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A new method using double distributed joint interface model for three-dimensional dynamics prediction of spindle-holder-tool system

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Abstract

The cutting process stability strongly depends on dynamics of the spindle-holder-tool system, which often changes and is determined by impact hammer testing in general. In order to avoid repeated and time-consuming impact hammer testing on different spindle-holder-tool combinations, this paper proposes a new method for three-dimensional dynamics prediction of spindle-holder-tool system. The system is modeled using Timoshenko’s beam theory and substructure synthesis method. The tool-holder connection is regarded as a double distributed joint interface model including a collet, a holder-collet joint interface and a tool-collet joint interface. The two joint interfaces are further modeled as two sets of independent spring-damper elements, while the collet and tool are modeled as Timoshenko beams with varying cross-sections. The substructure synthesis method is adopted to obtain the equation of motion of the spindle-holder-tool system. Finally, experiments of bending, torsional, and axial FRFs are carried out to verify the proposed method. Good agreements show that the new method is capable of predicting tool point FRFs more accurately compared with the existing methods.

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Abbreviations

H H(ω):

Receptance matrix of the spindle-holder subassembly with angular frequency ω

M c :

Mass matrix related to N c nodes of component c, where c = S,CorF

C c :

Damping matrix related to N c nodes of component c, where c = S,C,F,HCorTC

K c :

Stiffness matrix related to N c nodes of component c, where c = S,C,F,HCorTC

Q c :

=[q c,1T,q c,2T,...,q c,N c T]TDesignates the displacement vector of component c corresponding to N c nodes with c = H,S,C,orF

\(\mathbf {Q}_{{c}-\hat {c}}\) :

Displacement vector of nodes of component c which are in contact with component \(\hat {c}\) (c = S,C,F,HCorTC; \(\hat {c}=\textmd {H}, \textmd {S}, \textmd {C}, \textmd {F} \text {or} \textmd {TC}\) and \(\hat {c}\neq c\))

q c,i :

= [u c,i ,v c,i ,w c,i ,𝜃 c,i ,ϕ c,i ,ψ c,i ]TDesignates the displacement vector of the i th node of component c, where u c,i , v c,i , w c,i , 𝜃 c,i , ϕ c,i and ψ c,i (c = H, S, C, or F) denote translational and rotational displacements of the i th node of component c related to X,Yand Zaxes

\(\mathbf {F}_{{c-\hat {c}}}\) :

\(=[\mathbf {f}_{{c-\hat {c},1}}^{\textmd {T}}, \mathbf {f}_{{c-\hat {c},2}}^{\textmd {T}}, ... ,\mathbf {f}_{{c-\hat {c},} N_{c}}^{\textmd {T}}]^{\textmd {T}}\) Designates the load vector related to N c nodes of component c, and is applied by component \(\hat {c}\) (c = H,S,C,F,HCorTC; \(\hat {c}=\textmd {H}, \textmd {S}, \textmd {C}, \textmd {F}, \textmd {HC}\) or TCand \(\hat {c}\neq c\))

\(\mathbf {f}_{{c-\hat {c}},i}\) :

\(=[f_{\textmd {x},c-\hat {c},i},f_{\textmd {y},c-\hat {c},i},f_{\textmd {z},c-\hat {c},i},M_{\textmd {x},c-\hat {c},i},M_{\textmd {y},c-\hat {c},i}, M_{\textmd {z},c-\hat {c},i}]^{\textmd {T}}\) Designates the load vector related to the i th node of component c, and is applied by component \(\hat {c}\), where \(f_{\textmd {x},c-\hat {c},i}\), \(f_{\textmd {y},c-\hat {c},i}\), \(f_{\textmd {z},c-\hat {c},i}\), \(M_{\textmd {x},c-\hat {c},i}\), \(M_{\textmd {y},c-\hat {c},i}\) and \(M_{\textmd {z},c-\hat {c},i}\) (c = H,S,Cor F; \(\hat {c}=\textmd {H}, \textmd {S}, \textmd {C}, \textmd {F}, \textmd {HC} \text {or} \textmd {TC}\), and \(\hat {c}\neq c\)) Denote the forces and torques acting on the i th node of component c corresponding to X,Y,and Zaxes, and are applied by component \(\hat {c}\)

H:

spindle-holder subassembly

C:

collet component

S:

shank of tool component

F:

fluted part of tool component

TC:

tool-collet joint interface component

HC:

holder-collet joint interface component

References

  1. Tlusty J (1985) Machine dynamics. Chapman and Hall, New York, pp 49–153

    Google Scholar 

  2. Cao H, Zhang X, Chen X (2017) The concept and progress of intelligent spindles: A review. Int J Mach Tools Manuf 112:21–52

