In order to comprehensively consider the influence of geometric error caused by manufacturing defects and elastic error caused by the gravity of structural components on the static accuracy of machine tools, as well as the coupling relationship between them, this paper proposes an identification method of static error of three-axis machine tools. Taking the three-axis machine tool as the research object, the static error model of the machine tool is established according to the multi-flexible body system theory and the homogeneous transformation matrix (HTM), and the geometric error component and the elastic error component in the static error are qualitatively analyzed. The Chebyshev polynomials are used to establish the parametric model of static error. Based on the three-axis linkage experiment of the Double ball bar (DBB), all the static errors are decoupled. Then, the finite element method is used to discretize the machine tool into three subsystems. Based on the space beam element, the stiffness model of each subsystem is established, and the elastic error component in the static error is quantitatively analyzed. The results show that the elastic error affected by gravity is mainly reflected in seven straightness errors and angle errors, and is generally greater than the corresponding static error. It shows that the machine tool offsets the influence of geometric errors from the perspective of elastomer compensation in the design stage, and proposes a simplified static error model of the machine tool.

During the ground roll phase, an aircraft is subjected to various sources of uncertainty, including runway surface irregularities and stiffness degradation of landing-gear components, which may adversely affect ground-handling safety and passenger ride comfort. Accordingly, a six-degree-of-freedom nonlinear landing-gear model is developed, incorporating the aircraft mass, shock absorber, braking system, and strut, to investigate the effects of stochastic variations in key parameters on the dynamic response of the landing gear. The sparse generalized polynomial chaos expansion (SGPCE) is validated against Monte Carlo simulation (MCS) to demonstrate its effectiveness, and is subsequently employed to construct an efficient surrogate model for the landing-gear system. This approach significantly reduces computational cost while enabling rapid and accurate evaluation of the sensitivity of landing-gear responses to parametric uncertainties. Simulation results indicate that the peak frequencies of the vertical vibration response of the six-degree-of-freedom landing-gear model are mainly concentrated around 3 Hz, and that parameter uncertainties tend to broaden this frequency range. Variations in aircraft mass and shock-absorber stiffness have a pronounced influence on the vertical vibration response and ride comfort, whereas the strut stiffness predominantly governs the aircraft attitude. These findings provide useful guidance for uncertainty-aware landing-gear design by identifying the parameters that should be prioritized for improving ride comfort, attitude stability, and overall ground-handling performance.

A novel identification and correction method for position-independent geometric errors (PIGEs) is presented based on the unit dual quaternion (UDQ) differential motion linearization. First, a linearized kinematic error model based on UDQ differential motion representation is established, which is applied to the error identification and correction with the twist error vector and the correction parameters as the linearized targets, respectively. By combining the linearized model with the error projection principle, a PIGEs identification method based on double ball bar (DBB) test is proposed. The proposed error correction method solves the correction parameters of each motion axis simultaneously based on the UDQ Jacobian matrix, which effectively avoids the abrupt changes in correction parameters at singular points when separately correcting the orientation and position errors, due to the lack of constraints between the orientation and position error corrections. Further simulation and experiment verify the effectiveness of the proposed method.

A novel measurement method based on the double ball bar (DBB) is proposed to improve the positioning accuracy of industrial robots. The kinematic model is established based on the Modified Denavit-Hartenberg (MD-H) method. A measurement posture of the tool center point (TCP) tilted 30° is proposed to ensure that all joints can fully move, and a spherical spiral trajectory is adopted to increase the stroke in the Z direction. This paper combines the error sensitivity analysis with the identification to reduce the dimensionality of parameter identification. A sub-space identification based on the Levenberg-Marquardt algorithm is proposed, and the corresponding error model is established. The experiments are completed on the ABB IRB120 industrial robot. The experiment demonstrated that the sub-space identification method has better identification accuracy, and the full movement of all joints is conducive to improving the calibration effect. Compared with the conventional calibration method based on the DBB, the calibration effect of the proposed method is improved by 22.82%.

Remaining fatigue life prediction is vital for engineering structures to ensure safety and reliability. The successive and dynamic changes in morphology are valuable informational reminders of the remaining life of a material. This study proposed a novel strategy to monitor and predict the remaining life of materials in a successive and dynamic manner, incorporating the in-situ scanning electron microscope (SEM) and deep learning algorithm. Two in-situ SEM fatigue experiments were conducted to simulate the practical service conditions of additively manufactured Inconel 718 alloy. A series of SEM image sequences reflecting the changing morphology were collected and used for downstream deep learning-based remaining life prediction. Original SEM images were cropped and grouped for training, validation, and test purposes. Results showed that the deep learning-based method exhibited high prediction ability. The proposed method’s predicted life values were highly close to the experimental results. The visualization result showed that the microstructure evolution, such as accumulation of slip bands, surface fluctuation changes resulting from coordinated grain deformation, and fatigue crack growth, provide much information and decision support to the network. These results demonstrated the great promise of monitoring and predicting the remaining fatigue life of materials based on morphology. We believe this image and deep learning-based strategy will inspire current fatigue life prediction and facilitate the move toward successive, automatic, and accurate life monitoring in practical engineering structures.

