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\title{Effect of Dynamic Stiffness on Performance of Paddy Grain Losses in Axial-Flow Thresher}
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             \author[1]{Than Than  Htay}

             \affil[1]{  Mandalay Technological University}

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\date{\small \em Received: 6 December 2014 Accepted: 2 January 2015 Published: 15 January 2015}

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\begin{abstract}
        


The shaft of the thresher must be stiffness and strength to thresh efficiently for long duration. The objective of this study is to carry out the dynamic stiffness analysis of the shaft for thresher and performance of the thresher. The threshing scheme is used to change the operating speeds and moisture content of the paddy field (grain). Dynamic stiffness and performance were analyzed by using Hooke?s law. To enhance the threshing efficiency between dynamic stiffness of the shaft for thresher and losses as an unbalance weight was attached on the shaft. The analysis can be used for un-threshed losses and total losses. Performance due to dynamic stiffness was developed based on experimental performance. The most total grain losses of 12.263% were recorded at threshing thresher speed of 5.31 m/s at experiment. At 17% moisture content, un-threshed grain is 2.01% and threshing capacity is 97.99%.

\end{abstract}


\keywords{dynamic stiffness, moisture content, shaft, speeds, threshing, thresher.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
erformance test has based on dynamic analysis of the thresher. There are many sorts of the threshers to use for Combine Harvesters. This axial flow thresher is applied because it can give good performance for threshing and the least losses. Then, performance of that thresher is used by based on the shaft stiffness for this one.\par
The shaft is matched at the centre of it. While the shaft is operating with three forward engine speeds, the thresher will also do at the same condition. Based on the speeds, how the link of threshing losses and speeds at any positions that placed the unbalance weight on the shaft is considered.\par
Because of the high operating speeds and the performance from the shaft to the thresher, dynamic stiffness becomes a major design consideration. The need for dynamic analysis is especially important in the thresher of the shaft where an effective and efficient strength shaft is crucial in expending the shaft life. In the highest engine speed, the total threshing losses are very high.\par
It is therefore essential to be able to estimate the dynamic stiffness and ensure that the shaft can withstand such high model enables the thresher-shaft designer to modify the strength configuration for the optimum rate at high speeds level.\par
The result is impressive in that analysis but mathematical and dynamic model are complicated to consider. It is therefore proposed in this study a technique with consideration of any unbalance weight attachment in various speeds. 
\section[{II.}]{II.} 
\section[{Methodology a) Machine Configuration}]{Methodology a) Machine Configuration}\par
There are many sorts of the threshers in threshing the grain. This combine harvester operated axial-flow thresher was produced from KUKJE Machinery Co., ltd. (Korea). This thresher performs based on the shaft stiffness in this study. The shaft is matched at the centre of this thresher. While the shaft is operating with three forward engine speeds, the thresher also operates at the same condition. As well as harvesting method, threshing is the important practice which can affect the quantitative and qualitative losses of rice. In Myanmar's rice fields, four main types of paddy thresher are used, i.e; manual, tractor operated cross-flow type, small thresher equipped with wire loop threshing drum and combine harvester operated axial-flow thresher.\par
Recently, DKC-685 combine harvester operated axial-flow thresher adopted in many rice fields because of its easy application and better output for paddy thresher. It has wire-loop type peg-tooth. And, four comb types is attached entry of the thresher. All peg-teeth and drum (cover) are bolted by nuts at the threshing cylinder. It threshes the grain by axially. These are used for threshing the paddy crop. And, many different kinds of peg-tooth design and the shaft for this are applied to get good performance.\par
