Force Signals Research Articles

Tool Wear Condition Monitoring Method Based on Deep Learning with Force Signals.

Tool wear condition monitoring is an important component of mechanical processing automation, and accurately identifying the wear status of tools can improve processing quality and production efficiency. This paper studied a new deep learning model, to identify the wear status of tools. The force signal was transformed into a two-dimensional image using continuous wavelet transform (CWT), short-time Fourier transform (STFT), and Gramian angular summation field (GASF) methods. The generated images were then fed into the proposed convolutional neural network (CNN) model for further analysis. The calculation results show that the accuracy of tool wear state recognition proposed in this paper was above 90%, which was higher than the accuracy of AlexNet, ResNet, and other models. The accuracy of the images generated using the CWT method and identified with the CNN model was the highest, which is attributed to the fact that the CWT method can extract local features of an image and is less affected by noise. Comparing the precision and recall values of the model, it was verified that the image obtained by the CWT method had the highest accuracy in identifying tool wear state. These results demonstrate the potential advantages of using a force signal transformed into a two-dimensional image for tool wear state recognition and of applying CNN models in this area. They also indicate the wide application prospects of this method in industrial production.

Improvement of current-carrying tribological behaviour via laser surface texture

ABSTRACT Three kinds of laser surface texture (LST), i.e. square pit-textured surface (SPTS), round pit-textured surface (RPTS) and groove-textured surface (GTS), are fabricated on the flat brass (H65) sample surfaces. The current-carrying tribological behaviour of these surfaces are investigated. It is noticed the COFs of smooth surface, SPTS and RPTS are all greater than 0.6 after the test, while the GTS has the lowest COF, which remains around 0.2 throughout the test. The vibration signals detected from all surfaces indicate the larger COF will not trigger the FIV generation in this state. All the texture surfaces will not cause electrical contact breaks. Worn surface analysis indicates the wear level of GTS is the weakest, with slight damage and debris accumulation occurs along the groove edges. Finite element analysis is performed to calculate the variation of contact force, contact temperature and voltage signal, and the test results can be well explained.

Application of wavelet to strength log from scratch test

This paper proposes a methodology to construct logs of rock strength from the cutting force signal recorded in scratch tests conducted in the ductile regime. The approach, which is based on the application of discrete wavelet transforms, recognizes the existence of two length scales ℓc and ℓr. The strength length scale ℓc represents the length over which it is meaningful to measure strength, while the repeatability length scale ℓr is related to the resolution at which the force signal must be observed to become insensitive to the stochastic micro-failure events triggered by the motion of the cutter. It is postulated that the original cutting force signal, assumed to be sampled at a high enough frequency, can be decomposed into a deterministic signal intrinsic to the rock and a stochastic one resulting from discrete rock failure events. The technique of multiresolution analysis based on the maximal overlap discrete wavelet transform is applied as a low-pass filter to the original cutting force signals so as to wipe out the high-frequency components associated with the stochastic rock failure events. A criterion to determine the optimum cutoff frequency of the low-pass filter and the corresponding repeatability length scale is discussed in terms of the correlation coefficients between different filtered signals. It is shown that the low-pass filtered signals obtained at the optimum cutoff frequency have two salient features: (i) repeatability over different tests conducted at the same depth of cut on the same sample, and (ii) variability along the cutting distance. The excellent repeatability reveals that the deterministic background trend of the original force signals is relevant to the rock strength property, and the variability of the background trend captures the spatial variation of the rock strength.

Material Removal Rate Prediction Based on Broad Echo State Learning System for Magnetically Driven Internal Finishing

Material removal rate (MRR) modeling is crucial for process and quality control in abrasive finishing processes. In this paper, a novel broad echo state learning system (BESLS) is developed to predict MRR in the magnetically driven internal finishing process based on the force signal. This BESLS model employs reservoirs with echo state properties to replace the enhancement layer nodes of the conventional broad learning system. Three representative BESLS architectures are designed and experiments are conducted to validate the developed models. The effect of feature-fusion approaches on prediction accuracy is investigated. Results demonstrate that the prediction error of MRR is only 6.86% for the proposed BESLS model. The model has one reservoir with variable nodes (BESLS-III) and fuses extracted force features and process parameters as input. It also shows remarkable computational efficiency with a testing time of 0.134 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm s$</tex-math></inline-formula> , making it a potential candidate for online process control.

