The dynamic analysis of rotating beams is fundamental for the design and optimization of rotorcraft components, such as helicopter and tiltrotor blades. These structures exhibit high twist rates, geometric nonlinearities, and complex elastic and inertial coupling effects, making their modeling particularly challenging. This study presents a novel transfer matrix formulation for the analysis of rotating beams, developed by integrating the Finite Volume Beam formulation into the Transfer Matrix Method. The proposed model is fully three-dimensional and accounts for elastic and inertial coupling and centrifugal stiffening effect, ensuring an accurate representation of structural dynamics in rotorcraft applications. The resulting recursive formulation provides an efficient and effective alternative to global finite element methods to model rotating structures. The proposed method is validated against benchmark cases and a representative rotor blade. Comparisons with high-fidelity model demonstrate excellent agreement while highlighting the computational advantages of the transfer matrix approach. The results illustrate the critical influence of rotational speeds on natural frequencies and mode shapes. This study provides a powerful tool for analyzing rotating beams. The proposed formulation offers a computationally efficient and reliable tool for preliminary design and optimization, facilitating the study of complex structural dynamics in rotorcraft systems.

In advanced manufacturing fields such as aerospace, achieving high-precision cooperative positioning for dual-robot systems remains a critical challenge. Conventional calibration methods usually treat geometric error sources separately and calibrate them step by step, which can cause residual errors from one stage to propagate into the next and makes it difficult to compensate coupled system errors. This paper proposes a unified calibration framework to address this limitation. The master robot, the slave robot, and the base-to-base relationship are modeled as a single continuous kinematic chain. Based on this unified model, a cooperative error Jacobian matrix is derived for 78 geometric error parameters, and the Levenberg–Marquardt algorithm is used for parameter identification. Experimental results show that the mean absolute positioning errors in the x, y, and z directions decreased from 1.386 mm, 1.361 mm, and 0.341 mm to 0.391 mm, 0.387 mm, and 0.245 mm, corresponding to reductions of 71.8

This paper proposes a dynamics modeling method for industrial robots based on multibody systems transfer matrix method, aiming to overcome the computational complexity limitations of traditional dynamics modeling approaches in multi-degree-of-freedom systems. By decomposing the robot into modular subsystems (joints and links), the transfer matrices and equations that accurately characterize module’s mechanical properties are established. The system’s overall transfer equation is derived through sequential connection of component transfer matrices. The proposed method has the advantages of not requiring the global dynamics equations, high programmability and low system matrix order. A dynamics test platform for industrial robots is developed. First, the friction torque of each joint is identified using measured joint torque data. Subsequently, the dynamics model is combined to obtain the motion trajectory of the robot joint angle changes and joint angular velocity, and then verifies the simulation accuracy of the model.

The inherently low dynamic stiffness of industrial robots presents a fundamental obstacle to their full potential in high-precision milling applications, such as those in the aerospace sector. The resulting vibrations severely compromise machining quality and limit production efficiency. To address this problem, a high-bandwidth piezoelectric active damping toolholder is developed as a local micro-actuation unit for robotic milling. Distinct from conventional end-effector designs, the proposed toolholder adopts a local dynamic design strategy to reduce interference between the toolholder dynamics and the pose-dependent structural modes of the robot. Furthermore, a model-independent multi-harmonic adaptive feedforward control strategy is introduced to suppress spindle-related vibration harmonics without requiring real-time identification of the robot system. To evaluate the effectiveness and robustness of the proposed approach, milling experiments were conducted on two distinct industrial robot platforms under multiple validation scenarios. Initial validation on an ESTUN ER220 robot, machining a 5A06 aluminum alloy aerospace panel prototype, demonstrates maximum reductions in the root-mean-square values of vibration acceleration at the toolholder in the X, Y, and Z directions of 45.10%, 49.74%, and 50.61%, respectively, together with a surface roughness Sa reduction of up to 64.1%. Subsequent experiments on a KUKA KR500 heavy-duty robot further confirmed the effectiveness of the proposed toolholder under representative, posture-varying, chatter-prone, and variable-condition milling scenarios. The results support the robustness and cross-platform applicability of the proposed local active damping approach for improving vibration behavior and surface quality in robotic milling.

Curing process design is essential for producing high-quality composite parts. In conventional autoclave curing process, components are cooled to a predetermined temperature before pressure release. However, this approach is fundamentally incompatible with emerging curing techniques that utilize in-situ heating sources, where thermal insulation is employed to reduce heat loss and maintain uniform temperature distribution—significantly prolonging the cooling stage. To address this limitation, this study proposes a depressurized cooling process, in which high-pressure gas is vented immediately after curing. Subsequently, thermally insulated components, with vacuum maintained inside the vacuum bag, are removed from the equipment and allowed to cool gradually in ambient conditions until the temperature falls below the predetermined threshold. The effects of this process on cure quality were evaluated through comprehensive experimental analyses, including physicochemical characterization, mechanical testing, and assessment of cure-induced distortion. The results demonstrated that laminates processed via the depressurized cooling strategy exhibited comparable properties to those produced by the conventional pressurized cooling process. Notably, a reduction in cure-induced distortion was observed, particularly when female molds were used. These findings confirm the feasibility and effectiveness of the depressurized cooling strategy, offering a promising alternative for improving process efficiency and dimensional stability in advanced composite manufacturing.

