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In‐plane vibration of a balanced helicopter rotor is caused by variations with azimuth of the in‐plane forces acting on individual blades. These forces may be summarized under three headings: ‘Induced forces’ caused by the inclination of elemental lift vectors relative to the axis of rotation. ‘Profile drag forces’: variations are caused by changes with azimuth angle of the angle and airspeed of the individual blade elements. ‘Coriolis forces’, which are caused by blade flapping, which brings about a variation of blade moment of inertia about the axis of rotation. Equations are developed in this paper for the resultant hub force due to each of these forces, on the assumptions of small flapping hinge offset. It is assumed that blades are linearly twisted and tapered, an assumption which in practice can be applied to any normal rotor. It is shown that by suitably inclining the mechanical axis it is possible to balance out the worst induced and profile drag vibrations by the coriolis one, which can be made to have opposite sign. If the mechanical axis is fixed in the fuselage, this suppression is fully effective for one flight condition only. In multi‐rotor helicopters, vibration suppression can be extended over a much wider range by varying the fuselage attitude. The logical result of this analysis is, for single rotor helicopters, a floating mechanical axis which can be adjusted or trimmed by the pilot. This would be quite simple to do on a tip‐driven rotor, and has already been achieved with a mechanical drive on the Doman helicopter. The more important causes of vibration from an unbalanced rotor are next con‐sidered, attention here being confined principally to fully articulated rotors, which are the most difficult to balance because the drag hinges tend to magnify all in‐accuracies in finish and balance. From a brief discussion of the vertical vibration of an imperfect rotor it is shown that some contemporary methods of ‘tracking’ are fundamentally wrong. Finally the vibration due to tip‐mounted power units is described. In discussing the effect of a vibratory force on a helicopter a simple response chart is developed, and it is thought that its use could well be accepted as a simple standard for general assessment purposes. In the development of equations for vibration the following points of general technical interest are put forward: An equation for induced torque is developed which includes a number of hitherto neglected parameters. A new form of equation for mean lift coefficient of a blade is suggested. The simple Hafner criterion for flight envelopes is shown to give rise to considerable error, and the use of Eq. (28) is suggested in its place. The variation of profile torque with forward speed is given, and the increase due to ? varying round the disk is expressed as an explicit equation, thus allowing considerable improvement in the present methods of allowing for this effect.

This article examines the influence of centrifugal buoyancy on the hydrodynamic and thermal behaviour in fully developed flow through an orthogonally rotating duct of aspect ratio 2:1. A series of computations have been performed at rotation numbers ranging from 0 to 0.2, for constant‐density flows (no buoyancy) and also for different levels of outward and inward buoyancy. The resulting comparisons reveal that for a Reynolds number of 32,500, rotational buoyancy effects become significant at Rayleigh number values greater than 107. In outward flows, buoyancy is found to strengthen the effects of the Coriolis force on the mean motion and, by raising turbulence levels, buoyancy also enhances wall heat transfer along both the pressure and the suction side of the rotating duct. In inward flows, it is found that strong buoyancy can reverse the direction of the Coriolis‐induced secondary motion, which causes a strong rise in wall heat transfer along the suction side and a similarly significant fall in heat transfer along the pressure side. The computed effects on heat transfer are in qualitative agreement with the findings of a number of experimental studies. For both inward and outward flows, at a constant Reynolds number, the modifications of centrifugal buoyancy on the side‐averaged levels of heat transfer correlate reasonably well with the rotational Rayleigh number.

Deals with the flow reversal in a buoyancy‐opposed rotating duct that causes heat transfer deterioration. An active technique of trailing‐wall transpiration is adopted to check whether it can avoid the flow separation and subsequently improves the heat transfer deterioration. Finite‐difference method is employed to solve the three‐dimensional Navier‐Stokes equations and the energy equation. Periodic conditions are used between the entrance and exit of a typical two‐pass duct for the closure of the elliptic problem. The predicted results reveal that fluid withdrawal through the trailing wall can avoid the flow separation from the leading wall of the radial‐outward duct (ROD) and thus eliminate local hot spots. In addition, the trailing‐wall suction not only increases the peripherally averaged heat transfer but also reduces the friction loss in the ROD. In the radial‐inward duct (RID), both the peripherally averaged heat transfer and peripherally averaged friction factor are augmented by trailing‐wall injection and are degraded by the trailing‐wall suction.