Water-Mass Coordinates Isolate the Historical Ocean Warming Signal

Abstract Persistent warming and water cycle change due to anthropogenic climate change modifies the temperature and salinity distribution of the ocean over time. This “forced” signal of temperature and salinity change is often masked by the background internal variability of the climate system. Analyzing temperature and salinity change in water-mass-based coordinate systems has been proposed as an alternative to traditional Eulerian (e.g., fixed-depth, zonally averaged) coordinate systems. The impact of internal variability is thought to be reduced in water-mass coordinates, enabling a cleaner separation of the forced signal from background variability—or a higher “signal-to-noise” ratio. Building on previous analyses comparing Eulerian and water-mass-based one-dimensional coordinates, here we recast two-dimensional coordinate systems—temperature–salinity (T–S), latitude–longitude, and latitude–depth—onto a directly comparable equal-volume framework. We compare the internal variability, or “noise” in temperature and salinity between these remapped two-dimensional coordinate systems in a 500-yr preindustrial control run from a CMIP6 climate model. We find that the median internal variability is lowest (and roughly equivalent) in T–S and latitude–depth space, compared with latitude–longitude coordinates. A large proportion of variability in T–S and latitude–depth space can be attributed to processes that operate over a time scale greater than 10 years. Overall, the signal-to-noise ratio in T–S coordinates is roughly comparable to latitude–depth coordinates, but is greater in regions of high historical temperature change. Conversely, latitude–depth coordinates have greater signal-to-noise ratio in regions of historical salinity change. Thus, we conclude that the climatic temperature change signal can be more robustly identified in water-mass coordinates. Significance Statement Changes in ocean temperature and salinity are driven both by human-induced climate change and by modes of natural variability in the climate system, such as El Niño–Southern Oscillation. It can be difficult to isolate the human-induced “signal” of climate change from the natural fluctuations or “noise” in the climate system. Water-mass-based methods, which “follow” a parcel of water around the ocean, have been thought to improve on “Eulerian” (i.e., analyses performed at fixed latitude, longitude, and depth) frames of reference as they are less impacted by the noise. However, it is difficult to cleanly compare between water-mass-based methods and Eulerian methods. Here, we aim to quantify the extent to which water-mass-based frameworks improve on Eulerian frameworks in isolating the climate signal from the noise. We recast water-mass and Eulerian methods onto an equivalent grid, enabling a clean comparison between them, and find that doing so increases the signal-to-noise ratio in water-mass-based coordinates in regions of ocean warming. These results emphasize the utility of water-mass-based methods in analyzing long-term climatic temperature change in the ocean.

Dynamic force modeling and mechanics analysis of precision grinding with microstructured wheels

The application of structured surfaces on advanced tools is an effective method for enhancing the machining performance. The modeling of dynamic grinding force is of great significance for improving tool surface structure design and improving grinding accuracy. In this paper, a novel dynamic force modeling and mechanics analysis of precision grinding with microstructured wheels was put forward. A grinding wheel topography model was established by considering the non-simplified position-posture-shape-size multiple random grains morphological characteristics. On this basis, the material removal pattern of the microstructured multiple random abrasive grains was identified based on grinding kinematics and undeformed chip thickness. The grain diameter, average bearing width, flat surface area, friction coefficient and total number of active abrasive grains in the grinding area were considered. Their effects on the amplitude and frequency of grinding force were discussed in detail, and the precision grinding experiment was carried out. The results show that the dynamic force model proposed could accurately evaluate the influence of microstructure tools on forces with an error rate of 6.7% or less. Compared with the original grinding wheel, the addition of microstructure reduces the grinding force by 49.6%− 94.3%. By controlling the force components, the force frequency is more concentrated, and the disorder of the grinding force signal is suppressed. Furthermore, the carbon emission model was calculated, and it can be seen that microstructured wheels can obviously reduce carbon emission, which is a novel processing technology to realize low-carbon manufacturing.

