A new method for evaluating the firing precision of multiple launch rocket system based on Bayesian theory

How to effectively evaluate the firing precision of weapon equipment at low cost is one of the core contents of improving the test level of weapon system.A new method to evaluate the firing precision of the MLRS considering the credibility of simulation system based on Bayesian theory is proposed in this paper.First of all,a comprehensive index system for the credibility of the simulation system of the firing precision of the MLRS is constructed combined with the group analytic hierarchy process.A modified method for determining the comprehensive weight of the index is established to improve the rationality of the index weight coefficients.The Bayesian posterior estimation formula of firing precision considering prior information is derived in the form of mixed prior distribution,and the rationality of prior information used in estimation model is discussed quantitatively.With the simulation tests,the different evaluation methods are compared to validate the effectiveness of the proposed method.Finally,the experimental results show that the effectiveness of estimation method for firing precision is improved by more than 25%.

An efficient and modular modeling for launch dynamics of tubed rockets on a moving launcher

This paper develops a modular modeling and efficient formulation of launch dynamics with marching fire(LDMF)using a mixed formulation of the transfer matrix method for multibody systems(MSTMM)and Newton-Euler formulation.Taking a ground-borne multiple launch rocket systems(MLRS),the focus is on the launching subsystem comprising the rocket,flexible tube,and tube tail.The launching subsystem is treated as a coupled rigid-flexible multibody system,where the rocket and tube tail are treated as rigid bodies while the flexible tube as a beam with large motion.Firstly,the tube and tube tail can be elegantly handled by the MSTMM,a computationally efficient order-N formulation.Then,the equation of motion of the in-bore rocket with relative kinematics w.r.t.the tube using the Newton-Euler method is derived.Finally,the rocket,tube,and tube tail dynamics are coupled,yielding the equation of motion of the launching subsystem that can be regarded as a building block and further integrated with other subsystems.The deduced dynamics equation of the launching subsystem is not limited to ground-borne MLRS but also fits for tanks,self-propelled artilleries,and other air-borne and naval-borne weapons undergoing large motion.Numerical simulation results of LDMF are given and partially verified by the experiment.

Transfer matrix method for determination of the natural vibration characteristics of elastically coupled launch vehicle boosters

The analysis of natural vibration characteristics has become one of important steps of the manufacture and dynamic design in the aerospace industry. This paper presents a new scenario called virtual cutting in the context of the transfer matrix method of linear multibody systems closed- loop topology for computing the free vibration characteristics of elastically coupled flexible launch vehicle boosters. In this approach, the coupled system is idealized as a triple-beam system-like structure coupled by linear translational springs, where a non-uniform free-free Euler-Bemoulli beam is used. A large thrust-to-weight ratio leads to large axial accelera- tions that result in an axial inertia load distribution from nose to tail. Consequently, it causes the development of significant compressive forces along the length of the launch vehicle. Therefore, it is important to take into account this effect in the transverse vibration model. This scenario does not need the global dynamics equations of a system, and it has high computational efficiency and low memory requirements. The validity of the presented scenario is achieved through com- parison to other approaches published in the literature.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

A novel launch dynamics measurement system for multiple launch rocket system and comparative analysis with numerical simulations

In this paper,a novel launch dynamics measurement system based on the photoelectric sensor pair is built.The actual muzzle time(i.e.a time duration that originates from the initial movement to the rocket’s departure from the muzzle)and the muzzle velocity are measured.Compared with the classical methods,the actual muzzle time is obtained by eliminating the ignition delay.The comparative analysis method is proposed with numerical simulations established by the transfer matrix method for multibody systems.The experiment results indicate that the proposed measurement system can effectively measure the actual muzzle time and reduce the error of classical methods,which match well with the simulation results showing the launch dynamics model is reliable and helpful for further analysis and design of the MLRS.

Ballistic Trajectory Extrapolation and Correction of Firing Precision for Multiple Launch Rocket System

The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.

