Spindle Rotation Error Research Articles

Rotation Error Prediction of CNC Spindle Based on Short-Time Fourier Transform of Vibration Sensor Signals and Improved Weighted Residual Network.

The spindle rotation error of computer numerical control (CNC) equipment directly reflects the machining quality of the workpiece and is a key indicator reflecting the performance and reliability of CNC equipment. Existing rotation error prediction methods do not consider the importance of different sensor data. This study developed an adaptive weighted deep residual network (ResNet) for predicting spindle rotation errors, thereby establishing accurate mapping between easily obtainable vibration information and difficult-to-obtain rotation errors. Firstly, multi-sensor data are collected by a vibration sensor, and Short-time Fourier Transform (STFT) is adopted to extract the feature information in the original data. Then, an adaptive feature recalibration unit with residual connection is constructed based on the attention weighting operation. By stacking multiple residual blocks and attention weighting units, the data of different channels are adaptively weighted to highlight important information and suppress redundancy information. The weight visualization results indicate that the adaptive weighted ResNet (AWResNet) can learn a set of weights for channel recalibration. The comparison results indicate that AWResNet has higher prediction accuracy than other deep learning models and can be used for spindle rotation error prediction.

Performance evaluation and comparison of different types of full and partial texture of hydrostatic bearings

To reveal the influence of the different types of surface microtexture on the performance of hydrostatic bearing, microtexture (square, cylindrical, and composite texture) on the inner surface of the bearing were designed. The finite element model of bearing with textures was established. Under the condition of considering the cavitation effect, the influence of the different types of microtexture on performance of the bearing is studied based on the N-S equation. The SEA9 spindle rotation error analyzer is used to determine the eccentricity of the spindle in the machining process and to verify the accuracy of the theoretical simulation. The results demonstrates that the microtexture enhances the performance of hydrostatic bearing, when the eccentricity is in the range of 0∼0.3, compared with square, cylindrica, and smooth bearing, the performance of composite texture bearing can effectively improve the load capacity and reduce the friction coefficient. When the eccentricity is larger than 0.3, the partial textured bearing is analyzed. The initial angle is 120°, the load capacity of the partial microtextured bearing are greater than full microtextured bearing and smooth bearing, which can be used to improve the performance of the bearing. The optimal combination of structural parameters for the performance of the partial composite texture is provided, which has important theoretical significance and practical value for expanding the application range of the spindle system.

Indirect Prediction of Spindle Rotation Error Through Vibration Signal Based on Supervised Local Mean Decomposition Filter Fusion and Bi-LSTM Classification Network

Abstract Spindle rotation error directly correlates with the quality of mechanical processing. Currently, the error was mainly converted through measuring the distance information of standard component installed at the tool position, and it can't complete the normal machining because the tool is occupied. Therefore, a novel self-adaptive supervised learning method through easy-collected vibration signal that don't affect the machining to indirect predict the error. This method includes three steps: First, the original vibration signal is decomposed by local mean decompression (LMD) method to obtain two critical components; subsequently, the two components are fused as a signal by a weighted-average approach; finally, the fused signal and corresponding error are self-adaptive supervised trained by the setting termination condition to modify fusion coefficient and network parameters. The method is used to analyze the data-set of spindle platform, which has collected the experimental data at speeds 1000, 2000, 3000, and 4000 more than 170 groups, and the indirect prediction accuracy reached 94.12%, 92.35%, 97.68%, and 90.59%, respectively. Additionally, the experimental results were compared and demonstrated by three aspects with current different algorithms.

Roundness error separation based on singularity detection and exact-stop of spindle in on-machine measurement of spindle rotation error

At present, non-contact sensors are being extensively used for the measurement of spindle rotation errors. However, as the measuring target of the sensors, the roundness error of the artifact inevitably mixes into the error motion of the spindle. Moreover, the challenging nature of manufacturing high-precision artifacts has resulted in the separation of the roundness error of artifacts from the spindle rotation error being considered an urgent research prospect. In this study, a roundness error separation method based on singularity detection and exact-stop of spindle was proposed to perform on-machine measurement of spindle rotation error, wherein compared to the existing methods, the proposed method implements the Donaldson reversal method. It is independent of the index signal of the spindle encoder, which is usually unavailable on actual machine tools. The singularity of measured motion was detected using the wavelet transform modulus maximum (WTMM) ridges and their Lipschitz exponents, to locate the exact-stop and rotating stages of spindle in the measured motion. Consequently, a WTMM ridge extraction method was established to extract the continuous optimal WTMM ridges of the measured motion. Further, the synchronous motion of the measured motion was used for roundness error separation to promote the separation accuracy. Finally, the effectiveness of the proposed method was verified using the measurement results of a coordinate measuring machine (CMM). Thus, the measurement error caused by the roundness error of the artifact can be reduced significantly by applying the proposed method to the on-machine measurement of the spindle error motion.