Based on the speeds, the un-threshed and total grain losses also relate by any positions that placed the unbalance weight on the shaft. Dynamic Stiffness is a function of the excitation frequency. Hence, dynamic analysis is a simple extension of static analysis. All rotating shafts deflect during rotation.\par
Also, using thresher and its shaft in this machine are shown in Fig. \hyperref[fig_2]{2}   The specification of the used machine tabulates in Table  {\ref (1)}. Results data of the thresher from the design consideration are expressed in Table \hyperref[tab_9]{(}2) to apply for the next determination. The evaluation of threshing systems involves a number of experiment approaches and the dynamic stiffness into the following categories.  This thresher performance for all different types under study was evaluated measuring an un-threshed grain losses and total grain losses. A local long-grain paddy variety widely cultivated in Myittar Township was used for the performance. Physical characteristics of the variety are list in Table \hyperref[tab_9]{(}3). The crop was cut 45-55 cm above the ground and collected for the experiments.\par
The paddy moisture content at harvesting and threshing was measured using moisture meter. Four levels of paddy moisture contents of 25, 21.5, 20 and 17 \% (w.b.) were considered for the tests. Determination of grain moisture content accurately is important before decision of harvesting, storage and milling as shown in Table \hyperref[tab_9]{(4}  To obtain the percentage of broken grain, 10 samples of 100g were randomly chosen from the outlet of the thresher. The broken grains were separated by hand from the whole paddy grains and the weight of the broken grain was recorded. In order to determine the percentage of cracked grain, at each test runs, 10 samples of 50 grains were randomly selected from the outlet of the thresher and manually husked. The husked paddy grains (Ma Naw Thu Kha) were put on a crack tester and the number of cracked kernels was recorded[10Ali].\par
The second parameter is workability, which is calculated consideration the dynamic stiffness of the shaft for thresher, mainly, the stiffness and mass of threshing period and potential threshing process.\par
Visual investigation and manual separation of 10 samples each of 100 grams were used to calculate percentage of damaged and un-threshed grains. And, grain yield was estimated by manual harvesting 5plots each of (1×1 m) with high care from random locations. Thresher performance\par
ii. 
\section[{Workability}]{Workability}\par
iii. 
\section[{Percentage of total grain losses (Tgl)}]{Percentage of total grain losses (Tgl)}\par
The harvested plants were threshed by the thresher; the threshed grains were weight for each sample. The percentage of total grain losses was calculated from Equation (1), and (2) to determine of threshing efficiency, and then (3) for specific consumed energy:[09Els]\par
Where, (Pd) -Percentage of damage (Uth) -un-threshed grains (Pgl) -Percentage of grain losses where, W1 -weight of pure grain output (kg/hr), W2 -weight of residual grain in the straw (kg/hr).\par
The energy consumed was evaluated from the following formula, Where: Fc = fuel consumption, (L/h) Ap = Actual system productivity = Wg × Pr , (kg/hr) 
\section[{c) Performance Analysis with Dynamic Stiffness}]{c) Performance Analysis with Dynamic Stiffness}\par
Dynamic stiffness generally creates images of complicated equations with limited practical value. Vibration is merely a response to other conditions in a machine [09Els].   
\section[{d) Relation between dynamic stiffness and threshing losses based on positions and engine speeds}]{d) Relation between dynamic stiffness and threshing losses based on positions and engine speeds}\par
To determine natural frequency for the shaft with dynamic analysis, the total value of stiffness and mass of the shaft must be known. The natural frequency was calculated according to the following Equation (  {\ref 7} Optimum threshing operations as well as good systems is needed to minimize the loss and obtain maximum efficiency. So, the relation between dynamic   
\section[{Results and Discussion}]{Results and Discussion}\par
To determine how to relate dynamic stiffness and grain losses is the main contribution. It is important to be stiff because the shaft is attached inside the thresher. Operating the shaft, the thresher also operates in same time. It threshes the grain from the straw as the speed of the shaft. When the speed becomes higher suddenly, the threshing grain can be crush and damage. Also, if the stiffness of the shaft is weak, the shaft can twist and cannot operate well. So, the grain losses can be found due to weak performance.\par
