Errors Of Machine Tools Research Articles

The temperature-sensitive point screening for spindle thermal error modeling based on IBGOA-feature selection

Thermal error compensation is a simple and efficient method to reduce thermal errors of machine tools, and the compensation effect largely depends on the temperature-sensitive points screened for the thermal error modeling. In this paper, 5 spindle heating experiments are carried out, and a new temperature-sensitive point screening method based on the Improved Binary Grasshopper Optimization Algorithm (IBGOA) feature selection is proposed. Firstly, an optimal approximation criterion is added to the Binary Grasshopper Optimization Algorithm (BGOA) for ensuring the convergence of the algorithm. And the temperature measuring points are regarded as the feature of the thermal error. Then these feature temperature point subsets are generated by IBGOA. Next, the stepwise regression analysis is carried out to remove non-significant temperature points from these subsets. And each subset is evaluated to search the temperature-sensitive points based on the cross-validation result of the multiple linear regression (MLR). Finally, for further testing the applicability of the proposed temperature-sensitive points screening method, 3 common thermal error models are established with MLR, support vector regression, and back propagation neural network respectively. Compared with the traditional fuzzy C-means clustering (FCM) temperature-sensitive points screening method, the RMSE of these models could decrease by 30–50% in the thermal drift error of X-direction, 10%–30% in the thermal tilt error of Y-direction, generally 40%–60% in the thermal elongation of Z-direction and the thermal drift error of Y-direction. The results show the superiority of the proposed IBGOA-feature selection method.

A novel global sensitivity analysis method for vital geometric errors of five-axis machine tools

A novel global sensitivity analysis method for vital geometric errors of five-axis machine tools

The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning

Thermal error is one of the main sources of machining error of machine tools. Being a key component of the machine tool, the spindle will generate a lot of heat in the machining process and thereby result in a thermal error of itself. Real-time measurement of thermal error will interrupt the machining process. Therefore, this paper presents a machine learning model to estimate the thermal error of the spindle from its feature temperature points. The authors adopt random forests and Gaussian process regression to model the thermal error of the spindle and Pearson correlation coefficients to select the feature temperature points. The result shows that random forests collocating with Pearson correlation coefficients is an efficient and accurate method for the thermal error modeling of the spindle. Its accuracy reaches to 90.49% based on only four feature temperature points—two points at the bearings and two points at the inner housing—and the spindle speed. If the accuracy requirement is not very onerous, one can select just the temperature points of the bearings, because the installation of temperature sensors at these positions is acceptable for the spindle or machine tool manufacture, while the other positions may interfere with the cooling pipeline of the spindle.

Research on geometric error modelling and decoupling of machine tool based on NURBS projection curve

As a geometric measuring instrument of machine tool, double ball bar (DBB) instrument can effectively identify the geometric error of machine tool. In the existing literature, DBB mostly uses the two-dimensional circle as the identification trajectory to identify the geometric error continuously, and the most efficient way of single recognition is still in two-dimensional plane. Aiming at the low efficiency of DBB spatial geometric error recognition, the recognition range of DBB is extended from two-dimensional plane to spatial hemisphere. A method of space recognition and decoupling based on NURBS projection curve is proposed in this paper. The error decoupling of feed axis and rotation axis is realized in an experiment. The identification method has the characteristics of high efficiency, no secondary assembly and avoiding interference. It can decouple all the five-axis in hemispherical space at one time and get the effective solution.

A data-driven model for thermal error prediction considering thermoelasticity with gated recurrent unit attention

It is of great significance to reduce the thermal error of machine tools. However, there is a time lag between different temperature measurement points due to the thermoelastic effect, which causes inaccurate prediction when using only the current temperature. In this paper, the GRU time series neural network with an attention mechanism is employed to establish the thermal error model of the screw, which uses historical data and sets different weights for them. In addition, since the thermal error is closely related to the working condition, the electronic control data that reflect the working condition in the CNC system are considered. Compared with several state-of-art methods, such as RNN and LSTM, the prediction results demonstrate the superiority of the proposed method. The actual machining indicates that the compensation rate exceeds 75% and can reduce the thermal error from 20 µm to 5 µm.

