The transient changing of forces in interrupted milling
 207 Downloads
Abstract
The knowledge of cutting force in practical technology is increasingly important due to the growing quality and performance requirements. Therefore, especially in the case of milling, it also represents an important research area of cutting theory. The aim of the research in the project presented here was the study of transient processes assumed in milling. For this purpose, a model that describes cutting force in interrupted cutting realistically was developed. According to the initial hypothesis, cutting force reaches a stationary status in a finite time due to the fact that the thermodynamic processes of deformation are time consuming. This influences the energy characteristics of cutting significantly in the case of milling. It was assumed that the transient increase of cutting force can be described by a formula where Kienzle’s force formula is supplemented by an exponential function. The validation of this force model was performed by force measuring during the machining of normalized Csteel of C45 quality. One tool insert was used in the face milling tool. The measurements justified the applicability of the model; the Pearson index of the correlation was R^{2} > 0.9, moreover, it was higher than 0.95 in many cases.
Keywords
Cutting Transient force Milling modeling1 Introduction
Bayard, O. [1] listed 48 models through which the researchers of cutting theory wanted to describe chips formation and the accompanying mechanical and thermal processes. We can also add further researches which studied the formation of sheared chips using thermoplastic instability or fracture mechanics (see e.g., Komanduri et al. [2]) or hard turning, which is currently the subject of extensive research (e.g., Kundrák et al. [3]), as well as the extensive literature on interrupted cutting and milling. Thus, the otherwise interesting fact that cutting has been the continuous interest of the researchers of machining for about 150 years can be understood. Based on the above, two statements can certainly be made. One is that strong industrial interests are attached to these researches, and the second is that the seemingly simple technology comprises complicated processes.
This can be perceived in the summarizing work in which Cheng et al. [4] discuss machining dynamics in a comprehensive systematic manner. They demonstrate from multiple angles how important the theoretical modeling of multibody dynamic features of machines and the recognition of these are from the point of view of industrial practice. In turning, in its initial phase in certain special ways of machining, the cutting force varies rapidly [5]; however, milling is characterized by dynamic changes throughout the process [6]. They revealed that not only the shock effect of the cutting force, but also its rapid change strongly influences the stability of the machining system. In his comprehensive review of cutting theory and detailed investigation of milling, Altintas specified that, besides the shock effect of cutting force, its rapid change also influences the process [7].
Solid body physics have become a part of the tool kit of researchers. Turkovich [8] was able to rely on the considerable previous findings in the application of dislocation theory. These were supported by the material structure testing of Black, performed on steel chips by transmission and electron and scanning microscopes [9, 10, 11, 12]. There were researchers who investigated the movement of dislocations considering even the atomic structure [13, 14] while others studied the impact of the steel structure [15].
Ultimately, the microlevel processes determine the macrolevel behavior of the material. This has led to the broadscale application of constitutive equations in the plasticity theory or the increasingly popular FEM descriptions of chip formation. Essentially, this is a phenomenological method that describes the connection among stress, deformation, the speed of deformation, and temperature developing as a result of the force triggering deformation.
Although significant results have been achieved in the FEM simulation of the process of chip formation, the precision of these simulations raises constant concerns [13]. This must certainly be taken into consideration when cutting force is to be determined. It is important that the constitutive model describing the behavior of the machined material should be applied with correct material properties in calculations. This runs into difficulties that are hard to overcome owing to the significant, fast deformation and heat. Such extreme experimental conditions cannot be produced in material testing; therefore, measurement results need to be extrapolated outside the studied parameter range. This was also established by Zerilli [16] previously.
The experimental findings of Lazoglu et al. [23] in hard turning and Fan et al. [24] in the cutting of a Ti6Al4V alloy show the close relationship of the force and temperature that can be measured in cutting. Thandra és Choudhury [25] experienced this when applying an oxyacetylene hotmachined device under special circumstances.
