scholarly journals ESTABLISHING THE EQUATIONS THAT GENERATE THE VIBRATION MOVEMENT OF THE MAIN SPINDLE IN TRANSVERSAL DIRECTION AT CNC LATHE

2020 ◽  
Vol 4 (2) ◽  
pp. 25-30
Author(s):  
POPESCU DANIEL
Keyword(s):  
Mathematical Model ◽  
Variational Principle ◽  
Vibration Amplitude ◽  
Partial Derivatives ◽  
Transversal Vibration ◽  
First Order ◽  
Cnc Lathe ◽  
Main Spindle ◽  
Kinetic Moment

The paper presents a mathematical model for determining the movement equations that generate the transversal vibration of the main spindle at CNC lathe. For this purpose, we take into account the general equations which generate the vibration of the spindle, obtained by means of Hamilton’s Variational Principle as well as the impulse derivative and kinetic moment axioms. The solutions to the movement equations are arranged under the form of a system of first order partial derivatives equations, for which we determine the integration constants. This original way of establishing these equations allows further analysis of the main spindle vibrations in transversal direction and finding ways to decrease the vibration amplitude.

scholarly journals DETERMINING THE BALANCE CONFIGURATION, IN CASE OF THE OSCILLATING MOVEMENT OF THE MAIN SPINDLE AT CNC LATHE

2020 ◽  
Vol 7 (6) ◽  
pp. 41-46
Author(s):  
Daniel Popescu
Keyword(s):  
Variation Principle ◽  
Static Case ◽  
Cnc Lathe ◽  
Characteristic Points ◽  
Spindle Vibration ◽  
General Movement ◽  
The Stability ◽  
Main Spindle ◽  
Case Based ◽  
Kinetic Moment

In the paper we present a mathematical model through which are determined the balance conditions, needed for the stability analysis of the oscillating movement of the main spindle at CNC lathe. We take into account Hamilton's variation principle, the axiom of impulse derivative and the axiom of kinetic moment derivative. We present the general movement equations that generate the oscillations based on the calculus hypotheses, performing the introduction of the external solicitations. Establishment of the balance configuration is done by imposing the conditions that the system of forces that act upon the ensemble spindle – bearings - tool causes a deformation of the spindle, without producing spindle vibration. We obtain the new differential equations of the movement, in which the forces and moments are determined from the static case, based on which we can determine the integration constants in the characteristic points of the main spindle.

scholarly journals DETERMINING THE BALANCE CONFIGURATION, IN CASE OF THE OSCILLATING MOVEMENT OF THE MAIN SPINDLE AT CNC LATHE

2020 ◽  
Vol 7 (6) ◽  
pp. 41-46
Author(s):  
Daniel Popescu
Keyword(s):  
Variation Principle ◽  
Static Case ◽  
Cnc Lathe ◽  
Characteristic Points ◽  
Spindle Vibration ◽  
General Movement ◽  
The Stability ◽  
Main Spindle ◽  
Case Based ◽  
Kinetic Moment

In the paper we present a mathematical model through which are determined the balance conditions, needed for the stability analysis of the oscillating movement of the main spindle at CNC lathe. We take into account Hamilton's variation principle, the axiom of impulse derivative and the axiom of kinetic moment derivative. We present the general movement equations that generate the oscillations based on the calculus hypotheses, performing the introduction of the external solicitations. Establishment of the balance configuration is done by imposing the conditions that the system of forces that act upon the ensemble spindle – bearings - tool causes a deformation of the spindle, without producing spindle vibration. We obtain the new differential equations of the movement, in which the forces and moments are determined from the static case, based on which we can determine the integration constants in the characteristic points of the main spindle.

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. 

Dynamic Stability of an Axially Moving Yarn with Time-Dependent Tension

2014 ◽  
Vol 900 ◽  
pp. 753-756 ◽  
Author(s):  
You Guo Li
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Time Dependent ◽  
Second Law ◽  
Order Ordinary Differential Equation ◽  
Vibration Equation ◽  
Transversal Vibration ◽  
First Order ◽  
Homotopy Perturbation ◽  
Axially Moving

In this paper the nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin element. A partial differential equation governing the transversal vibration is derived from Newtons second law. Galerkin method is used to truncate the governing nonlinear differential equation, and thus first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result, the condition which should be avoided in the weaving process for resonance is obtained.