Therefore, it is vital to be stiff. In this paper, the stiffness of the shaft due to the attaching mass at any positions is determined. Moreover, the relationship of dynamic stiffness and grain losses are shown in the Fig ( \hyperref[fig_0]{14}, 15 and 16). To plot these, the relation of dynamic stiffness and losses via operating speeds is expressed in Fig ( \hyperref[fig_9]{6}). The required bode and polar plots are used to examine the response (vibration), dynamic stiffness and modal mass. These are shown in Fig.  {\ref 7}      approaches to the critical speed, the center of rotation begins to shift toward the CG. The phase angle between the exciting force (direction of the unbalance) and the actual vibration will be 90 degree. In this particular case, the vibration (response) amplitude lags the unbalance by 90°. So, dynamic stiffness for dynamic analysis is determined at 90° position calibration weight.\par
At 90 degree position, the values of stiffness decrease slightly in each engine speed (9.425, 10.2102 and 10.996 m/s. So, 903.47 N/m of stiffness can be accepted for this engine speed, 10.996 m/s. Table (8) refers to the effect of stiffness at various unbalance weight position by considering for each engine speeds. These relationships are shown by bar chart in Fig. \hyperref[fig_14]{10}. In this bar chart, the values of dynamic stiffness decrease steadily in the forward engine speeds (9.425, 10.2102 and 10.996 m/s). Also, these values become low from 30 degree to 180 degree. The highest dynamic stiffness can be found at the lowest speed.    Table  {\ref (10)} shows total stiffness including the value of calibration weight and shaft from design consideration depends upon engine speeds. The shaft for this thresher withstands strength, resist to unbalance weight so that it is stiffness dynamically. In dynamic analysis, the value of operating speed is determined based on natural frequency and frequency ratios. In Fig. \hyperref[fig_16]{12}, the total dynamic stiffness increased with decreasing engine speeds (9.425 m/s) for the reason that less feed rate into the threshing drum resulted in less impact force on the material. The forward engine speed of machine had significant effect on decreasing quality dynamic stiffness as speed increased. Table  {\ref (11)} shows the result of total mass (kg) with against to engine speed (rpm) and unbalanced weight position attachment (degree) on the shaft. The design requirement must be nearly the same with the critical speed for the operating speed to approach the C.G point of the shaft. During forward engine speeds (9.425, 10.2102 and 10.996 m/s), the values of un-threshed and total grain losses by changing operating speeds are shown in Fig. \hyperref[fig_0]{14}. According to this result chart, grain losses become increased steadily in each speed by dynamic stiffness consideration. These values also depend upon frequencies ratio. As the frequency ratio increases, the grain losses will follow. So, the grain losses need to adjust balance condition for frequency ratio.\par
At various speeds, losses are not different, nearly equal and the least in percentage in losses. So, it is satisfied to apply as a shaft of thresher in this combine harvester. Operating speeds, un-threshed and total losses are same each various positions attaching unbalance weight in three forward engine speeds. It can be seen that at each level of drum speed tested, the un-threshed and total grain losses increased significantly as the drum speed increased from 2.1 m/s to 39.84 m/s. However, higher value of grain losses was obtained at higher drum speed. The most un-threshed and total grain losses are 3.7 \% and 7.05 \% at 39.84 m/s, and then the least value of 0.19 \% and 0.37 \% by dynamic stiffness consideration were observed at drum speed of 2.1 m/s.   The results revealed that un-threshed grain losses increased steadily in the dynamic stiffness. By testing dynamic stiffness, the result of un-threshed grain losses increased significantly in experiment as the paddy moisture content decreased at 21.5, 20\% and 17 \% (w.b). It was observed that at each level of drum speed tested. But, the lower un-threshed grain losses observed at higher paddy moisture content with given drum speeds.\par
IV. 
