Modelling of the Influence of Tool Runout on Surface Generation in Micro Milling
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Abstract
Micro milling is a flexible and economical method to fabricate micro components with threedimensional geometry features over a wide range of engineering materials. But the surface roughness and micro topography always limit the performance of the machined micro components. This paper presents a surface generation simulation in micro end milling considering both axial and radial tool runout. Firstly, a surface generation model is established based on the geometry of micro milling cutter. Secondly, the influence of the runout in axial and radial directions on the surface generation are investigated and the surface roughness prediction is realized. It is found that the axial runout has a significant influence on the surface topography generation. Furthermore, the influence of axial runout on the surface micro topography was studied quantitatively, and a critical axial runout is given for variable feed per tooth to generate specific surface topography. Finally, the proposed model is validated by means of experiments and a good correlation is obtained. The proposed surface generation model offers a basis for designing and optimizing surface parameters of functional machined surfaces.
Keywords
Surface generation Roughness prediction Surface topography Runout Micro milling1 Introduction
Micro milling is recognized as one of the most versatile machining processes to fabricate micro components and micro features [1], due to the advantages including wide material choices, true 3D micro geometry machining capability, high accuracy, low cost and environmentally friendliness [2, 3, 4, 5]. Recently, micro milling has been employed to fabricate the microfluidic devices [6, 7, 8, 9, 10]. Microfluidic channels are the important part of microchemical devices, which is widely being used in microelectronic and biomedical applications. The characteristic scale of microfluidic channels is generally between a few to several hundred microns, and micromilling has a very high superiority in such scale machining. Tool diameters are downscaled in micro milling, unfortunately the surface roughness is not downscaled in micro milling, this is mainly due to the fact that cutting edge radius and machining dynamics such as tool runout are not downscaled and they are similar to those in conventional milling. Therefore, the relative surface roughness, i.e., the ratio of surface roughness to the machined feature size, is believed to be larger in micro milling. Research has shown that the wall roughness and micro topography can significantly affect the flow and drag along the microfluidic channel path [11], and microreactors often need to control the flow pattern to achieve enhanced mixing, to achieve enhanced mass transfer, and improve the reaction rate. And on the other hand, design and control of wall roughness and micro topography has become an effective means of microflow control [12, 13, 14]. In addition, the micro features size produced by micro milling makes the subsequent finishing processes, e.g., grinding or polishing, expensive or even impossible. Therefore, modelling surface generation in micromilling is significant and it provides a theoretical basis the design and manufacture of microfluidic channels.
Research has been carried out in micro milling surface generation in recent years. Vogler et al. [15] developed a model to predict the surface generation for singlephase materials based on the minimum chip thickness concept. investigated the effect of micro tool cutting edge radius on the surface roughness in the micro machining, and pointed out that larger cutting edge radius would increase the surface roughness due to the existence of the minimum chip thickness. Oliaei and Karpat [16] investigated the influence of machining parameters on the surface roughness of stainless steel machining. Bissacco et al. [17] studied the size effects on surface generation by ball nose and flat end micro milling of hardened tool steel, and the effects of the increased ratio between cutting edge radius and chip thickness have been observed. Sun et al. [18] studied the relationship among the surface roughness, the feed per tooth, as well as the cutter geometry. Li et al. [19] proposed a trajectorybased surface roughness model for microendmilling and proven capable of capturing the minimum chip thickness, micro tool geometry and process parameters. Based on this model, a surface roughness model with tool wear effect is developed by taking the material removal volume and cutting velocity into account and is experimentally validated. Weule et al. [20] investigated surface generation in microendmilling of steel and concluded that the surface roughness had the increasing trend when the feed rate was smaller than the cutting edge radius. Previous research studied the influence of geometry of the cutter, machining parameters, tool wear and minimum cutting chip thickness on the surface generation in micro milling. While the runout of the tool is ignored, which plays an important role in the surface generation in micro milling due to the fact that in micro milling the magnitude of tool runout is comparable with the feed per tooth. In this paper, a surface generation model is proposed considering the tool runout both in axial and radial directions, after that the influence of the runout on the surface generation is studied quantitatively.
2 Surface Generation Model in Micro Milling
2.1 Mathematical Model of the Cutter and Ideal Machined Surface Generation
 1.\(r_{\varepsilon } > 0\), \(f_{z} \le 2r_{\varepsilon } { \sin }k^{\prime}_{r}\), the machined surface is made up of the circular arc edge of the tool, as shown in Figure 3(a). The maximum height of residual area (peakvalley) is$$R_{{{\text{Imax}}1}} = r_{\varepsilon }  \sqrt {r_{\varepsilon }^{2}  \left( {\frac{{f_{z} }}{2}} \right)^{2} } \approx \frac{{f_{z}^{2} }}{{8r_{\varepsilon } }}.$$(2)
 2.
\(r_{\varepsilon } > 0\), \(f_{z} > 2r_{\varepsilon } { \sin }k^{\prime}_{r}\), the machined surface is made up of the circular arc edge of the tool and the end cutting edge, as shown in Figure 3(b). The maximum height of residual area (peakvalley) is
$$R_{{{\text{Imax}}2}} = r_{\varepsilon } \left( {1  { \cos }k^{\prime}_{r} } \right) + f_{z} { \sin }k^{\prime}_{r} \left( {{ \cos }k^{\prime}_{r}  { \sin }k^{\prime}_{r} \sqrt {\frac{{2r_{\varepsilon } }}{{f_{z} { \sin }k^{\prime}_{r} }}  1} } \right).$$(3)
2.2 Surface Generation Model Considering Tool Runout
From Figure 4 it can be found that the kth tooth removes more material than the (k+1)th, due to the runout in radial direction, which affect the uncut chip thickness of each feed per tooth. Thus, the runout in radial direction has a significant influence on cutting forces.
Figure 5 shows the influence of the runout in axial direction on surface generation. It can be found that the tool mark generates by the kth tooth was completely removed by the (k+1)th tooth due to the cutter runout in axial direction. The finial profile of the machined surface formed by the (k+1)th tooth. The period of the tool mark is around twice time of the feed per tooth. Thus, the cutter runout in axial direction affects the cutting depth directly and hence has a significant influence on surface generation.
 1.\(r_{\varepsilon } > 0\), \(f_{z} \le 2r_{\varepsilon } { \sin }k^{\prime}_{r}\), the machined surface as shown in Figure 6 is made up of the circular arc edge of the tool, the maximum height of residual area (peakvalley) is$$R_{\text{Amax}} = r_{\varepsilon }  \sqrt {r_{\varepsilon }^{2}  \left( {\frac{{2f_{z} }}{2}} \right)^{2} } \approx \frac{{f_{z}^{2} }}{{2r_{\varepsilon } }}.$$(4)
It can be found that in this case a slight axial runout (\(r_{\text{axial}} > \frac{{f_{z}^{2} }}{{2r_{\varepsilon } }}\)) will cause the emergence of singletooth cutting, which increases surface roughness significantly, i.e., almost 4 times larger than the ideal roughness as shown in Eq. (2). Considering that the magnitude of inevitable axial runout is comparable to feed per tooth, in this case the ideal roughness as shown in Figure 3(a) is difficult to achieve. This explains the reason why in micro milling actual surface roughness deviates substantially from theoretical surface roughness in most of the machining system and merely reducing feedrate cannot improve surface roughness.
 2.\(r_{\varepsilon } > 0\), \(f_{z} > 2r_{\varepsilon } { \sin }k^{\prime}_{r}\), the machined surface as shown in Figure 7 is made up of the circular arc edge of the tool and the end cutting edge. The second and third cases fall into this criterion and are illustrated as follows.
In the second case, the surface is composed by the two teeth, and the maximum roughness of the surface is
$$R_{{{\text{Amax}}1}} = r_{\varepsilon } \left( {1  { \cos }k^{\prime}_{r} } \right) + f_{z} { \sin }k^{\prime}_{r} \left( {{ \cos }k^{\prime}_{r}  { \sin }k^{\prime}_{r} \sqrt {\frac{{2r_{\varepsilon } }}{{f_{z} { \sin }k^{\prime}_{r} }}  1} } \right) + 2r_{\text{axial}} .$$(5)
It can be found that the R_{Amax1} is equal to the ideal R_{Imax2} as shown in Eq. (3) plus the axial runout of the cutter.
In this case, it can be found that the tool path on the machined surface is equal to the spindle rotation speed, rather than the spindle rotation speed multiplies the number of flutes.
The critical axial runout for the separation of the second case and the third case surface generation can be judged as follows:
when \(r_{\text{axial}} \le (R_{{{\text{Amax}}2}}  R_{{{\text{Imax}}2}} )/2\), the second case occur;
when \(r_{\text{axial}} > (R_{{{\text{Amax}}2}}  R_{{{\text{Imax}}2}} )/2\), the third case occur.
3 Experimental Validation
3.1 Determination of Tool Runout
From the judgment map as Figure 9, it can be found that for axial runout of 1 μm, when the feed per tooth less than 24 μm per tooth, the machined surface generation falls into the third case; and when the feed per tooth larger than 24 μm per tooth, the machined surface generation falls into the second case.
3.2 Simulation and Experimental Verification
Two set simulation and machining experiments are carried out with a 2 flutes micro milling cutter, the cutter diameter is 0.5 mm, the corner radius and the end cutting edge angle are measured as 5 μm and 5°, respectively. The machining parameters used in the experiments are 5 μm per tooth and 35 μm per tooth, respectively, at a spindle speed of 20000 r/min and an axial depth of cut of 20 μm.
4 Conclusions

