# Investigation of the Machining Stability of a Milling Machine with Hybrid Guideway Systems

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## Abstract

**:**

## 1. Introduction

## 2. Construction of Milling Machine

## 3. Modeling of the Milling Machine

#### 3.1. Modeling of the Joint/Interface

#### 3.1.1. Rolling Interface

_{h}represents the Hertz constant, which is determined by the contact geometry of the ball groove or raceway and the material properties of the contacting components. Details are available in the literatures [26,27]. The contact stiffness at the contact point can further be determined from Equation (2).

#### 3.1.2. Sliding Interface

_{n}isnormal deformation (mm), P

_{n}is normal pressure (N/mm

^{2}), C

_{n}is coefficient of normal contact flexibility, and m is coefficient of non-linearity of deformations. The contact stiffness in the normal direction can be obtained as

_{n}, K

_{s}]. K

_{n}and K

_{s}is the contact stiffness in normal and tangential directions of the contact interface.

#### 3.2. Modeling of Spindle Unit

^{3}. The overall contact stiffness of each bearing was calculated as 340 N/μm. The stiffness of each bearing is distributed on the spring elements circumferentially surrounding the spindle shaft created in the model. The tool holder with cutter was modeled as a solid cylinder and assumed to be firmly connected with the spindle nose, which was considered as a part of the spindle shaft.

#### 3.3. Finite Element Model of Milling Machine

_{n}in normal direction was 500 and 850 N/μm for normal and medium preloaded roller guides. Regarding to the sliding guideway with Turcite-B antifriction layer, the contact stiffness was measured as 750 kN/μm per unit area in meter [23]. The overall contact stiffness at ball groove was estimated as 1.62 kN/μm according to the specifications of the ball screw [24]. In order to obtain a whole analysis model of a milling machine, the spindle-bearing system created in the above section was incorporated in the spindle ram, as shown in Figure 4. Also, in finite element analysis, the materials used for structural components are made of gray cast iron with an elastic modulus E = 660 GPa, Poisson′s ratio μ = 0.3, and density ρ = 7200 Kg/m

^{3}. The materials of linear rolling components have an elastic modulus E = 210 GPa, Poisson′s ratio μ = 0.3, and density ρ = 7800 Kg/m

^{3}.The vibration mode shapes associated with the frequencies of the milling system were obtained by implementing the modal analysis into the finite element computation.

_{mr}, representing the structural damping factor, is calculated from 2 ξ

_{mr}/w

_{r}, where ξ

_{mr}is the modal damping ratio for spindle dominant vibration mode, about 2.5%.

## 4. Results and Discussions

#### 4.1. Frequency Response Function of Spindle Unit

#### 4.2. Natural Vibration Modes of Milling Machine

#### 4.3. Frequency Response Functions of the Milling Machine

#### 4.4. Machining Stability

_{min}) and the spindle speed (n) in end-mill operation as follows.

_{e}(w) + jI

_{m}(w), where R

_{e}and I

_{m}are, respectively, the real and imaginary parts of the transfer function of the spindle tool tip. The limit cutting depth Z

_{min}for stable machining at spindle speed n is defined as

_{t}is the cutting resistance coefficients in the tangential direction to the cutter, N is the number of cutter teeth, and k is the lobe number. The machining stability was calculated based on the vibration modes that cause the tool to deform greatly. Therefore, according to the tool end FRFs, the apparent peak vibrations at lower and high frequency were selected for prediction of the machining stability. The analysis of machining stability was used to evaluate how the linear guide preload will affect the dynamic behavior and machining. Considering that the yawing and twisting modes cause the tool to deform greatly and the two modes occur aligning in X and Y directions, therefore, the machining stability in X and Y directions are calculated, respectively. In this way, the coupled effect of the dominant vibration modes was ignored when calculating the stability lobe curves. A two-tooth carbide cutter was employed to machine the stock material of Al7075 alloys and titanium alloys Ti-6Al-4V alloys at high and low speed machining. The cutting resistance coefficients were calibrated as K

_{t}= 796 N/mm

^{2}of for Al7075 alloys and K

_{t}= 2000 N/mm

^{2}for Ti6Al4V alloys [28,29].