\section[{Conclusion}]{Conclusion}\par
The paddy moisture content and the drum (or shaft) speeds significantly affected the total losses during paddy threshing by placed the shaft in the axialflow thresher tested. The maximum total grain losses were obtained at shaft speed 39.84 m/s, frequency ratio 0.95 and moisture content 17 \% in Fig ( \hyperref[fig_0]{14}). values of total grain losses are 12.263 \% and 7.05\% for each theory with experiment in the paddy field and dynamic stiffness at 90 degree unbalance weight position.\par
The grain losses decrease in the suitable moisture content 20\% (w.b). So, threshing losses was more increase than determining by dynamic stiffness. Comparing these two results, the total grain losses due to the dynamic stiffness is more satisfied than experimental field condition.\par
In order to minimize the effect of shaft or drum speed on total grain losses in the axial-flow thresher, it is recommended that the threshing operation should be performed immediately after crop harvesting. Performances due to dynamic analysis of the shaft for thresher have been reviewed in this paper. The two main topics include: experimental measurement techniques and dynamic stiffness of the shaft with various operating speeds.\par
V.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-5.png}
\caption{\label{fig_4}©A}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3}\includegraphics[]{image-7.png}
\caption{\label{fig_6}Figure 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-8.png}
\caption{\label{fig_7}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-9.png}
\caption{\label{fig_8}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6}\includegraphics[]{image-10.png}
\caption{\label{fig_9}Figure 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-11.png}
\caption{\label{fig_10}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{78}\includegraphics[]{image-12.png}
\caption{\label{fig_12}Figure 7 :Figure 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-13.png}
\caption{\label{fig_13}For}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10}\includegraphics[]{image-14.png}
\caption{\label{fig_14}Figure 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{201511}\includegraphics[]{image-15.png}
\caption{\label{fig_15}2015 AFigure 11 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{12}\includegraphics[]{image-16.png}
\caption{\label{fig_16}Figure 12 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{13}\includegraphics[]{image-17.png}
\caption{\label{fig_17}Figure 13 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{201514}\includegraphics[]{image-18.png}
\caption{\label{fig_18}2015 AFigure 14 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{15}\includegraphics[]{image-19.png}
\caption{\label{fig_19}Figure 15 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{16}\includegraphics[]{image-20.png}
\caption{\label{fig_20}Figure 16 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.4572784810126582\textwidth}P{0.2636075949367088\textwidth}P{0.1291139240506329\textwidth}}
Parameter\tabcellsep Dimension\tabcellsep unit\\
L×W×H\tabcellsep 4430×\tabcellsep mm\\
\tabcellsep 1860×2330\tabcellsep \\
Total displacement\tabcellsep 2392\tabcellsep cc\\
Power / Revolution\tabcellsep 52 (70)/2800\tabcellsep kW(hp) /rpm\\
Number of reaping\tabcellsep 4\tabcellsep Row\\
lines\tabcellsep \tabcellsep \\
Reaping width\tabcellsep 1485 ± 50\tabcellsep mm\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.5676895306859207\textwidth}P{0.21173285198555955\textwidth}P{0.07057761732851986\textwidth}}
Type\tabcellsep Values\tabcellsep unit\\
Outside diameter of\tabcellsep 0.43\tabcellsep m\\
Thresher\tabcellsep \tabcellsep \\
Length of thresher\tabcellsep 0.6576\tabcellsep m\\
Diameter of shaft\tabcellsep 0.075\tabcellsep m\\