Launching ceremony of the International Society of Mechanical System Dynamics Convened in Beijing, China

The First General Assembly and the First Session of the First Executive Board Meeting of International Society of Mechanical System Dynamics(ISMSD),the ISMSD Launching Ceremony,the Second International Conference on Mechanical System Dynamics(ICMSD),the Second ICMSD Standing Steering Committee Meeting,the Third Editorial Board Meeting of the International Journal of Mechanical System Dynamics(IJMSD),and the IJMSD Expert Symposium 2023 were held as a series of international activities on mechanical system dynamics,during the period from August 31 to September 4,2023,at the Wyndham Beijing North,Beijing,China.

Study on the influence of projectile on muzzle disturbance

In order to make an efficient analysis of muzzle disturbance influenced by projectile mass, mass eccentricity, dynamic unbalance, load deviation, and clearance between projectile and bore, the orthogonal test method is extended to analyze the launch dynamics. Taking a tank as the research object, the launch dynamics equations of a tank system are established. Based on the stochastic simulation principle, the tank launch dynamic simulation system is constructed and through the development of the orthogonal test method, the influence of projectile on muzzle disturbance is studied. The study results provided both theoretical foundation and simulation approaches for improving the firing dispersion of the tank.

Adaptive control of track tension estimation using radial basis function neural network

Track tension is a major factor influencing the reliability of a track.In order to reduce the risk of track peel-off,it is necessary to keep track tension constant.However,it is difficult to measure the dynamic tension during off-road operation.Based on the analysis of the relation and external forces depending on free body diagrams of the idler,idler arm,road wheel and road arm,a theoretical estimation model of track tension is built.Comparing estimation results with multibody dynamics simulation results,the rationality of track tension monitor is validated.By the aid of this monitor,a track tension control system is designed,which includes a self-tuning proportional-integral-derivative(PID)controller based on radial basis function neural network,an electro-hydraulic servo system and an idler arm.The tightness of track can be adjusted by turning the idler arm.Simulation results of the vehicle starting process indicate that the controller can reach different expected tensions quickly and accurately.Compared with a traditional PID controller,the proposed controller has a stronger anti-disturbance ability by amending control parameters online.

Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response

The dynamic performances of an ultra-precision fly cutting machine tool(UFCMT)has a dramatic impact on the quality of ultra-precision machining.In this study,the dynamic model of an UFCMT was established based on the transfer matrix method for multibody systems.In particular,the large-span scale flow field mesh model was created;and the variation in linear and angular stiffness of journal and thrust bearings with respect to film thickness was investigated by adopting the dynamic mesh technique.The dynamic model was proven to be valid by comparing the dynamic characteristics of the machine tool obtained by numerical simulation with the experimental results.In addition,the power spectrum density estimation method was adopted to simulate the statistical ambient vibration excitation by processing the ambient vibration signal measured over a long period of time.Applying it to the dynamic model,the dynamic response of the tool tip under ambient vibration was investigated.The results elucidated that the tool tip response was significantly affected by ambient vibration,and the isolation foundation had a good effect on vibration isolation.

An Algorithm for Determination of Projectile Attitude Angles in Projectile Trajectory Prediction

A fast and accurate algorithm is established in this paper to increase the precision of ballistic trajectory prediction.The algorithm is based on the six-degree-of-freedom(6 DOF)trajectory equations,to estimate the projectile attitude angles in every measuring time.Hereby,the algorithm utilizes the Davidon-Fletcher-Powell(DFP)method to solve nonlinear equations and Doppler radar trajectory test information containing only position coordinates of the projectile to reconstruct the angular information.The″position coordinates by the test″and″angular displacements by reconstruction″at the end phase of the radar measurement are used as an initial value for the trajectory computation to extrapolate the trajectory impact point.The numerical simulations validate the proposed method and demonstrate that the estimated impact point agrees very well with the real one.Morover,other artillery trajectory can be predicted by the algorithm,and other trajectory models,such as 4 DOF and 5 DOF models,can also be incorporated into the proposed algorithm.

