The hardening is an important physical
process at the industrial production. The most famous examples are
pelletizing of iron ore or briquetting of coal and peat. We spoke about
the hardening kinetics in the articles [1-3].
Analytical curves of the hardening kinetics for the ore briquetting are shown in Fig.1.
Fig 1. The hardening kinetic curves obtained at the modeling [1-3] by formulas: (1) - artificial desiccation and (2) - native desiccation Time is presented in seconds
Now we shall deal with hardening velocity or hardening rate. What is that?
Hardening
velocity (rate) vS is ratio of the compressive strength of specimen Rs
to unit of time t. Hardening velocity is derivative of time vS = dRs
/dt (Pa / sec).
Our modeling approach to the hardening kinetics
allows carry direct calculation of the hardening velocity, pioneering
move. Formulas (1) and (2) of the hardening kinetics are presented in
articles [1-3].
I have proposed the following my own formula with
delay for the direct analytical calculations of the hardening velocity
vS (the differential equation in the operational form of Laplace).
The parameters Rs max, rs0, τ and T are determined from an experimental data of the hardening process.
The mathematical model (3) of the hardening velocity vS of the first order with delay is Transfer Function W(s), which is convenient for modeling using MATLAB. The mathematical model (3) has enough accuracy for engineering calculations.
The parameters Rs max, rs0, τ, τtr and T2 are determined from an experimental data of the hardening process.
The mathematical model (4) of the hardening velocity vc of the second order with delay is Transfer Function W(s), which is convenient for modeling using MATLAB. The mathematical model (4) provides very high accuracy of scientific calculations and engineering.
Analytical curves of the hardening velocity are shown in Fig. 2 and Fig. 3.
Fig 2. The hardening velocity curves obtained at the modeling by formulas
(3) - artificial desiccation and (4) - native desiccation. Time is presented in seconds
Fig 3. The hardening velocity curves obtained at the modeling by formulas
(3) - artificial desiccation and (4) - native desiccation. Time is presented in hours
The use of I. Bobin's operational formulas of the hardening kinetics and velocity allows:
1. Reduce the cost of obtaining products with the required strength.
2. Effectively manage the process of hardening of products.
3. Optimize the process of hardening finished products and semi-finished products.
4. Reduce the number of production areas.
5. Reduce the cost of drying and hardening products.
In
this manner the modeling of hardening kinetics is an indispensable tool
for analisis of the mineral technology and other. The immediate
analytical description and a visual representation of the hardening
velocity in time are very important for solving optimization problem of
production processing. The formulas of the hardening velocity can be
used everywhere with success where a product (or semi-product) acquires
strength over time.
Free pdf
References
1. Igor
Bobin, Natalia Petrovskaya. «THE MODELING OF THE HARDENING KINETICS»
News aggregation Linkedin Pulse. August 26, 2017
https://www.linkedin.com/pulse/modeling-hardening-kinetics-igor-bobin-ph-d-?lipi=urn%3Ali%3Apage%3Ad_flagship3_profile_view_base_post_details%3BFQp56PbETLirkMAYTZZg%2Fw%3D%3D
2. Igor Bobin, Natalia Petrovskaya «THE MODELING OF THE HARDENING
KINETICS» Web resurs "MINERAL MODELING". August 25, 2017
https://sites.google.com/site/mineralmodeling/hardening-modeling/the-modeling-of-the-hardening-kinetics
3. Igor Bobin, Natalia Petrovskaya. «THE MODELING OF THE HARDENING
KINETICS» Open publishing platform Scribd. August 25, 2017
https://ru.scribd.com/document/357243590/THE-MODELING-OF-THE-HARDENING-KINETICS
September 24, 2017
mineral.modeling@protonmail.com
No comments:
Post a Comment