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\title{Predictive Model of Orthotropic Un-Symmetric Box Cam Based On Deflection And countered by Segments of Circular-Arc Contact Profiles}
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             \author[1]{Dr. Fathi  Al-Shamma}

             \author[2]{Dr. Louay S.  Yousuf}

             \affil[1]{  baghdad university Iraq}

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\date{\small \em Received: 4 November 2011 Accepted: 24 November 2011 Published: 4 December 2011}

\maketitle


\begin{abstract}
        


In this paper the principal objective is to find the deflection of orthotropic box cam profile countered by segments of circular-arc due to the effect of contact loading which produce the generate force that induces high contact stress on the cam-surface especially in high-speed machine. In highspeed it can be used the composite cam, since it affects the whole machine performance to improve the wear resistance. Several researchers investigated the effects of cam profile in accuracy and system flexibility on the output motion experimentally; but there is a lake in the theoretical part. The theoretical part has been done with the solution of orthotropic circular plate equation using the harmonic deflection motion of the follower. The cam used in this paper can be seen in composite shifter cam for a motorcycle transmission, composite hollow cam-shafts, the running valve lift with roller followers of a composite camshaft, and heavy duty of marine engine. The aim of the present paper is to find the maximum deflection of orthotropic box cam on the boundaries of the three circular-arc contact profiles for flanks and noses of contact follower loadings. The results were arrangement into theoretical part and finite element using software ANSYS 12.1.

\end{abstract}


\keywords{Orthotropic Cam, Contact Loading, Circular Plate Equation, ANSYS Software, Un-Symmetric Pressure Angles, Box Cam.}

