Moment Balance Research Articles

Balance, barycentremetry and external shape analysis in idiopathic scoliosis: What can the physician expect from it?

ObjectiveOur objective was to establish a corridor of normality for the external shape 3D parameters and then to assess these variables in adolescent idiopathic scoliosis (AIS). MethodsAdolescent with mild and severe AIS were included prospectively, as well as a control group of asymptomatic subjects. A quasi‐automatic 3D reconstruction of the spine and manual 3D reconstruction of the external envelope was performed from biplanar radiography. The center of mass position, the axial intersegmental moment resulting at the apex and junctional vertebrae, and the coronal trunk balance were automatically computed. A normality corridor of asymptomatic subjects was calculated as the range [5th-95th percentiles] for external shape parameters at each vertebral level. ResultsForty-one asymptomatic subjects (19 females; 22 males; 21 yo, SD=4) and sixty AIS (56 females; 4 males; 13 years old, SD=1.9; 30 mild and 30 severe; 34 thoracic curves and 26 thoraco-lumbar or lumbar curves) were included. All parameters based on the external shape showed differences between AIS and controls, as well as between mild and severe scoliosis. For instance, the intersegmental moment applied to the upper junctional vertebra was above the 95th percentile of controls in 70% of AIS patient. The percentage of severe patients showing parameters higher than the normality corridor was significantly higher than mild patients (p<0.0001). ConclusionsThe analysis of center of mass, vertebral intersegmental moment and coronal trunk balance parameters appear to be relevant in characterizing the 3D deformity of adolescent idiopathic scoliosis. The upper junctional intersegmental moment seems to be able to distinguish the different stages of curvature severity.

Numerical simulation of atom transfer radical polymerization of styrene by moment and population balance models

Numerical simulation of atom transfer radical polymerization of styrene by moment and population balance models

Study on numerical simulation method of overtopping dam break of concrete faced sand-gravel dam

Based on the field investigation of dam break cases, a numerical simulation method of concrete faced sand-gravel dam overtopping break is proposed. The method is mainly composed of three parts: (1) Aiming at the erosion and scour of vortex flow on dam body, appropriate model is used to simulate the flow movement; (2) The interaction between water flow and sand particles in dam break process is accurately simulated; (3) Based on moment balance method, the failure process of concrete face slab under dead weight and water load is determined. The results show that the proposed mathematical simulation method can accurately simulate the reverse erosion of the dam and the detailed evolution of the face slab break during the dam break process. The relative error between the measured data and the calculated peak breach flow, the development of the breach of the rockfill body, the duration of the dam break and the length of the face slabs are all less than 15%, which verifies the rationality of the numerical model.

Upper-bound limit analysis on seismic rotational stability of waterfront retaining walls

The seismic rotational stability analysis of waterfront retaining walls can be found in the existing literature, which adopted the limit equilibrium theory and was based on the moment balance of the external force on the wall. However, the application location of the seismic earth pressure still lacks a recognized solution. This paper presented a new methodology for the rotational stability analysis of the waterfront retaining wall under earthquake conditions based on the multi-block upper bound approach. The seismic loads are determined by the pseudo-static method. The wall and soil wedge (not containing water within) are treated as a whole system and build an energy balance equation of this system, then an analytical expression for the seismic yield acceleration coefficient is deduced. Results showed that the water level on the downstream side exceeds 30% of the wall height, the seismic rotational stability of the waterfront retaining wall would decrease significantly. The seismic yield acceleration coefficient is decreasing by about 40% when the water level on the downstream side is increased from 3 m to 4 m. The results from the proposed method compared with those from Choudhury and Ahmad (2007) are slightly different but more reasonable.