Length of shaft\tabcellsep 0.2334\tabcellsep m\\
Thresher Weight\tabcellsep 105.6931\tabcellsep N\\
Threshing Speed\tabcellsep 5.31\tabcellsep m/s\\
Threshing Power\tabcellsep 2.1141\tabcellsep kW\\
Threshing Torque\tabcellsep 14.94\tabcellsep N-m\\
Torsional Moment\tabcellsep 14.9433\tabcellsep N-m\\
Total Weight (UD)\tabcellsep 69.5038\tabcellsep N\\
Total Mass\tabcellsep 7.085\tabcellsep kg\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.5442073170731707\textwidth}P{0.19695121951219513\textwidth}P{0.10884146341463415\textwidth}}
Item\tabcellsep Description\tabcellsep Unit\\
Paddy grain\tabcellsep 3438.61\tabcellsep kg/acre\\
Plant height\tabcellsep 80.8\tabcellsep cm\\
100 grains mass\tabcellsep 2.62\tabcellsep g\\
Length of panicle\tabcellsep 6.9\tabcellsep cm\\
Length of grain\tabcellsep 8.0\tabcellsep mm\\
Width of grain\tabcellsep 1.9\tabcellsep mm\\
Slenderness ratio\tabcellsep 3.4\tabcellsep -\end{longtable} \par
 
\caption{\label{tab_2}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.39171018276762404\textwidth}P{0.20639686684073105\textwidth}P{0.008877284595300261\textwidth}P{0.22526109660574412\textwidth}P{0.017754569190600523\textwidth}}
\multicolumn{2}{l}{Operation Desired}\tabcellsep Moisture\tabcellsep \multicolumn{2}{l}{Primary losses}\\
\tabcellsep Content\tabcellsep \tabcellsep \\
\multicolumn{2}{l}{Harvesting 20-25 \%}\tabcellsep \tabcellsep \multicolumn{2}{l}{Shattering if}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{grain is too dry}\\
Threshing\tabcellsep \multicolumn{2}{l}{20-25 \% for mechanical}\tabcellsep \multicolumn{2}{l}{Incomplete}\\
\tabcellsep threshing\tabcellsep \tabcellsep \multicolumn{2}{l}{threshing}\\
\tabcellsep \multicolumn{2}{l}{< 20\% for hand threshing}\tabcellsep \multicolumn{2}{l}{Grain damage}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{and cracking/}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{breakage}\\
Drying\tabcellsep \multicolumn{2}{l}{Final moisture content is}\tabcellsep \multicolumn{2}{l}{Spoilage, fungal}\\
\tabcellsep 14\% or lower\tabcellsep \tabcellsep \multicolumn{2}{l}{damage,}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Discoloration}\\
Storage\tabcellsep \multicolumn{2}{l}{<14\% for grain storage}\tabcellsep \multicolumn{2}{l}{Fungle, insect\&}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{rat damage}\\
\tabcellsep \multicolumn{2}{l}{<13\% for seed storage}\tabcellsep \multicolumn{2}{l}{Loss of vigor}\\
\tabcellsep \multicolumn{2}{l}{<9\% for long term seed}\tabcellsep \multicolumn{2}{l}{Loss of vigor}\\
\tabcellsep preservation\tabcellsep \tabcellsep \\
Milling\tabcellsep 14\%\tabcellsep \tabcellsep Grain\tabcellsep cracking\\
\tabcellsep \tabcellsep \tabcellsep and\tabcellsep breakage\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{over milling}\\
\multicolumn{2}{l}{At each level of paddy moisture, six level of}\tabcellsep \tabcellsep \\
\multicolumn{2}{l}{drum speed 5.89, 7.07, 8.25, 9.425, 10.603 and 11.781}\tabcellsep \tabcellsep \\
\multicolumn{2}{l}{m/s were examined. The drum speed was measured}\tabcellsep \tabcellsep \\
\multicolumn{2}{l}{with a digital tachometer (Lutron DT-2236). At each test}\tabcellsep \tabcellsep \\
\multicolumn{2}{l}{operate; five bundles of paddy crop were fed to the}\tabcellsep \tabcellsep \\
threshing chamber at a constant rate.\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.20529661016949152\textwidth}P{0.41779661016949154\textwidth}P{0.08043785310734464\textwidth}P{0.07443502824858757\textwidth}P{0.07203389830508473\textwidth}}
No.\tabcellsep Items\tabcellsep \tabcellsep Values\tabcellsep units\\
1\tabcellsep \multicolumn{2}{l}{Actual performance rate, P r}\tabcellsep 0.5625\tabcellsep acre/h\\