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\let\tabcellsep& 	 	 		 
\section[{NOMENCLATURES}]{NOMENCLATURES} 
\section[{INTRODUCTION}]{INTRODUCTION}\par
new type of composite cam-shafts that obtain an optimum condition valve lift running with roller followers based on it a new composite function cam profile emphatically is developed, in most cases the lobe profile needs to have a concave form (negative radii in the area of the cam lift profile) to improve fullness coefficient, positive and negative peak acceleration and cam-follower contact stress in cam tip; but at the same time the conventional grinding equipment is to suitable to manufacture this type of cam profile, \hyperref[b0]{[1,}\hyperref[b1]{2]}.Moreover the mechanical and microstructure properties of camshafts surfaces like Brinell, Rockwell, and Vickers hardness tests of Ti Al N/Al N composite film deposited on the profile surface of cam (made of chilled cast iron 45 steel) experimentally and numerically relating with the Ion Beam sputtering deposition, the solidification, and cooling rate technologies, in which the operation temperature can be controlled below the limitation of phases exchanging or at room temperature to avoid phase exchanging deformation and examined the rapid and slow cooling surfaces, rosette like graphite in pearlitic and low ferrite phase on cam hardness to improve the shape and dimension accuracy, \hyperref[b2]{[3,}\hyperref[b3]{4]}.In the other hand the cam material (ferrous P/M materials) of a composite shifter hollow cam-shafts for a sequential transmission includes portions formed of a wear resistant material and portions formed of a light weight material using laser surface quenching and discussed the static joining strength and fatigue strength of camshafts with different space between tooth. The destroying torsion of the shifter composite cam structure was (20-30) times as many as its actual work torsion, and its fatigue strength to allow the heavier, wear resistant material durable shifter cam, \hyperref[b4]{[5,}\hyperref[b5]{6]}. It can be studied a composite fabricated cam of Al-Sic using cold isostatic compaction and subsequent sintering die casting with a mixture of four different compositions \hyperref[b9]{(10,} {\ref 20,} {\ref 25,} {\ref 30})\% of Sic powder mixed with Al powders to obtain a high strength to weight ratio and low coefficient of thermal expansion and measured a cam properties like compressive strength, hardness, density and surface roughness, \hyperref[b6]{[7]}. The fatigue life and microscopic edge cracks is measured for two open-celled foamed polymers having different densities in compression impact using a cam-driven compound pendulum system and observed that the material measurements at constant incident energy included the static compression modulus and peak dynamic stress, which progressively degraded as the number of impacts approached one million, \hyperref[b7]{[8]}. 
\section[{II. BOX CAM SHAPE}]{II. BOX CAM SHAPE}\par
1. Plate cam or disk cam:\par
The follower moves in a plane perpendicular to the axis of rotation of the camshaft. A translating or a swing arm follower must be constrained to maintain contact with the cam profile.   
\section[{III. ANALYTICAL PROCEDURE}]{III. ANALYTICAL PROCEDURE}\par
The general circular plate equation as a function of (r, and?) coordinates is:? ? 2 ?r 2 + 2 r ? ?r ? * M r + ?? 1 r ? ?r + 1 r 2 ? 2 ?? 2 ? * M ? + ?? 2 r ? 2 ?r ?? ? 2 r 2 ? ?? ? * M r? + q = 0\textbf{(1)}\par
Where:\par
For orthotropic plate, the bending and twist moments are: The value of first term of eq. ( \hyperref[formula_0]{1}) is:M r = ?[ D r * ? 2 w ?r 2 + D 1 * ( 1 r ?w ?r + 1 r 2 ? 2 w ?? 2 )] M ? = ?[D ? ? 1 r ?w ?r + 1 r 2 ? 2 w ?? 2 ? + D 1 * ? 2 w ?r 2 ]\textbf{(2)}M r? = 2 * ?? ? 2 ?r 2 + 2 r ? ?r ? * M r = ?(D r * ? 4 w ?r 4 + D 1 r ? 3 w ?r 3 + D 1 r 2 ? 4 w ?r 2 ?? 2 ? 2 * D 1 r 3 ? 3 w ?r ?? 2 + 2 * D 1 r 4 ? 2 w ?? 2 + 2 * D r r ? 3 w ?r 3\par
)\par
And the value of second term of eq. ( \hyperref[formula_0]{1}) is:?? 1 r ? ?r + 1 r 2 ? 2 ?? 2 ? * M ? = ?(? D ? r 2 ? 2 w ?r 2 + D ? r 3 ?w ?r + 2 * D ? r 4 ? 2 w ?? 2 ? D 1 r ? 3 w ?r 3 + D ? r 4 ? 4 w ?? 4 + D 1 r 2 ? 4 w ?r 2 ?? 2 )\par
Also the value of third term of eq. ( \hyperref[formula_0]{1}) is:?? 2 r ? 2 ?r ?? ? 2 r 2 ? ?? ? * M r? = 2 * D r? (? 2 r 2 ? 4 w ?r 2 ?? 2 + 2 r 3 ? 3 w ?r ?? 2 ? 2 r 4 ? 2 w ?? 2 )\par
It can be put the three terms derived above in eq. ( \hyperref[formula_0]{1}) to obtain: \par
The homogenous solution of eq. ( \hyperref[formula_0]{1}) is as follows:w(r, ?) H = A * sin(r * ?) + B * cos(r * ?)\textbf{(4)}\par
Where:\par
A and B are constants.\par
It can be derived the homogenous solution (1, 2, 3, 4) times with respect to r and ? to obtain: And the particular solution is:w(r, ?) P = C * r * ?\textbf{(6)}\par
Put eq. ( \hyperref[formula_8]{6}) in plate equation eq. ( \hyperref[formula_0]{1}) and find the value of constant (C):C = q * r 3 ? * D ? w(r, ?) P = q * r 4 D ?\textbf{(7)}\par
The complementary solution of deflection is as below:\par
w?r, ?? = w(r, ?) H + w(r, ?) P w?r, ?? = \par
It can be applied the boundary conditions on eq. ( 8) to obtain the constants (A and B): Where: Atr = r 1 = 2.C 1 = 2 * D r * ? 1 3 * r 1 2 +6 * D 1 * r 1 2 * ? 1 +12 * D r? * r 1 2 * ? 1 ?D ? * ? 1 D r * ? 1 4 * r 1 3 +D ? * ? 1 2 * r 1 +2 * D 1 * r 1 3 * ? 1 2 +4 * D r? * r 1 3 * ? 1 2 ?2 * D 1 *C 1 * C 2 * (tan(r 1 * ? 2 ) * cos(r 1 * ? 1 )?sin(r 1 * ? 1 )) ? * sin(r * ?) + q * r 4 D ?\textbf{(9)}\par
It can be assumed that the two points of contact load are as the simply-supported beam subjected to distributed load (P o ) per unit length of point loading using superposition theory as illustrated in Fig.  {\ref (}3), \hyperref[b8]{[9]}:P o = 0.6 * ? y q = P o * 2 * ? 3 * L 2 8 * 1 L 1 * ? F (\textbf{10})\par
Where:\par
L: is the length of simply-supported beam.\par
L 1 :is the difference length between two points of contact.\par
? F : is the fiber volume fraction (? F = 0.3)\par
The elliptic equation is, \hyperref[b9]{[10]}: w(x, y) = q * (\par
Where: a 1 and b 1 is the major and minor distance axis of ellipse.\par
And; H = D 1 + 2 * D r? And the semi-circle equation is, \hyperref[b9]{[10]}:VII ( A ) w(r, ?) = ? [ 4 * q * r 4 ? * m 1 * ?16?m 1 2 ? * ?4?m 1 2 ? * D r + A 1m 1 * r m 1 + A 3m 1 * r m 1 +2 ] ? m 1 =1,3,5 * sin (m 1 * ?) (\textbf{12})\par
Where:  \hyperref[formula_1]{2}) : Cam Profile Specifications, [11].  IV.A 1m 1 = ?2 * q * (m 1 +1) * a 2 4?m 1 ? * m 1 * ?16?m 1 2 ? * ?4?m 1 2 ? * D r A 3m 1 = 2 * q * (m 1 ?1) * a 2 2?m 1 ? * m 1 * ?16?m 1 2 ? * ?4?m 1 2 ? * D r 
\section[{NUMERICAL PROCEDURE}]{NUMERICAL PROCEDURE}\par
For this problem, the (SHELL 99)element is used in this paper for the two-dimensional modeling of orthotropic un-symmetric cam shell structure carried out with ANSYS 12.1 program software and is defined byeight nodes having six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y , and z axes to find the maximum deflection on cam boundaries. The mesh generation of box cam can be indicated in Fig. (4).         Table \hyperref[b2]{(3)} shows the theoretical and ANSYS results for deflection vary with point's number of nose no. 2 and flank no. 3. The deflection of cam boundary profile decreased transiently with the increasing of point's number on orthotropic cam boundaries because varying the radius of curvature at these points from the point of beginning at nose no. 2 to the point of ending at flank no. 3. 
\section[{VI. CONCLUSIONS}]{VI. CONCLUSIONS}\par
1) The deflection of orthotropic cam is larger than the deflection in isotropic cam because the modulus of elasticity and Poisson's ratio for orthotropic cam is small for the same contact loading.\par
2) The maximum deflection occurs at nose no. \hyperref[b1]{(2)} because the radius of curvature is small. 3) The deflection on noses is larger thanthe deflection of flanks because the effect of the radius of curvatures.\begin{figure}[htbp]
\noindent\textbf{11}\includegraphics[]{image-2.png}
\caption{\label{fig_0}1 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-3.png}
\caption{\label{fig_1}2 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Fig. ( 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-5.png}
\caption{\label{fig_3}A 1 =}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-7.png}
\caption{\label{fig_6}( 2 *}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{231}\includegraphics[]{image-8.png}
\caption{\label{fig_7}2 Predictive 3 C 1 *}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-9.png}
\caption{\label{fig_8}2 ?}\end{figure}
          \begin{figure}[htbp]
\noindent\textbf{} \par 
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\caption{\label{tab_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{P{0.06706689536878216\textwidth}P{0.30471698113207546\textwidth}P{0.2624356775300171\textwidth}P{0.21578044596912518\textwidth}}
Points Number\tabcellsep Theoretical Results\tabcellsep ANSYS Results\tabcellsep Error (\%)\\
3\tabcellsep 0.005161615\tabcellsep 0.0056644\tabcellsep 8.876\%\\
4\tabcellsep 0.0058861\tabcellsep 0.006051\tabcellsep 2.725\%\\
5\tabcellsep 0.00606744\tabcellsep 0.0063089\tabcellsep 3.827\%\\
6\tabcellsep 0.00582013\tabcellsep 0.0064287\tabcellsep 9.466\%\\
7\tabcellsep 0.0060445\tabcellsep 0.006436\tabcellsep 6.083\%\\
8\tabcellsep 0.00661729\tabcellsep 0.0071268\tabcellsep 7.149\%\\
9\tabcellsep 0.00778991\tabcellsep 0.0073008\tabcellsep 6.278\%\\
10\tabcellsep 0.0083432\tabcellsep 0.0077435\tabcellsep 7.187\%\\
11\tabcellsep 0.00878378\tabcellsep 0.0083321\tabcellsep 5.142\%\\
12\tabcellsep 0.00903007\tabcellsep 0.0090455\tabcellsep 0.17\%\\
13\tabcellsep 0.0109305\tabcellsep 0.010322\tabcellsep 5.566\%\\
14\tabcellsep 0.0110767\tabcellsep 0.010799\tabcellsep 2.507\%\\
15\tabcellsep 0.0108222\tabcellsep 0.012067\tabcellsep 10.31\%\\
16\tabcellsep 0.0127715\tabcellsep 0.01377\tabcellsep 7.251\%\\
17\tabcellsep 0.01467905\tabcellsep 0.015786\tabcellsep 7.012\%\\
18\tabcellsep 0.0173589\tabcellsep 0.018493\tabcellsep 6.132\%\\
19\tabcellsep 0.01916212\tabcellsep 0.020308\tabcellsep 5.642\%\\
20\tabcellsep 0.0209437\tabcellsep 0.021801\tabcellsep 3.932\%\\
21\tabcellsep 0.0203995\tabcellsep 0.022859\tabcellsep 10.76\%\\
22\tabcellsep 0.0217526\tabcellsep 0.021979\tabcellsep 1.03\%\end{longtable} \par
 