Balancing of the Orthoglide Taking into Account Its Varying Payload

For fast-moving robot systems, the fluctuating dynamic loads transmitted to the supporting frame can excite the base and cause noise, wear, and fatigue of mechanical components. By reducing the shaking force completely, the dynamic characteristics of the robot system can be improved. However, the complete inertial force and inertial moment balancing can only be achieved by adding extra counterweight and counter-rotation systems, which largely increase the total mass, overall size, and complexity of robots. In order to avoid these inconveniences, an approach based on the optimal motion control of the center of mass is applied for the shaking force balancing of the robot Orthoglide. The application of the “bang–bang” motion profile on the common center of mass allows a considerable reduction of the acceleration of the total mass center, which results in the reduction of the shaking force. With the proposed method, the shaking force balancing of the Orthoglide is carried out, taking into account the varying payload. Note that such a solution by purely mechanical methods is complex and practically inapplicable for industrial robots. The simulations in ADAMS software validate the efficiency of the suggested approach.

A Dynamically Balanced Kinematically Redundant Planar Parallel Robot

AbstractA dynamically balanced robotic manipulator does not exert forces or moments onto the base on which it is fixed; this can be important for the performance of parallel robots as they are able to move at very high speeds, albeit usually have a reduced workspace. In recent years, kinematically redundant architectures have been proposed to mitigate the workspace limitations of parallel manipulators and increase their rotational capabilities; however, dynamically balanced versions of these architectures have not yet been presented. In this paper, a dynamically balanced kinematically redundant planar parallel architecture is introduced. The manipulator is composed of parallelogram linkages that reduce the number of counter rotary elements required to moment balance the mechanism. The balancing conditions are derived, and the balancing parameters are optimized using Lagrange multipliers, such that the total mass and inertia of the system is minimized. The elimination of the shaking forces and moments is then verified via a simulation in the multi-body dynamic simulation software msc adams.

Modeling and analysing of spring-loaded double parallelogram mechanism using moment balance

Double Parallelogram Lifting Mechanism (DPLM) is a multi-linkage mechanism adopted as the lifting mechanism of the designed robot in this paper. DPLM is designed based on Double Parallelogram Mechanism (DPM), making it a compact and stable multi-linkage mechanism with a low retracted height and a great working height. This paper investigates the condition in which DPLM obtains static equilibrium at any height using Hookean springs and the minimization of the motor’s required torque exertion against the gravitational moment of the weight of the mechanism. A mathematical model describing all the factors involved in moment balancing of DPLM is derived and established in MATLAB and is verified through experiments with a virtual prototype conducted in SOLIDWORKS. The obtained results show that the magnitude of the moment exerted by the tension of a spring can be determined not only by its exact installation positions but also by its D value, which is the difference in the distances between the two installation points of a spring and their respective rotation axes. An optimization method based on minimizing the RMSE of the unbalanced moment for DPLM is introduced.

Uniformly distributed lace design for hard rock TBMs

Optimization in TBM cutterhead design is essential for increasing its performance. Lace design for the cutters, buckets, and manholes in the cutterhead, is one of the major considerations in the design of the hard rock TBMs. An optimum lace design is necessary to avoid cutterhead deviation, vibration, and stress concentration during its operation. TBM manufacturers usually utilize two common lace designs of radial and spiral configurations. Despite the presence of many advantages for these two designs, each of them has its own disadvantages which may cause difficulties in achieving an efficient design of the cutterhead. This paper introduces a new TBM cutterhead lace design in which all three normal, side, and rolling forces are considered. The new force and moment balancing relationships are presented. With the consideration of the problems of the radial and spiral configurations, a new method of “uniformly distributed lace design” is introduced and the steps of achieving the final layout of the cutterhead is explained with its required parameters. On the basis of an example, a comparative study is made among three methods of applying radial, spiral, and uniformly distributed lace designs. The results show that the new method is very efficient in both uniformly and symmetrically distributing the cutters, buckets, and manholes on the cutterhead surface with no boundary conflicts. It also has the advantage to have low unbalanced forces and moments.