Direct compensation of the spindle rotation error with an active hydrostatic journal bearing system

Spindle rotation accuracy is important in machining process. Indirect compensation of spindle rotation error has been widely adopted in the field of machining accuracy improvement. However, there are some limitations on indirect compensation, and a little research on direct compensation can be found. This article utilizes active lubrication technology to improve the spindle rotation accuracy. Hydrostatic journal bearing with control recesses and servo valve drove by piezoelectric ceramics are adopted to compose the compensation element. The simple control strategy PID is adopted to provide control signal for servo valve. Both simulation and experiment are designed and conducted. The results show that proposed bearing system has the ability to improve the spindle rotation accuracy.

A virtual parallel two-point roundness error measurement system

As a typical artifact in machining, the roundness of shaft artifacts is an important tolerance standard. How to measure with high precision in ultra-precision machining is a difficult point. At present, the three-probe method is the most widely used method to measure spindle rotation error and artifact roundness error, which has the advantage of on-machine measurement, but the three-probe method has the critical problem of harmonic suppression. To completely separate the spindle error when measuring the roundness of the artifact, a new virtual parallel two-point measurement system is proposed in this paper. The probe is fixed on the flexible hinge stage, which is driven by a voice coil motor so that the measurement function of two probes can be realized only by using a single probe. Detailed numerical analysis and simulation analysis have been carried out to verify that the method can completely separate the spindle error in theory. Finally, the accuracy of the measurement system is tested through experiments. The new method results are compared with the single-point scanning method without error separation and the high-precision roundness instrument Talyrond 585LT. The comparison results show that the new method can separate the rotation error of the spindle and can improve the roundness measurement accuracy.

Prediction of Spindle Rotation Error through Vibration Signal based on Bi-LSTM Classification Network

One of the important indexes for high-precision machine tools is spindle rotation error, which is closely related to mechanical processing product quality. However, it’s difficult to directly acquire rotation error in the actual machining process. This literature proposed a novel uncompressed approach to predict spindle rotation error through vibration signal based on Bi-LSTM classification network, and this approach mainly consists of three steps, namely, pretreating original data; training Bi-LSTM classification network; predicting spindle rotation error. This approach adopts an uncompressed vibration signal method, which retains the time characteristic information into the predicted network, to build the relationship between easily collected vibration signal and the spindle rotation error. Finally, the proposed approach is applied in a spindle test rig, which has accomplished over 1700 hours of simulated load abrasion, and collected 170 days’ vibration signal and corresponding rotation error at RPM=1000, 2000, 3000, and 4000 conditions. The results show the proposed approach can effectively predict the spindle rotation error.

Uncertainty evaluation and reduction in three-probe roundness profile measurement based on the system transfer function

The three-probe method for separating the spindle rotation error and the specimen form error is extensively described in the literature. An attractive feature is its application in in-process measurement. However, the resulting uncertainty is studied far less extensively. In this paper, an evaluation and propagation method for the uncertainty, as well as for an uncertainty reduction, is given based on the system transfer function (S-function). First, utilizing the Laplace transform, the measurement system model is developed and expressed by an S-function. Second, the propagation laws of input uncertainties are analytically deduced by computing the partial derivatives of the S-function of roundness. Then, the laws are numerically validated by Monte Carlo simulations. The uncertainty propagation laws show that the uncertainties propagate with varying amplification over the harmonic domain, and moreover, they enable the quantification of both the harmonic and the total uncertainty of roundness. Taking the roundness uncertainty as a decisive parameter, three approaches are proposed for uncertainty reduction: (1) the hybrid 3-PM, where two roundness estimates are combined by taking individual harmonic estimate with the lowest uncertainty, (2) the fusion 3-PM, where the weighted average is taken over the harmonic domain, and (3) the angle optimization, which minimizes the total roundness uncertainty by properly arranging the sensor angles. The angle optimization is applied to the conventional 3-PM, as well as to the hybrid and the fusion 3-PMs. The genetic algorithm is adopted to speed up the optimization process. Finally, practical roundness measurements are performed.