The same statement can be made with regard to the research by Aurich et al. [26], who performed a 3D FEM analysis, and also regarding the endmilling research findings of Sato et al. [27]. The close relationship between the force and temperature in high and ultrahighspeed milling was shown by Cui et al. [28] with Abaqus/Explicit FEM software.
As the wear of the tool is determined by force and temperature together, as known, cutting force is used to monitor wear [29]. Suresh et al. [30] studied the relationship of the cutting force and the wear of the tool in hard turning. Li et al. [31] applied the cutting force for the monitoring of the tool wear in a way that they examined the irregular fluctuation of the force.
These examinations did not extend to the transient initial section of chip formation. This was equally ignored in theoretical analyses and in experiments. The initial phase of chip formation is also important from a practical angle since the entire process of milling can be regarded as transient. Zheng et al. [32] showed by the fractal analysis of cutting force and in force measurements registered with a microsecond time scale that the exponential growing phase of the force can be clearly seen beside the chaotic characteristics. This can be concluded from the results obtained by Zhang et al. [33] in hard milling.
So, the change of the cutting process in time has been the subject of intensive research for many years; however, we can conclude that the dynamics of the force’s change, which is also significant due to the close connection between temperature and force, has not been dealt with even in the latest publications. This paper discusses the findings of the work which aims to examine the transient, dynamic characteristics occurring in interrupted cutting.
2 The transient model of cutting force in milling
The force that is necessary for chip formation is basically determined by the chemical composition, structure, and condition of the workpiece’s material. The impacts of significant, fast deformation on the material structure were studied in detail by Zener and Holomon [34, 35] seven decades ago. They described the phenomena that influence the behavior of the material and determine the stress necessary for enforcing the expected deformation. According to Ashby [36], there are at least six distinguishable and independent ways in which a polycrystalline can be deformed and yet remain crystalline: a stress which exceeds the theoretical shear strength, then the glide motion of dislocations, the dislocation creep. Two independent kinds of diffusional flow originate from the flow of point defects through grains and round their boundaries: NabarroHerring creep and Coble creep. Finally, twinning provides a sixth mechanism.
The little pegs that can be seen in the lower part of the flow zone (2) deserve special attention. As the chip root was made by removing the tool with a blow in the direction of cutting speed v_{c}, these pegs suggest the development of local welding. This was a steel and hard metal material pair and it is obvious that such phenomenon does not happen, e.g., in TiNcoated inserts. Yet it must be concluded that friction speed can even be very small on the contact surface of the tool and the chip, and the internal friction of the flow zone determines the friction force.

the mobile dislocation density increases by the multiplication of the dislocations;

the average dislocation speed increases very quickly.
These cause a stress that is composed of two parts: one of them is dependent on temperature and the other that is athermal, i.e., independent of temperature. Nevertheless, it is true that the G shear modulus of the material also depends on temperature in the latter. Thus, it can be stated that stress and temperature are closely connected on the level of microstructure. Owing to the difficulties caused by complex processes, Lüthy and Whitte [15] studied the structural phenomenon like grain boundary sliding with a phenomenological method.
Examining the movement of dislocations on an atomic level, Lin et al. [13] concluded that dislocation density has a characteristic of increase that is similar to the charging of an electronic condenser. Similar phenomena occur on a macroscopic scale as well.
The calculations of Kalhori et al. [38], which were performed considering the dislocation density, the deformation localized on the shear zone, strain hardening, and thermal softening, also show the close relationship of temperature and shear stress.
The examination, carried out by Li et al. [39], is typical of the complex material structure characteristics of chip formation. The authors identified the various crystal axles in the chip root, and thus, they identified the significantly varying cutting forces belonging to various directions. It is clear how complicated the actual consideration of crystal structure is even in the case of a single crystal. The microstructural change or strengthening mechanism have been the subject of intensive research ever since, and the work has not been completed yet.
All these studies show that the significant deformation, the speed of deformation, and the fast thermal processes characteristic of chip formation are also shown in the change of the material structure. As we can see, it became obvious several decades ago that chip formation is characterized by extreme processes, whose physical observation is hindered by great difficulties. The extensive dislocation theory and material structure investigations concentrated on morphological, structural, and energetic features but a lot less attention was dedicated to kinematical characteristics.
