmap, also known as height map, a matrix/manifold of lines which are virtually cut when they interfere with the tool mesh [7]. A more advanced version of Zmap is the dexel approach [8] that can model overhangs in the geometry, thus supporting 5axis milling. The dexel approach may be improved to socalled tridexel model by introducing virtual grid lines in three directions to reduce dependence on grid directionality in the geometry accuracy for any cut direction [8, 9, 10].
4.2.2 Discretized Force Model
In order to predict cutting forces for arbitrary feed direction with arbitrary TWE, a discrete cutting force model is used. The model concept is shown in Fig. 4.1b, where cutting forces on a bull nose end mill act in different directions based on the cutter position and orientation. An example of the local cutting forces is shown at one section of the cutting edge, where the local radial force F_{r}, acts inward, normal to the cut surface, the tangent force, F_{t}, acts in the opposite direction of the cutter motion, and the axial force, F_{a}, acts tangent to the cut surface along to the tool profile.
The complex cut area from Fig. 4.1c is discretized into multiple elements in Fig. 4.1d. Each element has an effective cut width, b_{el}, along the tool profile, and thickness, h_{el}, normal to the tool profile. The global tool force is determined by combining the effects of all active cutting elements.
This section outlines the processes to determine the effects each tool element have on global cutting force.
4.2.2.1 Tool Discretization
The tool is discretized along the tool profile, L, into N_{L} elements, and circumferentially into N_{c}. The mesh structure is shown in Fig. 4.2c, with L mesh indices representing concentric circles radiating from the tooltip center and extending up the side of the tool. The element cut width, b_{el}, is the distance between two adjacent L elements. The Θ indices indicate the circumferential position of the elements. The elements are positioned with lag angles to follow the helical curve of the cutting edge, as shown in Fig. 4.2c. By creating the mesh along the helical curve, the indices of the TWE map always correspond directly to the cutting edge, and each Θ index corresponds to the elements of one flute at one rotational position.
Each element of the mesh has the indices, \({el}\left( {{\Theta} ,L} \right)\), and is defined by a set of position coordinates in Cartesian (X_{el}, Y_{el}, Z_{el}) and polar (r_{el}, θ_{el}, Z_{el}) coordinates and by an orientation angle, κ_{el} (see Fig. 4.2a).
4.2.2.2 Tool Coordinate Systems
Three coordinate systems (CS) are used in the cutting force analysis for each element of the cutting edge; {rta}, {R T A} and {XYZ}. {XYZ} is the tool global CS, in which tool motions and cutting forces are determined. {R T A} is the tool global polar CS, describing radial, tangent, and axial directions. {rta} is the local element CS and is used to account for the orientation of the cutting elements. The rta directions correspond to the force directions associated with the cutting force coefficients (CFCs), K_{e,rta} and K_{c,rta}, which are fixed relative to the orientation of the cutting element, but change direction based on the element orientation along a cutting edge (i.e., side or bottom of the tool profile).
4.2.2.3 Element Cutting Forces
Each tool element will contribute to the global cutting force if it is engaged in the cut. In this section, the element cutting forces are first calculated in the local {rta} CS and then transformed to the global tool {XYZ} CS.
4.2.2.4 Element Local Cutting Force
Equation (4.3) gives cutting forces in {rta} based on the element feed in the rta directions using the cutting force matrix, \(F_{c,rta,el} /f_{rta}\), or \(Q_{rta,el}\). The use of \(Q_{rta,el}\) is not a significant improvement on Eq. (4.1) in {rta}, however, though transformation of \(Q_{rta,el}\), the same force to feed relationship can be applied in any CS.
4.2.2.5 Cutting Force Transformations
4.2.3 Tool Cutting Forces
Cutting forces are determined by evaluating Eq. (4.11) for each flute position. As the tool rotates through the different positions, the components of Eq. (4.11) change to reflect the engaged elements in that section.