Diagnostic of spindle units on rolling bearings based on measuring of the housing vibrations

The analysis of modern methods of accuracy and technical condition evaluation of spindle units on rolling bearings has been performed. The prospectivity of measurements in the resonant vibrations zones is assessed. To evaluate the accuracy and technical condition of spindle units on rolling bearings at the stages of manufacturing and maintenance, it is proposed to use the previously developed method for indirect measurement of resonance vibrations of the spindle, based on spindle quill vibration measurement of the spindle units with subsequent calculation of spindle vibrations (mandrel installed in the spindle) using theoretical compliance function. Usage of this method in accuracy and diagnosing defects identification in manufacturing and assembly of the spindle units, a theoretical justification of the measurement schemes is given, the dynamic model of the test rig is adapted, and the corresponding research methods are developed. The general experimental part of research methods provides for: determining the first natural frequency of the test rig frame; determination of spindle speeds corresponding to frame resonant vibrations as a result of manifestation of manufacturing and assembling defects of the spindle unit; spindle quill vibrations measurement at these rotational speeds. The general theoretical part of the methods assumes: the calculation of dynamic compliance and the compliance function which connects mandrel and spindle quill subsystems vibrations; mandrel vibration spectra calculation from the experimental vibration spectra of the spindle quill and determination of the relative vibrations amplitudes of the mandrel at the forced vibrations characteristic frequencies. Based on the results, depending on the task, a 3D spectrum of vibrations or a spindle rotation error diagram in a given range of rotation frequencies is calculated. The results of evaluating the accuracy and technical condition of the grinding head at idle and under load are presented.

Four-Point Method in the Measurement and Separation of Spindle Rotation Error

For the spindle of machine tool, rotation error is a main factor affecting the machining quality, so many investigations have been focused on the measurement of the rotation error. In this article, a measurement and separation method of the rotation error is proposed to extract the orbit of spindle section center and to quantize the rotation error with a special measurement system. Thereinto, systematic measurement strategy has been especially designed to achieve the measurement and analysis of the rotation error. When the measurement does not conform to the small error conditions, the method can reduce the noise level from sensors and improve measurement accuracy in measuring the orbit of spindle section center. When it is necessary to accurately quantify the rotation error and the roundness error, the method also can effectively separate them with independent coordinate system and sensor bracket. Additionally, considering the effect of high temperature on spindle, the method can reduce the form error caused by thermal expansion in the measurement process, which is very important in industrial online measurement. Finally, the theoretical analyses are shown good agreement with experimental results, and these also reveal that it is an effective measurement method for the rotation error.

Characterization and Evaluation of Rotation Accuracy of Hydrostatic Spindle under the Influence of Unbalance

The paper studies the characterization and evaluation technology of rotation accuracy of hydrostatic spindle under the influence of unbalance. The dynamic model of the motion error of the hydrostatic spindle is established based on the dynamic parameters. The variation law of motion error of spindle rotor is analyzed under the unbalanced mass. The paper finds that with the increase of the spindle speed, the amplitude of the spindle error motion will increase, and the inclination angleθerror is more sensitive to the change in the rotational speed. In the total synthesis accuracy, the proportion of synchronization error decreases with the increase of the rotational speed. Finally, the least squares evaluation algorithm is used to evaluate the rotation error of the hydrostatic spindle, and a method for evaluating the rotation accuracy of the hydrostatic spindle with high calculation accuracy and calculation efficiency is proposed.

Influence of microscale effect on the radial rotation error of aerostatic spindle

This paper presents the influence of the microscale effect on the radial rotation error of aerostatic spindle, which is determined by the corresponding stiffness, damping, and unbalance mass. A microscale gas film flow model is used to simulate the static performance of the aerostatic bearing by introducing the microscale effect factor Q in this paper. Firstly, the radial stiffness and damping coefficients of aerostatic bearing were calculated considering microscale effect factor Q, therefore, the position of the rotating shaft in radial plane was deduced, and the corresponding rotation error was obtained. Finally, the simulation results of the stiffness and radial rotation error were verified by the experiment on the shaft test table, and the motion orbit was measured by a displace sensor with a high precision standard ball. The experimental results indicated that the simulated result considering the microscale effect factor Q was more consistent with the actual experimental value, which provided a reference for the design and optimization of the aerostatic spindle.

