The localized faults of rolling bearings can be diagnosed by the extraction of the impulsive feature. However, the approximately periodic impulses may be submerged in strong interferences generated by other components and the background noise. To address this issue, this paper explores a new impulsive feature extraction method based on the sparse representation. According to the vibration model of an impulse generated by the bearing fault, a novel impulsive wavelet is constructed, which satisfies the admissibility condition. As a result, this family of model-based impulsive wavelets can form a Parseval frame. With the model-based impulsive wavelet basis and Fourier basis, a convex optimization problem is formulated to extract the repetitive impulses. Based on the splitting idea, an iterative thresholding shrinkage algorithm is proposed to solve this problem, and it has a fast convergence rate. Via the simulated signal and real vibration signals with bearing fault information, the performance of the proposed approach for repetitive impulsive feature extraction is validated and compared with the noted spectral kurtosis method, the optimized spectral kurtosis method based on simulated annealing, and the resonance-based signal decomposition method. The results demonstrate its advantage and superiority in weak repetitive transient feature extraction.

A New Family of Model-Based Impulsive Wavelets and Their Sparse Representation for Rolling Bearing Fault Diagnosis

Benefits for your Students • Access to ASME student competitions/E-Fests, scholarships, internships and more • Exposure to the engineering community and real world situations, in and out of the classroom • Technical information & interactive tools to help with coursework and research • Mentoring by an experienced professional • Networking in person & online, locally & worldwide • Valuable relationships that can last a lifetime • Easy application process with no additional costs Benefits for your School • Supplements your curriculum and coursework • Provides targeted and relevant experiences beyond the classroom • Keeps you connected to the latest trends and industry developments • Offers exposure to international issues & perspectives • Exemplifies your exceptional commitment to your program and your students • Easy program administration, and the convenience of making a single payment

American Society of Mechanical Engineers (ASME)

This paper presents a new S trajectory kinematic measurement method to evaluate the dynamic accuracy of five-axis machine tools based on R-test measurements. The S trajectory is obtained by scaling the machining path of the S-shaped test piece to the measuring stroke of the R-test. A geometric and dynamic accuracy simulation model is established to analyze the influence of various error factors on the S trajectory test and compare with the conical kinematic test described in ISO10791.6 quantitatively. The simulation results shown that the S trajectory test is more sensitive to most geometric errors and dynamic errors than the conical test. Particularly, to reflect the dynamic error factors such as poor rigidity of machine tools, servo mismatch, reverse error and nonlinear error, the S trajectory test has obvious advantages. Meanwhile, compared with the actual S-shaped piece machining, which is under development for inclusion in ISO 10791.7, the proposed non-cutting kinematic test method can simply reflect the dynamic accuracy of five axis machine tools itself without the interference of other factors and does not require additional workpiece and testing equipment. The proposed method is verified through experiments on a five-axis machine tool.

Dynamic accuracy evaluation for five-axis machine tools using S trajectory deviation based on R-test measurement

The modelling of volumetric errors of machine tools has been widely used by the method of Homogeneous Transformation Matrix (HTM) based on rigid body kinematics analysis for a long time. Without spindle induced errors and thermal errors, to establish a closed-loop HTM for a three-axis machine tool, the total of 21 geometric errors are the primary elements to be known. It is well known that the measured points of translational errors are directly related to the volumetric error at the tool cutting point through rigid body kinematics. In the generalized HTM method, however, this relationship is missing. This report, therefore, proposes a new comprehensive approach to formulate the volumetric errors based on the famous Abbe principle in order to derive the error term in the motion direction, and Bryan principle to derive the error terms in orthogonal to the motion direction. The proposed methodology is simple in concept, rational in physical meaning and easy in implementation. Experimental results, including faster multi-degree-of-freedom error measurements, volumetric error analysis and compensation on a testbed of small machine tool, validate the correctness and effectiveness of this method.

A novel modeling of volumetric errors of three-axis machine tools based on Abbe and Bryan principles

The dynamic error of CNC machine tools, which often exceeds the quasi-static error at high-speed machining, becomes the main reason affecting the machining error of the sculptured surface parts. Although much research efforts have been dedicated to dynamic error, there is a lack of systematical summaries. In this review, firstly, the dynamic error is defined as the deviation of actual displacement of effector end of axis relative to reference displacement during feed motion. Secondly, according to the mechanical and control structure of the servo feed system, the dynamic error is divided into two components: dynamic error inside the servo loop (component 1) and dynamic error outside the servo loop (component 2). Based on the two components, the causes resulting in the dynamic error are analyzed from the points of view of the servo feed system itself and its input (setpoints). Thirdly, the basic strategies for reducing the dynamic error of individual axis, as well as for reducing the trajectory dynamic error by coordinating the dynamic error of individual axis, are summarized. Finally, the problems and future research directions on dynamic error are analyzed. It is concluded that resolving the contradiction between the setpoints and the servo feed system is still a great challenge for dynamic error in high-speed machining. To achieve high dynamic accuracy at high-speed machining, the control strategies on the dynamic error outside the servo loop should be further developed and integrated into dynamic error inside the servo loop-oriented control strategies. Meanwhile, the servo feed system itself and its input need to be investigated as a whole, so that the servo feed system of each axis can adapt to the differences and changes of the setpoints, and the differences in the servo dynamics of each axis can be considered in the setpoints.

Dynamic error of CNC machine tools: a state-of-the-art review

The manufacturing test part applications are essential for representations of machines’ capabilities. Commonly used NAS979 has been known to insufficiently evaluate the combination motions of rotary axes. Thus, a new test part, S part, has been presented to satisfy the increasing demand of a five-axis machine. In this paper, the model of S part is described in detail, which presents more characteristics in three-dimensional surface contours. According to the kinematics analysis, the speed of each axis and feed rate falls down and rises up on several positions. Each axis reverses the motion during the machining. Therefore, the S part makes high requirement on machine’s dynamic response.

