Qiang Cheng

A product module identification approach based on axiomatic design and design structure matrix

In terms of creating customized products rapidly, modularity is deemed to be an effective developmental strategy for handling product variety and intricacy. In order to develop reasonable modular product architecture with physically detachable modules, a new systematic and structured approach for product modularization based on axiomatic design and design structure matrix is proposed. The product is decomposed hierarchically into its functional, physical, and process domains using axiomatic design method. After transformation from design matrix to design structure matrix, the pertinence design structure matrices of design parameters describing function, structure, and manufacturing process are constructed. Besides, a manufacturing process similarity matrix of design parameters is established. Finally, a genetic algorithm combined with the minimal description length is employed to realize the modularization optimization after integration of the above matrices. To illustrate the effectiveness of the proposed methodology, an indoor air conditioner unit is presented as a demonstrative example.

An Analysis Methodology for Stochastic Characteristic of Volumetric Error in Multiaxis CNC Machine Tool

Traditional approaches about error modeling and analysis of machine tool few consider the probability characteristics of the geometric error and volumetric error systematically. However, the individual geometric error measured at different points is variational and stochastic, and therefore the resultant volumetric error is aslo stochastic and uncertain. In order to address the stochastic characteristic of the volumetric error for multiaxis machine tool, a new probability analysis mathematical model of volumetric error is proposed in this paper. According to multibody system theory, a mean value analysis model for volumetric error is established with consideration of geometric errors. The probability characteristics of geometric errors are obtained by statistical analysis to the measured sample data. Based on probability statistics and stochastic process theory, the variance analysis model of volumetric error is established in matrix, which can avoid the complex mathematics operations during the direct differential. A four-axis horizontal machining center is selected as an illustration example. The analysis results can reveal the stochastic characteristic of volumetric error and are also helpful to make full use of the best workspace to reduce the random uncertainty of the volumetric error and improve the machining accuracy.

Geometric accuracy allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory

Machining accuracy of a machine tool is influenced by geometric errors produced by each part and component. Different errors have varying influence on the machining accuracy of a tool. The aim of this study is to optimize errors to get a desired performance for a numerical control machine tool. Applying multi-body system theory, a volumetric error model was constructed to track and compensate effects of errors during operation of the machine, and to relate the functional specifications on volumetric accuracy to the permissible errors on the joints and links of the machine. Error sensitivity analysis was used to identify the influence of different errors (especially the errors which have large influences) on volumetric error. Based on First Order and Second Moment theory, an error allocation approach was developed to optimize allocation of manufacturing and assembly tolerances along with specifying the operating conditions to determine the optimal level of these errors so that the cost of controlling them and the cost of failure to meet the specifications is minimized. The approach developed was implemented in software and an example of the geometric errors budgeting for a five-axis machine was discussed. It is identified that the different optimal standard deviations reflect the cost-weighted influences of the respective parameters in the equations of the functional requirements. This study suggests that it is possible to determine the coupling relationships between these errors and optimize the allowable error budgeting between these sources.

An Analytical Robust Design Optimization Methodology Based on Axiomatic Design Principles

Robust design (RD) is an important method because it can reduce the variation of products or processes and improve their performances such as static and dynamic quality characteristics at a low cost. In order to obtain an efficient and universal RD solution, a novel analytical RD methodology is proposed based on axiomatic design principles. The covariance matrix of multiple functional requirements (FRs) that can reflect dependency relationship is obtained via the Talyor series expansion. Evaluation mechanism based on information axiom is introduced to select the better design scheme gained with different robust optimization models. The distinct characteristics of the proposed method are the implementation by matrix differential, and the ability that can deal with multiple FR optimization simultaneously. An RD optimization of a five roller coating head is illustrated. The results show that the proposed method can optimize the design parameters which meet the multiple FRs. Copyright

Fluctuation prediction of machining accuracy for multi-axis machine tool based on stochastic process theory

Geometric error has significant influence on the processing results and reduces machining accuracy. Machine tool geometric errors can be interpreted as a deterministic value with an uncertain fluctuation of probabilistic distribution. Although, the uncertain fluctuation can not be compensated, it has extremely profound significance on the precision and ultra-precision machining to reduce the fluctuation range of machining accuracy as far as possible. In this paper, a typical 3-axis machine tool with high precision is selected and the fluctuations in machining accuracy are studied. The volumetric error modeling of machine tool is established by multi-body system (MBS) theory, which describes the topological structure of MBS in a simple and convenient matrix form. Based on the volumetric error model, the equivalent components of the errors for the three axes are established by reducing error terms. Then, the fluctuations of equivalent errors and the machining accuracy in working planes are depicted and predicted using the theory of stochastic process, whose range should be controlled within a certain confidence interval. Furthermore, the critical geometric errors that have significant influence on the machining accuracy fluctuation are identified. Based on the analysis results, some improvement in the machine tool parts introduced and the results for the modified machine show that the prediction allow for reduction in errors for the precision and ultra-precision machining.