Time of Emergence for Altimetry‐Based Significant Wave Height Changes in the North Atlantic

AbstractSatellite observations of significant wave height (Hs) have recently reached 30 years of continuous record. Is this length sufficient to detect the effect of anthropogenically forced climate change on wave height trends? Wave height decadal variability is influenced by a combination of internal variability and forced variability caused by both anthropogenic and natural forcing. Using a statistical model to derive Hs from sea level pressure field and exploiting ERA‐5 reanalysis data as well as 80 members of the Community Earth System Model v2 large ensemble, we show that, over the North Atlantic (NA), altimetry‐based Hs trends are mostly caused by internal variability. This suggests that Hs changes computed over the satellite era are not yet controlled by anthropogenic climate change. Starting from 1993, the date of emergence, defined as the date when the forced signal becomes dominant over the internal variability, is later than 2050 for Hs in the NA.

Improvements on the Dynamical Behavior of a HiL-Steering System Test Bench

Shorter available development times and fewer available vehicle prototypes have increased the subsystem-based investigation on test rigs within the automotive development process. Steering systems exhibit a direct interface to the driver, therefore, posing high requirements to the control performance of a test bench, especially for the perception of steering feel. This work proposes three approaches to improve the force control performance of permanent magnet linear motors incorporated on a steering test bench. The first method improves control accuracy when a harmonic force signal is introduced into the steering system by adjusting the reference force signal based on the identified peak values of the measured and reference forces. The second method allows the inclusion of the actuator’s inertia and the occurring ratios between steering wheel angle and rack displacement into the control scheme to reduce performance deterioration due to inertia. The third approach considers delay time in the actuator control and estimates its future position for delay compensation. A validation of the proposed methods is conducted, displaying an improvement for all three applications. The proposed methods extend the applicability of a steering test bench within the automotive development process by enabling more accurate and reproductible control performance.

The robustness of driving force signals extracted by slow feature analysis

The slow feature analysis (SFA) can be used to extract potential driving force signals from a non-stationary time series. In recent years, although several studies have explored the applicability of SFA, the robustness of SFA to extract the driving forces is still an open question which is crucial to using it in practice. Based on this,the influence of three factors on the ability of SFA to extract the driving force signals is investigated in this paper, including spike noise, missing data, and sample size. Three classical chaotical models are used in our studies, namely, Logistic model, Henon model, and Lorenz model. The results show that SFA has a relatively strong anti-noise ability, but spike noise will cause high-frequency fluctuations in the extracted signals and weaken the extraction ability of SFA. Different degrees of missing data have a non-negligible influence on the performance of SFA to extract external forcing. As the degree of missing data increases, the extraction ability of SFA will be significantly reduced. However, the number of missing data from different dynamical systems has different effects on the extraction ability of SFA. In addition, the length of the sample size has a negligible effect on the ability of SFA to extract the driving force signals. The present research provides a more robust reference for the application of SFA in practice.

Isolating the speed factor is crucial in gait analysis for Parkinson's disease.

Parkinson's disease (PD) is characterized by an alteration of the walking gait, frequently including a slower self-selected walking speed (SSWS). Although the reduction of walking speed is inherent to people with PD, such speed reduction also represents a potential confounding factor that might partly explain the observed gait differences between PD and control participants. In this study, each participant walked along a 25 m level corridor during which vertical ground reaction force signals were recorded using shoes equipped with eight pressure sensors. Vertical ground reaction force signals (using statistical parametric mapping) and temporal and kinetic variables as well as their related variability and asymmetry (using Student's t-test) were compared between PD (n = 54) and walking-speed-matched control subjects (n = 39). Statistical parametric mapping did not yield significant differences between PD and control groups for the vertical ground reaction force signal along the walking stance phase. Stride time and single support time (equivalent to swing time) were shorter and peak vertical ground reaction force was larger in PD patients compared to controls (p ≤ 0.05). However, the single support time was no longer different between people with PD and healthy subjects when expressed relatively to stride time (p = 0.07). While single support, double support, and stance times were significantly more variable and asymmetric for PD than for the control group (p ≤ 0.05), stride time was similar (p ≥ 0.07). These results indicate that at matched SSWS, PD patients adopt a higher cadence than control participants. Moreover, the temporal subdivision of the walking gait of people with PD is similar to healthy individuals but the coordination during the double support phase is different. Hence, this study indicates that isolating the speed factor is crucial in gait analysis for PD.