It is broadly known that cutting temperature is usually measured at the contact surface of the tool and the chip. Salomon [17] did the same when taking his measurements and the known results were reached. So, the temperature and force analogy can be regarded as directly proven in the flow zone. This can also be established for the shear zone in another temperature range. Here, the important fact that a part of the heat produced flows opposite the direction of the movement of the material must be considered. As a result of this, the temperature of the material arriving at the shear zone changes rapidly at the beginning of the operation: it is initially low then starts increasing quickly. This generates a transient phenomenon, which ceases in continuous cutting. There is no time for this in milling, and so the forming stress in the material changes rapidly during the entire machining cycle.
It can be stated clearly that the critical nature of temperature in the deformation processes was also justified by these examinations. Based on the manysided material studies, it can also be established that the cutting force increases rapidly from the start of the process until it reaches a limit value.
As shown in Fig. 4, it can also be evidenced in down, up, and symmetric milling that the force converges on a curve that can be characterized by time constant τ ≈ 0 during the increase of the machined curve. Similar to turning, there is no transient phenomenon in this curve marked by a thin continuous line. It can also be seen from Fig. 4a that, due to the transient phenomenon, the maximum force does not develop at φ = 90^{o} but at angle φ_{max}, which is larger. This can be determined from Eq. (5) based on the dF/dt = 0 condition.
Here, the transient constant Γ can be determined by force measurement, then τ can be calculated with the numerical solution of Eq. (7).
3 Measuring the cutting force
The measurements were made in the laboratory of Institute of Manufacturing Science of the University of Miskolc, with a vertical machining center type PERFECT JET MCVM8 (H).
Dynamometer: type Kistler 9257A threecomponent dynamometer, 3 Kistler 5011A charge amplifier, type National Instrument Compact DAQ9171 four channel data acquisition unit, laptop. The measurement software was prepared in LabView programming language.
The workpiece was a normalized C45 unalloyed Csteel.
The type of the milling head: Sandvik R252.4408002715M face milling cutter, D = 80 mm.
The type of the milling insert: Sandvik R215.4415T308MWL GC4030
Edges: α = 11^{o}, γ_{f} = 20^{o}, λ_{s} = 4^{o}, κ_{r} = 90^{o}, κ_{r}’ = 1.5^{o}, r_{ε} = 0.8 mm.
Technological data: a_{p} = 0.4 mm, f_{z} = 0.1, 0.4, and 1.6 mm/rev, v_{c} = 100, 200, and 400 m/min.
The milling cutter cut with one edge so that the measurement of the cutting force should not be influenced by the other edges.
4 The validation of the transient model of the milling force and discussion
Chip removal occurs as a result of the distributed force system that develops on the contact surface between the tool and the workpiece and the chip. Based on the rules of statics, the resultant of this system of forces is a force and a torque vector. Considering the relatively small size of the surfaces in contact, the torque is usually ignored in cutting theory, and it is only the resultant cutting force that is taken into consideration. Essentially, it is the force developing in the chip root that determines the process, and this is the amount of force that is necessary to start and maintain the process. The fact that main cutting force F_{c}, thrust force F_{h}, and passive force F_{p} are generally distinguished is a practical method for the study of forces and energy relationships. However, it must be acknowledged in the study of processes actually taking place that the resultant cutting force is the primary characteristic of the process. For the purposes of the impact assessment, it is practical to divide this into two components, namely F_{xy} = (F_{x}^{2}+ F_{y}^{2})^{1/2} = F_{ch} = F_{c}^{2} + F_{h}^{2}) ^{1/2} in the basic plane and passive force F_{p} at right angles to cutting speed v. From an energetic point of view, F_{xy} is relevant from among these; therefore, validation was performed mainly with the analysis of F_{xy}.
