# Kinematic Analysis of the Slider-Crank Mechanism in Automated Vibration Sausage Feeder

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1 5 th World Conference on Applied Sciences, Engineering & Technology 0-04 June 016, HCMUT, Vietnam Kinematic Analysis of the Slider-Crank Mechanism in Automated Vibration Sausage Feeder NGUYễN HồNG NGÂN Department of Material Handling Equipment and Construction Machinery, Mechanical Engineering Faculty, Ho Chi Minh city University of Technology, VNU HCM, Ho Chi Minh City, Việt nam Abstract: The sausage feeder takes an important role in automated packaging systems. This paper presents the theoretical calculation, kinematic and dynamic characteristics of an automated sausage feeder using vibration technique and crank mechanism. The kinematics formulation of the crank mechanism is done using vector loop method and cosine rule are applied to describe the position of the mechanisms. Following the velocity of crank and necting rod is performed by differentiating the position in terms of the crank angle and necting rod angle respectively. The acceleration equation with brief form is derived from the velocity in the same principle. Based on the kinematics, the equations of motion of crank mechanism components are formulated for each moving link and platform then, all motion parameters of each component about its crank angle are readily derived. Furthermore the D model is provided by using D Auto CAD software in order to visualize the system and mathematical algorithm solved by using software MATLAB. The forces of sausage acting on the crank mechanism and system kinematic of sausage feeder from the crank to the sausage are also determined based on the angles of the crank and necting rod. The feeder has been fabricated, installed in the real production line. Keywor: Kinematics, Cranks Mechanism, Sausage Feeder, Automated Packaging System, Vibration Mechanism Introduction: In the sausage processing enterprises, sausage processing packaging has been automated in most companies, but issuance of sausage on packaging machines is still done mostly by hand, by automated equipment costs the entire system of foreign chains is very high, and requires extensive groun. At companies in Vietnam for granting sausage packaging machine to perform manually. This paper presents the theoretical calculation, kinematic and dynamic characteristics of an automated sausage feeder using vibration technique and crank mechanism. The feeder is the one important component of automation sausage feeder chain. Figure 1: Structural 3D of automation sausage feeder chain. Figure : Sausages movement in the chain. Automation sausage feeder chain: Automation sausage feeder chain is made as shown in fig 1, and sausages movement shown in fig. Chain structure includes the following major components: Lifting veyor 1; Intermediate feed veyor ; Distribution veyor 3; Inspired hopper 4; Vibration sausage feeder 5 (including crankshaft mechanism and vibration hopper); Packaging veyor 6. Chain is operating as follows: Workers poured sausages into the hopper of the lifting veyor 1, veyor lift sausage to intermediate veyor, intermediate veyor move sausage down distribution veyor 3, sausages through distribution veyor line, go to the hopper 4. From the hopper, sausages fall to the vibration feeder, the crank mechanism behind the feeder push sausage on the feeder to packaging veyor 6. WCSET Copyright 016 BASHA RESEARCH CENTRE. All rights reserved