In high-value manufacturing, dual-robot systems face a fundamental observability paradox: the very scenarios demanding precise cooperation are often those where physical occlusion prevents the dual-sided sensing required to achieve it. This bottleneck severely limits the application of flexible automation in complex tasks such as aircraft assembly. To address this challenge, this study proposes a cooperative control paradigm centered on model-based virtual sensing. This approach leverages a high-fidelity and precalibrated kinematic model of the dual-robot system as a virtual sensor, enabling the precise inference of the occluded robot's target pose using only single-sided physical measurements. We designed, integrated, and validated this paradigm on an industrial-scale dual-robot system for cooperative drilling and electromagnetic riveting (EMR). The experimental results demonstrate that the framework successfully constrains the cooperative attitude error to below 0.4 degrees. Compared to noncooperative methods, it reduces the average height of drilling exit burrs by 69.3% and improves the quality of EMR joints by decreasing the average perpendicularity error of the driven head by 34% and the coaxiality error by 64% . This work presents a robust and cost-effective solution that replaces infeasible or costly physical sensors with model-driven intelligence, advancing the frontier of flexible automation in aerospace manufacturing.

The transfer matrix method has long been recognized as a computationally efficient approach for the eigenanalysis of discrete and continuous dynamic systems, particularly in structural and rotor dynamics. In this study, the transfer matrix method framework is extended to incorporate parametric sensitivity analysis, providing the foundations required for continuation-based investigations. Sensitivity analysis is performed by evaluating the parametric derivatives of eigenvalues and eigenvectors directly from the system’s characteristic equation, clarifying the influence of parameter perturbations on system dynamics. To reduce computational effort, the intermediate terms required for the generic sensitivity matrix are accumulated and stored, enabling efficient evaluation of the overall sensitivity of the transfer matrix to frequency. Eigenvector normalization within the sensitivity analysis resolves the intrinsic non-uniqueness of eigenvectors and ensures consistent and stable computation of their sensitivities. The availability of consistent eigenvalue and eigenvector sensitivities naturally supports continuation procedures, enabling the systematic tracking of eigensolutions as system parameters vary and facilitating the identification of characteristic behaviors such as eigenvalue crossings and veering. Analytical sensitivity formulas inside the transfer matrix method framework and eigenvector normalization are used to address numerical challenges commonly encountered in transfer-matrix-based calculations. The methodology is verified through benchmark examples of increasing complexity, demonstrating its ability to capture critical system trends while preserving the compact structure of the transfer matrix formulation. Overall, the study demonstrates that integrating sensitivity analysis into the transfer matrix method significantly enhances its effectiveness for parametric investigations and early-stage design evaluations of complex dynamical systems, naturally supporting continuation-based analyses.

In mechanical systems, accurately calculating the frequency response function (FRF) is crucial for predicting the dynamic behavior of the system at various external excitation frequencies. This paper proposes a novel approach called the complex extended transfer matrix method (CETMM) for computing the FRF of mechanical systems. By introducing the concept of the complex extended state vector, this method streamlines the computation process of FRF. The governing equations for standard mechanical components, such as rigid bodies, beams, and elastic hinges, are derived. From these, the corresponding complex extended transfer equations and matrices are constructed. These are then assembled into the overall complex extended transfer equation and matrix for the entire mechanical system, ultimately enabling system's FRF computation. Using spindle-holder-tool and robotic milling systems from existing literature as case studies, the computational accuracy and efficiency of CETMM are validated, while its robustness and versatility in computing the FRF of mechanical systems are demonstrated.

To address the challenges of poor trajectory accuracy in industrial robots, which has emerged as a technological bottleneck hindering further robots’ applications in high-precision manufacturing industries, this paper proposes a method for the analysis and reliability-based optimization design for industrial robots’ trajectory accuracy considering parametric uncertainties. Firstly, the dynamic equation of an articulated industrial robot with six degrees of freedom is derived, incorporating the Stribeck joint friction model, followed by the uncertain parameter identification of this dynamic model. Subsequently, an uncertainty simulation system for the robot is established based on the constructed dynamic model and the sensitivity of system uncertain parameters to the robot trajectory accuracy is analyzed, where 10 key parameters are obtained among 54 uncertain parameters. Finally, a reliability-based multi-objective optimization design methodology is proposed synthesizing the robot trajectory accuracy, manufacturing cost, and quality loss, to achieve tolerance design of the robot's parameters, and enables minimizing costs and quality losses while ensuring the robot's trajectory accuracy reliability. The performance and practicality of the proposed method were validated using a six-degree-of-freedom rotary joint serial industrial robot as an example.