The nature of the curves shown in Fig. 6 corresponds to what can be seen in the basic function of the transient force model in Fig. 4b. This suggests a connection between the milling process examined by measurements and the assumed model.
The constants of the measured and calculated data shown in Fig. 10 (f_{z} = 0.4 mm/rev).
v (m/min)  C (N)  τ_{av} (μs)  a*  R^{2}** 

100  353  2.6  0.9835  0.9649 
200  360  2.6  1.0023  0.9671 
400  400  3  1.0074  0.9859 
The three feeds applied at a_{p} = 0.4 mm = const depth of cut in the experimental programme also mean that the chip ratios, being a_{p}/f_{z}: 4.0, 1.0, and 0.25 were significantly different in the three versions. It is important to consider that the shape of the cross section of the removed layer changes largely with the increase of the angle position of the milling cutter. In the case of the current a_{p}/f_{z}sinφ = 0...4 (if f_{z} = 0.1 mm/rev) chip ratio, it is really the undeformed thickness that is changing; however, the degree of change is considerably smaller and the nature of cutting is different as well if speed is f_{z} = 1.6 mm and chip ratio is a_{p}/f_{z}sinφ = 0 … 0.25. In this version, the undeformed thickness is constant and the width of the layer is changing.
Adjustment of function (5) to the results of force measurements
Milling  f_{z} (mm/rev)  Force  C_{F} (N)  τ_{av} (μs)  a*  R^{2}** 

Up  0.1  F _{ xy}  154  1.0  1.0009  0.9927 
F _{ z}  205  1.2  1.0029  0.9613  
0.4  F _{ xy}  345  3.5  1.0061  0.9989  
F _{ z}  312  1.2  0.985  0.9939  
1.6  F _{ xy}  970  5.3  1.0024  0.9983  
F _{ z}  548  1.9  1.0091  0.9982  
Symm  0.1  F _{ xy}  158  3.0  0.9949  0.9519 
F _{ z}  180  2.65  0.9909  0.9557  
0.4  F _{ xy}  368  2.7  1.0057  0.9472  
F _{ z}  310  2.5  1.0086  0.9525  
1.6  F _{ xy}  1020  1.8  0.9997  0.9872  
F _{ z}  573  1.8  0.999  0.9797  
Down  0.1  F _{ xy}  198  4.4  1.0032  0.9262 
F _{ z}  265  5.5  1.0081  0.9362  
0.4  F _{ xy}  435  3.4  1.0486  0.9208  
F _{ z}  376  4.4  1.0059  0.9219  
1.6  F _{ xy}  1450  4.0  1.0153  0.8993  
F _{ z}  1600  5.0  1.0027  0.89 
The fact that time constant τ continuously changes during the cutting process may lead to interesting conclusions regarding the causes of the transient phenomenon. This probably originates from the structural changes of the material that were mentioned in the introduction. However, this needs further research.
φ_{max} angles determined with local and average time constant τ
Milling  v (m/min)  f_{z} (mm/rev)  φ_{0} (°)  τ_{av}* (μs)  τ_{loc,max} (μs)  φ_{av,τ} (°)  φ_{loc,τ} (°)  φ_{loc,max} (°)  φ_{av,max} (°) 

Symm  100  0.4  43  2.6  5.0  6.2  12  95.5  90.5 
200  0.1  3.0  1.3  14.3  6  100.2  99.0  
0.4  2.6  1.9  12.4  9  91.5  96.8  
1.6  1.8  1.5  8.6  6.9  90.7  92.4  
400  0.4  3.0  3.8  28.7  36  114.6  110.4  
Down  200  0.1  90  4.4  6.7  21.0  32  134.7  131.0 
0.4  1.7  1.5  8.1  10  119.4  115.9  
1.6  4.0  1.5  19.1  10  119.4  128.0 
The results marked in Fig. 20 show the different effect of the average and local time constant of the transient process and the scatter of the measurements. The fact that τ_{av} and local time constant τ_{loc,max} at the maximum of the force differ can be understood based on Fig. 18. Moreover, the fact that this difference scatters can be traced back to the complexity of the cutting process.
