Moment Equilibrium Equations Research Articles

A two-muscle, continuum-mechanical forward simulation of the upper limb.

By following the common definition of forward-dynamics simulations, i.e. predicting movement based on (neural) muscle activity, this work describes, for the first time, a forward-dynamics simulation framework of a musculoskeletal system, in which all components are represented as continuous, three-dimensional, volumetric objects. Within this framework, the mechanical behaviour of the entire muscle-tendon complex is modelled as a nonlinear hyperelastic material undergoing finite deformations. The feasibility and the full potential of the proposed forward-dynamics simulation framework is demonstrated on a two-muscle, three-dimensional, continuum-mechanical model of the upper limb. The musculoskeletal model consists of three bones, i.e. humerus, ulna, and radius, an one-degree-of-freedom elbow joint, and an antagonistic muscle pair, i.e. the biceps and triceps brachii, and takes into consideration the contact between the skeletal muscles and the humerus. Numerical studies have shown that the proposed upper limb model is capable of predicting realistic moment arms and muscle forces for the entire range of activation and motion. Within the limitations of the model, the presented simulations provide, for the first time, insights into existing contact forces and their influence on the muscle fibre stretch. Based on the presented simulations, the overall change in fibre stretch is typically less than 3%, despite the fact that the contact forces reach up to 71% of the exerted muscle force. Movement-predicting simulations are achieved by minimising a nonlinear moment equilibrium equation. Based on the forward-dynamics simulation approach, an iterative solution procedures for position-driven (inverse dynamics) and force-driven scenarios have been proposed accordingly. Applying these methodologies to time-dependent scenarios demonstrates that the proposed methods can be linked to state-of-the-art control algorithms predicting time-dependent muscle activation levels based on principles of forward dynamics.

Improvement of lubrication characteristics in the reciprocating fuel pump of marine diesel engines

In this study, we apply circumferential grooves and taper shape to the plunger in order to improve the lubrication characteristics of reciprocating fuel pumps for marine diesel engines. We use the two-dimensional Reynolds equation to evaluate lubrication characteristics with variation of viscosity, clearance, groove and taper for an incompressible, unsteady state flow. Moreover, we use the equilibrium equation of moment and forces in the vertical and horizontal directions to determine the motion of the plunger. The validity of numerical model is verified through the fact that the position of wear is similar to that of minimum film thickness. We investigate the lubrication characteristics of the pump by comparing the dimensionless minimum film thickness, or film parameter. Through numerical analysis, we find that to improve the lubrication characteristics of the pump, applying both circumferential groove and taper shape to the plunger is more effective than applying just either one of them.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb (M-C) strength criterion and the initial normal stress without considering the inter-slice (or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price (M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

A new method for the stability analysis of geosynthetic-reinforced slopes

This paper is concerned with the stability analysis of reinforced slopes. A new approach based on the limit equilibrium principle is proposed to evaluate the stability of the reinforced slopes. The effect of reinforcement is modeled as an equivalent restoring force acting the bottom of the slice and added into the general limit equilibrium (GLE) method. The equations of force and moment equilibrium of the slice are derived and corresponding iterative solution methods are provided. The new method can satisfy both the force and the moment equilibrium and be applicable to the critical failure surface of arbitrary form. Furthermore, the results predicted by the proposed method are compared with the calculation examples of other researchers and the centrifuge model test results to validate its correctness and effectiveness.

Residual stress analysis with stress-dependent growth rate and creep deformation during oxidation

Abstract

Mechanical model of coupling rolling and sliding friction in real-time non-clearance precision ball transmission

In this paper, a new static mechanical model is established to study the rolling-sliding contact in the real-time non-clearance precision ball drive. Meshing forces at the main and the secondary transmission force points in two types of mechanical models are deduced shown in moment equilibrium equations and energy balance equations. Based on coupling coefficient determined by the Carter narrow theory, a new mechanical model of coupling rolling and sliding friction is established. The meshing force simulated by the finite element method has good matching with theoretical calculation with error less than 5.6%, which verifies the feasibility of the coupled model. Outcome of the research could be a theoretical support in improving the transmission accuracy of the drive.