4.2.4 Part Cutting Forces
4.2.5 Cutting Trials
Summary of CFCs used during cutting trials throughout this chapter
Test  K_{e,r} (N/mm)  K_{e,t} (N/mm)  K_{e,a} (N/mm)  K_{c,r} (N/mm^{2})  K_{c,t} (N/mm^{2})  K_{c,a} (N/mm^{2}) 

“M” machining tests  13.9  7.1  −1.3  619.9  1014.2  58.2 
Corner cut test  9.3  0.4  0.6  452.4  955.9  235.7 
SLE groove tests  7.4  −3  −2.7  128.4  965.5  85.34 
Prior to the start of the simulation, the tool mesh is created, and \(F_{e,XYZ,el}\) and \(Q_{XYZ,el}\) are determined for each tool mesh element (these only need to be calculated once for a given tool mesh and fixed set of cutting force coefficients). Then, for each CL point, the TWE is obtained for that move using ModuleWorks Software. Figure 4.9 shows examples of how the TWE maps obtained change throughout the operation. The TWE data for each move is then applied to obtain \(F_{e,XYZ} \left( {{{\Theta} }} \right)\) and \(Q_{XYZ} \left( {{{\Theta} }} \right)\), and the cutting forces are calculated using Eq. (4.11) at each angular position.
Note that the transformation between the tool CS and part CS is dependent on how the tool CS is defined in the part CS. In the step example shown in Fig. 4.8, the tool CS is the same as the part CS, so no transformation is needed (except to reverse the sign of the forces to represent forces acting on the part, where forces are calculated as acting on the tool). The transformation, \({T}_{{{T}2{P}}}\), for the 5axis example in Fig. 4.9, is more complex because it is a function of both the tool orientation and the feed direction of the tool.
Due to tracking errors in the tool feed velocity (despite fixing the A and C axes), the total machining time is measured as approximately 20% longer than expected. To account for this in the simulation, the feed per tooth was reduced to 0.078 mm per tooth to match the actual and simulation machine time (this effectively reduced the simulated average tool feed speed, and hence feed per tooth).
4.2.6 Cutting Force Model Summary
The cutting force model developed here was created to predict forces for complex machining operations where the tool/workpiece engagement is complex and highly variable throughout. The key feature of this model is that it treats the elements of a discretized tool as individual entities which have predetermined force characteristics (\(F_{e,XYZ,el}\) and \(Q_{XYZ,el}\)) which are independent of the feed rate and feed direction of the tool. When coupled with ModuleWorks TWE software to capture effect of changing cutting conditions on the TWE, it is possible to efficiently obtain complex cutting force predictions for 5axis milling operations.
The experiments discussed here have shown that this model is capable of predicting cutting force for a ball end mill in 3 and 5axis operations. The stair test resulted in accurate predictions of cutting force at varying cut depths. The “M” test demonstrated that this model is able to pair with Moduleworks TWE software and accounts for a high variation of cutting conditions effectively. The predictions from this test showed close agreement between simulated and measured forces.
4.3 Stability Roadmap
Chatter is one of the major limitations to machining processes that affects part quality and productivity. It has been extensively studied [12], and different approaches have been developed to predict and mitigate chatter. Several modelling techniques such as frequency domain solution [13], semidiscretization [14] and temporal finite element [15], and time domain solution [16] have been applied to predict stability in 3axis milling operations. These methods are used to create stability lobe diagrams (SLDs) which show the stable and unstable depths of cut at different spindle speeds.
The frequency domain solutions for flat end mills were later extended to general milling tools [17] and 5axis ball end milling operations [18]. Additional degrees of freedoms in 5axis milling complicate the calculation of tool and workpiece engagement which is a required input in modelling the mechanics and dynamics of the process. Ozturk and Budak [18] simulated the stability of 5axis ball end milling operation using both single and multifrequency solution. They used an analytical cutter workpiece engagement boundary definition [1]. In some complex toolpaths in 5axis milling, the definition of tool and process parameters such as cutting depth, step over, lead and tilt angles may not be enough to define the tool and workpiece engagements. For such cases, numerical geometric engagement calculation methods are required [19]. Ozkirimli et al. [20] calculated the SLDs by using a numerical engagement method employing the frequency domain solution.
In order to simulate stability of a complex toolpath, Budak et al. simulated stability lobe diagrams for different points along the toolpath [21] and generated 3D stability lobe diagrams. This approach is applicable for parameter selection while designing toolpath. By looking to the 3D stability lobe diagram, the most conservative cutting depth and spindle speed can be selected for the process to have a chatterfree process. On the other hand, there are practical issues with using 3D stability lobe diagrams.
