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Cutting force and chatter stability analysis for PKM-based helical milling operation

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Abstract

In order to enhance the manufacturing productivity, mobile machining with industrial robots is proposed as a cost-effective and portable manufacturing alternative to large-scale CNC machine tools in aircraft part machining. Combing the advantages of helical milling and parallel robot, the cutting forces and chatter stability of a novel 5-DOF hybrid PKM (named TriMule)-based helical milling process are first investigated in this paper. The cutting force and dynamic model of PKM-based helical milling operation are proposed, and the chatter stability diagrams at the seven representative machining positions are obtained based on the complete discretization scheme with Euler’s method approach. The predicted cutting forces and chatter stability diagrams are experimentally validated by the PKM-based titanium alloy helical milling. It can be found that the PKM machining position has a great influence on the corresponding limit stable axial depth of cut in the helical milling operation. Meanwhile, it was indicated that the spindle speed is an important factor affecting the helical milling stability difference at different machining positions. Meanwhile, it was found that the helical milling stability is only determined by second-, third-, and fourth-order modes of TriMule when the spindle speed is higher than 1000 rpm with the first 4 modes of the cutting system considered. The research results are expected to provide a basis for the helical milling parameter optimization and reasonable robot machining position selection.

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Abbreviations

Fx, Fy, Fz :

Cutting forces applied by the end effector

kx, ky, kz :

Stiffness of PKM end effector along the direction of cutting forces

F :

Cutting force caused by the peripheral cutting edges

F f :

Cutting force caused by the front cutting edges

h(θi):

Undeformed thickness of cutting chip of the tooth i

db :

Differential width of cut

dS i :

Differential edge length

Fa, Fr, Ft :

Cutting forces in the directions of axial, radial, and tangential

Krc, Ktc, Kac :

Cutting force coefficients associated with the thickness of cutting chips which are named shear effect coefficients for the radial, tangential, and axial direction

Kre, Kte,Kae :

Independent of the thickness of cutting chips which are named the friction (or plowing) effect coefficients for the radial, tangential, and axial direction

θ i :

Instantaneous immersion angle

θ P :

Pith angle of the tool

φ(z):

Lag angle for a particular disk

β :

Helix angle of cutting tool

R t :

Radius of cutting tool

α :

Ramp angle

g(ϕi):

Special function to indicate whether the tooth i is cutting or not

r :

Tool runout

λ :

Runout angle

m, c , k :

Mass, damping ratio, and stiffness of PKM-tool system along xw and yw

x,\( \dot{x} \),\( \ddot{x} \) :

Displacement, velocity, and acceleration of the tool in the direction of xw

y,\( \dot{y} \),\( \ddot{y} \) :

Displacement, velocity, and acceleration of the tool in the direction of yw

Fx(t),Fv(t) :

Cutting forces along the xw and yw

Δx , Δy :

Regenerative vibration terms during the present and the previous tooth period in the xw and yw directions

T :

Tooth period

ξ :

Relative damping ratio

ω n :

Angle natural frequency

w :

Cutting depth

m t :

Modal mass

τ :

Time delay

hxx(t), hxy(t), hyx(t),hyy(t) :

Specific cutting coefficients of 2-DOF

τ :

Time delay between two successive teeth of helical milling

n c :

Revolution speed

n :

Spindle speed

a :

Interpolation proportion parameter

C k :

Coefficient matrix

Φ :

Eigenvalues of transition matrix

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Funding

This work was supported by National key research and development program of China (grant number: 2017YFE0111300) and National Nature Science Foundation of China (grant numbers: 51705358, and 51775373) and EU H2020-RISE-ECSASDPE (grant number: 734272).

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Authors and Affiliations

  1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China

    Mengrui Shi, Xuda Qin, Hao Li, Shuai Shang & Tian Huang

  2. School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Belfast, BT5 9AH, UK

    Yan Jin

  3. School of Engineering, University of Warwick, Coventry, CV4 7AL, UK

    Tian Huang

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  1. Mengrui Shi
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Correspondence to Hao Li.

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Shi, M., Qin, X., Li, H. et al. Cutting force and chatter stability analysis for PKM-based helical milling operation. Int J Adv Manuf Technol 111, 3207–3224 (2020). https://doi.org/10.1007/s00170-020-06252-3

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