Dynamic error of multiaxis machine tools considering position dependent structural dynamics and axis coupling inertial forces

During the working process of high-speed multiaxis machine tools, inertial forces can cause vibration and deformation of mechanical structure, which lead to the dynamic error of tool center point (TCP) relative to worktable and can adversely affect the machining performance. Considering the varying feed positions and accelerations during machining, a parameter-varying multi-rigid-body dynamic model of a 3-axis gantry machine tool is proposed. This model represents the position dependent structural dynamics and inertial forces, which can simulate the dynamic error of TCP relative to worktable within the entire workspace. The results show that the dynamic error in one direction is affected by the feed motions of multiple feed axes. The magnitudes of the dynamic error significantly vary with the position of Z-axis. And the dynamic errors in Y- and Z-direction show different varying trends. Then the theoretical model is used to discuss the dynamic error and position dependency. The expressions of TCP dynamic response and inertial forces reveal the reason why the dynamic errors in Y- and Z-direction show different varying trends.

Research on shape error of microstructure array fabricated by fly cutting

Microstructural array optical elements have gained more and more attentions for its special properties in optics. Micro pyramid structure has been proved to be one of the most effective anti-reflective textures and has been extensively studied. Single point diamond cutting technology has been applied to the fabrication of microstructures with the advantages of high efficiency, low cost and high machining accuracy. This paper mainly studies the influence of machine tool error to the shape accuracy of pyramid fabricated by fly cutting. Analyzed the forms of shape error caused by cutting tool position shift, and proposed the method of restraining sub-groove error generation, through control the minimum single cutting depth to decrease the effect by machine tool error. The experiment results verified correctness of the theory, and fabricated micro pyramid array with no obvious shape error.

High-Efficient Calculation Method for Sensitive PDGEs of Five-Axis Reconfigurable Machine Tool

Sensitive geometric errors of a machine tool have significant influence on machining accuracy, and it is important to identify them. Complex modeling and analysis must be carried out to identify the sensitive geometric errors of a five-axis machine tool by using the traditional method. Once the configuration structure of the machine tools is reconstructed, repetitive error modeling and analysis are required, and the identification cycle of sensitive geometric errors is long. Therefore, this paper proposes a high-efficient calculation method for sensitive position-dependent geometric error (PDGEs) identification of a five-axis reconfigurable machine tool. According to the results of sensitive geometric errors of the RTTTR-type and TTTRR-type five-axis machine tools, the mapping expressions between sensitive PDGEs and the configuration structure of machine tools was established. In this method, sensitive PDGEs can be calculated directly according to the mapping expression, which eliminates the process of error modeling and analysis. Taking a RTTTR-type five-axis machine tool as an example, the sensitive PDGEs were calculated according to the presented mapping expressions without error modeling and analysis. A series of analysis points in the machining area were selected to compare the machining errors before and after sensitive PDGE compensation. The results show that this calculation method is accurate.

Thermal error prediction of machine tool spindle using segment fusion LSSVM

The key temperature points are the input variables of the thermal error model for prediction and compensation of thermal errors for precision CNC machine tools. However, the revealed time-varying characteristics of the key temperature points may jeopardize the robust prediction. To this end, the segment fusion least squares support vector machine (SF-LSSVM) thermal error modeling method is proposed. Firstly, the temperature data and thermal error data are divided into different segments according to time. Then, using the LSSVM with excellent nonlinear mapping capabilities as the basic model, the sub LSSVM thermal error model building and the corresponding key temperature points selection in each segment are fulfilled with genetic algorithm (GA) in a wrapper manner to preserve the corresponding local prediction characteristics. Finally, pick some of or all the sub LSSVM thermal error models to fuse together as the final thermal error model which may incorporate both the local and global prediction characteristics. The modeling and prediction experiment results on the spindle thermal error of a horizontal machining center demonstrate that the mean root-mean-square error (RMSE) on 5 spindle speeds after compensation is only 3.1 μm. Comparing with two traditional thermal error models, the prediction performance of the present model is improved by up to 51%. This research casts new light on both the mechanism of key temperature points and the prediction method of thermal errors.