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- To, Y. Modular Design for Machine Tools; McGraw Hill Professional: New York, NY, USA, 2008. [Google Scholar]
- Dhupia, J.S.; Powalka, B.; Ulsoy, A.G.; Katz, R. Effect of a nonlinear joint on the dynamic performance of a machine tool. J. Manuf. Sci. Eng. ASME
**2007**, 129, 943–950. [Google Scholar] [CrossRef] - Dhupia, J.; Powalka, B.; Katz, R.; Ulsoy, A.G. Dynamics of the arch-type reconfigurable machine tool. Int. J. Mach. Tools Manuf.
**2007**, 47, 326–334. [Google Scholar] [CrossRef] - Koren, Y.; Heisel, U.; Jovane, F.; Moriwaki, T.; Pritschow, G.; lsoy, G.; Brussel, H.V. Reconfigurable manufacturing systems. CIRP Ann. Manuf. Technol.
**1999**, 48, 527–540. [Google Scholar] [CrossRef] - Koren, Y.; Ulsoy, A.G. Reconfigurable manufacturing system having a production capacity method for designing same and method for changing its production capacity. U.S. Patents 6,349,237, 19 February 2002. [Google Scholar]
- Seo, Y.; Hong, D.P.; Kim, I.; Kim, T.; Sheen, D.; Lee, G.B. Structure modeling of machine tools and internet-based implementation. In Proceedings of the 2005 Proceedings of the Winter Simulation Conference, Orlando, FL, USA, 4 December 2005; IEEE: New York, NY, USA, 2005; pp. 1699–1704. [Google Scholar]
- Yigit, A.S.; Ulsoy, A.G. Dynamic stiffness evaluation for reconfigurable machine tools including weakly non-linear joint characteristics. Proc. Inst. Mech. Eng.
**2002**, 216, 87–101. [Google Scholar] [CrossRef] - Ravve, I.; Gottlieb, O.; Yarnitzky, Y. Nonlinear dynamics and stability of a machine tool traveling joint. Nonlinear Dynam.
**1997**, 13, 373–394. [Google Scholar] [CrossRef] - Lin, C.Y.; Hung, J.P.; Lou, T.L. Effect of preload of linear guides on dynamic characteristics of a vertical column-spindle system. Int. J. Mach. Tools Manuf.
**2010**, 5, 741–746. [Google Scholar] [CrossRef] - Hung, J.P. Load effect on the vibration characteristics of a stage with rolling guides. J. Mech. Sci. Technol.
**2009**, 23, 92–102. [Google Scholar] [CrossRef] - Chlebus, E.; Dybala, B. Modelling and calculation of properties of sliding guideways. Int. J. Mach. Tools Manuf.
**1999**, 39, 1823–1839. [Google Scholar] [CrossRef] - Fan, K.C.; Chen, H.M.; Kuo, T.H. Prediction of machining accuracy degradation of machine tools. Precis. Eng.
**2012**, 36, 288–298. [Google Scholar] [CrossRef] - Bianchi, G.; Paolucci, F.; van den Braembussche, P.; van Brussel, H.; Jovane, F. Towards Virtual Engineering in Machine Tool Design. CIRP Ann. Manuf. Technol.
**1996**, 45, 381–384. [Google Scholar] [CrossRef] - Altintas, Y.; Brecher, C.; Weck, M.; Witt, S. Virtual machine tool. CIRP Ann. Manuf. Technol.
**2005**, 54, 115–138. [Google Scholar] [CrossRef] - Sulitka, M.; Kolar, P. Calculation of spindle compliance considering it′s interaction with machine frame. MM Sci. J.
**2010**, 6, 180–185. [Google Scholar] [CrossRef] - Kolar, P.; Sulitka, M.; Janota, M. Simulation of dynamic properties of a spindle and tool system coupled with a machine tool frame. Int. J. Adv. Manuf. Technol.
**2011**, 54, 11–20. [Google Scholar] [CrossRef] - Law, M.; Altintas, Y.; Phani, A.S. Rapid evaluation and optimization of machine tools with position-dependent stability. Int. J. Mach. Tools Manuf.
**2013**, 68, 81–90. [Google Scholar] [CrossRef] - Hung, J.P.; Lai, Y.L.; Lou, T.L. Analysis of the machining stability of a milling machine considering the effect of machine frame structure and spindle bearings: Experimental and finite element approaches. Int. J. Adv. Manuf. Tech.
**2013**, 68, 2393–2405. [Google Scholar] [CrossRef] - Zulaika, J.J.; Campa, F.J.; de Lacalle, L.N.L. An integrated process-machine approach for designing productive and lightweight milling machines. Int. J. Mach. Tools Manuf.
**2011**, 51, 591–604. [Google Scholar] [CrossRef] - Huo, D.; Cheng, K.; Wardle, F. A holistic integrated dynamic design and modelling approach applied to the development of ultraprecision micro-milling machines. Int. J. Mach. Tools Manuf.
**2010**, 50, 335–343. [Google Scholar] [CrossRef] - Mousseigne, M.; Landon, Y.; Seguy, S.; Dessein, G.; Redonnet, J.M. Predicting the dynamic behaviour of torus milling tools when climb milling using the stability lobes theory. Int. J. Mach. Tools Manuf.
**2013**, 65, 47–57. [Google Scholar] [CrossRef][Green Version] - Seguy, S.; Arnaud, L.; Insperger, T. Chatter in interrupted turning with geometrical defects: An industrial case study. Int. J. Adv. Manuf. Technol.
**2014**, 75, 45–56. [Google Scholar] [CrossRef] - Aetna Plastics Corp. Turcite-B Slydway. Available online: http://www.aetnaplastics.com (accessed on 17 June 2013).
- Hiwin Technologies Corp. Ballscrews Technical Information. Available online: http://www.hiwin.com/online_cat (accessed on 11 June 2013).
- INA-Schaeffler Technologies Group UK. Flat Cage Guidance Systems. Available online: http:/www.ina.de (accessed on 14 May 2007).
- Brewe, D.E.; Hamrock, B.J. Simplified solution for elliptical-contact deformation between two elastic solid. ASME
**1997**, 99, 485–487. [Google Scholar] [CrossRef] - Greenwood, J.A. Analysis of elliptical Herztian contacts. Tribol. Int.
**1997**, 30, 235–237. [Google Scholar] [CrossRef] - Altintas, Y.; Budak, E. Analytical prediction of stability lobes in milling. CIRP Ann. Manuf. Technol.
**1995**, 44, 357–362. [Google Scholar] [CrossRef] - CUTPROV9.3, Advanced Machining Simulation Software. Available online: http://www.malinc.com (accessed on 1 March 2010).