Estimation and early prediction of grip force based on sEMG signals and deep recurrent neural networks

Hands are used for communicating with the surrounding environment and have a complex structure that enables them to perform various tasks with their multiple degrees of freedom. Hand amputation can prevent a person from performing their daily activities. In that event, finding a suitable, fast, and reliable alternative for the missing limb can affect the lives of people who suffer from such conditions. As the most important use of the hands is to grasp objects, the purpose of this study is to accurately predict gripping force from surface electromyography (sEMG) signals during a pinch-type grip. In that regard, gripping force and sEMG signals are derived from 10 healthy subjects. Results show that for this task, recurrent networks outperform nonrecurrent ones, such as a fully connected multilayer perceptron (MLP) network. Gated recurrent unit (GRU) and long short-term memory (LSTM) networks can predict the gripping force with R-squared values of 0.994 and 0.992, respectively, and a prediction rate of over 1300 predictions per second. The predominant advantage of using such frameworks is that the gripping force can be predicted straight from preprocessed sEMG signals without any form of feature extraction, not to mention the ability to predict future force values using larger prediction horizons adequately. The methods presented in this study can be used in the myoelectric control of prosthetic hands or robotic grippers.

STP-Net: A Signal Prediction Method of Laminar Decompression Robot Based on Swin Transformer

Spinal surgery robots have a great application value in laminar decompression surgery. For a safe surgery, the robot needs to accurately identify the cutting state of the lamina. Therefore, it is very important to deal with various sensing signals in the form of a time series. However, various state recognition algorithms proposed so far cannot completely avoid cutting through the lamina, leaving hidden dangers for nerve thermal damage caused by high-temperature liquid splashing. We propose a long time series prediction algorithm called STP-Net, which combined with the existing algorithms for recognizing the lamina cutting state can stop the lamina cutting in advance, thus preserving a thin inner layer of cortical bone and blocking high-temperature liquid splashing. STP-Net has the following advantages: (1) Dimension reduction is first performed on Swin (shifted window) Transformer to obtain 1D Swin Transformer, which was used to develop STP-Net for long time series prediction, which not only has high accuracy but also shows a linear relationship between computational complexity and input sequence length L, namely, O L . (2) The token merging layer is proposed and applied to the encoder of STP-Net, which reduces the computation cost and improves the global information extraction capability of the algorithm. (3) STP-Net uses a generative decoder to output the prediction sequence directly through a single operation, which not only has high efficiency but also avoids the accumulation of errors. Taking force signals as an example, when 400 numbers are used to predict 100 numbers, the average mean square error (MSE) and mean absolute error (MAE) of standard STP-Net are 1.22 × 10−3 and 2.42 × 10−2, respectively. STP-Net, combined with the existing method for recognizing the lamina cutting status, can stop the robot from cutting in advance in 87.14% of the cases. In addition, the results of practical lamina cutting experiments confirmed the effectiveness of STP-Net.

Noninductive Control of Permanent Magnet Synchronous Motor Based on Improved Synovial Observer

In the non-inductive control of permanent magnet synchronous motor, the rotor position information of the motor is usually estimated by the synovial film observer. Synovial observer has the advantages of simple control structure and short response time. The switch function of the control process of the synovial observer is usually the sign function. The back electromotive force signal is extracted by the filter, and then the rotor position information is estimated by the inverse tangent method. However, the traditional switching process of sign function contains a large number of high order harmonics, which will cause the problems of phase difference and amplitude attenuation after the signal is filtered by the filter, and the estimation error of arctangent method is large. Based on the above problems, the traditional switching function is improved in this paper. Continuous sigmoid function is used as the switching function, which can effectively solve the problem of excessive vibration during the operation of the motor. In addition, phase-locked loop technology is introduced to replace the traditional inverse tangential method for rotor position estimation, which further improves the estimation accuracy of the system.

Spatial Dependence of Log-Transformed Electromyography-Force Relation: Model-Based Sensitivity Analysis and Experimental Study of Biceps Brachii.