A New Method for Static Measurement of Two Axles Vehicle Centroid Height

Background: Vehicle centroid height is an important parameter in vehicle control systems. It plays an important role in vehicle roll stability and handling stability. At present, there are mainly static and dynamic measurement methods such as swing method, mass reaction method, marking method and so on. These static measurement methods often require a fixed suspension to make the measurement process time-consuming and laborious, and measurement errors will occur when the suspension is not fixed firmly, and it is impossible to measure the mass center position of spring-loaded mass and non-spring-loaded mass. Objective: Therefore, it is of great practical significance to study a high accuracy, low cost and fast measurement method of vehicle centroid height. We revised and summarized all patents relating to methods for estimating vehicle centroid height. And a new method of centroid measurement is designed in this paper. Methods: According to the change of tire flattening radius and suspension, the change of spring and non-spring mass center height when vehicle axle load changes, the method of delineation is used to calculate the change of tire flattening radius and suspension; According to the relationship between vehicle tilt angle and front and rear axle load, the principle of moment balance and the principle of mass balance, it determines the geometric relationship between the variables, and to take the moment of the contact point between the front wheel and the ground, the moment balance equation is established, and the height of the vehicle mass center, spring load and non-spring load mass center in the horizontal position of the vehicle are obtained. Results: This measurement method is different from the existing static measurement of vehicle centroid height, it does not need the fixed suspension, only need to measure several dimensions, we can avoid heavy labor and safety accidents brought by the fixed suspension, it can also reduce the measurement error caused by fixation, but also can draw the centroid location of the sprung mass and unsprung mass. The measurement method is simple, economical and accurate, and is widely applicable on two-axle vehicles. Conclusion: The purpose of this paper is to provide a static and accurate measurement method of vehicle centroid height, so as to solve the problem that the current static measurement method of vehicle centroid height needs fixed suspension, and measurement errors will occur when the suspension is not fixed properly, so it is impossible to measure the centroid position of spring-loaded mass and non-spring-loaded mass.

Determination of Catalyst Residence Time, Heat Generation, and Monomer Conversion via Process Variables during Propylene Polymerization by a Mathematical Model

Because of the inherent complexity of a Ziegler–Natta catalyst, its performance during propylene polymerization against the particular process variables, namely, the reaction temperature and hydrogen amounts, so far remains unclear. Obviously, these process variables directly affect the catalyst residence time, monomer conversion, and heat generation. Understanding these issues is essential for those working in the field such as catalyst chemists, polymer scientists, process engineers, designers, and producer licensors. The main aim of this work is to cover the existing gap in this field by proposing a mathematical kinetics model. The modeling approach is based on the polymer moment balance technique and validated via experimental data from a lab-scale reactor. The results of this study showed that the model has achieved the defined aims properly. Two significant conclusions were obtained. Firstly, only temperature increase has a significant effect on the conversion percent increase and hydrogen has no effect on it. Secondly, hydrogen not only increases the rate of polymerization, but also raises the deactivation constant and reduces the lifetime of the catalyst.

Reliability design of mechanical systems subjected to repetitive stresses

To enhance the design of mechanical systems, parametric Accelerated Life Testing (ALT) as a systematic reliability method is proposed as a way to evaluate the design of mechanical systems subjected to repeated impact stresses. It requires: (1) a parametric ALT scheme shaped on system BX lifetime, (2) a load inspection, (3) parametric ALTs with the associated design modifications, and (4) an assessment of whether the revised product design(s) reach the targeted BX life-time. We propose using a general life-stress model and sample size equation. A test example using both market data and parametric ALT was the redesign of a hinge kit system (HKS) in a refrigerator. To conduct parametric ALTs, a force and moment balance analysis was utilized. The mechanical impact loadings of the HKS were evaluated for an working refrigerator door. For the first ALT, the HKS failure happened in the crack/fracture of the kit housing and oil spilled from the damper when the HKS was disassembled. The failure modes and mechanisms constructed in the 1st ALT were similar to those of the unsuccessful samples found from the marketplace. The missing design parameters of the HKS included stress raisers such as corner roundings and the rib of the housing in HKS, the seal in the oil damper, and the material of the cover housing. In the second ALT, the cover housing fractured. The design defect of the cover housing in the HKS was the plastic material. As a corrective action plan, the cover housing was modified from plastic to aluminium. After the second ALT, the lifetime of the modified HKS was reassured to be B1 life 10 years with a yearly failure rate of 0.1%.