    Article  Google Scholar 

  3. Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. Ann CIRP 44:357–362

    Article  Google Scholar 

  4. Bayly P, Halley J, Mann B, Davies M (2003) Stability of interrupted cutting by temporal finite element analysis. Trans ASME - J Manuf Sci Eng 125:220–225

    Article  Google Scholar 

  5. Insperger T, Stepan G (2004) Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Methods Eng 61:117–141

    Article  MathSciNet  MATH  Google Scholar 

  6. Wan M, Wang Y-T, Zhang W-H, Yang Y, Dang J-W (2011) Prediction of chatter stability for multiple-delay milling system under different cutting force models. Int J Mach Tools Manuf 51(4):281–295

    Article  Google Scholar 

  7. Cao H, Li B, He Z (2012) Chatter stability of milling with speed-varying dynamics of spindles. Int J Mach Tools Manuf 52(1):50–58

    Article  Google Scholar 

  8. Wan M, Ma YC, Zhang WH, Yang Y (2015) Study on the construction mechanism of stability lobes in milling process with multiple modes. Int J Adv Manuf Technol 79(1-4):589–603

    Article  Google Scholar 

  9. Yang Y, Zhang W-H, Ma Y-C, Wan M (2016) Chatter prediction for the peripheral milling of thin-walled workpieces with curved surfaces. Int J Mach Tools Manuf 109:36–48

    Article  Google Scholar 

  10. Xu C, Feng P, Zhang J, Yu D, Wu Z (2017) Milling stability prediction for flexible workpiece using dynamics of coupled machining system. Int J Adv Manuf Technol 90(9):3217–3227

    Article  Google Scholar 

  11. Schmitz T, Donaldson R (2000) Predicting high-speed machining dynamics by substructure analysis. CIRP Ann-Manuf Technol 49:303–308

    Article  Google Scholar 

  12. Schmitz T, Duncan GS (2005) Three-component receptance coupling substructure analysis for tool point dynamics prediction. Trans ASME - J Manuf Sci Eng 127:781–790

    Article  Google Scholar 

  13. Park S, Altintas Y, Movahhedy M (2003) Receptance coupling for end mills. Int J Mach Tools Manuf 43:889–896

    Article  Google Scholar 

  14. Montevecchi F, Grossi N, Scippa A, Campatelli G (2016) Improved RCSA technique for efficient tool-tip dynamics prediction. Precis Eng 44:152–162

    Article  Google Scholar 

  15. Liao J, Yu D, Zhang J, Feng P, Wu Z An efficient experimental approach to identify tool point frf by improved receptance coupling technique, International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-017-0957-y

  16. Albertelli P, Goletti M, Monno M (2013) A new receptance coupling substructure analysis methodology to improve chatter free cutting conditions prediction. Int J Mach Tools Manuf 72:16–24

    Article  Google Scholar 

  17. Erturk A, Ozguven H, Budak E (2006) Analytical modeling of spindle-tool dynamics on machine tools using timoshenko beam model and receptance coupling for the prediction of tool point FRF. Int J Mach Tools Manuf 46:1901–1912

    Article  Google Scholar 

  18. Erturk A, Ozguven H, Budak E (2007) Effect analysis of bearing and interface dynamics on tool point FRF for chatter stability in machine tools by using a new analytical model for spindle-tool assemblies. Int J Mach Tools Manuf 47:23–32

    Article  Google Scholar 

  19. Mancisidor I, Urkiola A, Barcena R, Munoa J, Dombovari Z, Zatarain M (2014) Receptance coupling for tool point dynamic prediction by fixed boundaries approach. Int J Mach Tools Manuf 78:18–29

    Article  Google Scholar 

  20. Ozsahin O, Altintas Y (2015) Prediction of frequency response function (frf) of asymmetric tools from the analytical coupling of spindle and beam models of holder and tool. Int J Mach Tools Manuf 92:31–40

    Article  Google Scholar 

  21. Kivanc E, Budak E (2004) Structural modeling of end mills for form error and stability analysis. Int J Mach Tools Manuf 44:1151–1161

    Article  Google Scholar 

  22. Bediz B, Kumar U, Schmitz T, Ozdoganlar O (2012) Modeling and experimentation for three-dimensional dynamics of end mills. Int J Mach Tools Manuf 53:39–50