Aero-thermo-elastic Numerical Calculation and Analysis of Spinning Rocket

The application of computational fluid dynamics/computational solid method(CFD/CSM)on solving the aero-thermo-elastic problem of spinning rocket is introduced.Firstly,the aerodynamic coefficients of a rocket are calculated,and the results are compared with the available experimental data,which verified the accuracy of the CFD output.Then,analysis is carried using ANSYS Workbench multi-physics coupling platform,which includes fluid,thermal,and structural solvers.The results show that spinning causes a significant effect on the deformations and stresses.Furthermore,thermal stresses due to high temperature at the rocket warhead and tail edges have a dominated effect,even more than those produced by aerodynamic forces.Consequently,this important outcome should be taken into consideration during the rocket design stages.

Study on Launch Dynamics of the Tank Marching Fire

As an army main battle equipment, it is required that the tank should have high firing accuracy and high first round hit probability during marching. The initial disturbance of the projectile is the premier factor that takes effect on the marching fire accuracy of the tank. And the marching fire accuracy of the tank depends on the launch dynamics behaviors of the tank. In this paper, the launch dynamics theory of a tank marching fire is studied, and its launch dynamics model is established. Based on the transfer matrix method for multibody system(MSTMM) and the automatic deduction theorem of overall transfer equations, the overall transfer equation and the overall transfer matrix of a tank multibody system are deduced; the launch dynamics equations of the tank marching fire are deduced, and the dynamic response of the tank system, the motion of projectile in barrel, the initial disturbance of the projectile and the vertical target dispersion are exactly simulated; meanwhile, the results of simulation are verified by tests. This work provides both theoretical foundation and simulation approaches for improving the marching fire accuracy of the tank.

Discrete time transfer matrix method for dynamics analysis of complex weapon systems

Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.

Substructuring Technique for Dynamics Analysis of Flexible Beams with Large Deformation

In this paper, the substructuring technique is extended for the dynamics simulation of flexible beams with large deformation. The dynamics equation of a spatial straight beam undergoing large displacement and small deformation is deduced by using the Jourdain variation principle and the model synthesis method. The longitudinal shortening effect due to the transversal deformation is taken into consideration in the dynamics equation. In this way, the geometric stiffening effect, which is also called stress stiffening effect, is accounted for in the dynamics equation. The transfer equation of the flexible beam is obtained by assembling the dynamics equation and the kinematic relationship between the two connection points of the flexible beam. Treating a flexible beam with small deformation as a substructure, one can solve the dynamics of a flexible beam with large deformation by using the substructuring technique and the transfer matrix method. The dynamics simulation of a flexible beam with large deformation is carried out by using the proposed approach and the results are verified by comparing with those obtained from Abaqus software.

Eigenvalue analysis of planar linear multibody system under conservative force based on the transfer matrix method

The linear multibody system transfer matrix method(LMSTMM)provides a powerful tool for analyzing the vibration characteristics of a mechanical system.However,the original LMSTMM cannot resolve the eigenvalues of the systems with ideal hinges(i.e.,revolute hinge,sliding hinge,spherical hinge,cylindrical hinge,etc.)or bodies under conservative forces due to the lack of the corresponding transfer matrices.This paper enables the LMSTMM to solve the eigenvalues of the planar multibody systems with ideal hinges or rigid bodies under conservative forces.For a rigid body,the transfer matrix can now consider coupling terms between forces and kinematic state perturbations.Also,conservative forces that contribute to the eigenvalues can be considered.Meanwhile,ideal hinges are introduced to LMSTMM,which enables the treatment of eigenvalues of general multibody systems using LMSTMM.Finally,the comparative analysis with ADAMS software and analytical solutions verifies the effectiveness of the proposed approach in this paper.