About Identifiability of Oil and Water Relative Permeability Curves and Reservoir Heterogeneity through Integrated Well Test Study

Relative permeabilities (RP) play an important role in reservoir engineering. RP functions together with the permeability anisotropy coefficient predetermine waterflooding efficiency and oil/water ratio in production forecast. Traditionally multiphase flow parameters are estimated from core analysis data. But such measurements suffer from small representative elementary volume (REV) and limited characterization of reservoir properties. Therefore using core data in 3D reservoir modelling could lead to distorted description of actual flow conditions. Despite those functions (RP) could be history matched with assimilated production data, such a procedure would require long history of waterflooding. So the authors’ idea is to apply integrated well test study to estimate the displacement efficiency and/or relative permeability functions at downhole conditions. Well testing is traditionally applied in reservoir engineering for single-phase reservoir parameters estimation. Our approach is extended to multi-phase flow and is based on data collection at well bottomholes and subsequent data assimilation in flow model.In this paper we summarize both features of mathematical problem statement and identifiability of multiphase parameters through inverse problem solution, but also discuss 10+ -year experience in interpretation of two-phase well testing using our technologies. To estimate multiphase parameters, we have to jointly consider complex data of well logging and dynamic data of well testing. Both data sets are used in the inverse problem quality criteria, where the least squares method has been applied. Forward problem corresponds to a 3D multiphase fluid flow model in porous media. The latter consists of continuity equation with multiphase Darcy equation instead of moment balances. For data assimilation modern methods of optimal control theory were successfully applied. For all synthetic test cases real reservoir parameters were accurately recovered through the use of forward simulation data.In order to estimate reservoir heterogeneity, we applied a single-phase model to get the ratio of vertical to horizontal permeability. Data of well self-interference testing were used for vertical permeability estimation. Depending on the depth of reservoir pressure perturbation, reservoir properties could be properly inferred from observations. Two other options of 3D interference testing using vertical and horizontal wells are also presented.In other words, all the problems considered are identifiable, and the level of their correctness is completely predetermined by the amount and quality of observed data. And transition to digital (intelligent) oil-and-gas production and closed-loop reservoir management [1] provides a possibility to remove discussed restrictions and all inverse problems considered should be accounted as fully identifiable.

Predicting Molecular Weight Distribution, Melt Flow Index, and Bulk Density in a Polypropylene Reactor via a Validated Mathematical Model

One of the main goals of polymer science has been to relate the process variable to their vital macroscopic properties in order to obtain tailor-made products. In particular, this goal is significant when we have to use a catalyst that has a unique and unknown behavior with its own complex kinetics such as a Ziegler–Natta catalyst for polypropylene production. Today, computer simulation with acceptable accuracy has come to the aid of polymer science. The final product properties are highly dependent on the crucial factors comprising the average molecular weight, its dispersity, and bulk density of a polymer, and these factors also depend on process variables with the complexity of a kinetic reaction. A mathematical model can be a worthy replacement to the conventional manner, experiment by trial and error, for designing a favorite product. In this study, a mathematical model is proposed to fulfill this aim. By the model with its offered algorithm, kinetic constants can be easily adjusted with fairly good prediction of the desired product. The modeling approach is a polymer moment balance technique (population balance) in a slurry semibatch reactor and coded in MATLAB/SIMULINK software. The model has been validated via experimental data from a laboratory scale reactor with an acceptable margin of error.

A Mechanics Study on the Self-Righting of Abalone from the Substrate.