Tool runout has a significant influence of the surface roughness, and axial tool runout limits the achievable surface roughness. Three typical surface topography generation cases of the machined surface in micro milling are presented by considering tool runout, and the emergence conditions for each surface generation cases are investigated quantitatively.

The tool runout in axial direction has significant influence on the machined topography generation.

Proposed surface generation model has been verified by the micro milling experiments over a wide range of feedrate, and the results show that it provides accurate surface topography prediction.
Notes
Authors’ Contributions
DH and WC were in charge of the whole trial; WC wrote the manuscript; YS and XT assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Authors’ Information
Wanqun Chen, born in 1987, is currently an associate professor at School of Mechatronics Engineering, Harbin Institute of Technology, China. He is also a Research Associate at School of Mechanical and Systems Engineering, Newcastle University, UK. He received his PhD degree from Harbin Institute of Technology, China, in 2014. His research interests include ultraprecision machine design and dynamic analysis.
Yazhou Sun, born in 1968, is currently a professor at School of Mechatronics Engineering, Harbin Institute of Technology, China. He received his PhD degree from Harbin Institute of Technology, China, in 2005. His research interests include ultraprecision machine design and dynamic analysis.
Dehong Huo, born in 1975, is currently a Senior Lecturer at School of Mechanical and Systems Engineering, Newcastle University, UK. He received his PhD degree from Harbin Institute of Technology, China, in 2004. His research interests include micro machining process and precision machine design.
Xiangyu Teng, born in 1991, is currently a PhD candidate at School of Mechanical and Systems Engineering, Newcastle University, UK.
Competing Interests
The authors declare that they have no competing interests.
Funding
Supported by Engineering and Physical Sciences Research Council (Grant No. EP/M020657/1), National Natural Science Foundation of China (Grant No. 51505107) and Project of Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (Grant No. HIT.NSRIF.2017029).
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