In robotic milling for aerospace large and complex cabin structural components, chatter can significantly impair the surface quality of workpieces, and in severe cases even result in tool damage. To mitigate chatter-related issues, the selection of appropriate process parameters using Stability Lobe Diagrams (SLDs) is a widely employed and effective strategy. Nevertheless, most prior investigations have primarily focused on regenerative chatter in specific robotic configurations, often disregarding the impact of low-frequency chatter originating from the inherent structural modes of the robot and its configuration-dependent dynamics. A novel approach for predicting the multi-modal stability of milling robots across their entire workspace is presented in this study. By integrating multibody dynamics model and regenerative chatter theory, this approach comprehensively accounts for the vibrations of the robotic milling system, which encompasses both the robotic structure and the tool, as well as the influence of multi-order modal variations. Moreover, a new representation method for the stability cloud map is suggested. Utilizing the multibody system transfer matrix method, a dynamics model is formulated to accommodate alterations in configurations. Additionally, a grid-based dynamic parameter identification method is proposed to predict frequency response functions under different robotic configurations. The chatter stability prediction model is integrated with the dynamics model to establish a multi-modal driven SLD. Finally, the correctness of the proposed robotic dynamics model and the effectiveness of the multi-modal SLDs with variable configurations are validated through modal and milling experiments conducted on an industrial robot.

Accurate analysis of the dynamic characteristics of a mobile industrial robot (MIR) is essential for evaluating and enhancing its machining performance. In the case of mobile heavy-load milling industrial robots, the significant weight of the end-effector and periodic external excitations highlight the flexibility of joints and links. This flexibility considerably affects the vibration characteristics and milling quality of the system. This work proposes a new multi-rigid-flexible coupling dynamics model for the MIR that employs the multibody systems transfer matrix method. The overall transfer equations and dynamics response equations for the system are derived. This method is distinguished by its high programmability, low system matrix order, and strong versatility. To validate the proposed method, modal experiments and excitation response tests have been designed in this work. Additionally, the influence of joint stiffness, joint angle, and link flexibility on the dynamic characteristics of the MIR is thoroughly analyzed. An evaluation index is developed to enhance the system's stiffness during milling that integrates both static and dynamic characteristics based on the analysis of these influencing factors. Finally, the feasibility and effectiveness of the stiffness enhancement model are verified after performing various milling experiments.

Thin-walled parts are important parts in determining the performance of aircraft. In order to solve the problem of easy deformation and generalized clamping, this paper proposes a vibration suppression method for thin-walled parts machining by combining magnetorheological damping module and flexible fixture. Firstly, the dynamic response characteristics of large thin-walled parts and flexible fixture under machining excitation are experimentally investigated. Then an intelligent vibration damping fixture is designed for the vibration characteristics of the parts, and the response surface optimization method is adopted to optimize the structural parameters of the fixture with the goal of reducing the deformation of thin-walled parts under machining excitation, so as to improve the vibration suppression effect of the intelligent vibration damping fixture.

Industrial robots often face challenges in high-precision tasks due to low absolute positioning accuracy. While model-based parameter identification is commonly used for calibration due to its simplicity and cost-effectiveness, it lacks a clear basis for quantifying multifactor influences and conducting sequential error identification. This article proposes a novel stepwise calibration method that leverages sensitivity analysis to address multisource errors. The method identifies primary factors affecting accuracy, evaluates correlated parameters, and conducts sequential identification of errors. Experimental validation on the CR 20 and other robots demonstrates the method’s superior performance in both accuracy and robustness, highlighting its universality and suitability for heavy-load applications. Across all experiments, this method reduces the average error by over 86%, significantly outperforming conventional calibration techniques.

Tiltrotor aircraft integrate the advantages of vertical takeoff and landing (VTOL) capability of helicopters with the forward speed and range of fixed-wing aircraft. However, rotor control systems experience significant load variations across flight modes, posing challenges for accurate load predictions. To address the challenge, this study develops a coupled multibody dynamic model of the rotor control system analyzing pitch link loads in multiple flight modes. The simulation results align well with flight test data, validating the model's reliability. Furthermore, accuracy improves when compared with CAMRAD computational results. At low airspeed in helicopter mode, pitch link loads exhibit periodic oscillation patterns. As forward speed increases, there is a noticeable rise in pitch link loads, with particularly significant amplification in high-frequency components. In conversion mode, the load amplitude decreases as the rotor tilting angle increases, accompanied by rapid attenuation of high-frequency components. In airplane mode, steady axial flow conditions yield predictable load trends. The validated framework provides critical insights into control load mechanisms in multiple flight modes.

