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9It is good that industrial enterprises carry out the plan in time and economic indicators and profits of workers and laborers are high there. But the dream of carrying out the plan can destroy the environment and on these cases the people who live near these enterprises lose their health and during the treatment of illnesses and diseases enterprises have to pay salary during their sick period and it is one of the economical outcomes too. The best way is to decrease the pollution of environment to the least level, to create healthy condition, succeed in getting fresh water and air. In good conditions it is easy to fulfill the plan of enterprises and support the health of workers.
Concluding the above mentioned issues, we can say that there are complicated relation between the nature and society and all are connected with the influence and character of men. The properly and carefully used natural resources and purposely farm management create closely link between nature and humanity. The non-following to the nature rules and go against them may create negative outcomes and they may be dangerous.
RELATIONSHIP BETWEEN THE VELOCITY COEFFICIENT AND MOMENT OF FORCE TO CUTTING WITH A DISC
KNIFE
Abstract. A number of food products are effectively cut with disc knives with smooth cutting edge. Due to the elasticity of the food products, the deformation that arises during their dissection causes friction forces between the side walls of the knife and the product. Given these frictional forces formulas are derived for the resultant friction power and friction torque [1].
This article is a continuation of previous studies [1; 2; 3; 4]. A study is proposed on the influence of the parameter X, representing the ratio of the cutting velocity of the disc to the feeding velocity, on the resultant friction moment.
Keywords: moment of force, friction, velocity coefficient, disc knife, food
Introduction. With the expansion of the modern food industry it is required to optimize and increase the quantity and quality of the final product. In this regard, various technological processes in food production are examined theoretically and experimentally in order to improve them.
Subject of the present theoretical study is the mechanical cutting process, which is one of the most common processes in different sectors of the food industry. Cutting devices using disc knives are discussed. Their main advantages are in the relatively simple construction and convenience in operation. The disc blades provide quality food processing combined with high cutting speeds. That is why they are the subject of a number of studies.
Cutting food products is accompanied by elastic compression of the material. The deformation creates significant frictional forces between the side walls of the knife and the material getting cut.
In previous studies [1] a formula is derived for the resultant moment as friction is reported between the side walls of the knife and the product getting cut:
where
^ - coefficient of friction
E - modulus of elasticity of the product getting cut, Pa a - half of the disc knifes width, m
l - width of the product getting cut from the one side of the knife, m r - radius of the disc knife, m B - thickness of the product getting cut, m
A - height of the disc blade s part, which is incised in the board, m
Parameters J6 and J7 are called third and fourth resistance characteristics and are given by the following elliptic integrals
Ilieva I.
Bulgaria, Plovdiv, University of Food Technologies
(1)
A- cosm T № A- cosm
J6 = I 1 , ; j7 = 1 —-— =dm.
Jm' + A2 - 2Acosm Jmi cos3 mV 1 + A,2 - 2Acosm
v —"
Here A = —1L is a velocity coefficient, which is the ratio between the cutting velocity vc and
feeding velocity vf of the disc knife.
The limits of the integrals J6 and J7 are determined by:
r-A r-A-B
9, = arccos- ; mu = arccos-.
r r
Parameters ^, E , a and 1 depend on the nature of the product getting cut and are derived experimentally. The values of r , B, A and A are still subject to both theoretical and experimental studies.
This work offers a study on the influence of the velocity coefficient A on the resulting friction moment.
Output data
Object of the current research is a double bevelled disc knife with smooth edge. Numerical analysis for a raw material meat has done with the following parameters:
• coefficient of friction ^ = 0.05;
• modulus of elasticity of the product getting cut E = 12.103 Pa;
• half of the disc knife's width a = 0.15.10-3 m;
• width of the product getting cut from the one side of the knife 1 = 0.45.10-3 m;
• radius of the disc knife r = 0.105 m ;
• thickness of the product getting cut B = 0.07 m;
• height of the disc blade's part, which is incised in the board A = 0.007m. Results
Resistance characteristics and the moment of force are solved and shown when the velocity coefficient is A = 10,20,30,40 and 50. The received results are shown in a table 1 and figures 1, 2 and 3.
Table 1. Values of the resultant resistances when A e [10,50]
A 10 20 30 40 50
J6 0,9308 0,933 0,9333 0,9335 0,9336
J7 7,35 7,3735 7,3777 7,3792 7,3799
Mfr, Nm 0,0926 0,09287 0,09291 0,09293 0,09294
20 № 2(6), Vol.1, February 2016
WORLD SCIENCE
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20 30 40 50
Fig. 2 Relationship between the fourth resistance characteristic and the velocity coefficient X
20 30 40 50
Fig. 3 Relationship between the resultant moment of force and the velocity coefficient X
Conclusion. When X increases, the resultant moment of force during disc knife cutting of food products caused by the friction between the material and the knife side walls increases as well. The slope of the tangent at any point of the graph of M fr = Mfr (X) decreases as X increases.
The relationship between the moment of force and the velocity coefficient is not a linear. It is close to an elliptic curve.
REFERENCES
1. Vasilev S., Modelirane i dinamichen analiz na mehanichni protsesi i sistemi v hranitelno vkusovata promishlenost, Habilitatsionen trud, Plovdiv, 2010
2. Boyadzhiev D., S. Vasilev, I. Ilieva, Analitichen metod za opredeliane na silata na syprotivlenie pri riazane s diskov nosh, porodena ot trieneto mezhdu materiala I stranichnite steni na nozha, Nauchni trudove na SUB, Plovdiv, p.119-122.
3. Ilieva I., S. Vasilev, D. Boyadzhiev, Opredeliane na vyrtiashtia moment, pri riazane na hranitelni produkti s diskov nosh s otchitane na trieneto mezhdu product i stranichnite steni na nozha, Nauchni trudove na SUB, Plovdiv, 2013, p.43-48.
4. Ilieva I., D. Boyadzhiev, S. Vasilev, Izsledvane na vlianieto na skorostnia koeficient vyrhu resultantnata sila na triene mezhdu stranichnite steni na nozha i razriazvania product pri riazane s diskov nosh, Nauchni trudove na SUB, Plovdiv, 2014, p.29-33.