This paper presents a novel synchronous motion trajectory based on the unit dual quaternion (UDQ) to identify the position-independent geometric errors (PIGEs) of the dual rotary axes of a hybrid five-axis machine tool using a Double ball-bar (DBB). A general irregular trajectory equipartition method is presented to deal with the asynchronous matching between DBB data sampling and trajectory points. The kinematic model is effectively simplified by redefining the PIGEs of linear/rotary axes. The installation errors of the DBB are obtained by circular/spherical fitting trajectories, which are brought into the error model for elimination. The simulation of the UDQ kinematic model combined with preset error value shows that the non-uniform variation of DBB motion will lead to the deviation of PIGEs decoupling results. A compensation strategy of major orientation errors based on the UDQ is proposed, which is verified by simulation and compensation experiments.

In this paper, a general error identification and compensation method is proposed for the position-independent geometric errors (PIGEs) of dual rotation axes of cradle-type five-axis machine tools with non-intersecting rotation axes. A unique hole machining specimen is designed to evaluate the compensation effect. First, the kinematic error model of the five-axis machine tool is established based on the dual quaternion, and the correlation between the PIGEs defined based on the dual quaternion and the PIGEs in ISO 230–7 is analyzed. Then, eight PIGEs of the two rotation axes are simultaneously identified by using a double-ball bar (DBB) through the synchronous motion trajectory of the A- and C-axes. Moreover, an error compensation strategy based on the principle of tool pose approximation is proposed, which preferentially compensates for the direction error. The direction and position vector errors of the tool are directly compensated by establishing the ideal and actual relative pose difference model between the tool and workpiece. Finally, a unique hole machining experiment on a circular cone surface is proposed according to the position structure of the rotation axis of the target machine tool. The machining of the hole on the conical surface is realized by controlling the tool through the motion of the rotation axis, thus effectively avoiding the influence of the translational axis. The effectiveness of the proposed compensation strategy is verified by the measurement and fitting of the points on the machining hole wall by a three-coordinate measuring machine. The average residual error after compensation is reduced by about 88.65

为解决三轴机床在球杆仪误差敏感方向上直线度误差缺项建模与误差辨识精度问题,以三轴数控机床为研究对象,根据指数积理论与三轴数控机床运动链,结合混阶切比雪夫多项式预拟合模型,构建综合误差系数模型.在双正交轴检测实验基础上,对综合误差系数模型进行Moore-Penrose逆矩阵求解,使得18项误差能够在球杆仪误差敏感方向上得到全部辨识,无需在非运动轴向进行解耦,提高辨识精度和效率.在某三轴数控机床上进行双正交轴检测实验和NC代码补偿实验,补偿后XY、XZ、YZ双正交轴实验综合误差分别减少82.02％、91.63％、70.6％,验证了所提方法的有效性.对改进前后的切比雪夫多项式预拟合模型进行残差对比,结果表明混阶切比雪夫多项式预拟合模型精度更高.

A universal identification method for position independent geometric errors (PIGEs) of dual rotary axes of fiveaxis machine tools with arbitrary rotary axis position structures is proposed based on the unit dual quaternion (UDQ). The PIGEs of translational/rotary axes are redefined based on UDQ transformation, which effectively reduces the transformation parameters and avoids the unitization process of UDQ compared with the existing UDQ kinematics model. Based on the redefined PIGEs, a kinematic error model of a five-axis machine tool is established for error identification. Taking the cradle-type five-axis machine too with non-intersecting rotary axes as the research objective, a novel method for identifying PIGEs through the synchronous motion of dual rotary axes using a double ball bar (DBB) is proposed. Compared with BK1 and BK2 in ISO10791-6 and other existing methods, the advantage of the proposed method is that it can greatly reduce the complexity of the experiment and the operation steps by directly constructing the relative kinematic relationship between the tool and the workpiece based on the error model. Only one installation and one measurement trajectory are needed to simultaneously identify the eight PIGEs of the dual rotary axes. In addition, a trajectory equalization algorithm is proposed to effectively solve the asynchronous problem of motion and data sampling in DBB trajectory operation. By combining the simplified error model with the sampling data of DBB, the pseudo-inverse matrix is used for decoupling. The effectiveness of the proposed method is verified by DBB compensation comparison experiment. The proposed error identification method can be applied to other types of five-axis machine tools with a few changes in the configural parameters, which is ideal for periodic checks and calibration to ensure the machining accuracy.