In this study, we aim to probe the self-righting behavior of abalone on a substrate based on experiments and mechanistic analyses. A successful self-righting process of abalone is observed, and its critical condition in theory can be given in terms of the rotation angle. Then, according to the moment balance and potential energy minimization, the required tension force of the abalone foot for self-righting is derived with respect to the rotation angle. The experimental result also shows that in many cases the abalone cannot finish this self-righting process. Then, measurements on the tolerant strength of abalone muscle and tolerant adhesion strength of the foot on substrate are both conducted. It is judged that the abalone muscle is strong enough, which can provide enough tension force, and thus, the self-righting mainly depends on the adhesion area of the foot on substrate. These findings cast new light on engineering new types of biomaterials and devices, such as marine equipment and soft robotics.

Thermodynamically consistent thermoelastic plate and shell formulations for small deformation and small strain using non-classical continuum mechanics incorporating internal rotations

The work presented in a recent paper by the authors [35] for a thermodynamically consistent and kinematic assumption free plate and shell formulation for small deformation and small strain based on the conservation and balance laws of classical continuum mechanics (CCM) is extended here for non-classical continuum mechanics (NCCM). This formulation incorporates additional physics due to internal rotations that arise due to the deformation gradient tensor. This physics is neglected in CCM, hence is absent in the plate and shell formulation of reference [35]. Consideration of this new physics requires modifications of the current balance laws as well as consideration of a new balance law “balance of moment of moments” (BMM) [2, 3]. Cauchy stress tensor becomes non-symmetric. Cauchy moment tensor is conjugate to the symmetric part of the rotation gradient tensor which exists now due to new physics. Balance of angular momenta yields additional three differential equations as part of the mathematical model. The new balance law (BMM) establishes symmetry of the Cauchy moment tensor. The new physics considered here exists in all deforming solid continua as it is due to the deformation gradient tensor, but is ignored in CCM. The consequence of this new physics is additional stiffness, hence additional strain energy storage and change in the time history of displacements and stress field compared to formulations based on CCM. The basic mathematical model for the plate and shell deformation consists of conservation and balance laws in $$\mathbb {R}^3$$ based on NCCM incorporating internal rotations. The associated finite element formulations for obtaining the solution of the mathematical model consists of : (i) geometry of the plate or shell described by the flat or curved middle surface (as done conventionally) and nodal vectors locating the top and bottom faces of the plate/shell (ii) the displacement field approximation that is p-version hierarchical in the plane as well as in the transverse direction (iii) integral form is constructed using Galerkin Method with Weak Form (GM/WF) and the corresponding element equations. The formulation presented here remains valid and accurate for thin as well as thick plate/shell and naturally reduces to the formulation of reference [35] based on classical continuum mechanics. Model problem studies and comparisons with the studies based on CCM formulation [35] will be presented in a follow up paper.

Static modeling and analysis of soft manipulator considering environment contact based on segmented constant curvature method

PurposeThe purpose of this paper is to estimate the deformation of soft manipulators caused by obstacles accurately and the contact force and workspace can be also predicted.Design/methodology/approachThe continuum deformation of the backbone of the soft manipulator under contact is regarded as two constant curvature arcs and the curvatures are different according to the fluid pressure and obstacle location based on piecewise constant curvature framework. Then, this study introduces introduce the moment balance and energy conservation equation to describe the static relationship between driving moment, elastic moment and contact moment. Finally, simulation and experiments are carried out to verify the accuracy of the proposed model.FindingsFor rigid manipulators, environmental contact except for the manipulated object was usually considered as a “collision” which should be avoided. For soft manipulators, an environment is an important tool for achieving manipulation goals and it might even be considered to be a part of the soft manipulator’s end-effector in some specified situations.Research limitations/implicationsThere are also some limitations to the presented study. Although this paper has made progress in the static modeling under environmental contact, some practical factors still limit the further application of the model, such as the detection accuracy of the environment location and the deformation of the contact surface.Originality/valueBased on the proposed kinematic model, the bending deformation with environmental contact is discussed in simulations and has been experimentally verified. The comparison results show the correctness and accuracy of the presented SCC model, which can be applied to predict the slender deformation under environmental contact without knowing the contact force.