A model of triple friction pendulum bearing for general geometric and frictional parameters

SummaryCurrent models describing the behavior for the triple friction pendulum (TFP) bearing are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply as a direct consequence of equilibrium.This paper presents a revised model of behavior of the TFP bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact. To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces. Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior.The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity and temperature can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made. This paper presents (a) the development of the revised TFP bearing model, (b) the analytic solution for the force–displacement relations of two configurations of the TFP bearing, (c) a model that incorporates inertia effects of the TFP bearing components and other effects that are useful in advanced response history analysis, and (d) examples of implementation of the features of the presented model. Copyright © 2016 John Wiley & Sons, Ltd.

Improvement of Lubrication Characteristics in Fuel Injection Pump for Medium-Speed Diesel Engines: Part I - Application of Profile Shape

Engine & Machinery Division, Hyundai Heavy Industries(Received August 15, 2015; Revised September 20, 2015 ; Accepted September 21, 2015)Abstract − In this research, effects of profile changes of stem section of the plunger on the lubrication char-acteristics of a fuel injection pump (FIP) were evaluated by hydrodynamic lubrication analysis. The clearancebetween plunger and barrel was divided into two regions, head and stem. The head was not involved in pre-venting a decrease of fuel oil pressure. So, research efforts were focused on both edges of the plunger’s stem.The two -dimensional Reynolds equation was used to evaluate lubrication characteristics with variations in vis-cosity, clearance and profile for a laminar, incompressible, unsteady-state flow. Moreover, the equilibrium equa-tion of moment and forces in the vertical and horizontal directions were used to determine the motion of theplunger. The equations were discretized using the finite difference method. Lubrication characteristics of the FIPwere investigated by comparing the dimensionless minimum film thickness, or film parameter, which is the ratioof minimum film thickness to surface roughness. Through numerical analyses, we showed that the profile of thelower edge of the stem had no effect on lubrication characteristics, but the profile of the upper edge had a sig-nificant influence on lubrication characteristics. In addition, changes in the profile were more effective in improvinglubrication characteristics under low viscosity conditions.Keywords − medium-speed diesel engine, fuel injection pump, profile, minimum film thickness

Residual Stress Analysis Due to Chemomechanical Coupled Effect, Intrinsic Strain and Creep Deformation During Oxidation

Metal oxidation at high temperature is often accompanied with the stress generation both in the metal substrate and the growing oxide scale. In this paper, taking into account the growth strain, intrinsic strain and creep deformation, a new analysis model to characterize the residual stress evolutions during an isothermal oxidation process is developed on the basis of the mechanical-balance and moment-equilibrium equations. In this model, the growth strain and the stress are coupled based on an evolving equation, which reduces to the Clarke’s assumption if the stress influence on the growth strain of the oxide scale is ignored. The curvature describing the bending of the system is expressed. Euler numerical method is adopted to simulate the stress evolution and the comparisons among the present model, Zhang’s creep solution and the experimental results are also performed. Finally, effects of creep constants, substrate thickness and intrinsic strain on the residual stress distribution in the oxide scale/metal substrate are discussed.

부하를 고려한 직선운동유니트의 정밀도 시뮬레이션 기술

This paper presents the motion accuracy simulation considering loads such as workpiece weight, cutting force, cogging force of a linear motor, and force caused by misalignment and runout error of a ballscrew in linear motion units. The transfer function method is basically utilized to estimate 5-DOF motion errors, together with the equilibrium equations of force and moment on the table. The transfer function method is modified in order to consider clearance changed according to the loads in the double sided hydrostatic/aerostatic bearings. Then, the analytic model for predicting the 5-DOF motion errors is proposed with the modified transfer function method. Motion errors were simulated under different loading conditions in the linear motion units using hydrostatic, aerostatic, and linear motion bearings, respectively. And the proposed analytic model was verified by comparing the estimated and measured motion errors.

