In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides a concise representation for the two kinds of uncertainties simultaneously. In this paper, a generalized Markov chain model (GMCM), based on the generalized interval probability theory, is proposed to improve the reliability of prediction. In the GMCM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. A case study for predicting the average dynamic compliance in machining processes is provided to demonstrate the effectiveness of proposed GMCM. The results show that the proposed GMCM has a better prediction performance than that of MCM.
Cutting chatter is a violent self-excited vibration between a tool and a workpiece.Its negative effects mainly include poor surface quality,inferior dimensional accuracy,disproportionate tool wear or tool breakage,and excessive noise.Therefore,early recognition and online suppression of chatter vibration are necessary.This paper proposes a novel synthetic criterion(SC)for early chatter recognition.The proposed SC integrates standard deviation(STD)and one-step autocorrelation function(OSAF).Moreover,this paper revised the fast algorithm of OSAF.We can quantitatively divide a chatter vibration signal into three stages,which are stable stage,transition stage and chatter stage according to the SC.Compared with STD,the SC can improve the reliability of chatter recognition and the threshold of SC is not sensitive to variable cutting conditions.This paper presents an original algorithm of SC and its fast algorithm in detail.The fast algorithm of SC in this paper improves the computation efficiency compared with the original algorithm of SC.To validate the effectiveness of the proposed SC,a series of milling experiments were conducted under different cutting conditions.In these experiments,the vibration signals were acquired by two accelerometers mounted on the spindle house.The experimental results showed that the proposed SC could effectively recognize chatter vibration at an early stage of chatter vibration,which saved valuable time for online chatter suppression.
Research of thermal characteristics has been a key issue in the development of high-speed feed system. Most of the work carried out thus far is based on the principle of directly mapping the thermal error against the temperature of critical machine elements irrespective of the operating conditions. But recent researches show that different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated was similar. As such, it is important to develop a generic thermal error model which is capable of evaluating the positioning error induced by different operating parameters. This paper ultimately aims at the development of a comprehensive prediction model that can predict the thermal characteristics under different operating conditions （feeding speed, load and preload of ballscrew） in a feed system. A novel wavelet neural network based on feedback linearization autoregressive moving averaging （NARMA-L2） model is introduced to predict the temperature rise of sensitive points and thermal positioning errors considering the different operating conditions as the model inputs. Particle swarm optimization（PSO） algorithm is brought in as the training method. According to ISO230-2 Positioning Accuracy Measurement and ISO230-3 Thermal Effect Evaluation standards, experiments under different operating conditions were carried out on a self-made quasi high-speed feed system experimental bench HUST-FS-001 by using Pt100 as temperature sensor, and the positioning errors were measured by Heidenhain linear grating scale. The experiment results show that the recommended method can be used to predict temperature rise of sensitive points and thermal positioning errors with good accuracy. The work described in this paper lays a solid foundation of thermal error prediction and compensation in a feed system based on varying operating conditions and machine tool characteristics.