Surface fractal topography-based contact stiffness determination of spindle-toolholder joint

Accurate modeling of contact stiffness is crucial in predicting the dynamic behavior and chatter vibration of spindle–toolholder system for high-speed machining centers. This paper presents a fractal theory-based contact model of spindle–toolholder joint to obtain the contact stiffness and its real contact area. Topography of the contact surfaces of spindle–toolholder joint is fractal featured and determined by fractal parameters. Asperities in micro-scale are considered as elastic or plastic deformation. Then, the contact stiffness, the real contact area, the elastic contact force, and the plastic contact force of the whole contact surface are calculated by integrating the micro asperities. The relationship of the contact stiffness and the drawbar force follows a power law, in which the power index is determined by the fractal parameters. Experiments are conducted to verify the efficiency of the proposed model. The results from the fractal contact model of spindle–toolholder joint have good agreement with those of experiments.

Robust geometric accuracy allocation of machine tools to minimize manufacturing costs and quality loss

With increasing demands of machining accuracy, designing of machine tools for satisfactory performance using cost-effective geometric accuracy configurations is becoming a complex problem to the machine tool manufacturers. In this paper, a novel robust accuracy allocation method is proposed for multi-axis machine tools based on multi-objective quality and cost trade-offs. To model the volumetric accuracy of machine tool based on geometric errors, the multi-body system theory was introduced. A manufacturing cost model for the machine tool components with a significant effect on geometric errors was established based on the machining features. The quality loss of the machine tool was also integrated into a single optimization objective. After identifying the relationship between the accuracy grade parameters of the feeding components and the geometric errors, the maximum in the Euclidean norm of all the accuracy parameters was defined as another optimization objective. The robust accuracy allocation was performed using Isight software and the Non-Dominated Sorting Genetic Algorithm-II built in the MATLAB. The optimization results for a four-axis horizontal machining center showed that the proposed method can realize the optimization of geometric accuracy and can determine the optimal accuracy grade of the feeding components satisfying the machining accuracy requirements.

A product modular design method based on axiomatic design

In order to develop reasonable modular product architecture with physically detachable modules, a new systematic method for product modularization is proposed based on axiomatic design (AD). In the proposed method, the product is decomposed hierarchically in its functional, physical and process domains according to AD. After the transformation from design matrices to design structure matrices, the correlation design structure matrices of design parameters about function, structure and manufacturing process are constructed. Finally, a genetic algorithm combined with the minimal description length is introduced to solve the modularization optimization problem. To illustrate and validate the effectiveness of the proposed methodology, an indoor air conditioner unit is presented as a demonstrative example.

Characteristics evaluation of gas film in the aerostatic thrust bearing within rarefied effect

The characteristic of gas film is a key factor in the performance of the aerostatic bearing. Because the gas film flow is in the slip regime, influence of the rarefied effect is significant. The modified Reynolds equation suitable for compressible gas in the rarefied effect is deduced through introducing the flow factor in the rarefied effect to the Reynolds equation. Pressure distribution, capacity, and stiffness of the gas film under the rarefied effect are analyzed. With the increase of gas pressure, the gas film capacity and stiffness of bearing would also increase. However, the greater the gas supply pressure, the more intense the gas film vibration, so it was important to select a reasonable gas supply pressure for achieving the optimal gas film characteristic. Finally, the gas rarefied effect is verified by the experiment indirectly, which agreed well with the analytical results and provided a theoretical guidance for the machining accuracy of the machine tool.

Contact characteristic analysis of spindle–toolholder joint at high speeds based on the fractal model:

Due to the influence of centrifugal force, accurate contact stiffness model of spindle–toolholder joint at high speeds is crucial in predicting the dynamic behavior and chatter vibration of spindle–toolholder system. In this paper, a macro–micro scale hybrid model is presented to obtain the contact stiffness of spindle–toolholder joint in high speeds. The hybrid model refers to the finite element model in macro-scale and three-dimensional fractal model in micro-scale. The taper contact surface of spindle–toolholder joint is assumed flat in macro-scale and the finite element method is used to obtain the pressure distribution at different speeds. In micro-scale, the topography of contact surfaces is fractal featured and determined by fractal parameters. Asperities in micro-scale are considered as elastic and plastic deformation. Then, the contact ratio, radial and torsional contact stiffness of spindle–toolholder joint can be calculated by integrating the micro asperities. Experiments with BT40 type toolholder–spindle assembly are conducted to verify the proposed model in the case of no speed. The reasonable intervals of spindle speed and drawbar force can be obtained based on the presented hybrid model, which will provide theoretical basis for the application and optimization of the spindle–toolholder system.