MATHEMATICAL MODELING AND EXPERIMENTAL STUDY ON SIT-TO-STAND PROCESS BASED ON ASSISTIVE STANDING-UP ROBOT

The new assistive standing-up robot followed the rule of sit-to-stand movement was developed. Mathematical model during standing-up motion was built by using Newton-Euler approach for kinetics analysis. Force and moment equilibrium equations were obtained and simulation model was built in Simulink by standing up with robot-aided, robot and arms supported and robot, arm and lower limbs of weakness of muscle strength. By means of assistive standing-up robot and sensors, force and moment were measured and analyzed. The results show that standing-up robot can be efficiently used to assist the rising, especially in initial stage, in spite of sit-to-stand aided-method. Arm-supported standing-up maneuver can keep the posture balance and stable, and has compensation ability of necessary force and moment of lower extremity, particularly close to upright standing posture,and force and moment can be predicted accurately by the standing posture simulation model. Lower limbs of deficient muscle strength play limited role to assist the rising.

Design and Research of Electromagnetic Drive Pulley Type Downhole Blowout Preventer

A new electromagnetic drive rope and pulley type downhole blowout preventer is proposed. The moment equilibrium equation of downhole blowout preventer is established. The structural dimensions of the valve plate connecting position of blowout preventer and pulley rope location are optimized. The dynamic simulation of pulley type downhole blowout preventer is carried out to improve the parameters of this new blowout preventer and to improve its motion performance and mechanical properties.

Identification of bearing load by three section strain gauge method: Theoretical and experimental research

Reasonable bearing load distribution is important for the safe and reliable operation of rotating machinery. However, it is difficult to measure bearing load in field. This paper puts forward a bearing load identification method based on the measured three section strain values. Shaft is divided into several sections at strain gauge locations. The force and moment equilibrium equations are set up and assembled to form bearing load solving equations. This method can reduce the modeling error, especially for the machines with irregular rotating parts. It can also be applied for the entire shaft system bearing load distribution study with high accuracy and fault tolerant. Test was done on a rotor-bearing system rig. Bearing load distribution in different shaft alignment states is identified and analyzed. Test results show that the bearing load distribution varies sensitively and linearity to the change of bearing elevation. Further research shows that the accuracy of the method depends on the strain gauge locations. It would be best to place the strain gauge at location where the bending moment is sensitive to the change of bearing load. Moreover, mounting the strain gauge further from the bearing reduces the relative error due to the exact reaction point location is not known, which influences the accuracy of beading moment arm from the strain gauge location to the reaction point.

Determination of the response distributions of cantilever beam under sinusoidal base excitation

As a kind of base excitation, shaking table is often used to test the dynamic characteristics of structures. However, the prediction of response to base excitation hasn't been solved effectively, which limits the further research on the test and analysis method with respect to base movement. This article is based on a cantilever beam and focuses on its response prediction under sinusoidal base excitation. By moment and force equilibrium equations, an analytical model is built for this cantilever beam, and then a method to predict dynamic response at base excitation is proposed. Finally, the method is used to solve the vibration response distributions of the cantilever beam at base excitation. Correctness of this method is also proved by comparing the result with experimental data.

Quantifying catch‐and‐release: The extensor tendon force needed to overcome the catching flexors in trigger fingers

The extensor tendon forces required to overcome the catching flexors in trigger fingers are unknown. A biomechanical model with moment equilibrium equations and method of least squares was developed for estimating the tendon force at triggering in trigger fingers. Trigger fingers that exhibited significant catching and sudden release during finger extension were tested. A customized "pulling tester" was used to pull the finger from flexion to extension and provide synchronic measurement of the pulling force. The displacement of the tested finger was measured by a motion capture system. This preliminary study presents kinematic and kinetic data at triggering of 10 trigger fingers. The distal and proximal interphalangeal (PIP) joints presented sudden release while the metacarpophalangeal (MCP) joint started extension in the early phase of finger extension. The tendon tension of flexor digitorum profundus was greater than that of flexor digitorum superficialis (FDS) in six fingers, and less than that of FDS in three fingers. The tension of two flexor tendons was almost equal in one finger. At the PIP and MCP joints, 1.54 times the force of flexors was needed for the extensors to overcome the catching flexors in trigger fingers. This biomechanical model provides clinicians with a clearer idea of the tendon force at triggering. The quantitative results may help in the understanding of movement characteristics of trigger fingers. These findings are useful to better understand the etiology and nature of trigger finger development, and thus aid in further development of better assessments and treatments related to this.