    Article  Google Scholar 

  23. Yang Y, Zhang WH, Ma YC, Wan M (2015) Generalized method for the analysis of bending, torsional and axial receptances of tool-holder-spindle assembly. Int J Mach Tools Manuf 99:48–67

    Article  Google Scholar 

  24. Qi B, Sun Y, Li Z (2017) Tool point frequency response function prediction using rcsa based on timoshenko beam model. Int J Adv Manuf Technol 92(5):2787–2799

    Article  Google Scholar 

  25. Namazi M, Altintas Y, Abe T, Rajapakse N (2007) Modeling and identification of tool holder-spindle interface dynamics. Int J Mach Tools Manuf 47:1333–1341

    Article  Google Scholar 

  26. Schmitz T, Powell K, Won D, Duncan GS, Sawyer WG, Ziegert JC (2007) Shrink fit tool holder connection stiffness/damping modeling for frequency response prediction in milling. Int J Mach Tools Manuf 47:1368–1380

    Article  Google Scholar 

  27. Movahhedy M, Gerami J (2006) Prediction of spindle dynamics in milling by sub-structure coupling. Int J Mach Tools Manuf 46:243–251

    Article  Google Scholar 

  28. Ahmadi K, Ahmadian H (2007) Modelling machine tool dynamics using a distributed parameter tool-holder joint interface. Int J Mach Tools Manuf 47:1916–1928

    Article  Google Scholar 

  29. Ahmadian H, Nourmohammadi M (2010) Tool point dynamics prediction by a three-component model utilizing distributed joint interfaces. Int J Mach Tools Manuf 50:998–1005

    Article  Google Scholar 

  30. Park S, Chae J (2008) Joint identification of modular tools using a novel receptance coupling method. Int J Adv Manuf Technol 35:1251–1262

    Article  Google Scholar 

  31. Matthias W, Ozsahin O, Altintas Y, Denkena B (2016) Receptance coupling based algorithm for the identification of contact parameters at holderctool interface. CIRP J Manuf Sci Technol 13:37–45

    Article  Google Scholar 

  32. Xu C, Zhang J, Wu Z, Yu D, Feng P (2013) Dynamic modeling and parameters identification of a spindle–holder taper joint. Int J Adv Manuf Technol 67(5):1517–1525

    Article  Google Scholar 

  33. Cao H, Li B, He Z (2013) Finite element model updating of machine-tool spindle systems. J Vib Acoust 135(2):024503–024503–4

    Article  Google Scholar 

  34. Cao H, Xi S, Cheng W (2015) Model updating of spindle systems based on the identification of joint dynamics. Shock Vib 2015:10

    Google Scholar 

  35. Yang Y, Wan M, Ma Y-C, Zhang W-H (2016) An improved method for tool point dynamics analysis using a bi-distributed joint interface model. Int J Mech Sci 105:239–252

    Article  Google Scholar 

  36. Schmitz T, Duncan GS (2006) Receptance coupling for dynamics prediction of assemblies with coincident neutral axes. J Sound Vib 289(4):1045–1065

    Article  Google Scholar 

  37. Rao SS (2011) Mechanical vibrations, 5th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  38. Yokoyama T (1990) Vibrations of a hanging timoshenko beam under gravity. J Sound Vib 142(2):245–258

    Article  Google Scholar 

  39. Schmitz T (2010) Torsional and axial frequency response prediction by RCSA. Precis Eng 34:345–356

    Article  Google Scholar 

  40. Schmitz T, Smith KS (2009) Machining dynamics: frequency response for improved productivity. Springer, New York

    Book  Google Scholar 

  41. Ozguven H (1990) Structural modifications using frequency response functions. Mech Syst Signal Process 4:53–63

    Article  MATH  Google Scholar 

Download references

Funding

This research has been supported by the National Natural Science Foundation of China (Grant Nos. 51705427, 11432011, and 51675440) and the Fundamental Research Funds for the Central Universities (Grant No. 3102017ZY006).

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Authors and Affiliations

  1. School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Yun Yang, Min Wan, Ying-Chao Ma & Wei-Hong Zhang

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  1. Yun Yang
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  2. Min Wan
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  3. Ying-Chao Ma
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  4. Wei-Hong Zhang
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Correspondence to Min Wan or Wei-Hong Zhang.

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Yang, Y., Wan, M., Ma, YC. et al. A new method using double distributed joint interface model for three-dimensional dynamics prediction of spindle-holder-tool system. Int J Adv Manuf Technol 95, 2729–2745 (2018). https://doi.org/10.1007/s00170-017-1394-7

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