5 The energy effect of the transient process
This way, two opposite effects prevail in milling. One of them is the consequence of the wellknown fact that the undeformed thickness of material continuously changes during machining. This considerably influences the specific cutting force, which significantly increases, often even due to rather small layer thickness. This is accompanied by the effect of the transient process shown above, as a result of which less energy is necessary for chip formation in the initial phase than in continuous cutting. So, this double effect jointly determines the energy need of the cutting of a given amount of material.
It is understandable that the energy need is smaller in the case of greater feed and the beneficial effect of the decrease of cutting ratio a_{p}/f_{z}, which was shown by Karpuschewski [40]. The same can be established for milling. The new piece of information is that the relationship of energy need in the two methods of cutting can vary. It can be seen that milling is more advantageous at f_{z} = 0.1 mm/rev feed; however, this changes at larger feeds. All in all, it can be established that the energy need of turning and the symmetrical milling presented herein are approximately the same due to the opposite effect of the two phenomena mentioned, i.e., the change of band thickness and the transient phenomenon.
6 Summary
The measurement and calculation of cutting forces in manufacturing has been studied by researchers of cutting theory for a long time. Turning removing a permanent diameter was studied for many years, but lately more and more attention has been given to the cutting of a changing cross section, i.e., milling. This paper gives an account of the research whose objective was to examine the transient processes assumed in milling. A model that describes the actual cutting force in shorttime interrupted cutting was elaborated for this. The hypothesis was that the thermodynamic processes of deformation in the chip root are time consuming; therefore, the cutting force reaches the stationary status during a finite time. A model function where the usual Kienzle function was supplemented with an exponential part was applied in the qualitative description of the assumed transient process.
The force measurements were performed during the milling of normalized C45 steel. There was only one insert in the milling tool so that the process changing quickly in time could be examined better. The symmetrical, down and up milling were conducted with a_{p} = 0.4 mm depth of cut, f_{z} = 0.1, 0.4 and 1.6 mm/rev feed, and v_{c} = 100, 200, and 400 m/min cutting speeds. The diameter of the milling cutter was D = 80 mm, the width of the workpiece was B = 58 mm.
Based on the experiment, the following conclusions can be drawn:
It was clearly proven that the assumed transient phenomenon does exist and it can be described approximately by an exponential function, which shows the speed of the process by a time constant τ. The deformation of the material in cutting is the result of such complicated processes that can be described by the exponential function only approximately; time constant τ changes during the process. Nevertheless, an average time constant τ_{av} can be determined for the whole cutting cycle. This time constant characterizes the cycle well.
The model function fit in well with the measured F_{xy} forces and k_{xy} specific cutting forces determined based on the forces. The Pearson score of the correlation was R^{2} > 0.9, or often even higher than 0.95.
The traditional Kienzle power function of the specific cutting force in milling cannot be used because it fails to consider the transient process. However, it can be applied well if supplemented with an exponential part.
The transient phenomenon in milling leads to the consequence that the specific energy need of the material’s cutting is smaller than in the case of a stationary process.
There is a considerable difference between the energy processes of the removal of the chip root in the case of cutting with varying specific cutting ratio a_{p}/f_{z}. If cutting ratio a_{p}/f_{z} is smaller, the specific energy use is also smaller.
The fact that the specific energy need of cutting based on measurements is smaller in symmetrical milling than in down or up milling, it can also be attributed to the impact of the transient phenomenon.
If milling is compared with turning from an energy point of view, it can be concluded that the specific energy use is nearly the same because the opposite effects mostly offset each other.
The physical content of time constant τ has not been explored in depth yet in the presented phenomenological model of the cutting force in milling. Further research is required in this respect, which may make the model more precise.
Notes
Acknowledgements
Open access funding provided by University of Miskolc (ME).
