Prediction of Frequency Response Function for Cylindrical Thin-Walled Workpiece with Fixture Support Constraints

Auxiliary fixtures are widely used to enhance the rigidity of cylindrical thin-walled workpieces (CTWWs) in the machining process. Nevertheless, the accurate and efficient prediction of frequency response function (FRF) for the workpiece-fixture system remains challenging due to the complicated contact constraints between workpiece and fixture. This paper proposes an analytical solution for the comprehensive FRF analysis of the CTWW-fixture system. Firstly, based on the vector mechanics, the mode shape functions of the workpiece are presented using the classical theory of thin shell. The variable separation method is utilized to deal with the inter-mode coupling of the workpiece. Secondly, the motion equation of the CTWW with fixture constraints is established using analytical mechanics from the viewpoint of energy balance. Finally, the FRFs of the CTWW-fixture system are derived by means of modal superposition. Experimental modal tests verify that the predicted FRFs are in good agreement with the measured curves.

WRITING OUT OF FORMULAS FOR CALCULATING FORCES IN THE JOINTS OF MANIPULATORS IN STATICS

The problem of bulkiness of mathematical models of manipulative systems of industrial robots is solved. Here we consider formulas for calculating static reactions in joints and formulas for active forces that balance the forces of gravity acting on the manipulator's bodies in its stationary state. The manipulator can be in such a state when it is before capturing the object of manipulation and releasing it, or when it is performing some assembly operations, or it is during spot welding and in slow (quasi-static) arc-welding and painting processes. Aim. The aim is to derive general recur-rence and finite formulas for calculating the reaction forces in joints and their projections to the ax-es of the coordinate system rigidly connected with the selected body. Express the formulas of force projections in terms of guiding cosines and justify their optimality in terms of the minimum of arithmetic operations. Derive general inverse recurrence formulas for writing out the guide cosines of the axes associated with the moving bodies of the coordinate system with respect to the stationary coordinate system. Research methods. The methods of research relate to vector mechanics and sys-tems analysis, and the algorithmization of calculations by reducing them to the use of recurrent formulas. Results. A systematic analysis of general formulas, in which all possible regular expres-sions are highlighted which are corresponding unambiguously to the kinematic parameters of ma-nipulators, is performed. These regular expressions are used in software for analytical modeling of manipulator, in particular, for the analytical solution of problems of statics of a manipulator. The method of analytical verification of the prescribed formulas is described. The tasks of writing out optimal formulas for calculating the projections of static reaction forces in joints have been solved. And the tasks of writing out optimal formulas for calculating active forces in progressive joints of universal manipulators with six degrees of freedom, operating in Cartesian, cylindrical, spherical and angular coordinate systems, have been solved also. Analytical verification of the derived equations of stat-ics is performed. Examples of the reuse of the derived formulas for manipulators with the same kin-ematic schemes of their subsystems. Conclusion. Expressions of the equations of statics of manipu-lators through the guide cosines of the axes of the associated coordinate systems of their bodies al-low us to write these equations through the known parameters of body orientation. The recurrent formulas for calculating directional cosines allows to use recursive functions in their software im-plementation, i.e. to increase the computational efficiency of the software.

Modeling and Analysis of a Generic Internal Cargo Airdrop System for a Tandem Helicopter

This article describes the results of modeling and analysis of a generic internal cargo system using a discretization method of the vector mechanics. The model can be easily incorporated into a tandem helicopter model and is intended for use of simulation and investigating the problems of flight dynamics, control, etc., both in flight operation loading a cargo and flight operation in the process of airdrops. The model is derived by considering the main descriptions of the cargo, including the linear and rotational dynamics, the kinematics, and the forces and moments acting on the helicopter. A simulation method embedded with a numerical trim algorithm is developed for the complete coupling helicopter/cargo nonlinear dynamics system. The simulation application of the model is illustrated, including the case of flight operation loading a cargo by considering three mass configurations of 3000, 4500, and 6000 kg, and the case of flight operation in the process of airdrops at velocities of 0, 40, 80, 120, and 160 knots. Stabilities of the helicopter in the process of airdrops are also analyzed. The major conclusions drawn are: (i) the tandem helicopter has a good attitude maintaining ability in the whole flight velocity envelope when it conducts a flight operation loading a cargo; (ii) in the process of airdrops, the increase in flight velocity will constantly decrease the helicopter pitching attitude and increases the total airdrop time and decreases the backward moving velocity of the cargo, and helicopter flying at a velocity between 80 and 120 knots might be acceptable; (iii) the stabilities of both the longitudinal and lateral periodic modes are continuing to decrease during the backward movement of the cargo.

Heavy Military Land Vehicle Mass Properties Estimation Using Hoisting and Pendulum Motion Method

Mass properties such as the centre of gravity location, moments of inertia, and total mass are of great importance for vehicle stability studies and deployment. Certain parameters are required when these vehicles need to be arranged inside an aircraft for the carrier to achieve proper mass balance and stability during a flight. These parameters are also important for the design and modelling process of vehicle rollover crash studies. In this study, the mass properties of a military armoured vehicle were estimated using hoisting and pendulum method. The gross total weight, longitudinal and vertical measurements were recorded by lifting the vehicle using a mobile crane and the data were used to estimate the centre of gravity. The frequency of vehicle oscillation was measured by applying swing motion with a small angle of the vehicle as it is suspended on air. The centre of gravity and mass moment of inertia were calculated using the vector mechanics approach. The outcomes and limitations of the approach as discussed in details.

Dynamic Nonlinear Analysis of Semi-Rigid Steel Frames Based on the Finite Particle Method

The Finite Particle Method (FPM), based on the Vector Mechanics, is a new structural analysis method. This paper explores the possibility of the proposed method being applied in the dynamic nonlinear analysis of semi-rigid steel frames. Taking the two dimensional beam element as an example, the formulations of the FPM to calculate the dynamic and geometric nonlinear problems are derived. Spring model with zero-length is adopted to simulate the relationship between internal forces and deformations of the semi-rigid steel connections. The nonlinear strengthen spring model is used to analyze the nonlinear behavior of the semi-rigid connection. Explicit time integrations are used to solve equilibrium equations. Comparing to traditional Finite Element Method, iterations and special modifications are not needed during the dynamic nonlinear analysis, which is more advantageous in structural complex behavior analysis. Two numerical examples are presented to analyze the behaviors of rigid and semi-rigid steel frames, and behaviors of linear and nonlinear semi-rigid connections, which demonstrate the accuracy and applicability of this method in dynamic nonlinear analysis.

Dynamics Analysis of Drag Rope Base on Lagrange Equation

Drag rope is a kind of soft body. Now the analysis method of rigid-Body mechanics is not suitable for drag rope mechanics to analysis. This paper compares the two branches of the theoretical mechanic, who are the vector mechanics and the analysis mechanics, then put forward a kind of mechanical analysis method which uses the Lagrange-equation which belongs to the analysis mechanics, to analysis the movement and stress of drag rope.