LiMin Zhu

An alternative time-domain index for condition monitoring of rolling element bearings—A comparison study

Abstract Statistical moments have been widely used for detection and diagnosis of rolling element bearing damage. Among them, Kurtosis and Honarvar third moment S r are the major parameters. In this paper a new statistical moment, from the viewpoint of Renyi entropy, is derived, which is shown to be as effective as kurtosis and S r . Comprehensive comparisons of kurtosis, S r and this moment are performed, and the results from simulations and experiments show the new moment has a better overall performance than kurtosis and S r . On the one hand, this moment behaves much like kurtosis but is less susceptible to spurious vibrations, which is considered to be one of the main shortcomings of higher statistical moments including kurtosis. On the other hand, from the viewpoint of sensitivity to incipient faults, which is the major drawback of lower statistical moments including S r , the new moment is superior to S r . Moreover, the sensitivity of this new moment to changes of bearing speed and load is also less than kurtosis and is close to that of S r .

A steepest descent algorithm for circularity evaluation

This paper presents a novel algorithm for evaluating the circularity of a mechanical part by using measurement points obtained with a coordinate measuring machine (CMM). Following the minimum zone criterion set forth in the current ANSI and ISO standards, evaluation of circularity is formulated as a non-differentiable unconstrained optimization problem, and based on the geometric representation of the necessary and sufficient condition for the optimal solution, an efficient steepest descent optimization procedure is proposed to find the circularity value. The steepest descent direction is determined by the method of calculating the minimum translational distance between two convex polygons, which is initially introduced in the field of robot path planning, and the length of the moving step is exactly determined by a presented geometrical method. A computational geometry-based method for pre-processing the measured data is also proposed. In comparison with existing methods, this algorithm has the advantages of computational efficiency and high precision. Simulations and practical example confirm the validity of the presented algorithm.

Application of kinematic geometry to computational metrology: distance function based hierarchical algorithms for cylindricity evaluation

This paper applies kinematic geometry to investigate the problem of determining the cylindricity error of a mechanical part by using measurement points obtained with a coordinate measuring machine. For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its increment with respect to the differential motion of the surface is derived. On this basis, four commonly used cylindricity evaluation methods, i.e., minimum zone cylinder method, maximum inscribed cylinder method, minimum circumscribed cylinder method and least-squares cylinder method, are formulated as nonlinear constrained optimization problems and nonlinear least-squares problem, and efficient sequential approximation algorithms are developed to solve them. For enhancing the performance of the algorithms, two relevant optimization problems and corresponding algorithms, i.e., localization of cylinder and minimum variance fitting of cylinder, are introduced to analytically provide proper initial solutions. By organizing all involved algorithms in a hierarchical structure, four complete cylindricity evaluation algorithms are presented. Comparing with existing methods, they have the advantages of implementational simplicity, computational efficiency and robustness. Examples confirm the validity of the proposed hierarchical algorithms.

Tool path optimisation for flank milling ruled surface based on the distance function

This paper deals with optimised tool path generation for five-axis flank milling using signed point-to-surface distance function. The main idea is that the geometrical deviations between the design surface and the machined surface are minimised by fine tuning the cutter locations. Based on the tangency conditions in envelope theory, the analytic representation of the envelope surface of a cutter undergoing five-axis motion is first obtained. Then the geometrical deviations between the envelope surface (i.e. machined surface) and the design surface are calculated. Optimisation of the five-axis tool path is modeled as the fine tuning of the initial cutter locations under the minimum zone criterion recommended by ANSI and ISO, which requires minimisation of the maximum geometrical deviation between the design surface and the envelope surface. Using the signed point-to-surface distance function, tool path optimisation for finish milling is formulated as a constrained optimisation problem. Based on the first-order Taylor approximation of the signed distance function, two sequential approximation algorithms for the Minimax and Least Square optimisations are developed. Numerical examples, in which a conical tool is chosen as a special case of flank machining ruled surface, verify the proposed strategy.

On a novel approach to planning cylindrical cutter location for flank milling of ruled surfaces

This paper presents a novel approach to planning cylindrical cutter location for flank (or side) milling of ruled surfaces. It contains two steps: tool positioning and re-positioning. In the former step, first an adaptive mesh is constructed on the designed ruled surface with the existing algorithm, and then a sequence of initial cutter locations (CLs) is determined using the offset points of the grid sampled points via semidefinite programming (SDP). In the latter step, a smooth tool axis surface is generated by interpolating the initial CLs using the dual mapping theory; afterwards, the tool is re-positioned by adjusting the offset value of each sampled point on the designed surface according to the predicted cutting errors. The cutter positioning methods for rough and finish milling are both developed in this framework. Example and numerical simulation illustrate the efficiency of the novel strategy.