In complex cutting cases, definition of cutting depth can be vague. Even if the process planner has the 3D stability lobe diagram for a given process, it will be difficult for the process planner to identify whether the process is stable at a given point. First, they need to determine the cutting depths at each point in the toolpath and spindle speed and compare them with the 3D stability lobe diagram. Moreover, once the toolpath is generated it is not possible to change the cutting depth without generating the toolpath again. For these reasons stability lobe diagrams are less practical for the visualization of the stability and changing the cutting depth without changing the toolpath. In order to visualize the stability of a given process, the stability roadmap (SRM) is proposed. It plots the stable speeds for a given part program considering the changing cutting conditions.
The purpose of the SRM is to efficiently obtain and represent stability information for complex 5axis operations. Once a part program is created, the TWE is assumed to be fixed for each cutter location (CL) point of the program. Apart from regenerating the part program, the most effective way to reduce chatter is through spindle speed control. The SRM, thus, can be used by process planners to identify the best spindle speeds throughout the program.
The force and stability formulation required to generate SRMs are presented in this section, along with validation tests in which the model predictions are compared with measured results.
4.3.1 Dynamic Force Model
The dynamic force in Eq. (4.15) has timevarying coefficients due to the tool rotation angle dependence of \(Q_{xyz} \left( {{{\Theta} }} \right)\) (each rotation angle can be expressed as a function of time as the tool rotates). Equation (4.15) is made timeinvariant by approximating the timevarying term as an average value [12]. Averaging the \(Q_{xyz} \left( {{{\Theta} }} \right)\) over the tooth passing period, or over the range of rotation angles, \({{{\Theta} }}\), is analogous to the approximation of timevarying coefficients through the zeroth order Fourier series term in [12]. The average Q matrixes over one tool revolution, \(Q_{0}\), are calculated in Eq. (4.16), where N_{c} is the total number of circumferential elements in the tool mesh.
4.3.2 Stability Roadmap Generation
4.3.3 Stability Roadmap Trials
Stability roadmaps are generated for two example part programs and cutting trials are performed to compare the stability predictions with stability measurements. The first trial is a 5axis ball end milling of a 3D “M” character in which the A and C axes are fixed, and the second is a continuously varying lead and tilt corner cut. The stability predictions from both examples are tested experimentally.
4.3.3.1 Stability Roadmap Trial 1
Cutting trials are run at 12,250 and 10,850 RPM. After each test, a spectrogram of the microphone signal is generated to identify tooth passing and chatter frequencies throughout the cut. Dominant frequencies, excluding tooth passing harmonics, are considered to be a result of chatter.
The 10,850 RPM test results (Fig. 4.13b) match the predicted chatter frequencies near 2300 Hz, and no chatter is observed near 1500 Hz. Predictions from the 10,850 rpm test are again most accurate for the first 850 CL points.
Both machined “M” parts are shown in Fig. 4.13 with locations of visible chatter on the part surface labelled. The CL points corresponding to the chatter locations are indicated both on the SRM and on the photos of the part for sections A1 and A2 at 12,250 RPM and B1 and B2 at 10,850 RPM. It can be seen that these chatter locations agree with the spectrogram measurements and SRM predictions for the first 850 points.
In both tests, the tool motion path begins at point P1 in Fig. 4.13 and follows the “M” path until it reaches point P2 (P2 corresponds the CL point 850). As the A and C axes positions are constant, the lead angle on the tool becomes negative from P2 to P3 and tip of the tool is engaged with the workpiece. One potential cause of chatter prediction errors starting at P2 is the indentation effects caused by tooltip engagement start at this point. This indentation effect, which results in underprediction of the stability, is not considered in this model.
4.3.3.2 Stability Roadmap Trial 2
The second trial is conducted on a Starrag Ecospeed with data logging capability for the collection of true axis positions and spindle speeds throughout the cut. During the edge cutting trials, force measurements are collected using a Kistler 9139AA dynamometer. During the tests, the logged machine data and measured force data are synced so that force results can be tracked based on tool position. Further, the measured position data is applied directly to the stability model so that the stability predictions can be directly correlated to the measured force data. Note that the use of measured tool motion data does not change the SLM and is only used here to more easily compare simulation and measurement.