2\tabcellsep \multicolumn{2}{l}{Percentage of damage, P d}\tabcellsep 19.231\tabcellsep \%\\
3\tabcellsep Un-threshed grains, U th\tabcellsep \tabcellsep 2\tabcellsep \%\\
4\tabcellsep \multicolumn{3}{l}{Percentage of grain losses, P gl 5.263}\tabcellsep \%\\
5\tabcellsep \multicolumn{2}{l}{Percentage of total grain}\tabcellsep 12.263\tabcellsep \%\\
\tabcellsep losses,T gl\tabcellsep \tabcellsep \\
6\tabcellsep Field efficiency, ? t\tabcellsep \tabcellsep 77.49\tabcellsep \%\\
7\tabcellsep Cutting efficiency, ? c\tabcellsep \tabcellsep 62.87\tabcellsep \%\\
8\tabcellsep Cleaning efficiency, ? cl\tabcellsep \tabcellsep 90\tabcellsep \%\\
9\tabcellsep Threshing efficiency, ? cl\tabcellsep \tabcellsep 97.77\tabcellsep \%\\
10\tabcellsep \multicolumn{3}{l}{Specific consumed energy, S e 7.8×}\tabcellsep kW.h\\
\tabcellsep \tabcellsep \tabcellsep 10 -3\tabcellsep /kg\\
11\tabcellsep \multicolumn{2}{l}{Fuel consumption per hour}\tabcellsep 3.08\tabcellsep gal/ hr\\
12\tabcellsep Fuel Cost per Acre\tabcellsep \tabcellsep 31,197\tabcellsep kyats/ac\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep re\\
13\tabcellsep Labour Cost par Acre\tabcellsep \tabcellsep 13750\tabcellsep Kyat/acr\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep e\\
\multicolumn{2}{l}{The results at 90 degree position are shown in}\tabcellsep \multicolumn{3}{l}{stiffness and modal mass from design and unbalance}\\
\multicolumn{2}{l}{Table (6). These results are determined based on Fig 7,}\tabcellsep \multicolumn{2}{l}{weight condition.}\\
\multicolumn{2}{l}{8 and 9. Table (7) is to compare for the values of}\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.03891566265060241\textwidth}P{0.4977108433734939\textwidth}P{0.0983132530120482\textwidth}P{0.2150602409638554\textwidth}}
Item\tabcellsep Parameters\tabcellsep Symbol\tabcellsep Values\\
s 1 2 3 4 5\tabcellsep Original response (mil p-p) New response (mil p-p) Response due to calibration weight Applied force of calibration weight Synchronous dynamic stiffness\tabcellsep s ? O + = ? F DS C ? C ? K O ? R ? ?\tabcellsep 2.98 ? 90.6° 3.8 ? 180.6° 4.8 ? 218.71 ° 0.2902 ? 90° 4730.9 ? 129°\\
6\tabcellsep Modal mass (kg)\tabcellsep M\tabcellsep 0.0451\\
7\tabcellsep Modal stiffness (N/m)\tabcellsep K\tabcellsep 903.4586\\
8\tabcellsep Modal damping\tabcellsep D\tabcellsep 12.539\\
9\tabcellsep (N.s/m) Influence vector (mil\tabcellsep H ?\tabcellsep 26.83 ? 129°\\
\tabcellsep p-p)\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_5}Table 6 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{7} \par 
\begin{longtable}{P{0.20705128205128204\textwidth}P{0.2833333333333333\textwidth}P{0.3596153846153846\textwidth}}
Items\tabcellsep Modal mass\tabcellsep Stiffness\\
Shaft\tabcellsep 34.68 kg\tabcellsep 3.9716 ×10 9 N/m\\
unbalance\tabcellsep 0.1398kg\tabcellsep 2799 N/m\end{longtable} \par
 
\caption{\label{tab_6}Table 7 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{8} \par 
\begin{longtable}{P{0.17739130434782607\textwidth}P{0.25130434782608696\textwidth}P{0.2291304347826087\textwidth}P{0.19217391304347825\textwidth}}
Engine\tabcellsep 9.425\tabcellsep 10.2102\tabcellsep 10.996\\
speeds\tabcellsep \tabcellsep \tabcellsep \\
(m/s)\tabcellsep \tabcellsep \tabcellsep \\
Position\tabcellsep Stiffness\tabcellsep Stiffness\tabcellsep Stiffness\\
(degree)\tabcellsep (N/m)\tabcellsep (N/m)\tabcellsep (N/m)\\
30\tabcellsep 3143.427\tabcellsep 2941.34\tabcellsep 2799\\
60\tabcellsep 1696.7251\tabcellsep 1587.6\tabcellsep 1511\\
90\tabcellsep 1014.6117\tabcellsep 949.33\tabcellsep 903.47\\
120\tabcellsep 600.5195\tabcellsep 561.934\tabcellsep 534.81\\
150\tabcellsep 287.5591\tabcellsep 269.0757\tabcellsep 256.15\\
180\tabcellsep 20.0446\tabcellsep 18.7543\tabcellsep 17.851\end{longtable} \par
 
\caption{\label{tab_7}Table 8 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{9} \par 