Soil Persistence of Dinitramine

Weed Science ◽  
1980 ◽  
Vol 28 (6) ◽  
pp. 650-654 ◽  
Author(s):  
J. A. Poku ◽  
R. L. Zimdahl
Keyword(s):  
Mathematical Model ◽  
Soil Moisture ◽  
Field Data ◽  
Soil Moisture Content ◽  
Sandy Loam ◽  
Clay Loam ◽  
First Order ◽  
Soil Persistence ◽  
Herbicide Concentration ◽  
Increasing Temperature

The effects of soil temperature, moisture, and herbicide concentration on the rate of degradation of dinitramine (N4,N4-diethyl-α,α,α-trifluoro-3,5-dinitrotoluene-2,4-diamine) were measured in clay loam and sandy loam in the laboratory. In sandy loam, the rate of degradation increased with increasing temperature. In clay loam, the rate of degradation increased from 10 to 30 C and decreased at 40 C. Soil moisture content influenced the rate of degradation in the following order: 22>11>>2.2% (air-dry) for clay loam and 12.0 = 6.0>>0.5% (air-dry) for sandy loam. First-order half-lives ranged from 3.2 at 30 C to 47 weeks at 10 C in clay loam, and 2.3 at 40 C to 31 weeks at 10 C in sandy loam. Applications in 2 yr did not cause buildup of dinitramine in the field. A mathematical model was used in an attempt to correlate laboratory and field data.

scholarly journals A Dynamic Model of PI3K/AKT Pathways in Acute Myeloid Leukemia

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yudi Ari Adi ◽  
Fajar Adi-Kusumo ◽  
Lina Aryati ◽  
Mardiah S. Hardianti
Keyword(s):  
Mathematical Model ◽  
Acute Myeloid Leukemia ◽  
Numerical Simulations ◽  
Signaling Pathways ◽  
Myeloid Leukemia ◽  
Akt Signaling ◽  
Dimensional System ◽  
First Order ◽  
Immature Myeloid Cells ◽  
Acute Myeloid

Acute myeloid leukemia (AML) is a malignant hematopoietic disorder characterized by uncontrolled proliferation of immature myeloid cells. In the AML cases, the phosphoinositide 3-kinases (PI3K)/AKT signaling pathways are frequently activated and strongly contribute to proliferation and survival of these cells. In this paper, a mathematical model of the PI3K/AKT signaling pathways in AML is constructed to study the dynamics of the proteins in these pathways. The model is a 5-dimensional system of the first-order ODE which describes the interaction of the proteins in AML. The interactions between those components are assumed to follow biochemical reactions, which are modelled by Hill’s equation. From the numerical simulations, there are three potential components targets in PI3K/AKT pathways to therapy in the treatment of AML patient.

scholarly journals FRICTION ANALYSIS IN CASE OF THE CARRIAGE- FEED SHAFT CINEMATIC COUPLING AT CNC LATHE

2020 ◽  
Vol 7 (5) ◽  
pp. 30-37
Author(s):  
Daniel Popescu
Keyword(s):  
Mathematical Model ◽  
Rational Design ◽  
Normal Force ◽  
Stick Slip ◽  
Disturbing Force ◽  
Dimensional Precision ◽  
Cnc Lathe ◽  
Elastic Systems ◽  
Friction Analysis ◽  
Slip Phenomenon

The paper presents a mathematical model for analysis of friction between the tool bearing saddle and conductor at CNC lathe. The analysis of longitudinal advance movement laws is performed taking into account the appearance and development of disturbing harmonic forces created by auto-vibrations determined by the interaction between the partial elastic systems of tool and workpiece. The friction force is emphasized as product of two components depending on the sliding speed and on the normal disturbing force. By establishing the dynamic response of the system, when the normal force depends linearly on speed, acceleration and mobile ensemble position, the premises are created for stability analysis of the friction movement, obtaining the limit speeds under which the stick-slip phenomenon occurs. Thus, it is provided for a rational design of CNC lathe elastic structure, in order to improve the surface quality and the dimensional precision.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

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