This paper aims to propose a forcefree control algorithm that is based on a dynamic model with full torque compensation is proposed to improve the compliance and flexibility of the direct teaching of cooperative robots.

Dynamic parameters identification is performed first to obtain an accurate dynamic model. The identification process is divided into two steps to reduce the complexity of trajectory simplification, and each step contains two excitation trajectories for higher identification precision. A nonlinear friction model that considers the angular displacement and angular velocity of joints is proposed as a secondary compensation for identification. A torque compensation algorithm that is based on the Hogan impedance model is proposed, and the torque obtained by an impedance equation is regarded as the command torque, which can be adjusted. The compensatory torque, including gravity torque, inertia torque, friction torque and Coriolis torque, is added to the compensation to improve the effect of forcefree control.

The model improves the total accuracy of the dynamic model by approximately 20% after compensation. Compared with the traditional method, the results prove that the forcefree control algorithm can effectively reduce the drag force approximately 50% for direct teaching and realize a flexible and smooth drag.

The entire algorithm is verified by the laboratory-developed six degrees-of-freedom cooperative robot, and it can be applied to other robots as well.

A full torque compensation is performed after parameters identification, and a more accurate forcefree control is guaranteed. This allows the cooperative robot to be dragged more smoothly without external sensors.

The purpose of this paper is to simulate flow inside differentially heated rotating cavity using two different formulations; one using Navier‐Stokes (NS) equations derived in non‐inertial (rotating) frame of reference and the other using NS equations in inertial frame of reference. Then to compare the results obtained from these formulations to find their merits and demerits.

The NS equations for both non‐inertial and inertial formulations are written in artificial compressibility form before discretizing them by a high resolution finite volume method. The dual time steeping approach of Jameson is used for time accuracy in both the formulations. Arbitrary Lagrangian Eulerian (ALE) approach is used for taking care of moving boundary problem arising in the inertial formulation. A newly developed HLLC‐AC Riemann solver for discretizing convective fluxes and central differencing for discretizing viscous fluxes are used in the finite volume approach. Results for both the formulations are first validated with test cases reported in literature. Then the results of the two formulations are compared among themselves.

Results of the non‐inertial formulation obtained by the proposed method are found to match well with those reported in literature. The results of both the formulations match well for low rotational speeds of the cavity. The discrepancies between the results of the two formulations progressively increase with the increase in rotational speed. Implicit treatment of the source term is found to reduce the discrepancies.

The present approach is useful for accurate prediction of flow feature and heat transfer characteristic in case of applications such as manufacturing of single wafer crystal for semiconductor and in numerous metallurgical processes.

The ALE formulation is used for the first time to simulate a differentially heated rotating cavity problem. The attempt to compare non‐inertial and inertial formulations is also reported for the first time. Implicit treatment of the source term leading to change in solution accuracy is one of the important findings of the present investigation.

A numerical study of a quantitative analogy of fully developed turbulent flow in a straight square duct rotating about an axis perpendicular to that of the duct and a stationary curved duct of square cross‐section was carried out. In order to compare the two flows, the dimensionless parameters K_TR=Re^1/4/√Ro and the Rossby number, Ro=w_m/Ωd_h, in the rotating straight duct flow corresponded to K_TC=Re^1/4/√λ and the curvature ratio, λ=R/d_h, in the stationary curved duct flow, so that they had the same dynamical meaning as those parameters for fully developed laminar flow. For the large values of Ro or λ, the flow field satisfied the “asymptotic invariance property”; there were strong quantitative similarities between the two flows, such as in the flow patterns and friction factors for the same values of K_TR and K_TC. Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa.