\caption{\label{tab_1}Table ( 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_2}Table ( 1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{P{0.07619047619047618\textwidth}P{0.30238095238095236\textwidth}P{0.2642857142857143\textwidth}P{0.20714285714285713\textwidth}}
Points Number\tabcellsep Theoretical Results\tabcellsep ANSYS Results\tabcellsep Error (\%)\\
68\tabcellsep 0.0030505\tabcellsep 0.0031101\tabcellsep 1.916\%\\
69\tabcellsep 0.004008805\tabcellsep 0.0038517\tabcellsep 3.918\%\\
70\tabcellsep 0.00466814\tabcellsep 0.0045842\tabcellsep 1.798\%\\
71\tabcellsep 0.004986\tabcellsep 0.0048537\tabcellsep 2.653\%\\
72\tabcellsep 0.0049904\tabcellsep 0.0051238\tabcellsep 2.603\%\\
73\tabcellsep 0.00519162\tabcellsep 0.0054449\tabcellsep 4.651\%\\
74\tabcellsep 0.0055525\tabcellsep 0.0055893\tabcellsep 0.658\%\\
75\tabcellsep 0.00594125\tabcellsep 0.005553\tabcellsep 6.691\%\\
1\tabcellsep 0.00480574\tabcellsep 0.0052705\tabcellsep 8.818\%\\
2\tabcellsep 0.005125194\tabcellsep 0.0052481\tabcellsep 2.342\%\\
3\tabcellsep 0.005301403\tabcellsep 0.0050653\tabcellsep 4.453\%\end{longtable} \par
 