\begin{longtable}{P{0.18888888888888888\textwidth}P{0.20856481481481481\textwidth}P{0.22824074074074074\textwidth}P{0.22430555555555556\textwidth}}
Engine\tabcellsep 9.423\tabcellsep 10.2102\tabcellsep 10.996\\
speeds\tabcellsep \tabcellsep \tabcellsep \\
(m/s)\tabcellsep \tabcellsep \tabcellsep \\
Position\tabcellsep Modal\tabcellsep Modal\tabcellsep Modal\\
(degree)\tabcellsep mass\tabcellsep mass\tabcellsep mass\\
\tabcellsep (kg)\tabcellsep (kg)\tabcellsep (kg)\\
30\tabcellsep 0.157\tabcellsep 0.1469\tabcellsep 0.1398\\
60\tabcellsep 0.0848\tabcellsep 0.0793\tabcellsep 0.0755\\
90\tabcellsep 0.0507\tabcellsep 0.0474\tabcellsep 0.0451\\
120\tabcellsep 0.03\tabcellsep 0.0281\tabcellsep 0.0267\\
150\tabcellsep 0.0144\tabcellsep 0.0134\tabcellsep 0.0128\\
180\tabcellsep 0.001001\tabcellsep 0.000937\tabcellsep 0.000892\end{longtable} \par
 
\caption{\label{tab_8}Table 9 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_9}Table ( 9}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{10} \par 
\begin{longtable}{P{0.1275\textwidth}P{0.23640625\textwidth}P{0.24437499999999998\textwidth}P{0.24171874999999998\textwidth}}
Engine\tabcellsep 9.425\tabcellsep 10.2102\tabcellsep 10.996\\
speeds\tabcellsep \tabcellsep \tabcellsep \\
(m/s)\tabcellsep \tabcellsep \tabcellsep \\
Position\tabcellsep Stiffness×1\tabcellsep Stiffness×1\tabcellsep Stiffness×10 9\\
(degree)\tabcellsep 0 9\tabcellsep 0 9\tabcellsep (N/m)\\
\tabcellsep (N/m)\tabcellsep (N/m)\tabcellsep \\
30\tabcellsep 3.971603143\tabcellsep 3.971602941\tabcellsep 3.971602799\\
60\tabcellsep 3.971601697\tabcellsep 3.971601588\tabcellsep 3.971601511\\
90\tabcellsep 3.971601015\tabcellsep 3.971600949\tabcellsep 3.971600903\\
120\tabcellsep 3.971600601\tabcellsep 3.971600562\tabcellsep 3.971600535\\
150\tabcellsep 3.971600288\tabcellsep 3.971600269\tabcellsep 3.971600256\\
180\tabcellsep 3.97160002\tabcellsep 3.971600019\tabcellsep 3.971600018\end{longtable} \par
 
\caption{\label{tab_10}Table 10 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{11} \par 
\begin{longtable}{P{0.1837837837837838\textwidth}P{0.21058558558558557\textwidth}P{0.2412162162162162\textwidth}P{0.2144144144144144\textwidth}}
Engine\tabcellsep 9.425\tabcellsep 10.2102\tabcellsep 10.996\\
speeds\tabcellsep \tabcellsep \tabcellsep \\
(rpm)\tabcellsep \tabcellsep \tabcellsep \\
Position\tabcellsep Modal\tabcellsep Modal\tabcellsep Modal\\
(degree)\tabcellsep mass\tabcellsep mass\tabcellsep mass\\
\tabcellsep (kg)\tabcellsep (kg)\tabcellsep (kg)\\
30\tabcellsep 34.84\tabcellsep 34.8269\tabcellsep 34.82\\
60\tabcellsep 34.7648\tabcellsep 34.7593\tabcellsep 34.76\\
90\tabcellsep 34.7307\tabcellsep 34.7275\tabcellsep 34.7251\\
120\tabcellsep 34.71\tabcellsep 34.7081\tabcellsep 34.7067\\
150\tabcellsep 34.6944\tabcellsep 34.6934\tabcellsep 34.6928\\
180\tabcellsep 34.681\tabcellsep 34.68094\tabcellsep 34.681\end{longtable} \par
 
\caption{\label{tab_11}Table 11 :}\end{figure}
 			\footnote{© 2015 Global Journals Inc. (US)} 			\footnote{Effect of Dynamic Stiffness on Performance of Paddy Grain Losses in Axial-Flow Thresher} 		 		\backmatter   			 
\subsection[{Acknowledgement}]{Acknowledgement} 			  			 \par
First of all, the author is particularly intended to  {\ref Dr} Moreover, the author would like to thank to Principal and staffs from Mechanization Training Centre (Meikhtila) and then, Managers and staffs from Heavy Industry(18), Inngon (Kyaukse) for their help and permit to study for this research. Special thanks are given to her parents, brothers, sisters and her friends for their constant understanding, encouragement and support to make this research without difficulty.			 			  				\begin{bibitemlist}{1}
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\end{document}