2 NGUYỄN HỒNG NGÂN Automated sausage feeder with crank mechanism: Vibration automated sausage feeder is a most important part in the system. Structure shown in Figure 3. It includes hopper taining sausages, hopper vibration mechanism and slider crank mechanism. Need to understand the characteristics and dynamics kinetics of the automated sausage feeder with crank mechanism to achieve the optimal parameters. Crank mechanism comprises of piston, necting rod and crank shaft. In formulation of the crank mechanism such as piston kinematics and necting rod kinematics of already existing sausage feeder need parameters, the given parameters are stated in table 1 Figure 3. Vibration automated sausage feeder:1- hopper taining sausages; - vibration mechanism; 3- slider crank mechanism. Figure 4. Diagram principle of crank mechanism with sausage: 1- engine: : transmission belt; 3- crankshaft; 4-rod; 5- slider; 6-piston of crank mechanism; 7-sausage on the top piston; 8 sausage go to piston; 9 - sausage leave the piston. Table1. Parameter of feeder with slider crank mechanism Parameters Unit Values Connecting rod length mm 300 Crank radius mm 100 Piston diameter mm 0 Stroke mm 00 Speed of Crank rpm 140 Sausage weight on feeder kg 5 Figure 5. Slider crankshaft structure Kinematic analysis of the slider- mechanism: Kinematic Modeling of Piston Motion: Piston is one of the main parts in the system and its purpose is to transfer force from engine to the crankshaft via a necting rod Piston Pin Position. The displacement of the piston with respect to crank angle can be derived from simple trigonometry. This can then be differentiated to yield velocity and acceleration of the piston. The expressions obtained tend to be very complicated and can be simplified into the expression taining only first order (once per revolution), sed order (twice per revolution), and a negligible fourth order. The piston pin position is the position from crank center to the piston pin center in fig. 5 and can be formulated from cosine rule of the trigonometry s l cosr sin lsin rsin rsin r sin, let, therefore l l The piston position as follows s r l (1) () cos 1 sin (3) 4.1. Piston Pin Velocity. Piston pin velocity is the upward velocity from crank center along cylinder bore center and can be calculated as the first derivative of equation 3 with respect to angle theta v t piston pin velocity. To express the velocity with respect to time v We have v rsin( t) l sin( t)cos( t) 1 sin ( t) (4) Piston Pin Acceleration: Piston pin acceleration is the upward acceleration from crank center along cylinder bore center and can be calculated as the sed derivative of equation 3 with respect to angle theta June 016, HCMUT, Vietnam, ISBN 13: , pp 34-38

3 Kinematic analysis of the slider-crank mechanism in automated vibration sausage feeder To express the acceleration with respect to time can be express as a Then a r t l cos( ) ( ) sin ( t) 4 1 sin ( t) (5) r t t ( sin ( ) cos ( )) 1 sin ( t) (6) Survey process of restructuring activities pushed sausages level. The purpose of the structure is pushed sausage levels are sure to provide sufficient quantities of sausages and is part of the veyor belt to automatic packaging machine, the speed level is adjusted by the servo motor speed sync with speed packing. The feeding is done by structural push rod to the crankshaft. Chart principle diagram of the structure calculation pushing presented in figure 4, and figure 5. The results received are presented in the table below. Piston Pin Velocity Piston Pin Acceleration Figure 5. displacement, velocity and acceleration of the piston when the frequency ω = 10 rad / sec r=110 mm; l=30 mm Crank rotation ω=10 rad/s. ω= 1 rad/s Max Piston Pin Velocity Piston Pin Acceleration in forward Piston Pin Acceleration in return 150mm/s 1500 mm/s 8000 mm/s 100 mm/ s 1600 mm/ s 4000 mm/ s Piston Pin Position. Piston kinematic Piston Pin Velocity Piston Pin Position. Piston Pin Acceleration Figure 6. The displacement, velocity and acceleration of the piston when the frequency ω = 1 rad / sec 0-04 June 016, HCMUT, Vietnam, ISBN 13: , pp 34-38