\caption{\label{tab_3}Table ( 2}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_4}Table ( 2}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{(} \par 
\begin{longtable}{P{0.0794234592445328\textwidth}P{0.2957256461232604\textwidth}P{0.2517892644135189\textwidth}P{0.22306163021868788\textwidth}}
Points Number\tabcellsep Theoretical Results\tabcellsep ANSYS Results\tabcellsep Error (\%)\\
22\tabcellsep 0.0458897\tabcellsep 0.040823\tabcellsep 11.041\%\\
23\tabcellsep 0.0458858\tabcellsep 0.043772\tabcellsep 4.606\%\\
24\tabcellsep 0.0418067\tabcellsep 0.045346\tabcellsep 7.805\%\\
25\tabcellsep 0.0440422\tabcellsep 0.046558\tabcellsep 5.403\%\\
26\tabcellsep 0.0479334\tabcellsep 0.047361\tabcellsep 1.194\%\\
27\tabcellsep 0.04459053\tabcellsep 0.047317\tabcellsep 5.762\%\\
28\tabcellsep 0.0470031\tabcellsep 0.046831\tabcellsep 0.3661\%\\
29\tabcellsep 0.04224056\tabcellsep 0.045533\tabcellsep 7.231\%\\
30\tabcellsep 0.0460082\tabcellsep 0.043685\tabcellsep 5.049\%\\
31\tabcellsep 0.0405565\tabcellsep 0.041455\tabcellsep 2.167\%\\
32\tabcellsep 0.0360775\tabcellsep 0.038849\tabcellsep 7.134\%\\
33\tabcellsep 0.0387652\tabcellsep 0.035871\tabcellsep 7.466\%\\
34\tabcellsep 0.029147\tabcellsep 0.032265\tabcellsep 9.663\%\\
35\tabcellsep 0.0256657\tabcellsep 0.028528\tabcellsep 10.033\%\\
36\tabcellsep 0.02435666\tabcellsep 0.025104\tabcellsep 2.977\%\\
37\tabcellsep 0.02280797\tabcellsep 0.021889\tabcellsep 4.029\%\\
39\tabcellsep 0.0170958\tabcellsep 0.018668\tabcellsep 8.421\%\end{longtable} \par
 