Analysis of aerostatic spindle radial vibration error based on microscale nonlinear dynamic characteristics

This paper presents a method of predicting the radial rotary error of an aerostatic spindle based on the microscale-effect to investigate the influence of gas film fluctuation on the rotation accuracy of the aerostatic spindle. First, the gas bearing of the spindle is simplified as a spring-damping system with two degrees of freedom perpendicular to each other. Additionally, the aerostatic spindle bearing-rotor system is established by considering the forced vibration and deflection vibration of the rotor. Subsequently, the microscale-effect is introduced into the dynamic model of the gas film flow, and the dynamic Reynolds equation of the gas film is established in the microscale. Moreover, the nonlinear dynamic stiffness and dynamic damping coefficient are obtained by the perturbation method. The nonlinear dynamic parameters in the microscale are introduced into the dynamic model of the bearing-rotor system and all the vibration errors are obtained. By comparison with the conventional case, it is found that the spindle gyration error increased and that the response delay occurred when the microscale-effect is considered. Moreover, the influence of the supply pressure and speed on the vibration of the spindle is also analyzed. An experiment measuring the spindle rotation error is carried out. The experimental results reveal that the prediction method of the nonlinear spindle rotation error in the microscale is more accurate, and that the errors are 5.8% and 9.6%.

Measurement of Spindle Tilt Error Based on Interference Fringe

The spindle rotation error is one of the important factors that affect the precision of the machined parts. The study of spindle rotation error is of great significance for finding the source of error, predicting the surface shape error of machining parts and improving the machining accuracy of ultra-precision machine tools. The structural of the aerostatic spindle this article focuses on is motorized spindle and the spindle tilt error has the maximum effect on the machining precision. A new method for measuring the rotation error of ultra-precision aerostatic spindle based on interference fringes is proposed in this paper. By using the principle of phase shifting interferometry, the mathematical model between the shape of interference fringes and the motion law of the spindle rotor is established by theoretical modeling. The interference fringes are processed with gray, smooth filtering, expansion corrosion, and edge detection and so on. The distance and direction of the interference fringes are calculated in the coordinate system, so as to get the spindle tilt error. Finally, the measurement system for the spindle rotation error of the aerostatic spindle is developed. The accuracy and effectiveness of this method are shown based on the experimental results.

Measurement and analysis of the radial motion error of aerostatic ultra-precision spindle

The measurement of the rotation error of an aerostatic ultra-precision spindle is critically important to evaluate and hence ensure the precision of machine tools. The Donaldson reversal method, which was taken as the efficient method for error separation theoretically, has been widely used to separate shape errors of standard artifact. However, the accuracy analysis of the Donaldson reversal method has not been fully studied and understood. In this study, a nanometer system for measuring the radial rotation error of aerostatic ultra-precision spindle was constructed based on the Donaldson reversal method. The comparative experiments were carried out to investigate the effects of the motor drive, and an angle correction algorithm was proposed to alleviate the effect of angle deviation. The method of harmonic analysis was applied to investigate the effect of artifact eccentricity, and the relationship between the axial motion and measuring error was also studied. The measuring accuracy can be improved by reducing the cogging torque of motor, the angle deviation, artifact eccentricity and spindle axial motion. Experimental results showed that the measurement uncertainty of both the spindle rotation error and artifact form error can be controlled in nanometer level. Besides, the separated value of the artifact form error was very close to the nominal roundness, which verifies the accuracy of the measurement system and the validity of the error separation method.

Investigation of non-uniform preload on the static and rotational performances for spindle bearing system

In order to eliminate the deflection of spindle under external loading, a new non-uniform preload for spindle bearing system is proposed in this paper, and the effect of non-uniform preload on the static and rotational performances of the spindle system is explored both theoretically and experimentally. Seeking to reveal the role of non-uniform preload in spindle static and rotational performances under external radial loading, the equivalent transformation model is firstly built to simplify the non-uniform preload applied on the bearing. Then a simulation model is employed to analyze the variable static and rotational performances of spindle under different preload conditions. A test rig is designed to equip with spindle bearing system, inside which the measurement system is arranged to experimentally investigate how the spindle static and rotational accuracy are influenced by non-uniform preload, varying external load and rotating speeds. The results under different preload conditions show that the non-uniform preload with reasonable equivalent magnitude and direction can effectively adjust the spindle rotating center and compensate the spindle rotation error, and thus improves the rotational accuracy of the spindle system under complicated and alternating working conditions. This provides a new compensation method to the spindle deflection and rotational motion error through adjusting the non-uniformly distributed preload on the spindle bearing system.

