Development of Mathematical Model for Top Roller Displacement of Three-Roller Bending Machine Using Dimensional Analysis

2018 ◽  
pp. 125-132 ◽  
Author(s):  
Prafull S. Thakare ◽  
Sandip M. Salodkar ◽  
C. C. Handa
Keyword(s):  
Mathematical Model ◽  
Dimensional Analysis

FORMULATION OF MATHEMATICAL MODEL FOR MAINTENANCE COST OF A STONE CRUSHING PLANT BASED ON DIMENSIONAL ANALYSIS AND MULTIPLE REGRESSION

2013 ◽  
pp. 1-6
Author(s):  
PROF. ANJALI J. JOSHI ◽  
DR. JAYANT P. MODAK
Keyword(s):  
Mathematical Model ◽  
Multiple Regression ◽  
Dimensional Analysis ◽  
Least Square Method ◽  
Least Square ◽  
Maintenance Cost ◽  
Design Data ◽  
Static And Dynamic Analysis ◽  
Dimensionless Equation ◽  
Crushing Plant

This paper presents the approach for the mathematical modeling of maintenance cost for the set up of new Stone Crushing Plant based on the dimensional analysis and multiple regression. Presented maintenance cost mathematical model is derived based on the generated design data. Design data is generated from actual design of all stone crushing plants followed by static and dynamic analysis. Estimation of design data is carried out based on the assumed plant layout. Dimensional analysis is used to make the independent and dependent variables dimensionless and to get dimensionless equation. Later, multiple regression analysis is applied to this dimensionless equation to obtain the index values based on the least square method. The mathematical model of maintenance cost is formulated using these obtained index values. Finally, the formulated model is evaluated on the basis of correlation and root mean square error between the computed values by model and the estimated values.

Corner Reproduction Accuracy in Electro-Chemical Drilling (ECD) of Blind Holes

1984 ◽  
Vol 106 (1) ◽  
pp. 55-61 ◽  
Author(s):  
V. K. Jain ◽  
Vinod Kumar Jain ◽  
P. C. Pandey
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Regression Analysis ◽  
Dimensional Analysis ◽  
Analysis Of Variance ◽  
Process Parameters ◽  
Important Process ◽  
Electrochemical Drilling ◽  
Experimental Findings ◽  
Shape And Size

Little information is available about the corner shape and size produced in electrochemical drilling of blind holes. On this account prediction of the complete anode shape analytically, in ECD, is not possible. This paper reports the experimental findings regarding the shape and size of the corners copied, in the anode during electrochemical drilling of blind holes using a tool of specified geometry. An equation evolved by regression analysis of experimental data has been suggested for this purpose. With a view to improve results, an equation based on dimensional analysis has also been presented. Finally, a comprehensive mathematical model accounting for the independent, higher order, and the interaction effects of different important process parameters on the yield (anode radius) has been proposed and its adequacy has been tested by the analysis of variance and accuracy against experimental data.

A Mathematical Model for Predicting the Extrusion Efficiency of a Vertical Column Shaft Palm Oil Extrusion Machine using Dimensional Analysis

2016 ◽  
Vol 6 (1) ◽  
pp. 001-008
Author(s):  
Victor Chijioke Okafor ◽  
◽  
Princewill Kelechi Ejesu ◽  
Dennis Chukwunonye Chinweuba ◽  
Reginald Nnaemeka Nwakuba
Keyword(s):  
Mathematical Model ◽  
Dimensional Analysis ◽  
Palm Oil ◽  
Vertical Column

Model Development for a Composite Core-Pulling Mechanism

2014 ◽  
Vol 494-495 ◽  
pp. 387-390 ◽  
Author(s):  
Yan Fang Yin ◽  
Hua Shun Hu
Keyword(s):  
Mathematical Model ◽  
Mechanical System ◽  
Dimensional Analysis ◽  
Simple Structure ◽  
Simulation Analysis ◽  
Model Development ◽  
Plastic Part ◽  
One Dimensional ◽  
Safety And Reliability ◽  
Plastic Parts