This study investigated electromyography (EMG)-force relations using both simulated and experimental approaches. A motor neuron pool model was first implemented to simulate EMG-force signals, focusing on three different conditions that test the effects of small or large motor units located more or less superficially in the muscle. It was found that the patterns of the EMG-force relations varied significantly across the simulated conditions, quantified by the slope (b) of the log-transformed EMG-force relation. b was significantly higher for large motor units, which were preferentially located superficially rather than for random depth or deep depth conditions (p < 0.001). The log-transformed EMG-force relations in the biceps brachii muscles of nine healthy subjects were examined using a high-density surface EMG. The slope (b) distribution of the relation across the electrode array showed a spatial dependence; b in the proximal region was significantly larger than the distal region, whereas b was not different between the lateral and medial regions. The findings of this study provide evidence that the log-transformed EMG-force relations are sensitive to different motor unit spatial distributions. The slope (b) of this relation may prove to be a useful adjunct measure in the investigation of muscle or motor unit changes associated with disease, injury, or aging.

Influence of microstructure and phase morphology on the stability of high temperature irradiation resistant thermocouples

Development of in-core instrumentation is driven by the pursuit of safer and more economic energy production from both existing nuclear reactors and Generation IV reactor designs. Idaho National Laboratory (INL) has developed high temperature irradiation resistant thermocouples (HTIR-TCs) for temperature sensing inside Generation IV nuclear reactors. These thermocouples are composed of phosphorus-doped niobium (Nb-P) and lanthana-doped molybdenum (Mo-LaO) thermoelements, an alumina (Al2O3) insulation, and a niobium sheath. HTIR-TCs require an initial heat treatment exceeding the maximum service temperature to stabilize the generated electromotive force (EMF) signal; however, the mechanism behind this stabilization is not well understood. This work evaluates the impact of the stabilization heat treatment on the thermoelements' microstructures, chemical stability, and electrical properties to determine the mechanisms by which the EMF signal stabilization occurs. Accordingly, during the preliminary heat treatment, a secondary Nb3P phase formed within the Nb-P, along with an interaction region at the Al2O3/niobium interface. The formation of secondary phases within the niobium leg of the thermocouple causes an increase in the Seebeck coefficient. Stabilization of the HTIR-TC EMF signal was found to be dependent upon both the equilibrium of a diffusion interaction region at the Nb-P/Al2O3 interface and the formation of Nb3P precipitates.

A new aerodynamic identification technology for short-time hypersonic wind tunnels while considering inertial force interference

When aerodynamic force tests are performed in hypersonic wind tunnels, the test model in the force measurement system (FMS) will be subjected to transient impact and induced transient vibration due to the high-speed airflow generated during start-up. The output signal of the FMS will contain the real aerodynamic signal and the inertial force signal caused by model vibration. The inertial force signal completely overcomes the aerodynamic signal, strongly influencing the test accuracy of the aerodynamic force and even making the aerodynamic force signal completely unusable. Therefore, this study develops a novel intelligent aerodynamic identification method based on deep residual shrinkage network (DRSN) deep learning technology and applies this method to aerodynamic force tests in hypersonic wind tunnels. This method can achieve intelligent identification and filtering of inertial force interference signals and instrument noise signals, and improve the test accuracy of aerodynamic forces. Also, this study performed a numerical simulation experiment and a test-bed experiment; verified the results through hypersonic wind tunnel test signals; and compared the identification results of the DRSN network method with the identification results of the traditional CNN network method, the mean method and the FFT method. From comparison results, the aerodynamic force identification accuracy of the DRSN network method proposed in this paper is shown to be nearly ideal and always remains above 95%. Thus, the proposed method effectively reduces the interference of instrument noise and inertial force, markedly improving the accuracy and reliability of the hypersonic wind tunnel aerodynamic force test.

Multi-dimensional features based data-driven state of charge estimation method for LiFePO4 batteries

The flat open-circuit voltage (OCV) curve of LiFePO4 (LFP) batteries poses a significant challenge to state of charge (SOC) estimation. To solve this problem, this paper proposes a data-driven SOC estimation method based on multi-dimensional features, especially incorporating force signals. The significant force variation at the middle SOC region section compensates for the flat OCV problem. A long short-term memory (LSTM) neural network model is established to estimate SOC. Battery voltage, current, temperature, and force data sampled only in 5 s are taken as input. The proposed method is validated under different dynamic testing profiles and different temperatures. Experimental results indicate that this method can highly improve SOC estimation accuracy in the middle SOC region, with less than 0.5% root mean square errors and less than 2.5% maximum errors. The validation results at different temperatures also maintain high accuracy with the same model, showing strong robustness and excellent generalization performance. Additionally, the model training process of this method only takes 1.5 h, and the online estimation time is less than 1 s, considerably reducing time cost.