**Figure 1.**Schematics of a horizontal milling machine with moving column and hybrid guideways. (

**a**) Main structure modules of the milling machine, (

**b**) Y-axis guideway system, (

**c**) X and Z-axis guideway system.

**Figure 2.**Modeling of the rolling and sliding interfaces. (

**a**) Schematic of angular contact bearing, (

**b**) Modeling of the contact interface between rolling ball and groove, (

**c**) Schematic of sliding guideway and the modeling of the antifriction sliding interface.

**Figure 6.**Comparisons of the frequency response functions measured from the spindle unit and predicted by the spindle model. (

**a**) Amplitude of the FRFs, (

**b**) Real part of the FRFs.

**Figure 8.**Comparisons of the predicted frequency response functions at tool end of milling machine modelin X and Y directions. (

**a**) Amplitude of the FRFs, (

**b**) Real part of the FRFs.

**Figure 9.**Predicted stability lobe diagrams in X and Y directions based on the vibration mode associated with the machine tool structure. (

**a**) Stability lobes in X direction, (

**b**) Stability lobes in Y direction.

**Figure 10.**Predicted stability lobe diagrams in X and Y directions based on the vibration mode associated with the spindle structure. (

**a**) Stability lobes in X direction, (

**b**) Stability lobes in Y direction.

**Figure 11.**Comparisons of the tool end FRFs predicted for milling machine with different preloaded linear guides mounted on spindle head and movable column. (

**a**) FRFs in X direction, (

**b**) FRFs in Y direction.

**Figure 12.**Comparisons of the stability lobe diagram predicted at the vibration mode associated with machine tool structure with different preloaded guideways. (

**a**) Stability lobes in X direction, (

**b**) Stability lobes in Y direction.

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**MDPI and ACS Style**

Hung, J.-P.; Lin, W.-Z.; Chen, Y.-J.; Luo, T.-L. Investigation of the Machining Stability of a Milling Machine with Hybrid Guideway Systems. *Appl. Sci.* **2016**, *6*, 76.
https://doi.org/10.3390/app6030076

**AMA Style**

Hung J-P, Lin W-Z, Chen Y-J, Luo T-L. Investigation of the Machining Stability of a Milling Machine with Hybrid Guideway Systems. *Applied Sciences*. 2016; 6(3):76.
https://doi.org/10.3390/app6030076

**Chicago/Turabian Style**

Hung, Jui-Pin, Wei-Zhu Lin, Yong-Jun Chen, and Tzou-Lung Luo. 2016. "Investigation of the Machining Stability of a Milling Machine with Hybrid Guideway Systems" *Applied Sciences* 6, no. 3: 76.
https://doi.org/10.3390/app6030076