\caption{\label{tab_5}Table ( 3}\end{figure}
 			\footnote{December} 			\footnote{© 2011 Global Journals Inc. (US)} 			\footnote{Predictive Model of Orthotropic Un-Symmetric Box Cam Based On Deflection And countered by Segments of Circular-Arc Contact Profiles © 2011 Global Journals Inc. (US)} 			\footnote{Predictive Model of Orthotropic Un-Symmetric Box Cam Based On Deflection And countered by} 		 		\backmatter  			  				\begin{bibitemlist}{1}
\bibitem[Müller et al.]{b0}\label{b0} 	 		‘Composite Camshaft-Avoid Lobe Grinding Using PM Lobes’.  		 			Harald Müller 		,  		 			J Mahle 		,  		 			Pleuco Wizemann 		,  		 			Andreas Gmbh 		,  		 			Kaiser 		.  	 	 		\textit{Journal of SAE}  		 (970001)  p. .  	 
\bibitem[Chappelear and Hacker ()]{b5}\label{b5} 	 		‘Composite Shifter Cam for A Motorcycle Transmission’.  		 			Eric M Chappelear 		,  		 			William J Hacker 		.  	 	 		\textit{Track new patents and Technologies},  				2006.  	 
\bibitem[Kong Fan-Feng1 et al.]{b1}\label{b1} 	 		‘Design and Study of New Composite Function Cam Profile’.  		 			Chu Kong Fan-Feng1 		,  		 			Wang Chao-Meil 		,  		 			L I Bo2 		,  		 			Zhao-Jian1 		.  	 	 		\textit{Chinese Journal}  		p. .  	 
\bibitem[Purohit and Sagar ()]{b6}\label{b6} 	 		‘Fabrication of A Cam using Metal Matrix Composites’.  		 			R Purohit 		,  		 			R Sagar 		.  	 	 		\textit{Journal of Advanced Manufacturing Technology}  		2001. 17  (9)  p. .  	 
\bibitem[Wilson ()]{b7}\label{b7} 	 		‘Impact-Induced Fatigue of Foamed Polymers’.  		 			James F Wilson 		.  	 	 		\textit{Journal of Impact Engineering}  		2007.  (34)  p. .  	 
\bibitem[Leventcenkkumruo?lu ()]{b2}\label{b2} 	 		‘Mechanical and Microstructure Properties of Chilled Cast Iron Camshaft: Experimental and Computer Aided Evaluation’.  		 			Leventcenkkumruo?lu 		.  	 	 		\textit{Journal of Materials and Design}  		2009.  (33)  p. .  	 
\bibitem[Hearn ()]{b8}\label{b8} 	 		\textit{Mechanics of Materials},  		 			E J Hearn 		.  		1985. 2.  	 	 (Book of second edition) 
\bibitem[Quanguq et al. (2010)]{b3}\label{b3} 	 		‘Microstructure and Properties of Ti Al N/Al N December Composite Film Deposited on Cam's Profile by Ion Beam Sputtering Technique’.  		 			Pei Quanguq 		,  		 			Shouren Wang 		,  		 			Huan Yong Cui 		.  	 	 		\textit{Journal of Key Engineering Materials}  		June 2010. 443 p. .  	 
\bibitem[Lee ()]{b10}\label{b10} 	 		‘Size Optimization of Cam Mechanisms with Translating Roller Followers’.  		 			Yu 		,  		 			H P Lee 		.  	 	 		\textit{Journal of Mechanical Engineering Science}  		1998. 212  (C5) .  	 
\bibitem[Zhang Chi et al.]{b4}\label{b4} 	 		‘The Study of Cam Materials and Assembling Technology of Composite Hollow Camshafts’.  		 			Zhang Chi 		,  		 			Yang Yue-Ying 		,  		 			Liu Shen-Hua 		,  		 			Yong-Bing 		.  	 	 		\textit{Chinese Journal (Material Science and Technology}  		p. .  	 
\bibitem[Ventsel and Krauthammer ()]{b9}\label{b9} 	 		‘Thin Plates and Shells’.  		 			Eduard Ventsel 		,  		 			Theodor Krauthammer 		.  	 	 		\textit{Book of Theory, Analysis and Application},  				2001.  	 
\end{bibitemlist}
 			 		 	 
\end{document}