The CFCs used for the AL7075T6 workpiece and the twofluted 30° ball end mill with 6 mm radius (Sandvik R216.4212030AK22A H10F) are found experimentally to be: K_{e,r} = 9.3, K_{e,t} = 0.4, K_{e,a} = 0.6 N/mm, and K_{c,r} = 452.4, K_{c,t} = 955.9, and K_{c,a} = 235.7 N/mm^{2} (also see “corner cut tests” in Table 4.1). Note that the CFC trials were repeated on the EcoSpeed with a new tool. Note that the tool used here is the same type but not the same tool used in the previous tests. New CFC tests are conducted with the current tool which better reflects the region of the tool used in the edge cutting trials, resulting in values which differ from the prior CFC tests.
The results from Fig. 4.17 show that the stability regions do not line up exactly, as there is a shift in RPM between the predicted and measured stability regions. The cause of this shift is not known for certain; however, it is possible that this shift is a result of changes in the spindle dynamic parameters as a result of spindle speed. Despite these differences and the highly transient nature of this operation, the measured regions of stability of the corner machining example closely follow the stability roadmap, and the chatter vibration amplitudes follow the qualitative predictions of the system eigenvalues.
4.3.4 Stability Roadmap Summary
The SRM provides an effective means of representing stability information for complex machining operations. Application of the zeroorder approximation method to a discretized cutting force model allows for efficient stability prediction regardless of the engagement or the tool feed direction. When coupled with TWE simulation software, this approach can be used to represent the entire process virtually for a specific part program with a specific tool.
The experiments from this paper show that the SRM can accurately predict chatter locations, even with a tool with nonsymmetric direct FRFs and significant cross FRFs. However, the experimental results have shown that the current model is only effective when the tooltip center is not engaged in the cut.
Moving forward, the current SRM model can be expanded to include additional machining considerations, such as surface finish, surface location error, and workpiece dynamics.
4.4 Surface Location Error Model
During machining processes, cutting forces cause the tool to displace relative to the workpiece due to flexibility in the tool and/or workpiece. These relative displacements result in form errors in the part geometry, known as surface location errors (SLE). SLEs differ from chatter in that they are a result of periodic cutting forces (the forces calculated in the static cutting force module) and not regenerative effects. As such, SLEs are prevalent for both stable and unstable cutting conditions.
The prediction of surface location error has been made using various techniques in prior research. In these works, the motion of the tool in response to the cutting force is predicted, and this motion is imposed onto the rotating cutting edge to predict the true surface left behind. A closed form solution to predict SLE as a function of the tool FRF and forcing function is developed in [23]. Time domain simulations have also been used to predict tool motions in more complex cases, such as runout [24], or 2DOF milling dynamics [25]. Others used a truncated Fourier solution to determine tool motions based on modal parameters [26]. They then simulated the full 3D “morphed” cutting edge path, which then used to model the final machined surface.
Ozturk et al. [1] developed an approach for predicting form error for 5axis ball end milling operations. Their approach predicts form error based simulation of static tool deflections, and these predictions were shown to closely agree with single point measurements in machining trials.
In this section, the strategy used to approximate SLE based on the discrete tool model is developed. This model is able to predict 5axis SLE for complex tool geometries, tool/workpiece engagements, based on dynamic displacement and rotation of the tool. Cutting trials are conducted to compare predicted and measure SLE for a 5axis ball end mill operation.
4.4.1 Form Error Prediction
Surface location error is predicted by first simulating tool displacements based on the cutting force profile and the system dynamic parameters. These displacements are combined with the rotary motion of the tool to model the true path of the cutting edge (helical or straight). The true cutting edge locations are compared with nominal (with no relative displacement) edge locations to determine the edge position error at each location of the tool.
Once the tool displacements are known, they are combined with the rotary motion of the cutting edge, as shown in Fig. 4.19b. With no tool displacements, the helical cutting edges nominally follow a path that forms a cylindrical shape. The addition of the tool vibrations causes the helical cutting edges to form a new shape, which represents the actual profile of the tool. By following the shape traced by the cutting edges, which is plotted with green points, the deviation of each point can be determined and the surface location error identified at each point of the tool. In the example in Fig. 4.19b right, the tool edge trace is oriented so that the tool is feeding out of the page, and the machined surface left behind is the leftmost side of the tool profile. Nominally, the tool removes material along the cylindrical shape, leaving behind the straight, blue edge. When vibrations are included, the resulting machined surface is curved, resulting in overcut along the upper surface, and undercut at the lower surface.
