Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar

A nonlinear dynamic analysis of the cutting process of a nonextensible composite cutting bar is presented. The cutting bar is simplified as a cantilever with plane bending. The nonlinearity is mainly originated from the nonextensible assumption, and the material of cutting bar is assumed to be viscoelastic composite, which is described by the Kelvin–Voigt equation. The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. The steady forced response of the cutting system under periodically varying cutting force is approximately solved by the multiscale method. Meanwhile, the effects of parameters such as the geometry of the cutting bar (including length and diameter), damping, the cutting coefficient, the cutting depth, the number of the cutting teeth, the amplitude of the cutting force, and the ply angle on nonlinear lobes and primary resonance curves during the cutting process are investigated using numerical calculations. The results demonstrate that the critical cutting depth is inversely proportional to the aspect ratio of the cutting bar and the cutting force coefficient. Meanwhile, the chatter stability in the milling process can be significantly enhanced by increasing the structural damping. The peak of the primary resonance curve is bent toward the right side. Due to the cubic nonlinearity in the cutting system, primary resonance curves show the characteristics of typical Duffing’s vibrator with hard spring, and jump and multivalue regions appear.

Download Full-text

Nonlinear Dynamics of Cutting Process considering Higher-Order Deformation of Composite Cutting Tool

Shock and Vibration ◽

10.1155/2021/8699218 ◽

2021 ◽

Vol 2021 ◽

pp. 1-23

Author(s):

Donghui Yao ◽

Yongsheng Ren ◽

Yuhuan Zhang ◽

Bole Ma

Keyword(s):

Cutting Force ◽

Nonlinear Dynamic ◽

Cutting Tool ◽

Primary Resonance ◽

Higher Order ◽

Forced Response ◽

Cutting Process ◽

Structural Damping ◽

Superharmonic Resonance ◽

Cutting System

In this paper, the nonlinear dynamic analysis of the cutting process of composite cutting tool is performed. The cutting tool is simplified to a nonplanar bending rotating shaft. The higher-order bending deformation, structural damping, and gyroscopic effect of cutting tool are considered. It is assumed that cutting tool is subjected to a regenerative two-dimensional cutting force containing the first and second harmonic components. Based on the Hamilton principle, the motion equation of nonlinear chatter of the cutting system is derived. The nonlinear ordinary differential equations in the generalized coordinates are obtained by Galerkin method. In order to analyze the nonlinear dynamic response of cutting process, the multiscale method is used to derive the analytical approximate solution of the forced response for the cutting system under periodic cutting forces. In the forced response analysis, four cases including primary resonance and superharmonic resonance, i.e., Ω ¯ = ω 1 , Ω ¯ = ω 2 , 2 Ω ¯ = ω 1 , and 2 Ω ¯ = ω 2 , are considered. The influences of ratio of length to diameter, structural damping, cutting force, and ply angle on primary resonance and superharmonic resonance are investigated. The results show that nonlinearity due to higher-order bending deformation significantly affects the dynamic behavior of the milling process and that the effective nonlinearity of the cutting system is of hard type. Multivalued resonance curves and jump phenomenon are presented. The influences of various factors, such as ratio of length to diameter, ply angle, structural damping, cutting force, and rotating speed, are thoroughly discussed.

Download Full-text

STUDY OF CUTTING AERIAL PMMA WITH MINIATURE DETONATION CORD

International Journal of Modern Physics B ◽

10.1142/s0217979208050826 ◽

2008 ◽

Vol 22 (31n32) ◽

pp. 5566-5571

Author(s):

Z.Q. LI ◽

L.M. ZHAO ◽

Y.G. ZHAO

Keyword(s):

Experimental Study ◽

Dynamic Analysis ◽

Nonlinear Dynamic ◽

Linear Density ◽

Nonlinear Dynamic Analysis ◽

Plate Versus ◽

Cutting Depth ◽

Simulation Results ◽

Relationship Of ◽

The Relationship

In order to shorten the time of through-the-canopy-ejection, and to ensure pilot safely escape and survive. The application of linear cutting technique using miniature detonation cord( MDC) in through-the-canopy-ejection-system is proposed. A series of different kinds of MDC are designed. Firstly experimental study on the cutting process of the PMMA plate wiht MDC is carried out. Material of metal cover explosive types and the range of charge quantities are determined. Consequently the phenomena of spallation is observed, and the relationship between the cutting depth and charge quantities is obtained. For the comparison, the process of explosion cutting PMMA plate is simulated by means of nonlinear dynamic analysis code LS-DYNA. Spallation phenomena which occurs in the experiment, is also observed in the simulation. Simulation results present the relationship of cutting depth of PMMA plate versus charge linear density, which well agree with experimental ones.

Download Full-text