Mechanical Performance of External Fixators With Wires for the Treatment of Bone Fractures—Part I: Load-Displacement Behavior

1993 ◽  
Vol 115 (1) ◽  
pp. 29-36 ◽  
Author(s):  
C. Delprete ◽  
M. M. Gola
Keyword(s):  
Mathematical Model ◽  
Mechanical Performance ◽  
Bone Fractures ◽  
Fracture Site ◽  
External Fixators ◽  
Axial Loads ◽  
Linear Estimate ◽  
The Common ◽  
Displacement Behavior ◽  
The Mathematical Model

Using matrix algebra, a mathematical model is formulated for a particular type of external fixator with wires (system developed by Ilizarov) for the treatment of bone fractures. The mathematical model is used to give a linear estimate of the stiffness under lateral and axial loads in a representative number of practical conditions. Relative displacements of the bone ends at the fracture site are calculated not only in the common case of a gap, but also for various angles of inclined sliding contact; in this case, a realistic load is applied and nonlinear stiffening of the wires under transversal loads is iteratively taken into account.

Design of the Conjugate Cam Induction Hardening Mechanism and Establishment of the Motion Controlling Mathematical Model

2012 ◽  
Vol 155-156 ◽  
pp. 726-730
Author(s):  
Zhong Hua Li ◽  
Qian Tang ◽  
Di Yan ◽  
Jie Wu
Keyword(s):  
Mathematical Model ◽  
Induction Hardening ◽  
Uniform Motion ◽  
Hardening Mechanism ◽  
Kinematic Relationship ◽  
Nc Machine ◽  
The Common ◽  
Relationship Of ◽  
The Mathematical Model ◽  
Basic Motion

The common methods of cam induction hardening are discussed at present. By analyzing the basic motion law of conjugate cam, a new induction hardening mechanism is designed. The motion controlling mathematical model is built on the basis of the kinematic relationship of the transmission of the induction hardening mechanism. Through the mathematical model calculation, we can get angular velocity of the workbench, then realize that single axis on NC machine controls the inductor to make isometric uniform motion relative to the cam surface, so that the cam hardening depth distribution is uniform.

scholarly journals Biomechanical assessment of composite versus metallic intramedullary nailing system in femoral shaft fractures: A finite element study

2021 ◽  
Author(s):  
Saeid Samiezadeh ◽  
Pouria Tavakkoli Avval ◽  
Zouheir Fawaz ◽  
Habiba Bougherara
Keyword(s):  
Mechanical Performance ◽  
Bone Fractures ◽  
Stress Shielding ◽  
Femoral Shaft ◽  
Delayed Union ◽  
Fracture Site ◽  
Long Bone ◽  
Fe Model ◽  
Non Union ◽  
Shaft Fractures

Background: Intramedullary nails are the primary choice for treating long bone fractures. However, complications following nail surgery including non-union, delayed union, and fracture of the bone or the implant still exist. Reducing nail stiffness while still maintaining sufficient stability seems to be the ideal solution to overcome the above mentioned complications. Methods: In this study, a new hybrid concept for nails made of carbon fibers/ fl ax/epoxy was developed in order to reduce stress shielding. The mechanical performance of this new implant in terms of fracture stability and load sharing was assessed using a comprehensive non-linear FE model. This model considers several mechanical factors in nine fracture configurations at immediately post-operative, and in the healed bone stages. Results: Post-operative results showed that the hybrid composite nail increases the average normal force at the fracture site by 319.23 N ( P b 0.05), and the mean stress in the vicinity of fracture by 2.11 MPa ( P b 0.05) at 45% gait cycle, while only 0.33 mm and 0.39 mm ( P b 0.05) increases in the fracture opening and the fragments' shear movement were observed. The healed bone results revealed that implantation of the titanium nail caused 20.2% reduction in bone stiffness, while the composite nail lowered the stiffness by 11.8% as compared to an intact femur. Interpretation: Our results suggest that the composite nail can provide a preferred mechanical environment for healing, particularly in transverse shaft fractures. This may help bioengineers better understand the biomechanics of fracture healing, and aid in the design of effective implants.

scholarly journals Biomechanical assessment of composite versus metallic intramedullary nailing system in femoral shaft fractures: A finite element study

2021 ◽  
Author(s):  
Saeid Samiezadeh ◽  
Pouria Tavakkoli Avval ◽  
Zouheir Fawaz ◽  
Habiba Bougherara
Keyword(s):  
Mechanical Performance ◽  
Bone Fractures ◽  
Stress Shielding ◽  
Femoral Shaft ◽  
Delayed Union ◽  
Fracture Site ◽  
Long Bone ◽  
Fe Model ◽  
Non Union ◽  
Shaft Fractures

Background: Intramedullary nails are the primary choice for treating long bone fractures. However, complications following nail surgery including non-union, delayed union, and fracture of the bone or the implant still exist. Reducing nail stiffness while still maintaining sufficient stability seems to be the ideal solution to overcome the above mentioned complications. Methods: In this study, a new hybrid concept for nails made of carbon fibers/ fl ax/epoxy was developed in order to reduce stress shielding. The mechanical performance of this new implant in terms of fracture stability and load sharing was assessed using a comprehensive non-linear FE model. This model considers several mechanical factors in nine fracture configurations at immediately post-operative, and in the healed bone stages. Results: Post-operative results showed that the hybrid composite nail increases the average normal force at the fracture site by 319.23 N ( P b 0.05), and the mean stress in the vicinity of fracture by 2.11 MPa ( P b 0.05) at 45% gait cycle, while only 0.33 mm and 0.39 mm ( P b 0.05) increases in the fracture opening and the fragments' shear movement were observed. The healed bone results revealed that implantation of the titanium nail caused 20.2% reduction in bone stiffness, while the composite nail lowered the stiffness by 11.8% as compared to an intact femur. Interpretation: Our results suggest that the composite nail can provide a preferred mechanical environment for healing, particularly in transverse shaft fractures. This may help bioengineers better understand the biomechanics of fracture healing, and aid in the design of effective implants.

Mechanical Performance of External Fixators With Wires for the Treatment of Bone Fractures—Part II: Wire Tension and Slippage

1993 ◽  
Vol 115 (1) ◽  
pp. 37-42 ◽  
Author(s):  
C. Delprete ◽  
M. M. Gola
Keyword(s):  
Mechanical Performance ◽  
Marked Decrease ◽  
Bone Fractures ◽  
Transverse Load ◽  
External Fixators ◽  
Transverse Loading ◽  
Ilizarov External Fixator ◽  
Single Wire ◽  
Wire Tension

The work shows correct procedures needed in order to gather reliable data from measurement of displacements versus axial load in a laboratory mounting of the Ilizarov external fixator. The mechanism of settling after load cycling is investigated. Detension under load is a major problem of wires. By means of vibration frequency measurements, tests on single wire allow determination of reduction in wire tension due to transverse loading: it is found that, almost independently from the amount of clamp tightening, the tension reaches a lower limit related only to the transverse load and not related to pretension. It is shown that, for higher clamp tightening torques, wire detension must be attributed to permanent plastic deformation of the wires; moreover, it is shown that the unavoidable errors in the spacing of the tensioned wires lead to marked decrease of their stiffness under transverse load.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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