The drivetrain system of tiltrotor aircraft is a complicated multibody system. Traditionally, rotorcraft drivetrain systems are modeled by the finite element method using an equivalent mathematical model with all the elements spinning at the same rotational velocity and structural properties scaled according to gear ratios. Such a process can be complex and computationally expensive, especially for large-scale problems. This paper proposes the dynamic analysis of a tiltrotor drivetrain, coupled with flexible blades’ lagwise motion, using a novel multibody system modeling and analysis method based on the transfer matrix method. The proposed method eliminates the need for equivalent processing of the drivetrain system components and does not require the derivation of the overall governing equations based on the Hamilton principle. Instead, they are directly formulated according to the system’s topology graph. Virtual branch and geometric elements are introduced to decouple any topological structure of the drivetrain system into multiple independent chain systems, further reducing the modeling complexity.

Industrial robots (IRs) have become powerful alternatives for milling large and complex components to computerized numerical control machine tools due to their low cost, wide adaptability, and large workspace. However, the significant low stiffness of IRs makes them more prone to vibration under machining forces, especially in milling operations with large cutting volumes, restricting the development of IRs in high-quality and high-efficiency machining fields. Robot configuration and process parameters are the direct and typical factors affecting the vibration in robotic milling. Reasonable selection of these parameters can significantly reduce the vibration in robotic milling, and then the machining quality and efficiency can thus be improved. In this paper, a multibody dynamics model of milling IRs is established and then validated through experimental modal analysis, hammer impact test, and milling experiments. Based on this foundation, the effects of machining parameters including robot configuration, spindle speed, feed speed, depth of cut, and width of cut on vibration in robotic milling are investigated, which provides the guidance for the vibration suppression and the improvement of efficiency for robotic milling.

Purpose This study aims to propose a calibration method to enhance the positioning accuracy in dual-robot collaborative operations, aiming to address the challenge of drilling hole spacing errors in spacecraft core cabin brackets that require an accuracy of less than 0.5 mm. Design/methodology/approach Initially, the cooperative error of dual robots is defined. Subsequently, an integrated model is constructed that encompasses the kinematic model errors of the dual robots, as well as the establishment errors of the base and tool frames. A calibration method for optimizing the cooperative accuracy of dual robots is proposed. Findings The application of the proposed method satisfies the collaborative drilling requirements for the spacecraft core cabin. The average cooperative positioning error of the dual robots was reduced from 0.507 to 0.156 mm, with the maximum value and standard deviation decreasing from 1.020 and 0.202 mm to 0.603 and 0.097 mm, respectively. Drilling experiments conducted on a core cabin simulator demonstrated that after calibration, the maximum hole spacing error was reduced from 1.219 to 0.403 mm, with all spacing errors falling below the 0.5 mm threshold, thus meeting the requirements. Originality/value This paper addresses the drilling accuracy requirements for spacecraft core cabins by using a calibration method to reduce the cooperative error of dual robots. The algorithm has been validated through experiments using ER 220 robots, confirming its effectiveness in fulfilling the drilling task requirements.

Vibration characteristic is an important factor affecting the motion of rocket in the launcher and its firing performance. In this paper, a rocket-launcher coupling dynamics model is proposed by applying the transfer matrix method for multibody systems. Considering manufacturing error and nonlinear contact force, the dynamics equations of the rocket-launcher coupling system during the whole process of firing are deduced. Combined with the dynamics model and equations, a dynamics simulation system is developed with uncertain parameters. The uncertain parameter description scheme and probability sampling scheme are proposed to obtain dynamics characteristic and firing performance of the system. The relevant tests are carried out to verify simulation results. Then, the factors affecting the firing performance are discussed. In view of the analysis results, the influence weight of initial disturbance on firing precision is 85% under the condition of full-loading continuous firing, and the swing angular velocity of rocket at muzzle is the main influence factor.

This paper establishes a multibody dynamics model of a milling robot system based on the transfer matrix method of multibody systems, forming the total transfer matrix and total transfer equation of the system. According to the vibration characteristics and dynamic responses of industrial robots, we studied the LQR (Linear Quadratic Regulator) optimal active vibration control method and verified its effectiveness through modal control simulation. The simulation results show that the LQR optimal active vibration control method based on the multibody dynamics model of the milling robot can reduce the vibration at the robot's tool tip, providing support for the feasible and effective implementation of the LQR control method in vibration suppression during robot milling.

Industrial robots are crucial in aerospace manufacturing for their precision, efficiency, and flexibility. However, vibrations during machining can impact product quality. This study introduces a piezoelectric-driven tool handle to suppress the machining vibration of the robot. It details the design process from structure to optimization and concludes with simulation verification of its feasibility.