Position independent geometric errors (PIGEs) of rotary axes, which are caused by imperfections during assembly of machine tools, are proved to be one of the major error sources of a five-axis machine tool. In this paper, PIGEs’ characterization method through hybrid motion of linear-rotary axes using a double ball bar (DBB) is proposed. The coordinated motions involving the motion of a linear and rotary axes are designed, namely, the XC, YC, and ZB motion pairs. The comprehensive error model of the machine tool is established using the screw theory based on the machine tool topology. The asynchronization between the synthetized velocity of the spindle tool cup relative to the workpiece tool cup during the coordinated motions has been resolved based on optimal motion trajectories. The PIGEs are identified using the particle swarm optimization method and simulated using the comprehensive machine tool model. A compensation strategy of the identified errors is proposed using the machine inverse kinematics. The effectiveness of the proposed characterization method is proved by the compensation results.

This paper presents a novel method to identify the squareness errors of computer numerical control (CNC) machine tools based on double ball bar (DBB) measurements. A series of spherical S-shaped paths are proposed to measure the squareness errors, instead of the generally used circular detection paths since the presented method requires only one experimental setup, and three translation axes are linked, which is more convenient and comprehensive. In this article, the coordinate transformation method and the method for dividing experimental paths evenly are used to solve the asynchronization between actual motion and DBB sampling process. The experimental data is then combined with the product of exponential (POE) model to calculate the three CNC machine tool squareness errors and applied to a spherical spiral testing path with the compensation of the diagnosed errors. The effectiveness of the method is verified by comparing the experimental results before and after the compensation.

Reliability allocation is one of the most important factors to consider when determining the reliability and competitiveness of a product. The feasibility-of-objectives (FOO) technique has become the current standard for assessing reliability designs for military mechanical-electrical systems. However, the FOO method has several drawbacks: For instance, it requires that the value of reliability allocation factors is single linguistic variables, and it does not consider the ordered weight of reliability allocation factors, but simply multiplies the ISPE (Complexity (I), State of Art (S), Performance Time (P), and Environment (E)) values one by one. This can lead to erroneous results. To address these issues, this paper combines the fuzzy allocation method with the maximum entropy ordered weighted averaging method (ME-OWA) to achieve a flexible allocation of system reliability. To verify the effectiveness of the proposed method, the CNC machine tool is taken as an example. The FOO method and the fuzzy allocation method and the proposed method were used to assign reliability to the eight subsystems of a CNC machine tool, and the results were compared to draw conclusions: The proposed method is more flexible and accurate for reliability allocation.

Geometric error is the main error that affects the machining accuracy of complex five-axis machine tool. Therefore, tracing analysis of error influence for a complex machine tool has been carried out based on an S-shaped workpiece in this study. A method of judging the error parameters which is the biggest influence on machining errors is established. In this method, the machining error of S-shaped workpiece and shaping motions of complex machine tool are comprehensively considered. Cubic B-splines surface has been applied to characterization of the curved surface. The actual position of tool center can be deduced by projecting the B-splines surface in its normal direction. The mapping relationship between the actual tool position and the actual machining curve has established. The machining errors generation model has established. The error expression equation has been deduced. Those five key parameters that have great influence on machining errors are determined according to the contribution which have been computed using the sensitivity and measured values of error parameters. Experimental results show that the error of each point is not more than ±1.5 μm by comparing the five error parameters and all parameters under the action of at the same time. The biggest errors which influence on the machining errors are \( {\varepsilon}_{yC_1} \), δ z (B), ε y (C 1), ε x (C 1), and \( {\varepsilon}_{x_1{C}_1} \).

To better understand the dynamic characteristics of a hydrostatic spindle in fluid-structure coupling, the impact of oil film slip on the 4 dynamic stiffness and damping coefficients of the spindle is studied. On the basis of modified Reynolds equation, which considers the microscale velocity slip effect, rotation error of the spindle is calculated. To solve the rotor axis orbit under the existence of eccentric quality, 4 dynamic stiffness and damping coefficients of the oil film, which describe the dynamics of a rotor axis orbit, are calculated by using load increment method and the pressure perturbation method. The research results show that velocity slip caused a certain impact on dynamics of bearing stiffness and damping performance. The experiment of the measuring path of the shaft verifies the correct and effect of the orbit of shaft center model.