Effect of shape formation on the accuracy of grinding ends while compensating for machine tool errors

There are several general methods for correcting errors related to positioning the machine tool structural units. The task to achieve optimal manufacturing accuracy can be resolved by using a compatible solution to vector equations, a variation of the shape formation function, or applying a matrix of transfer coefficients. However, there is no mutual relationship between various calculation methods for the case of grinding flat surfaces. The methods should be simplified and tested for the elongated shape formation function while considering the links’ dimensions. This paper reports a study into the accuracy of grinding flat surfaces, determining and reducing the share of manufacturing errors. The content of variation matrices and transfer coefficients has been substantiated. The comparison of the orientation angles of the grinding machine headstock relative to the machine tool bed has demonstrated close results from all methods. These angles were taken as machine tool errors. The calculation error does not exceed 1.5 %. The experiments are consistent with the calculations. Different signs of the transfer coefficients in the orientation angles of grinding machine headstocks in the matrix make it possible to mutually compensate for the overall impact. The calculations have shown that the accuracy of the side-end machining is largely affected by a change in the orientation angle in the vertical plane. The effect exerted on the accuracy of individual mated parts by the machine tool structural units has been estimated. The calculations show that the error of positioning a part in the drum window acquires the highest absolute values and is random in nature, which requires a more accurate base positioning. The findings from both theoretical and experimental studies have been applied. The mathematical model makes it possible to determine the degree of scattering the end surface around the base plane via its variance. The measured trajectory provides diagnostic information about the sources of error in the machine tool assembly. A task to calculate the accuracy of the end-grinding machine tool can be solved for other models of machine tools in the same way

Dynamic positioning error analysis and modeling of CNC machine tool guideway system

The dynamic characteristics of the XY worktable are thoroughly analyzed in this study to accurately compensate the measurement errors of on-machine measurement systems caused by the dynamic and static characteristics under multiple factors. The dynamic positioning error model of the XY worktable motion components is established, and the theoretical model of the dynamic positioning error of the XY worktable is derived. The actual parameters of the experimental platform for the correlation error of CNC machine tools are substituted into the model for theoretical calculation and analysis. Results show that the motion speed of the worktable, the weight of the measured workpiece, the installation position of the workpiece, and the friction force are the main factors causing the dynamic positioning error. Dynamic positioning error analysis and verification experiments were conducted to verify the validity of the proposed theoretical model. Experimental results show that a regular change occurs between the dynamic positioning error and the movement speed of the XY worktable, and the actual measurement results are basically consistent with the theoretical calculation results. The research results can lay a good foundation for establishing the measurement error prediction and compensation model of on-machine measurement systems of CNC machine tools and improving its measurement accuracy.

Tolerance analysis of the volumetric error of heavy-duty machine tool based on interval uncertainty

Tolerance design is one of the main stages in the robust design process of machine tool. For heavy-duty machine tools, traditional tolerance analyses based on probabilistic methods may not be suitable because it is generally difficult and costly to obtain the accurate probability distribution of error by the limited geometric error measurements in large dimension. In this paper, a new tolerance analysis method for heavy-duty machine tools is proposed based on the interval uncertainty. Considering independent geometric error components have certain bounds but accurate distributions are unknown, the interval theory is introduced to the kinematic modeling of the static volumetric error of heavy-duty machine tools based on the multi body system (MBS) and homogeneous transformation matrix (HTM). Geometric error components are described in forms of interval numbers to extend the error model to the interval number system. The interval extension of the volumetric error function is further modified so that the variation interval of the volumetric error is thus accurately evaluated by the interval arithmetic. Comparative studies on tolerance analyses of different typical probabilistic/non-probabilistic methods are conducted through numerical simulations. It is found that under the given computational condition, the tolerance analysis based on the interval uncertainty can accurately evaluate the variation range of the volumetric error.

Error Analysis and Fault Diagnosis of CNC Machine Tools under Artificial Intelligence Technology

With the development of technology and the arrival of the era of artificial intelligence, the relationship between machine and human is becoming closer and closer. This paper mainly studies the error analysis and fault diagnosis of CNC machine tools based on artificial intelligence technology. The detection of machine tool error is mainly completed by laser interferometer. In this paper, a dual frequency laser interferometer is used. In order to ensure the efficiency of the program, the display image is refreshed in 20ms. According to the structure analysis, the error branches of CNC machine tools are determined, and the position feature relationship and motion feature relationship between adjacent bodies in each error branch are analyzed. In this paper, the fault tree analysis method is used to establish the fault tree model of computerized numerical control machine tool, and the fault reasoning method based on fault tree is given. On this basis, the deep neural network model is used to classify and identify the difficult to identify features such as fault degree, so as to achieve the purpose of deep fault diagnosis. The data show that the average recognition rate of BP network before feature reduction is 82%, and the average recognition rate of BP network after feature reduction is 86%. The results show that artificial intelligence technology can improve the accuracy of error analysis of CNC machine tools.