A new test part to identify performance of five-axis machine tool—part I: geometrical and kinematic characteristics of S part

A new test part, the S part, has been further discussed on its validation. Researches have shown dynamic errors, especially for follow-up errors that mainly contribute to dimensional errors of the S part. The models of mechanical system, servo system, are set up to find out the key dynamic machine factors. Coupled with the motions of five axes, the follow-up errors, the actual positions of the tool center, and the contouring error are calculated, which are used to analyze the effect of factors. Results show that different machine factors have different error curves on the S part surface. So the algorithm to track the cause of the processed error has been developed. Then, the S part cutting experiments are carried out to testify the analysis results. Both analysis and experiment results have a good agreement. Finally, the characteristics of the S part are compared with the commonly used test part NAS979. Obviously, the S part presents more machine abilities than NAS979, which test well the performance of a five-axis machine center.

A new test part to identify performance of five-axis machine tool-Part II validation of S part

In this paper, a convenient way to detect machining precision of five-axis CNC machine tool is suggested in theory. In a general way, NAS979 is cut to test machine tool; however, it fails to evaluate the combination motions of rotary axes sufficiently. Therefore, a novel S-shape test part, called ‘S’ test piece, has been presented to demonstrate the machine tool’s capabilities. As a new test specimen, ‘S’ test piece has some advantage to exhibit the machining precision of five-axis machine tool. There are some visible marks related to performance of machine tool experimentally, however, the reasons for these abnormal marks are uncertain theoretically, the performance of the servo system may be one of the causes. In order to figure out the definite cause of the abnormal morphology, a simulated platform with the servo system is set up to amplify and the normal errors that come from the tracking of axes are presented. The simulation results of the abnormal morphology of ‘S’ test piece is provided. And the surface quality is evaluated by the peak-to-peak value (Vpp). There are obvious marks in four special regions of ‘S’ test piece that simulated with poor performance servo system, and these marks are invisible in the surface of ‘S’ test piece that simulated with good performance servo system. Vpp in these four regions changes greater than the other regions of ‘S’ test piece. The Vpp that simulated by the poor performance servo system is about 15 times larger than the error simulated by the optimized performance servo system in these four special regions. While, Vpp of other regions is essentially invariant. Then, the machining experiments of ‘S’ test piece are conducted with the standard suggested process. The abnormal morphology of machined ‘S’ test piece is so obvious that it can be observed by the naked eyes, without any test equipment. And the result of the experiment is consistent with the simulation result, which means that tracking errors of servo system have direct influence on surface morphology abnormality, and the surface quality of ‘S’ test piece could display the dynamic performance of the servo system intuitively in theory. As a standard comparison object, the surface quality of NAS979 test piece is analyzed through the same platform with the poor performance servo system, the largest Vpp is about 0.00022 mm, one eightieth smaller than ‘S’ test piece at least. And machining experiment is also carried out with the poor performance machine tool, the surface is so smooth that unexpected texture cannot be observed by the naked eyes, it should be test by the special measurements. The simulation results and experiment results both show that the surface quality of ‘S’ test piece is hugely worse than NAS979. Besides, there are several special regions of ‘S’ test piece to exhibit the surface texture waving with certain parameters. In a word, ‘S’ test piece is high effectively to exhibit the dynamic performance of the servo system of five-axis machine tool.

Modeling and simulation of surface morphology abnormality of ‘S’ test piece machined by five-axis CNC machine tool

To improve the machine tool accuracy, geometric error identification is required for volumetric error compensation. This paper presents a method for the geometric error identification of a five-axis machine tool that considers the optimised distribution of measurement points and accurate description of geometric errors. The measurement is performed using a laser tracker that permits rapid error data collection over a large measurement range. In the volumetric error modelling, the geometric errors are described as position-dependent Chebyshev polynomials. Hence, the identification of geometric errors is converted into the identification of polynomial coefficients. In the identification process, a distribution method for measurement points is proposed to improve the identification accuracy by minimising the influence of measurement error on the identification result. At the same time, an adaptive approach is introduced to accurately define the polynomial orders of geometric errors to improve the identification accuracy. Simulations and experiments are conducted to verify the geometric error identification method. In addition, the proposed method is compared with other methods. Based on the identification result of geometric errors and the volumetric error model, the volumetric error of any position in a workspace can be predicted and further compensated.

Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process

Geometric errors have a comprehensive influence on the volumetric error of the five-axis machine tool. The identification of the vital geometric errors that have major effect on the volumetric error is the key problem to improve the machine tool accuracy. Therefore, a sensitivity analysis method to identify the vital geometric errors is proposed in this paper. The volumetric error model of a five-axis machine tool with 41 geometric errors is established based on the multi-body system method. Through the projection of the error vectors and the introduction of the effective cutting length, LSIL and GSIL are defined as the sensitivity indices for the local and global sensitivity analysis, respectively. Simulations are conducted for the local and global sensitivity analysis in which the LSIL and GSIL are used. And the analysis results have proven the validity of the proposed sensitivity analysis method. Compared with the conventional sensitivity analysis method, the proposed sensitivity analysis method has considered the position and posture error of the cutting tool simultaneously, which is more effective and efficient. The analysis results are helpful to improve the accuracy of the five-axis machine tool.

Zhong Jiang

Papers

A new test part to identify performance of five-axis machine tool—part I: geometrical and kinematic characteristics of S part

A new test part to identify performance of five-axis machine tool-Part II validation of S part

Modeling and simulation of surface morphology abnormality of ‘S’ test piece machined by five-axis CNC machine tool

Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process

A sensitivity method to analyze the volumetric error of five-axis machine tool