To investigate the effect of aspect ratio on the quantitative analogy between developing laminar flows in orthogonally rotating straight ducts and stationary curved ducts

A fractional step method is used to obtain the numerical solution of the governing equations by decoupling the solution of the momentum equations from the solution of the continuity equation. In order to clarify the similarity of the two flows, dimensionless parameters K_LR and Rossby number, Ro, in a rotating straight duct were used as a set corresponding to Dean number, K_LC, and curvature ratio, λ, in a stationary curved duct.

Under the condition that the aspect ratio was larger than one and that the magnitude of Ro or λ was large enough to satisfy the “asymptotic invariance property” the quantitative analogy between the two flows was established clearly.

As the aspect ratio decreased below one, the difference between the secondary flow intensities of these two flows increased, and therefore, the analogy between the two flows was not as evident as that for the larger aspect ratios.

Based on this methodology, the characteristics of the developing flow in orthogonally rotating ducts of higher aspect ratio can be predicted by considering the flow in stationary curved ducts, and vice versa.

The results obtained in this study will suggest an optimal criterion for the application of this approach to the flow similarity analysis in rectangular ducts with arbitrary aspect ratios.

The sensorless external force estimation of robot manipulator can be helpful for reducing the cost and complexity of the robot system. However, the complex friction phenomenon of the robot joint and uncertainty of robot model and signal noise significantly decrease the estimation accuracy. This study aims to investigate the friction modeling and the noise rejection of the external force estimation.

A LuGre-linear-hybrid (LuGre-L) friction model that combines the dynamic friction characteristics of the robot joint and static friction of the drive motor is proposed to improve the modeling accuracy of robot friction. The square root cubature Kalman filter (SCKF) is improved by integrating a Sage Window outer layer and a nonlinear disturbance observer (NDOB) inner layer. In the outer layer, Sage Window is integrated in the square root Kalman filter (W-SCKF) to dynamically adjust noise statistics. NDOB is applied as the inner layer of W-SCKF (NDOB-WSCKF) to obtain the uncertain state variables of the state model.

A peg-in-hole contact experiment conducted on a real robot demonstrates that the average accuracy of the estimated joint torque based on LuGre-L is improved by 4.9% in contrast to the LuGre model. Based on the proposed NDOB-WSCKF, the average estimation accuracy of the external joint torque can reach up to 92.1%, which is improved by 4%–15.3% in contrast to other estimation methods (SCKF and NDOB).

A LuGre-L friction model is proposed to handle the coupling of static and dynamic friction characteristics for the robot manipulator. An improved SCKF is applied to estimate the external force of the robot manipulator. To improve the noise rejection ability of the estimation method and make it more resistant to unmodeled state variable, SCKF is improved by integrating a Sage Window and NDOB, and a NDOB-WSCKF external force estimator is developed. Validation results demonstrate that the accuracy of the robot dynamics model and the estimated external force is improved by the proposed method.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

The paper aims to reduce the low-frequency resonance and residual vibration of the robot during the operation, improve the working accuracy and efficiency. A reduced weight and large load-to-weight ratio can improve the practical application of a collaborative robot. However, flexibility caused by the reduced weight and large load-to-weight ratio leads to low-frequency resonance and residual vibration during the operation of the robot, which reduces the working accuracy and efficiency. The vibrations of the collaborative robot are suppressed using a modified trajectory-planning method.

A rigid-flexible coupling dynamics model of the collaborative robot is established using the finite element and Lagrange methods, and the vibration equation of the robot is derived. Trajectory planning is performed with the excitation force as the optimization objective, and the trajectory planning method is modified to reduce the vibration of the collaborative robot and ensure the precision of the robot terminal.

The vibration amplitude is reduced by 80%. The maximum torque amplitude of the joint before the vibration suppression reaches 50 N·m. After vibration suppression, the maximum torque amplitude of the joint is 10 N·m, and the resonance phenomenon is eliminated during the operation process. Consequently, the effectiveness of the modified trajectory planning method is verified, where the vibration and residual vibration in the movement of the collaborative robot are significantly reduced, and the positioning accuracy and working efficiency of the robot are improved.

This method can greatly reduce the vibration and residual vibration of the collaborative robot, improve the positioning accuracy and work efficiency and promote the rapid application and development of collaborative robots in the industrial and service fields.