Synthetic positioning error modelling of a feed axis for a precision CNC machine tool

The linear feed system is a kernel movement component in a CNC machine tool. Because of thermal generation principally caused by motor and frictional action between motion pairs, such as cutter-workpiece and ball-raceway pairs, positioning errors have not only geometrical errors but also thermal errors, which plays an important role on the machining accuracy of parts. Geometrical errors solely related to position can be extracted through coordinate rotation transformation and expressed in the form of a polynomial. Many temperature sensors are allocated at different places to acquire the overall temperature changes in the feed system. To eliminate the correlation between some temperatures, the K-means clustering algorithm is employed to categorize the temperature measurement points, and key points are selected based on grey correlation analysis to achieve representative measurements. Consequently, a thermal error model is implemented by a BP neural network to establish the relationship between temperature and thermal deformation. A synthetic model is obtained through superposition of the above two error models to predict the positioning error. A thermal characteristic experiment of the linear feed axis carried out on a precision CNC machine verifies the effectiveness of the positioning error modelling method and provides a feasible and reliable reference to compensate for feed axis positioning errors in CNC machine tools.

CGHMM based fault identification for single point diamond flycutting machines

The ultra-precision single point diamond flycutting method is commonly used to produce fine optical surfaces. But the motion errors of machine tool are very weak, it is hard to achieve the error detection for single point diamond flycutting machines. To solve this problem, different measuring data such as vibrations and temperatures of different components were collected synchronously, and then we established the fault identification method based on hidden Markov model (HMM) to analyse the acquired measuring signals. The method includes signal analysis of raw data, fault recognition based on continuous Gaussian mixture density hidden Markov model (CGHMM) and information fusion. It combines the advantages of HMM and information fusion, to identify fault information accurately. Results show that the identification rates of the temperature signals to classification status by GRMS can reach 92% and vibration signals are little related to the surface quality of the workpieces classified by GRMS.

Identification of 11 position-independent geometric errors of a five-axis machine tool using 3D geometric sensitivity analysis

In this paper, a method is proposed for identification of 11 position-independent geometric errors (PIGEs) of five-axis machine tools with a tilting/rotary table via single-ball measurements and three-dimensional (3D) geometric sensitivity analysis. Eleven PIGEs were identified, including three squareness errors between three linear axes, two offset errors, and two squareness errors for the tilting/rotary axis. The approach uses a set-up of a ball and three circular measurements involving simultaneous control of two linear axes and a tilting/rotary axis. A 3D geometric sensitivity analysis is carried out to investigate the effects of the 11 PIGEs on each of the measurement’s paths and between the measurement paths. The particular measurement paths used allow the radius of the circular path at the first measurement, and the distance between the circular paths of the second and third measurements, to be increased for accurate identification of the 11 PIGEs. The proposed method was also used to derive root-sum-square values of sensitivity coefficients, and then applied to a commercial five-axis machine tool for experimental verification. It calculates the peak-to-valley values of the positional deviations in the x-, y-, and z-directions along the test paths as 152.1, 118.2, and 47.1 μm, respectively, without compensation for the identified PIGEs, and as 17.6, 15.0, and 11.4 μm, respectively, with compensation. The results confirm the validity of our proposed method.

A mapping model between the workpiece geometric tolerance and the end pose error of CNC machine tool considering structure distortion of cutting process system

Aiming at the problem that the geometric accuracy design index of machine tools is difficult to be determined reasonably in the geometric precision design process of CNC machine tools, this paper presents a mapping model between geometric tolerance of the workpiece and end pose error (positional and orientational error of the tool relative to the workpiece) of the machine tool considering structure distortion of cutting process system. Only considering the factors of the machine tool geometric errors, this paper first establishes the relationship between the geometric tolerance requirements of the workpiece and relative pose error at the end of machine tools, and completes the estimation of the machine tools end pose error. Then this paper analyzes the elastic deformations of the cutting process system caused by the cutting force. These elastic deformations produce machining errors. Based on the above analysis, the estimated variation range of the end pose error can be adjusted by the emulation of the geometric tolerance of the workpiece and used as the geometric accuracy design index of machine tools. This paper takes the international standard small size contour processing test piece as an example to explain the application process of the proposed model.