In the current model, dynamic displacements are derived using a frequency domain solution. Compared with time domain simulation, the frequency domain approach is intended to be more efficient and robust. Further, this approach can be applied using system FRFs directly without the need to identify modal parameters, which is a requirement for time domain models. The frequency domain solution does not account for regenerative force effects which lead to chatter, so it is run under the assumption of stability (chatter is considered using a Stability Roadmap).
4.4.2 Surface Location Error Calculation
4.4.3 Surface Location Error Trials
Figure 4.23b shows both the nominal surface (with no vibrations) and the simulated surface with vibrations. From this view, the simulated surface is offset from the nominal surface by the surface location error (SLE) values which are predicted for each element based on the cutting edge trace.
Since we are comparing error results at many points along the simulated part surface, a best fit error approach is used to characterize surface errors. As the nominal shape of the ball end mill machined grooves is circular, circular fit errors are used.
Once a simulated surface is obtained, a circle is fitted to the simulated surface points (see best fit circle in Fig. 4.23b), and best fit errors are determined for each point (see in Fig. 4.23c). Even though SLE errors from the nominal surface are simulated directly, the best fit error approach allows for the simulated surface shape to be evaluated independently of a known reference (i.e., the nominal surface). This is useful for comparing simulated surface errors to the measured surface errors, which do not have an easily obtainable absolute reference. Both the simulated and experimental surfaces are evaluated using the same process based on a best fit circle.
A 12mmdiameter ball end mill with two flutes and helix angle of 30° (Sandvik R216.4212030AK22A H10F) is used for this trial. The tool is mounted using a Bilz ThermoGrip T1200/HSKA63 tool holder with a tool overhang of 67.2 mm. The machine used for the tests is a MAG FTV52500, and force measurements are collected using a Kistler 9139AA dynamometer. The workpiece material is AL 7075 T6 and PTFE nylon. The CFCs used for the AL7075T6 workpiece are found experimentally using a ball end mill mechanistic model [11], to be: K_{e,r} = 7.43, K_{e,t} = −2.98, K_{e,a} = −2.7 N/mm, and K_{c,r} = 128.35, K_{c,t} = 965.49, and K_{c,a} = 85.34 N/mm^{2} (also see “corner cut tests” in Table 4.1). Note that average CFC values identified experimentally are used for all elements regardless of local oblique and rake angles.
Summary of cutting conditions for SLE experiments
Test #  Feed/tooth (mm)  Spindle speed (RPM)  Lead (Degrees)  Tilt (Degrees)  Cut depth (mm) 

1  0.15  13,050  15  15  0.5 
2  0.1  13,050  15  15  0.5 
3  0.15  20,800  15  15  0.5 
4  0.1  20,800  15  15  0.5 
5  0.15  13,050  15  −15  0.5 
6  0.1  13,050  15  −15  0.5 
7  0.15  20,800  15  −15  0.5 
8  0.1  20,800  15  −15  0.5 
9  0.15  13,050  15  15  1 
10  0.1  13,050  15  15  1 
11  0.15  20,800  15  15  1 
12  0.1  20,800  15  15  1 
13  0.15  13,050  15  −15  1 
14  0.1  13,050  15  −15  1 
After the tests, an Alicona Infinite Focus G5 is used to measure the shape of the machined grooves. This machine and an example of a surface produced during the measurement are shown in Fig. 4.24b, c. Surface data generated in these measurements are used to characterize the true form of the grooves. As they are all machined with a 6 mm radius ball end mill, the nominal surface generated should also have a circular form with a radius of 6 mm.
One challenge for SLE experiments is determining an absolute reference from which to measure the errors in the true surface. For example, it is difficult to define the nominal center of the tool from which to compare the measured surfaces. For this reason, the best fit circles are used as a reference to measure errors for both simulated and measured surface data.
The results from these tests show that the SLE model can provide a good indication of surface error for simple 5axis operations using a ball end mill.
4.5 Process Model Simulation Interface
The process models discussed in this chapter have been developed in MATLAB. In order to make use of these models accessible to TwinControl partners, a MATLAB graphical user interface (GUI) has been developed. The GUI contains all of the process models, and the interface allows users to execute any or all of the models from a single setup. This section describes the basic features of the TwinControl process model GUI.
