This paper presents an analytical stability prediction method in milling chatter analysis with mu... more This paper presents an analytical stability prediction method in milling chatter analysis with multiple delays. The improved full-discretization method is used to determine the critical boundary of chatter stability. The proposed method can take many practical factors into consideration, such as helix angle, non-constant pitch, and cutter runout, etc. The influence of the multiple delays is explored in detail and the simulation results show that the cutter runout has the great influence on the elevation of the stability boundary. The finding proves the validity of the proposed method by experiment verification.
International Journal of Machine Tools & Manufacture
Machining stability analysis is important for chatter avoidance and machining efficiency improvem... more Machining stability analysis is important for chatter avoidance and machining efficiency improvement. To accurately predict the stability, the chatter mechanism must be recognized. Chatter is a kind of self-excited vibrations and the two most widely used theories explaining chatter in milling are the regenerative effect and the mode coupling effect. However, these two mechanisms are always separately considered in the previous stability researches, and none of them can explain the great difference between the stability prediction results with the classical model and the experimental results in many cases. This paper investigates the structural mode coupling effect in the regenerative milling stability analysis. Based on lots of experimental data, we found that these two mechanisms actually co-exist during the practical milling process, and the usually neglected structural mode coupling effect has a great effect on the stability lobe diagram in many practical milling cases. The theoretical prediction taking the cross coupled terms into account alters the stability boundary and such prediction is verified by the chatter experimental results.► Regenerative effect and mode coupling effect co-exist in practical milling process. ► Structural mode coupling effect has a great effect on the stability lobe diagram in practical milling cases. ► The experimental data of the cross coupled terms are given for the first time. ► Asymmetric modal matrices of the machine–tool structure are due to imperfect physical constraints. ► Milling stability boundary can be lifted by increasing the cross coupled mass and damping.
International Journal of Machine Tools & Manufacture, Jan 1, 2010
This paper presents a full-discretization method based on the direct integration scheme for predi... more This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.
This paper presents an analytical stability prediction method in milling chatter analysis with mu... more This paper presents an analytical stability prediction method in milling chatter analysis with multiple delays. The improved full-discretization method is used to determine the critical boundary of chatter stability. The proposed method can take many practical factors into consideration, such as helix angle, non-constant pitch, and cutter runout, etc. The influence of the multiple delays is explored in detail and the simulation results show that the cutter runout has the great influence on the elevation of the stability boundary. The finding proves the validity of the proposed method by experiment verification.
International Journal of Machine Tools & Manufacture
Machining stability analysis is important for chatter avoidance and machining efficiency improvem... more Machining stability analysis is important for chatter avoidance and machining efficiency improvement. To accurately predict the stability, the chatter mechanism must be recognized. Chatter is a kind of self-excited vibrations and the two most widely used theories explaining chatter in milling are the regenerative effect and the mode coupling effect. However, these two mechanisms are always separately considered in the previous stability researches, and none of them can explain the great difference between the stability prediction results with the classical model and the experimental results in many cases. This paper investigates the structural mode coupling effect in the regenerative milling stability analysis. Based on lots of experimental data, we found that these two mechanisms actually co-exist during the practical milling process, and the usually neglected structural mode coupling effect has a great effect on the stability lobe diagram in many practical milling cases. The theoretical prediction taking the cross coupled terms into account alters the stability boundary and such prediction is verified by the chatter experimental results.► Regenerative effect and mode coupling effect co-exist in practical milling process. ► Structural mode coupling effect has a great effect on the stability lobe diagram in practical milling cases. ► The experimental data of the cross coupled terms are given for the first time. ► Asymmetric modal matrices of the machine–tool structure are due to imperfect physical constraints. ► Milling stability boundary can be lifted by increasing the cross coupled mass and damping.
International Journal of Machine Tools & Manufacture, Jan 1, 2010
This paper presents a full-discretization method based on the direct integration scheme for predi... more This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.
Uploads
Papers