Funding information
The authors greatly appreciate the (financial) support of the National Research, Development and Innovation Office–NKFIH (No. Of Agreement: OTKA K 116876), Hungary
References
 1.Bayard O (2000) Investigation of the verification techniques for modelling turning processes. Royal Institute of Technology, Dept. Material Processing, Production Engineering, StockholmGoogle Scholar
 2.Komanduri R (1993) Machining and grinding: a historical review of the classical papers. Appl Mech Rev 46(3):80–132CrossRefGoogle Scholar
 3.Kundrák J, Gyáni K, Tolvaj B, Pálmai Z, Tóth R (2017) Thermomechanical modelling of hard turning: a comptational fluid dynamics approach, simulation modelling practice and theory, vol 70, pp 52–64Google Scholar
 4.Cheng K (ed) (2008) Machining dynamics: theory, applications and practices. Springer, LondonGoogle Scholar
 5.Ezugwu EO, Sales WF, Landre J (2008) Machining dynamics in turning processes. In: Cheng K (ed) Machining dynamics: theory, applications and practices. Springer, London, pp 151–166Google Scholar
 6.Liu X (2008) Machining dynamics in milling processes. In: Cheng K (ed) Machining dynamics: theory, applications and practices. Springer, London, pp 167–231Google Scholar
 7.Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool vibrations and CNC design, 2nd Edition. Cambridge University PressGoogle Scholar
 8.Turkovich BF (1967) Dislocation theory of share stress and strain rate in metal cutting, Advanced in Machine Tool Design and Research, Proceedings of the 8th international M.T.D.R. conference (incorporating the 2nd international CIRP production engineering research conference), University of Manchester, Institute of Science and Technology, pp. 531–542Google Scholar
 9.Black JT (1971) On the fundamental mechanism of large strain plastic deformation, electron microscopy of metal cutting chips. J Eng Ind 93:507–526CrossRefGoogle Scholar
 10.Black JT (1972) Shear frontlamella structure in large strain plastic deformation processes. J Eng Ind 94:307–316CrossRefGoogle Scholar
 11.Ramalingam S, Black JT (1973) An electronmicroscopy study of chip formation. Metallurgical Transactions 4:1103–1112CrossRefGoogle Scholar
 12.Black JT (1979) Flow stress model in metal cutting. Journal of Engineering for Industry 101:403–415CrossRefGoogle Scholar
 13.Lin ZC, Chen ZD, Hua C (2007) Establishment of a cutting force model and study of the stressstrain distribution in nanoscale copper material orthogonal cutting. Int J Adv Manuf Technol 33:425–435CrossRefGoogle Scholar
 14.Li QJ, Li J, Shan ZW, Ma E (2016) Strongly correlated breeding of highspeed dislocations. Acta Mater 119:229–241CrossRefGoogle Scholar
 15.Lüthy H, Whitte RA (1979) Grain boundary sliding deformation mechanism maps. Mater Sci Eng 39:211–216CrossRefGoogle Scholar
 16.Zerilli FJ, Armstrong RA (1987) Dislocationmechanicsbased constitutive relations for material dynamics calculations. Journal of Applied Physics 61(5):1816–1825CrossRefGoogle Scholar
 17.Salomon C (1929) Schnittdruck und Schneidtemperatur Erscheinungen an der Werkzeugschneide, Die Werkzeugmaschine, Zeitschrift für Metallbearbeitung und Maschinenbau, 33. Jahrg. Heft 23. pp. 477–496Google Scholar
 18.Longbottom JM, Lanham JD (2006) A review of research related to Salomon’s hypothesis on cutting speeds and temperatures. Int J Mach Tools Manuf 46:1740–1747CrossRefGoogle Scholar
 19.Pálmai Z (1987) Cutting temperature in intermittent cutting. Int J Mach Tools Manuf 27(2):261–274CrossRefGoogle Scholar