Anthropogenic Influence on Temperature Change in China over the Period 1901–2018

Abstract Human influence on regional warming since 1901 has received little attention because of limited data during the early period. This study investigates the relative contribution of different external forcings to observed annual, summer, and winter warming in China over the period 1901–2018. First, four observational datasets were compared to validate data representativeness, particularly during the early twentieth century. Observed temperature changes were then compared with outputs from phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) based on an optimal fingerprinting method. Generally, both generations of climate models were able to reliably reproduce long-term warming in China over the period 1901–2018; however, they slightly underestimate the amplitude of annual and winter temperature increases. The observed annual warming of 1.54°C from 1901 to 2018 was more rapid than the global mean and was mostly attributable to the anthropogenic forcing signal. The three-signal detection analyses, including greenhouse gas (GHG), anthropogenic aerosol (AA), and natural external (NAT) forcings, indicated the detectable and distinct influence of GHG and AA signals on annual, summer, and winter temperatures during 1901–2018. For annual mean temperature, the GHG and AA contributed to 2.06°C (from 1.58° to 2.54°C) and −0.45°C (from −0.17° to −0.73°C) of observed change, respectively. The GHG signal was detectable from individual CMIP6 models and thus was indicative of the robustness of this influence. While during 1951–2018, GHG and AA were simultaneously detected in the summer temperatures based on the CMIP6 models; here, the AA cooling effects offset approximately 25% of GHG-induced warming.

Effects of Single/Compound Pit Texture on the Friction-induced Vibration and Noise of Thrust Cylindrical Roller Bearings

To improve the reliability and service life of thrust cylindrical roller bearings (TCRBs), the effects of single/compound pit texture on tribological properties and on friction-induced vibration and noise were studied. Laser marking equipment was used to create compound pit texture on a shaft washer. A universal friction and wear test rig was used to measure the friction force, vibration acceleration, and noise signals of TCRBs. The differences between the single/composite pit-textured and non-textured surfaces were studied in terms of the friction, wear, and vibration noise properties. The results revealed that the friction force and wear loss of the single/composite pit-textured surface were markedly lower than those of the non-textured surface. Compared to non-textured surface bearings, the friction force and wear loss for textured surface bearings were reduced by 39.6 % and 59.6 %, respectively, when the diameter, depth, and area density of the pit were 300 μm, 10 μm, and 10 %, respectively. The single/composite pit-textured surface exhibited good potential for vibration absorption and noise suppression. It could effectively interfere with the self-excited vibration of the TCRBs friction pair system, thereby reducing the degree of vibration noise of the TCRBs.

Dynamics and stability analysis of five-axis ball end milling with low radial immersion considering cutter runout

The inevitable cutter runout has an important influence on the cutter dynamic properties and transient cutting condition, whereas it is usually neglected in analyses of mechanics and dynamics in five-axis ball end milling for lack of efficient mechanism modeling methods. This paper presents a novel mechanical and dynamic model considering runout to develop stability analysis suitable in five-axis ball end milling with low radial immersion. Firstly, the mathematical modeling of the cutting edge trajectory is derived from the cutting process considering runout effect. The impact of runout on the motility pattern of the cutter center and cutting edge is clarified. Then, the optimized tool coordinate system independent on runout parameters is defined to decompose the cutter complex elliptical or quasi elliptical motion caused by runout into two regular circular motion combinations. One is the center of cutter rotates around spindle, and the other is the cutting edge of cutter rotates around cutter center. Taking advantage of this strategy, the mechanics and dynamics of five-axis ball end milling considering runout are determined. A new analytic method is developed to extract the cutter and workpiece engagement (CWE) for five-axis ball end milling considering runout effect based on the transient cutting force signal. The superiority of the proposed dynamic and CWE models are both immune from the runout parameters. Thereafter, generalized precise integration method (GPIM) is presented to deduce dynamic system with multiple time delays into the state transition matrix. The axial angle of cutting edge acts as a bridge between transition matrix and the limit cutting positions defined by the analytic CWE to develop stability analysis for five axis ball end milling. The accuracy and efficiency of the GPIM is validated by the classic benchmarks and experimentally verified examples. Finally, five-axis ball-end milling experiments are performed to confirm the effectiveness of the proposed mechanical and dynamic models.