Motion Analysis of Timing Belt Used in Control Systems

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Increase the speed of opening and closing valves, gave the savings in fuel consumption, exhaust emissions and reduced engine noise emissions. The use of timing belts in electric servo steering system has also contributed to a reduction in fuel consumption of vehicles. Currently, the number of gear timing belts, in motor vehicles approaching twenty ^[10].

Figure 2. Storage vials in pharmaceutical factory

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A more rapid development can be observed in industrial applications. The accuracy of movement in the drive axis CNC machines robots and manipulators resulted in the need to increase the quality and accuracy of production of toothed belts. The entire group of such systems can only drive belts made to the highest standard of precision.

Presented "magazine vials in motion" show that the inaccuracy of the carrier must be compensated straps (Figure 2). Another example is the bottling system whose construction involves filling 40 thousand. bottles per hour. In such applications the standard belt does not achieve the desired accuracy of the motion and speed of 20 thousand. bottles per hour (Figure 3).

Very important is the choice of strips made of the right materials. In the presented application creep caused by significant inaccuracies of motion and rapid damage the belt (Figure 4). Therefore, in this case, the selected edge solution. (color belt means a belt newest generation) ^[11].

Figure 3. Control system of bottle filling system

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Figure 4. Timing belts i robotics

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Figure 5. Willis principle

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Analysis of the kinematics of the toothed belt started from the comparison with the chains. This sufficed in the first constructions belts of trapezoidal teeth. They differed only on the properties of the cord chain which was not elastic. In subsequent constructions belts rounded teeth and began to look for analogies to helical gears. Perpendicular at the point where mating teeth “B” runs through the central point of engagement “C” (Figure 5). Trajectories targeted tooth movement in relation to the wheel usually rays, because the curve of the helical known not suitable for the description. The main advantage of such an engagement is lack sliding friction, gear teeth sweep up after yourself. This is the kind of cooperation it seeks in gear with the timing belts, as limited by this wear volume of teeth due to friction in the process of conjugation ^{[12, 13]}.

The problem is also belt drives internal friction. Can be reduced by reducing the waist under the neutral axis, while increasing the susceptibility of bent. Reduce the amount of material for the carrier layer, it can also be accomplished by the use of toothed belts have the same pitches while a different type of cords ^[14].

3. Description of the Belt Tooth Movement

The gear units with timing belts, can be distinguished equivalent focal point meshing, but the point “C” is moving with the movement of the wheels. Calculating the Lagrange difference kinetic and potential energy (Figure 6).

(1)

Figure 6. Schematic representation of the power transmission with timing belt [8]

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after the above analysis we get:

Lagrange equation takes the form:

(2)

Transmission dynamics occurring variability depends on the size and mass of the individual teeth. Possible collision belt teeth and wheels introduce additional vibration, and that it should be used to limit the right materials for the backing layer to strip underwent the smallest elongation. Should analyze the geometric form of rebate in a circle and the tooth at the waist ^{[4, 5]}. The beginning and the end of cooperation should take place without mutual slip. Assuming that managed to reduce the tendon elongation, in the case of one scale can be omitted to describe the process of engaging the belt wheel, you can use the Lagrange description of the pendulum with variable coupling point (Figure 7).

Figure 7. Movement of the teeth in the coupling

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(3)

or:

(4)

In the present equation, m is the mass of a tooth-belt, l₀ - distance from the center of the tooth belt from the central point of engagement "C", Δl- value scale belt or wheel (depending on whether the movement takes the wheel or belt).

It is very important for the proper conduct of the process is to maintain the proper pitch diameter which in these transmissions is measured at the height of the neutral axis of the carrier layer ^[6]. Changing the position of the belt or cord diameter changes to unfavorable feedback. This also applies to the diameter of the surfaces on which they are co-belt wheels and in part, the diameter of the gear tooth tips of the feet in diameter part ^[7].

In order to improve the liquidity of engagement should first analyze the coverage ratio of teeth in the process of conjugation. While maintaining a small belt pitch while increasing the number of teeth of the pulley is obtained a situation in which several tooth is involved in the coupling to the wheel.

(5)

X-coverage factor D_p-foot diameter pulley teeth, tooth height, h_l-axis of the cord, h-height of the belt tooth.

Figure 8. Changing the torque caused by the coupling

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