 20.Pálmai Z (2017) Mathematical analysis of transient temperature changes in the chip root during milling. Int J Adv Manuf Technol 91(912):4219–4232CrossRefGoogle Scholar
 21.Crookall JR, Raine T (1971) Cutting forces, temperatures and surface characteristics for CIRP nickelchrome steels. Ann CIRP XVIV:183–189Google Scholar
 22.Zheng HQ, Li XP, Wong YS, Nee AYC (1999) Theoretical modelling and simulation of cutting forces in face milling with cutter runout. Int J Mach Tools Manuf 39:2003–2018CrossRefGoogle Scholar
 23.Lazoglu I, Buyukhatipoglu K, Kratz K, Klocke F (2006) Forces and temperatures in hard turning. Mach Sci Technol 10:157–179CrossRefGoogle Scholar
 24.Fan Y, Zheng M, Zhang D, Yang S, Cheng M (2014) Static and dynamic characteristic of cutting force when highefficiency cutting Ti6Al4V. Adv Mater Res 305:122–128CrossRefGoogle Scholar
 25.Thandra SK, Choudhury SK (2010) Effect of cutting parameters on cutting force, surface finish and tool wear in hot machining. Int J Mach Mach Mater 7(3–4):260–273Google Scholar
 26.Aurich JC (2006) 3D finite element modelling of segmented chip formation. Ann CIRP 55:47–50CrossRefGoogle Scholar
 27.Sato M, Tamura N, Tanaka H (Apr. 2011) Temperature variation in the cutting tool in end milling. J Manuf Sci Eng 133:021005–02116CrossRefGoogle Scholar
 28.Cui X, Zhao B, Jino F, Zheng J (2016) Chip formation and its effects on cutting force, tool temperature, tool stress, and cutting edge wear in high and ultrahighspeed milling. Int J Adv Manuf Technol 83:55–65CrossRefGoogle Scholar
 29.Ghani MU, Abukhshim NA, Sheikh MA (2008) An investigation of heat partition and tool wear in hard turning of H13 tool steel with CBN cutting tools. Int J Adv Manuf Technol 39:874–888CrossRefGoogle Scholar
 30.Suresh R, Basavarajappa S, Samuel GL (2012) Predictive modelling of cutting forces and tool wear in hard turning using response surface methodology. Proc Eng 38:73–81CrossRefGoogle Scholar
 31.Li Z, Wang G, He G (2017) Milling tool wear state recognition based on partitioning around medoids (PAM) clustering. Int J Adv Manuf Technol 88:1203–1213CrossRefGoogle Scholar
 32.Zheng G, Zhao J, Song X, Cheng X (2014) A fractal analysis of cutting forces in simulation and experiment. Key Eng Mater 589590:122–127CrossRefGoogle Scholar
 33.Zhang S, Li J, Lv H, Chen W (2014) An experimental investigation of cutting forces in hard milling of H13 steel under different cooling/lubrication conditions. Key Eng Mater 589590:13–18CrossRefGoogle Scholar
 34.Zener C, Holomon JH (Jan) Effect of strain rate upon plastic flow of steel. J Appl Phys 15, 1944:22–32Google Scholar
 35.Zener C, Hollomon JH (1946) Problems in non elastic deformation of metals. J Appl Phys 17(2):69–82CrossRefGoogle Scholar
 36.Ashby MF (1972) A first report on deformationmechanism maps. Acta Metall 20:887–897CrossRefGoogle Scholar
 37.Leslie WC (1961) The physical metallurgy of steels. McGrawHill Book Company, LondonGoogle Scholar
 38.Kalhori V, Wedberg D, Lindgren LE (2010) Simulation of mechanical cutting using a physical based material model. International Journal of Material Forming 3(Supp. 1):511–514CrossRefGoogle Scholar
 39.Li Q, Gong Yd, Sun Y, Liu Y, Liang Cx (2018) Milling performance optimization of DD5 Nibased singlecrystal superalloy. Int J Adv Manuf Technol 94(5–8):2875–2894CrossRefGoogle Scholar
 40.Karpuschewski B, Batt S (2007) Improvement of dynamic properties in milling by integrated stepped cutting. Ann CIRP 56(1):85–88CrossRefGoogle Scholar
Copyright information
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided 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.