The main purpose of this work was to develop a mathematical model and computer programs for design analysis in composite core-pulling mechanism. The injection mould with slanted guide pillar for two-step core-pulling from the side of the product effects significantly the quality and efficiency of plastic part. The study is a one-dimensional analysis of secondaryejector mechanism, based on a forward marching technique of solution for the simple structure and high safety and reliability. Using the simulation analysis of mechanical system based on Pro/E, the mechanism can solve the problem that plastic parts are difficult to side core pulling in different directions by the use of bevel pillar.

scholarly journals FORMULATION OF MATHEMATICAL MODEL FOR PRODUCTION TURNOVER OF BIODIESEL PLANT BASED ON DIMENSIONAL ANALYSIS AND MULTIPLE REGRESSION

2012 ◽  
pp. 268-276
Author(s):  
ASHWIN S. CHATPALLIWAR ◽  
DR. VISHWAS S. DESHPANDE ◽  
DR. JAYANT P. MODAK ◽  
DR. NILESHSINGH V. THAKUR
Keyword(s):  
Mathematical Model ◽  
Multiple Regression ◽  
Dimensional Analysis ◽  
Least Square Method ◽  
Least Square ◽  
Design Data ◽  
Dimensionless Equation ◽  
Set Up ◽  
The Mathematical Model ◽  
Data Design

This paper presents the approach for the mathematical modeling of production turnover for the set up of new Biodiesel plant based on the dimensional analysis and multiple regression. Presented production turnover mathematical model is derived based on the generated design data. Design data is generated from the estimated design data. Estimation of design data is carried out based on the assumed plant layouts of different capacities. Dimensional analysis is used to make the independent and dependent variables dimensionless and to get dimensionless equation. Later, multiple regression analysis is applied to this dimensionless equation to obtain the index values based on the least square method. The mathematical model of production turnover is formulated using these obtained index values. Finally, the formulated model is evaluated on the basis of correlation and root mean square error between the computed values by model and the estimated values.

Modeling the tool wear rate in powder mixed electro-discharge machining of titanium alloys using dimensional analysis of cryogenically treated electrodes and workpiece

2016 ◽  
Vol 231 (2) ◽  
pp. 271-282 ◽  
Author(s):  
Sanjeev Kumar ◽  
Rupinder Singh ◽  
Ajay Batish ◽  
TP Singh
Keyword(s):  
Mathematical Model ◽  
Wear Rate ◽  
Tool Wear ◽  
Titanium Alloys ◽  
Dimensional Analysis ◽  
Electric Discharge ◽  
Cryogenic Treatment ◽  
Tool Wear Rate ◽  
Electric Discharge Machining ◽  
X Ray

Three grades of titanium alloy TITAN 15, TITAN 21, and TITAN 31 were machined using powder mixed electric discharge machining to study the effect of cryogenic treatment and its effect on tool wear rate (TWR). Thereafter, an attempt has been made to develop a mathematical model for predicting TWR using dimensional analysis using the outcome of the Taguchi model and thermo-physical properties of tool materials. The model shows the significant role of thermal conductivity on TWR in electric discharge machining of titanium alloys. The predicted values from the developed mathematical model were validated and were found to be in good agreement with the experimental results. Microscopic investigations on selected tool samples were performed using scanning electron microscope, energy-dispersive X-ray spectrometer, and X-ray diffraction. The results showed transfer of material on the tool surface from the workpiece, dielectric, and the powder.