The influence of dynamic error outside servo-loop on the trajectory error

The moon-shaped trajectory is designed as to study the influence of dynamic error outside servo loop (DEOS) on the trajectory error of CNC machine tool. Firstly, the system identification method is used to build up the transfer function from the setpoint position (SP) to the linear encoder feedback position (LEFP), as well as the transfer function from the SP to the effector end position (EEP). Inputting the setpoints of the moon-shaped trajectory into these transfer functions, the LEFP and EEP can be predicted. Secondly, the setpoint trajectory, trajectory at LEFP, and trajectory at EEP are generated by D-H method. In addition, the trajectory errors are solved. Finally, the influence of DEOS on the trajectory error at EEP is investigated. The results show that there is a clear difference between the trajectory error at LEFP and the trajectory error at EEP, which causes the moon-shaped trajectory to be overcut and undercut. At a feed rate of 10000 mm/min, the difference between the two errors can reach a maximum of 0.03 mm. The main reason for the inconsistency is that the DEOS causes the trajectory at LEFP and the trajectory at EEP to not coincide.

Deterministic error compensation for slow tool servo-driven diamond turning of freeform surface with nanometric form accuracy

• A deterministic process flow was proposed for error compensation in free from surface turning. • All the main error factors were modeled, simulated and compensated before machining. • The method enabled achieving nanometer-level form accuracy without trial-and-error. • A two-dimensional sine wave grid was generated on single-crystal silicon by a single cut. • The form error was reduced to 8 nm peak-to-valley with surface roughness of ∼ 1 nm Sa. Slow tool servo (STS) turning takes an important role in fabrication of freeform optical elements. However, in conventional STS turning, it is technologically difficult to obtain nanometer-level form accuracy due to multiple error factors such as tool trajectory errors, tool alignment errors and dynamic follow-up errors of machine tools used. In this study, a deterministic process flow was proposed where all the main error factors were comprehensively analyzed, simulated and then compensated before machining based on the feedforward method, and the workpiece form error after compensation was predicted accurately. The proposed process flow enabled achieving nanometer-level form accuracy by a single cut without the necessity of repetitive trial-and-error. To demonstrate the effectiveness of the proposed method, cutting tests of a two-dimensional sine wave grid were attempted on single-crystal silicon and the proposed error compensation was applied. As a result, the form error was reduced to 8 nm P–V (peak to valley) with a surface roughness of 1 nm Sa by a single cut.

Application of Multisensor Information Fusion Technology in the Measurement of Dynamic Machining Errors of Computer Numerical Control (CNC) Machine Tools

A CNC machine tool is process control equipment integrating machine, electricity, and liquid, which makes its fault diagnosis complex and special due to its own advanced, complex, and intelligent characteristics. Traditional diagnostic methods rely on the engineering experience of technical personnel, which incorporates human subjective factors, and can only perform qualitative analysis, resulting in low diagnostic efficiency. And through a single sensor to detect and diagnose the machine tool, the accuracy and credibility of the decision are low, and the system is also weak against interference. In this paper, we first summarize the composition and working principle of CNC machine tools and analyze the working condition signals generated by CNC machine tools and the sensors that collect the signals and decide to use a multisensor multisignal fusion‐based approach to monitor the machine tool status. It is possible to obtain more effective and valuable information from the observed information through multiple sensors so that the goal of fusion can be achieved. In this paper, a multisensor fusion technique based on wavelet transform and neural network fusion is applied to a machine tool condition monitoring system. The theoretical basis of wavelet analysis and neural network is introduced, and the composition of the condition monitoring system and the process of applying multisensor fusion technology based on wavelet analysis and neural network in the condition monitoring system are given. A complete software and hardware system for online monitoring of CNC machine tools is established. In order to improve the accuracy of the mathematical model, the use of a neural network to fit the nonlinear data and the use of coarse set theory to simplify the relevant data can effectively solve the accurate establishment of the mathematical model in the error compensation method. The thermal error compensation method for CNC machine tools is proposed based on rough set theory, ant colony algorithm, and neural network. This paper first investigates the current development of error compensation technology for CNC machining centers, analyzes the various error sources of CNC machine tools, and finds out the influencing factors affecting the errors of CNC machine tools.