Ligang Cai

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 Improved Force Feedback Control Algorithm for Active Tendons

An active tendon, consisting of a displacement actuator and a co-located force sensor, has been adopted by many studies to suppress the vibration of large space flexible structures. The damping, provided by the force feedback control algorithm in these studies, is small and can increase, especially for tendons with low axial stiffness. This study introduces an improved force feedback algorithm, which is based on the idea of velocity feedback. The algorithm provides a large damping ratio for space flexible structures and does not require a structure model. The effectiveness of the algorithm is demonstrated on a structure similar to JPL-MPI. The results show that large damping can be achieved for the vibration control of large space structures.

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.

Stiffness Identification of Spindle-Toolholder Joint Based on Finite Difference Technique and Residual Compensation Theory

The chatter vibration in high-speed machining mostly originates from the flexible connection of spindle and toolholder. Accurate identification of spindle-toolholder joint is crucial to predict machining stability of spindle system. This paper presents an enhanced stiffness identification method for the spindle-toolholder joint, in which the rotational degree of freedom (RDOF) is included. RDOF frequency response functions (FRFs) are formulated based on finite difference technique to construct a completed spatial FRF for the joint, where the measured data can be obtained from the piezoelectric acceleration sensors. In order to depress the influence of “modal truncation” and measurement noises, residual compensation theory is introduced to regenerate the RDOF FRF. Experiments are conducted to demonstrate the efficiency of the proposed model in stiffness identification of spindle-toolholder joint, and the accuracy is significantly improved compared to the traditional model.

An improved dynamic model for angular contact ball bearings under constant preload

Abstract High-speed spindles are typically installed with angular contact ball bearings. This research has established a dynamic model for angular contact ball bearings under constant preload. By analyzing the constant preload mechanism, and the gyroscopic and centripetal forces, a dynamic non-linear model for angular contact ball bearings was proposed using Hertz contact theory. The model was solved by numerical iteration to obtain the dynamic parameters of an angular contact ball bearing which included: the dynamic normal contact force and contact angle, the maximum compressive stress and axial displacement, the contact pattern, stiffnesses, etc. To validate the model, a test device was designed which was equipped with a constant preloaded bearing group. By measuring the relative displacement of the bearings’ inner and outer rings under different conditions, the accuracy of the model was proved. This modeling method provided a theoretical basis for calculating bearing thermal characteristics, fatigue life, and an optimized radius of curvature of the bearing ring channel.

Rapid Control Prototyping of an Automated Clutch Using dSPACE and Matlab/Simulink

Parameter uncertainty and measuring noise are still very challenging work in developing an appropriate controller for the automated clutch system due to the effect of the external disturbances. This paper introduces a robust control method for automated clutch system. A nonlinear dynamic model for the screw-nut actuator associated with clutch is derived, and then a dynamic sliding mode controller for automated clutch of AMT vehicle is presented. The chattering phenomenon is alleviated and the robustness is improved by adopting the proposed controller. Based on dSPACE and Matlab/Simulink, the rapid control prototyping (RCP) of automated clutch is used to demonstrate the efficiency and robustness of the proposed algorithm via the comparison with both the PID controller and the conventional sliding mode controller (CSMC).

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.

Stiffness and damping model of bolted joint based on the modified three-dimensional fractal topography

The machine tools are consisted of many parts and most of them are connected by the bolts. Accurate modeling of contact stiffness and damping for bolted joint is crucial in predicting the dynamic performance of machine tools. This paper presents a modified three-dimensional fractal contact model to obtain the stiffness and damping of bolted joint. Topography of the contact surface of bolted joint is fractal featured and determined by fractal parameters. Asperities in microscale are considered as elastic, elastic–plastic, and full plastic deformation. The expand coefficient ψ is introduced to the size-distribution function of asperities. The real contact area, contact stiffness, and damping of the contact surface can be calculated by integrating the microasperities. The relationship of contact stiffness, damping, fractal dimension D, and fractal roughness parameter G can be obtained. Experiments are conducted to verify the efficiency of the proposed model. The results show that the theoretical mode shapes are in good agreement with the experimental mode shapes. The relative errors between the theoretical and experimental natural frequencies are less than 3.33%, which is less than those of the W-K model and L-L model. The presented model can be used to accurately predict the dynamic characteristic of bolted assembly in the machine tools.

A review of hydrostatic bearing system: Researches and applications:

Hydrostatic bearing is a key part that provides precision and long life to machine tools. It is one of the embodiments of tribology, mechanics, optimization method, and structural design in engineering practice. Articles about hydrostatic bearings since 1990 are collected in this review. Researching status is evaluated in two aspects: basic theory and typical application. This article presents a review of research articles related to introducing developments in hydrostatic bearings. Basic theory contains equations and analysis methods which include analytic, numerical, and experimental methods. Typical applications are based on rectangular oil pad, circular oil pad, and journal bearings. Moreover, this article focuses on the analysis of the relevant model, solution, and optimization and summarizes the hotspots and development directions.