Prediction of residual burst strength of worn casing by theoretical and numerical modelling

Casing wear is a serious problem affecting casing integrity and casing strength, especially in ultra-deep wells, directional wells and horizontal wells. After casing is worn, degraded casing strength will lead to such hazardous problems as casing deformation, sustained casing pressure and even casing failure. Therefore, it is crucial and meaningful to predict residual casing strength and design casing string considering wear effect. Residual strength calculation model of worn casing, however, is still a challenge in casing design and safety evaluation. The purpose of this paper is to explore a simple and accurate model to predict the residual burst strength of crescent-shaped worn casing. The most commonly used mathematical models are discussed and compared in this paper. Through investigation and derivation, it is found that API (American Petroleum Institute) standard model assumes a uniform wear reduction around casing inner wall, while eccentric wear model simplifies worn casing as an eccentric pipe in bipolar coordinate. Then this paper presents a crescent-shaped wear model based on the force balance and moment balance of crescent-shaped worn casing. Finite element analysis proves that crescent-shaped wear model is more rigorous and accurate for residual burst strength prediction of worn casing. The work presented in this paper can provide a theoretical foundation and technical basis for casing wear evaluation and casing string design in directional wells.

Investigating Growth of Molecular Weight and Its Dispersity of Polypropylene during Polymerization by a Validated Mathematical Model

In this study, we investigate the effect of temperature reaction and hydrogen amount as the most effective process variables on Ziegler–Natta catalysts; with the aim of evaluating their effects on how to grow molecular weight and its dispersity during polypropylene polymerization with the aid of a validated mathematical model. The used approach in modeling is polymer moment balance technique (population balance approach) in MATLAB/SIMULINK environment, and then the model has been validated by experimental data come from a laboratory scale reactor. The main target of this study is to gain considerable insight into Ziegler–Natta catalyst performance against changing of the variables. The model might be applicable for the catalyst makers to evaluate and to improve their catalysts and also could be useful for process chemical engineers to easily operate the plant, to replace a new catalyst, to optimize process conditions and to generate new formulation for a new grade.

Selection and strength check on fasteners of protective structure in cryogenic wind tunnel

Protective structure, acted as a substructure of internal insulation system in cryogenic wind tunnel, is in possession of such advantages of isolating insulation unit from cryogenic medium and reducing cold energy loss. However, the protective structure is continuously subjected to alternating pressure during the operation of cryogenic wind tunnel. Thus, the type selection and strength check on connecting fastener, acted as weak bearing component in protective structure, are investigated. Firstly, according to the composition of protective structure, three key connecting positions are determined and the corresponding connecting fasteners are selected. Then, according to the cryogenic wind tunnel working condition, the theoretical mechanical models of connecting fasteners are built under different working conditions. Finally, involving the force and moment balance, mechanics analysis and strength check are conducted on connecting fasteners. The obtained results show that the selected fasteners are conformed to the strength requirement of cryogenic wind tunnel in service, which paves the way for building the cryogenic wind tunnel in the future.

Mathematical Modeling of Propylene Polymerization with Ziegler-Natta Catalyst and Hydrogen Response Validation

Hydrogen in spite of having a chain transfer agent role is one of the most important factors which directly affecting on kinetic of propylene polymerization. Hydrogen causes to dramatically increase the percentage of activated sites in proportion to being total potential sites on the catalyst surface. On the other hand, the chain transfer agent role of hydrogen gives rise to changing some vital indices of final product properties. This study has attempted to present a validated mathematical model that able to predicting profile polymerization rate and also calculating some of the vital indices of the final product, properties to be derived from kinetic equations. Furthermore, in this paper, we present a developed model that calculates fraction activated sites catalyst via hydrogen concentration based on dormant site theory and determining the best process condition. The modeling approach is based on the polymer moment balance method, i.e. population balance technique, and validated by experimental works. The main aim of this study is assigned to investigate the behavior change of polymerization rate to hydrogen. The experimental data and model outputs were compared and concluded that the global errors were in the acceptable range.