Cylindricity Error Measuring and Evaluating for Engine Cylinder Bore in Manufacturing Procedure

On-line measuring device of cylindricity error is designed based on two-point method error separation technique (EST), which can separate spindle rotation error from measuring error. According to the principle of measuring device, the mathematical model of the minimum zone method for cylindricity error evaluating is established. Optimized parameters of objective function decrease to four from six by assuming thatcis equal to zero andhis equal to one. Initial values of optimized parameters are obtained from least square method and final values are acquired by the genetic algorithm. The ideal axis of cylinder is fitted in MATLAB. Compared to the error results of the least square method, the minimum circumscribed cylinder method, and the maximum inscribed cylinder method, the error result of the minimum zone method conforms to the theory of error evaluation. The results indicate that the method can meet the requirement of engine cylinder bore cylindricity error measuring and evaluating.

Rotation error measurement technology and experimentation research of high-precision hydrostatic spindle

The hydrostatic spindle is widely applied in the field of high-precision machine tools, which has some advantages such as high stiffness, high rotary precision, and the high damping shock absorption. The spindle rotation error is an important index to measure the machining accuracy of machine tools. Due to the installing eccentric error of the test bar, conventional method based on the standard test bar to measure the rotation error indirectly is applied to the precision machine tools and common machine tools whose rotation error is greater than 1 μm only. In order to eliminate the installing eccentric error of the standard test bar, it presents a self-reference approach that takes the online finish turning test bar, rather than that of the standard test bar, as the measuring datum. Using the capacitive micro-displacement sensor and the LMS data acquisition equipment as the test platform, it designs a set of spindle rotation error measurement system. Then it studies the frequency domain three-point method and has the rotation error and roundness error of high-precision hydrostatic spindle separated. Experimental study shows that the rotation error and the roundness error of the spindle are 0.9 and 0.3 μm, respectively, under the circumstance of conventional standard test bar as the measuring datum. However, if it takes the online finish turning test bar as the measuring datum, the rotation error and the roundness error of the spindle are only 0.3 and 0.1 μm, respectively. The self-reference method is able to eliminate the installing eccentric error of standard test bar directly, and the measurement system has realized the accurate measurements of the rotation error and roundness error of the high-precision hydrostatic spindle.

Single-step spatial rotation error separation technique for the ultraprecision measurement of surface profiles

To improve the measurement accuracy of the profilometer for large optical surfaces, a new single-step spatial rotation error separation technique (SSEST) is proposed to separate the surface profile error and spindle spatial rotation error, and a novel SSEST-based system for surface profile measurement is developed. In the process of separation, two sets of measured results at the ith measurement circle are obtained before and after the rotation of error separation table, the surface profile error and spatial rotation error of spindle can be determined using discrete Fourier-transform and harmonic analysis. Theoretical analyses and experimental results indicate that SSEST can accurately separate spatial rotation error of spindle from the measured surface profile results within the range of 1-100 upr and improve the accuracy of surface profile measurements.

Error analysis of compensation cutting technique for wavefront error of KH2PO4 crystal

Considering the wavefront error of KH(2)PO(4) (KDP) crystal is difficult to control through face fly cutting process because of surface shape deformation during vacuum suction, an error compensation technique based on a spiral turning method is put forward. An in situ measurement device is applied to measure the deformed surface shape after vacuum suction, and the initial surface figure error, which is obtained off-line, is added to the in situ surface shape to obtain the final surface figure to be compensated. Then a three-axis servo technique is utilized to cut the final surface shape. In traditional cutting processes, in addition to common error sources such as the error in the straightness of guide ways, spindle rotation error, and error caused by ambient environment variance, three other errors, the in situ measurement error, position deviation error, and servo-following error, are the main sources affecting compensation accuracy. This paper discusses the effect of these three errors on compensation accuracy and provides strategies to improve the final surface quality. Experimental verification was carried out on one piece of KDP crystal with the size of Φ270 mm×11 mm. After one compensation process, the peak-to-valley value of the transmitted wavefront error dropped from 1.9λ (λ=632.8 nm) to approximately 1/3λ, and the mid-spatial-frequency error does not become worse when the frequency of the cutting tool trajectory is controlled by use of a low-pass filter.