4 NGUYỄN HỒNG NGÂN Kinematics Modeling of Connecting Rod Motion: The necting rod is a major link inside of a engine. It nects the piston to the crankshaft and is responsible for transferring power from the piston to the crankshaft and sending it to the transmission. Connecting rod as one component of the crank mechanism it is crucial to formulate the kinematics of necting rod Instantaneous Velocity Connecting Rod v (7) dt dt where v instantaneous velocity of necting rod. Differentiate equation () with respect to angle theta cos,cos 1, (8) cos v cos (9) 4... Instantaneous Acceleration. Connecting Rod Figure 8. Model of the impact of the piston on sausages 5. Kinematic parameters of the slider-crank mechanism and sausage: Based on the model of the impact of the piston into the sausage (Figure 8), matlab - simulink diagram was built to determine the kinetic parameters of the piston and sausages in Figure 9. From then determine the relationship between the parameters of a rotation with the distance between the piston and the original given sausages. Figure 10 is a graph of relationships piston displacement - velocity sausage, and figure 11 is a graph relationships piston displacementdisplacement sausag a dv dv, dt dt Differentiating equation 9 with respect to time a sin (10) Kinematic analysis of the slider-crank mechanism and sausage: Kinematics Modeling of Sausage motion Figure 9. matlab - simulink diagram to determine the kinetic parameters of the piston and sausages. Figure 7. The relationship between the structural position of the crankshaft necting rod and sausage The relationship between the position of the crankshaft necting rod structure and sausage is shown in Figure 7. At the back of the piston, the top piston will leave from the sausage, the forward, at first piston not touching to sausages, the next the piston will compressed sausage in elastic limit, then push sausage up to the sausage packaging. The forces on the sausage are the weight of sausage above (P) and the friction with platform (Fms). Model of the impact of the piston on sausages is presented in Figure 8. From equation (3), building on the mat chart lab simulation, kinematic parameters of crankshaft systems - sausage will be determined. : sausage velocity; piston displacement. Figure 10. Graph relationships piston displacement - sausage velocity 0-04 June 016, HCMUT, Vietnam, ISBN 13: , pp 34-38

5 Kinematic analysis of the slider-crank mechanism in automated vibration sausage feeder : sausage displacement; piston displacement Figure 11 graphs relationships piston displacement - sausage displacement Results and Discussion: The clusions are drawn as follows: 1. The modeling methodology for kinematics of crank mechanism has been derived systematically by sidering the geometric figuration of the crank mechanism of the automated feeder system. The forces of the sausage applied to the crank mechanism also properly analysed. Through sideration of the crank mechanism the position, velocity and acceleration is properly formulated. 3. From the chart matlab - simulink we can survey system kinematic of sausage feeder from the crank to the sausage, identify the impact of the crankshaft speed, the relative position of sausages, speed of sausage during the working piston. References: [1] Zinovjav, V.A., (199) Mechanisms and Machine Theory. Моscou, - 384p. (in Russian) [] Krewer, (1995) Conveyor arrangement for a sausage packaging machine, Bulletin 1998/18. [3] Righele, (199) Machine for the separation of one tinuous sausage into individual sausages., Bulletin 9/38. [4] Michaud, Presseau, Drolet, (1994) Sausage link handling and packaging machine., Bulletin 91/46. [5] Zinovjav, V. A. (199) Mechanisms and Machine Theory. Моscou,- 384p. (in Russian). [6] Sumskii, S.N. (1980) Calculation of Cinematic and Dynamic Properties of Flat Lever Mechanisms. Мoscou, 310 p. (in Russian). [7] Paulauskas, L. (00) Theoretical basics of automated packa-ging machine package closing modules. Balttexmasch 00, Каliningrad, p [8] Paulauskas, L. (00) Calculation of packing automatic machines with rotation slide-block., Int. Scientific Practical Conf. New tren in quality food production. Jelgava, Latvia, p [9] Henry, J., Topolsky, J., and Abramczuk, M., (015), Crankshaft Durability Prediction A New 3D Approach, SAE Technical Paper No , Society of Automotive Engineers. Mechanics, Materials Science & Engineering, October 015 ISSN [10] Anusha B and Reddy C. Vijaya Bhaskar, (013) Modeling and Analysis of Two Wheeler Connecting Rod by Using Ansys, Journal of Mechanical and Civil Engineering, Vol.6, Page 83-87, May. - Jun. [11] Norton R.L., (01) Kinematics and Dynamics of Machinery, Tata McGraw Hill Education (P) Ltd., New Delhi. Conclusion: Through computational and experimental shows automation sausage feeder chain were operating in sync with automatic packaging machines, frequency pushing of the feeder always adjusted in line with the frequency packaging machines, working frequency of crankshaft follow packaging speed. The parameters of sausage feeder calculated to ensure the sistent with sausage packaging requirements 0-04 June 016, HCMUT, Vietnam, ISBN 13: , pp 34-38

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