Vibration Characteristics of an Elastic Linkage With Elastic Input and Output Shafts

1984 ◽  
Vol 106 (3) ◽  
pp. 272-277 ◽  
Author(s):  
A. Garcia-Reynoso ◽  
W. P. Seering
Keyword(s):  
Mathematical Model ◽  
Dimensional Analysis ◽  
Lumped Parameter Model ◽  
Mode Shapes ◽  
System Response ◽  
Constant Input ◽  
Input And Output ◽  
Continuous Parameter ◽  
Lumped Parameter ◽  
Four Bar Linkage

This paper develops a mathematical model of the linearized vibrations of a four-bar linkage with a flexible rocker link and flexible input and output shafts. The model assumes constant input velocity and includes inertial masses at the ends of the input and output shafts. The assumed modes technique is used to model the rocker link. Exact rocker mode shapes are derived from an analysis of the continuous parameter model and are then used in a lumped parameter model to predict system response. Finally, a dimensional analysis is presented which develops the concept of families of mechanisms whose dynamic behaviors are similar.

scholarly journals Model Matematis Hubungan antara Kadar Air Akhir Bahan dengan Variabel Proses Pengeringan pada Pneumatic Conveying Recirculated Dryer

2018 ◽  
Vol 38 (2) ◽  
pp. 217
Author(s):  
Abadi Jading ◽  
Nursigit Bintoro ◽  
Lilik Sutiarso ◽  
Joko Nugroho Wahyu Karyadi
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Dimensional Analysis ◽  
Final Moisture Content ◽  
Sago Starch ◽  
Pneumatic Conveying ◽  
Drying Process ◽  
Vertical Pipe ◽  
The Mathematical Model ◽  
The Relationship

Flour drying could be conducted by using pneumatic conveying dryer (PCD) or flash dryer, but generally it is required a high vertical pipe. The high of vertical pipe may be replaced with a recirculation process to produce a required final moisture content of the material. This study had designed pneumatic conveying recirculated dryer (PCRD) to dryi of wet sago starch. Later, the design was used to determine a mathematical model of the relationship between the variables of drying process with final moisture content of the material. The purpose of this study was to develop a mathematical model of the relationship between the final moisture content of wet sago starch  with variables drying process and recirculation continuously in the pneumatic conveying recirculated dryer (PCRD) using dimensional analysis. Buckingham Phi Theorem methods of dimensional analysis was used to find the relationship variables that affect the final moisture content of wet sago starch on the PCRD machine. The mathematical model generated in this study is      The coefficient of determination (R2) of the mathematical model was 0.948, or 94.8 %, indicated that the model was valid to predict the final moisture content of wet sago starch in designing PCRD machines. While the sensitivity of the test results showed that the dimensionless product of the most influential are , , and . The model was applicable for drying wet sago starch or other starch material which is similat to the physical properties of wet sago starch. ABSTRAKPengeringan bahan-bahan tepung dapat dilakukan dengan pneumatic conveying dryer (PCD) atau flash dryer, namun umumnya memerlukan pipa vertikal yang cukup tinggi. Pipa vertikal yang tinggi dapat diganti dengan proses resirkulasi untuk menghasilkan kadar air akhir bahan yang disyaratkan. Pada penelitian ini telah dirancang pneumatic conveying recirculated dryer (PCRD) untuk mengeringkan pati sagu basah, serta dicari model hubungan matematis antara variabel-variabel proses pengeringan dengan kadar air akhir. Tujuan penelitian ini adalah mengembangkan model matematis hubungan antara kadar air akhir pati sagu basah dengan variabel-variabel proses pengeringan resirkulasi secara kontinyu pada pneumatic conveying recirculated dryer (PCRD) menggunakan analisis dimensi. Metode Buckingham Phi Theorem dalam analisis dimensi digunakan untuk mencari hubungan variabel-variabel yang berpengaruh terhadap kadar air akhir pati sagu basah pada mesin PCRD. Model matematis yang dihasilkan pada penelitian ini adalah      Nilai koefisien determinasi (R2) dari model matematis tersebut adalah 0,948 atau 94,8 %, menunjukkan bahwa model tersebut valid digunakan untuk memprediksi kadar air akhir pati sagu basah dalam merancang mesin PCRD. Sedangkan hasil uji sensitivitas menunjukkan bahwa dimensionless product yang paling berpengaruh adalah , , dan . Model tersebut berlaku untuk pengeringan pati sagu basah atau bahan-bahan tepung lainnya yang sifat fisiknya identik dengan pati sagu basah.

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