Deep-learning-assisted online surface roughness monitoring in ultraprecision fly cutting

Surface roughness is one of the most critical attributes of machined components,especially those used in high-performance systems.Online surface roughness monitoring offers advancements comparable to post-process inspection methods,reducing inspection time and costs and concurrently reducing the likelihood of defects.Currently,online monitoring approaches for surface roughness are constrained by several limitations,including the reliance on handcrafted feature extraction,which necessitates the involvement of human experts and entails time-consuming processes.Moreover,the prediction models trained under one set of cutting conditions exhibit poor performance when applied to different experimental settings.To address these challenges,this work presents a novel deep-learning-assisted online surface roughness monitoring method for ultraprecision fly cutting of copper workpieces under different cutting conditions.Tooltip acceleration signals were acquired during each cutting experiment to develop two datasets,and no handcrafted features were extracted.Five deep learning models were developed and evaluated using standard performance metrics.A convolutional neural network stacked on a long short-term memory network outperformed all other network models,yielding exceptional results,including a mean absolute percentage error as low as 1.51%and an R2value of 96.6%.Furthermore,the robustness of the proposed model was assessed via a validation cohort analysis using experimental data obtained using cutting parameters different from those previously employed.The performance of the model remained consistent and commendable under varied conditions,asserting its applicability in real-world scenarios.

Tool-tip vibration prediction based on a novel convolutional enhanced transformer

Superior surface finish remains a fundamental criterion in precision machining operations,and tool-tip vibration is an important factor that significantly influences the quality of the machined surface.Physics-based models heavily rely on assumptions for model simplification when applied to complex high-end systems.However,these assumptions may come at the cost of compromising the model's accuracy.In contrast,data-driven techniques have emerged as an attractive alternative for tasks such as prediction and complex system analysis.To exploit the advantages of data-driven models,this study introduces a novel convolutional enhanced transformer model for tool-tip vibration prediction,referred to as CeT-TV.The effectiveness of this model is demonstrated through its successful application in ultra-precision fly-cutting(UPFC)operations.Two distinct variants of the model,namely,guided and nonguided CeT-TV,were developed and rigorously tested on a data set custom-tailored for UPFC applications.The results reveal that the guided CeT-TV model exhibits outstanding performance,characterized by the lowest mean absolute error and root mean square error values.Additionally,the model demonstrates excellent agreement between the predicted values and the actual measurements,thus underlining its efficiency and potential for predicting the tool-tip vibration in the context of UPFC.

Optimal design of 6-DOF vibration isolation platform based on transfer matrix method for multibody systems

The structure parameters of 6-degree of freedom(DOF)vibration isolation platform have a significant effect on its performance.To make the designed vibration isolation platform perform well,non-dominanted sorting genetic algorithm version II(NSGA-II)was applied to optimize its structure based on the transfer matrix method for multibody systems.Firstly,the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics.Secondly,the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems.And the formula of its natural frequency was derived according to the boundary conditions of the system.Thirdly,the manipulability index was constructed based on a dimensionless Jacobian matrix.And a new performance index function was established considering the influence of dynamic isotropic and legs mass.Fourthly,genetic algorithm(GA)and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions,respectively.It showed that NSGA-II had higher optimization efficiency,better calculation accuracy and shorter optimization time than that of GA.Finally,NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions.Optimal Pareto solutions were obtained,which provides structural parameters for subsequent design work.Therefore,the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism.

Dynamic modeling and H_∞ independent modal space vibration control of laminate plates

In this paper, combining the transfer matrix method and the finite element method, the modified finite element transfer matrix method is presented for high efficient dynamic modeling of laminated plates. Then, by constructing the modal filter and the disturbance force observer, and using the feedback and feedforward approaches, the H ∞ independent modal space control strategy is designed for active vibration control of laminate plates subjected to arbitrary, immeasurable disturbance forces. Compared with ordinary dynamic modeling and control methods of laminated plate structures, the proposed method has the low memory requirement, high computational efficiency and robust control performance. Formulations as well as some numerical examples are given to validate the method and the control performance.