4.5.1 Process Model GUI Layout, Inputs and Options

A database of tool geometries used (*.csv file),

A database of cutting force coefficients used (*.csv file),

An *.stl file of the stock part geometry (must be geometry before machining operation),

A part program file containing tool motion and tool number data.
 A.
Users can select FRF files for up to ten tools used in the part program. The FRF data for all tools is plotted when the user selects “Show FRF Data”.
 B.
The user selects which models to run during the simulation.
 C.
The user can control the resolution of the tool mesh and the tool path resolution at which all analysis is performed (analysis is performed at fixed distance points along the toolpath, and not an every CL point). The user can also select which section of the part program to analyze based on CL move number using Max/Min Move.
 D.
Once options are set, the user selects “Start Analysis” to start the simulation. During simulation, the status of the simulation is updated in the “Status” box. Once the simulation is complete, the user has the option to view all tool/workpiece engagements along the toolpath by selecting “Check Engagements”.
 E.
After simulation, the results can be plotted based on the selections in the box. Forces and torques can be plotted as tool rotation angle dependent, or as average values over one revolution. They can be plotted against simulated time or against CL move number. Finally, the type of analysis results can be selected.
 F.
Selections in this box show the results rendered against the toolpath instead of time (see next section for examples).
 G.
Shows a plot of the tool mesh resolution and geometry.
 H.
Plot of simulation results against toolpath.
 I.
Main display window used during simulation setup and to show simulation results.
4.5.2 Process Model GUI Outputs
The method of display for the results in Fig. 4.31 is intended to allow process planners to quickly and easily interpret simulation data for a specific process. These results concisely show what issues may appear during the part program, and where they will occur on the part geometry.
4.6 Conclusions
The process models developed to model interactions between the tool, and the workpiece provide important predictions about the final outcome of an operation. The models developed here are all based on a discrete tool cutting force model which provides flexible and efficient solutions for complex machining operations. It has been shown through validation testing that these models are capable of predicting force and torque, as well as chatter and surface location error. By combining all of these separate model components into a single environment, we can efficiently simulate and view results for complex operations in a concise format. We will see in the following chapters how this system has been used to improve example machining operations from both the automotive and aerospace industries.
Notes
Acknowledgements
This chapter is based on the publication at Procedia CIRP (Volume 58, 2017, Pages 445–450) of the work “Discrete Cutting Force Model for 5Axis Milling with Arbitrary Engagement and Feed Direction” presented by Luke Berglind, Erdem Ozturk and Denys Plakhotnik at the 16th CIRP Conference on Modelling of Machining Operations (https://www.sciencedirect.com/science/article/pii/S221282711730433X).
References
 1.Ozturk, E., Budak, E.: Modelling of 5axis milling processes. Mach. Sci. Technol. 11(3):287–311 (2007)Google Scholar
 2.Budak, E., Ozturk, E., Tunc, L.T.: Modelling and simulation of 5axis milling processes. Mach. Sci. Tech. (2007)Google Scholar
 3.Lazoglu, I., Boz, Y., Erdim, H.: Fiveaxis milling mechanics for complex free from machining. CIRP Ann. Manuf. Technol. 60, 117–120 (2011)Google Scholar
 4.Boz, Y., Rdim, H., Lazoglu, I.: Modeling cutting forces for 5axis machining of sculptured surfaces. In: 2nd International Conference, Process Machine Interactions (2010)Google Scholar
 5.Layegh, S., Erdim, H., Lazoglu, I.: Offline force control and feedrate scheduling for complex free form surfaces in 5axis milling. In: CIRP Conference on High Performance Cutting (2012)Google Scholar