On a virtual work consistent three-dimensional Reissner–Simo beam formulation using the quaternion algebra

In the paper, we present the Reissner–Simo beam theory in which the rotations are represented by quaternions. From the generalized virtual work principle, where the unity constraint of the rotational quaternion is properly considered and the consistent energy complements of the rotational quaternions are employed, we derive the weak kinematic equations in the quaternion-based description. These equations are then employed in the extended virtual work principle to obtain the consistent governing equations of the three-dimensional beam in terms of the quaternion algebra. The quaternion moment equilibrium equation is analyzed, discussed, and interpreted. In numerical implementation, the standard Galerkin discretization is used to obtain the quaternion-based finite-element formulation. Various examples prove the suitability of the formulation.

Cylinder Position Servo Control Based on Fuzzy PID

The arbitrary position control of cylinder has always been the hard challenge in pneumatic system. We try to develop a cylinder position servo control method by combining fuzzy PID with the theoretical model of the proportional valve-controlled cylinder system. The pressure differential equation of cylinder, pressure-flow equation of proportional valve, and moment equilibrium equation of cylinder are established. And the mathematical models of the cylinder driving system are linearized. Then fuzzy PID control algorithm is designed for the cylinder position control, including the detail analysis of fuzzy variables and domain, fuzzy logic rules, and defuzzification. The stability of the proposed fuzzy PID controller is theoretically proved according to the small gain theorem. Experiments for targets position of 250 mm, 300 mm, and 350 mm were done and the results showed that the absolute error of the position control is less than 0.25 mm. And comparative experiment between fuzzy PID and classical PID verified the advantage of the proposed algorithm.

Slope Stability Analysis Based on Limit Equilibrium and Numerical Analysis

Based on the background of a foundation pit slope of the tertiary strong weathered basalt(TSWB), a quantitative analysis of the slope stability is proposed by combination of the limit equilibrium and the numerical analysis. The analysis also considers the effects of the natural state and soaking state Then, as an example, an ultra-deep foundation pit slope (UFPS) is analyzed under the background of TSWB. The Janbu method is used in the limit equilibrium because it can meet all the equilibrium conditions, including the force and moment equilibrium equation. The Lagrangian difference method which based on shear strength reduction is adopted in numerical analysis. Some meaningful conclusions can be obtained through comparing analysis the calculation results of Janbu method with finite difference method. These conclusions can be given a reference to similar projects.

Consideration of equilibrium equations at the hip joint alongside those at the knee and ankle joints has mixed effects on knee joint response during gait

Accurate estimation of muscle forces during daily activities such as walking is critical for a reliable evaluation of loads on the knee joint. To evaluate knee joint muscle forces, the importance of the inclusion of the hip joint alongside the knee and ankle joints when treating the equilibrium equations remains yet unknown. An iterative kinematics-driven finite element model of the knee joint that accounts for the synergy between passive structures and active musculature is employed. The knee joint muscle forces and biomechanical response are predicted and compared with our earlier results that did not account for moment equilibrium equations at the hip joint. This study indicates that inclusion of the hip joint in the optimization along the knee and ankle joints only slightly (<10%) influences total forces in quadriceps, lateral hamstrings and medial hamstrings. As a consequence, even smaller differences are found in predicted ligament forces, contact forces/areas, and cartilage stresses/strains during the stance phase of gait. The distribution of total forces between the uni- and bi-articular muscle components in quadriceps and in lateral hamstrings; however, substantially alter at different stance phases.

Analysis of Bearing Loads for Scroll Compressor Considering Phase-Angled Counterweights

In order to improve the dynamic characteristics of scroll compressor, according to the crankshaft bearing characteristics of scroll compressor, based on the forces and moment equilibrium equations of the crankshaft and compressor frame body, used the frame body forces and crankshaft bearing loads as a variable, analyzed the frame body forces in the best of conditions by changing the counterweights installation angle to control the crankshaft bearing design formulas, thus obtained counterweights quality and phase angle and other parameters, ensured the service life of the bearing, and obtained effective control of the crankshaft bearing load and frame body force, improve the operation reliability of scroll compressor, prolonging the service life. This paper puts forward a set of formulas, which are derived based on analysis of the loads at crankshaft of scroll compressor. The formulas can be used to determine the parameters of installation angle of the counterweight and the forces of loads at crankshaft for scroll compressor.