 6.Taner, T.L., Ömer, Ö., Erhan, B.: Generalized cutting force model in multiaxis milling using a new engagement boundary determination approach. Int. J. Adv. Manuf. Technol. 77, 341–355 (2015)Google Scholar
 7.Kim, G., Cho, P., Hu, C.: Cutting force prediction of sculptured surface ballend milling using Zmap. Int. J. Mac. Tools Manuf. 40, 277–291 (2000)Google Scholar
 8.Boess, V., Ammermann, C., Niederwestberg, D., Denkena, B.: Contact zone analysis based on multidexel workpiece model and detailed tool geometry representation. In: 3rd CIRP Conference on Process Machine Interactions (2012)Google Scholar
 9.Erkorkmaz, K., Hosseinkhani, A.K.Y., Plakhotnik, D., Stautner, M., Ismail, F.: Chip geometry and cutting forces in gear shaping. CIRP Ann. Manuf. Technol., 133–136 (2016)Google Scholar
 10.Siebrecht, T., Kersting, P., Biermanna, D., Odendahla, S., Bergmann, J.: Modeling of surface location errors in a multiscale milling simulation system using a tool model based on triangle meshes. In: CIRPe 2015—Understanding the Life Cycle Implications of Manufacturing (2015)Google Scholar
 11.Gradisek, J., Kalveram, M., Weinert, K.: Mechanistic identification of specific force coefficients for a general end mill. Int. J. Mach. Tools Manuf. 44, 401–414 (2004)CrossRefGoogle Scholar
 12.Altintas, Y., Weck, M.: Chatter stability of metal cutting and grinding. CIRP Ann. Manuf. Technol. 53(2), 619–642 (2004)Google Scholar
 13.Altintas, Y., Budak, E.: Analytical prediction of stability lobes in milling. CIRP Ann. Manuf. Technol. 44(1), 357–362 (1995)Google Scholar
 14.Insperger, T., Mann, B., Stépán, G., Bayly, P.: Stability of upmilling and downmilling, part 1: alternative analytical methods. Int. J. Mach. Tools Manuf. 43(1), 25–34 (2003)CrossRefGoogle Scholar
 15.Mann, B., Bayly, P., Davies, M., Halley, J.E.: Limit cycles, bifurcations, and accuracy of the milling process. J. Sound Vib. 277(1), 31–48 (2004)CrossRefGoogle Scholar
 16.Campomanes, M.L., Altintas, Y.: An improved time domain simulation for dynamic milling at small radial immersions. ASME J. Manuf. Sci. Eng. 125, 416–422 (2003)CrossRefGoogle Scholar
 17.Altintas, Y., Engin, S.: Generalized modeling of mechanics and dynamics of milling cutters. CIRP Ann. Manuf. Technol. 50(1), 25–30 (2001)CrossRefGoogle Scholar
 18.Ozturk, E., Budak, E.: Dynamics and stability of fiveaxis ballend milling. J. Manuf. Sci. Eng. 132, 1–13 (2010)CrossRefGoogle Scholar
 19.Gong, X., Feng, H.: Cutterworkpiece engagement determination for general milling using triangle mesh modeling. J. Computat. Des. Eng. 3(2), 151–160 (2016)Google Scholar
 20.Ozkirimli, O., Tunc, L., Budak, E.: Generalized model for dynamics and stability of multiaxis milling with complex tool geometries. J. Mater. Process. Technol. 238, 446–458 (2016)CrossRefGoogle Scholar
 21.Budak, E., Tunc, L., Alan, S., Özgüven, H.: Prediction of workpiece dynamics and its effects on chatter stability in milling. CIRP Ann. Manuf. Technol. 61(1), 339–342 (2012)CrossRefGoogle Scholar
 22.Schmitz, T.L., Smith, K.S.: Machining Dynamics, Frequency Response to Improved Productivity. Springer Science, New York, NY (2009)Google Scholar
 23.Schmitz, T.L., Mann, B.P.: Closedform solutions for surface location error in milling. Int. J. Mach. Tools Manuf. 46, 1369–1377 (2006)CrossRefGoogle Scholar
 24.Schmitz, T.L., Couey, J., Marsh, E., Mauntler, N., Hughes, D.: Runout effects in milling: Surface finish, surface location error. Int. J. Mach. Tools Manuf. 47, 841–851 (2007)CrossRefGoogle Scholar
 25.Insperger, T., Gradisek, J., Kalveram, M., Stepan, G., Winert, K., Govekar, E.: Machine tool chatter and surface location error in milling processes. J. Manuf. Sci. Eng. 128, 913–920 (2006)CrossRefGoogle Scholar
 26.Bachrathy, D., Insperger, T., Stepan, G.: Surface properties of the machined workpiece. Mach. Sci. Technol. 13, 227–245 (2009)CrossRefGoogle Scholar
Copyright information
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.