# Analysis of the working condition of the hottest b

2022-10-14
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Working condition analysis of belt transmission

1 force analysis in belt transmission

1 The force transmitted by the belt

the belt is annular, and it is sleeved on the pulley with a certain tension F0, so that the belt and the pulley are pressed against each other. At rest, the tension on both sides of the belt is equal, both of which are F0 (Fig. 11.5a); During transmission, due to the friction between the belt and the wheel surface, the tension on both sides of the belt is no longer equal (Fig. 11.5b). When winding into one side of the driving wheel, the tension increases from F0 to F1, which is called tight side tension; The tension of the other belt is reduced from F0 to F2, which is called loose edge tension. The difference between the pulling forces on both sides f = F1-F2 is the effective pulling force of the belt, which is equal to the sum of the friction forces on the contact arc along the pulley. Under certain conditions, the friction has a limit value. If the working resistance exceeds the limit value, the belt will slip on the wheel surface and the transmission will not work normally

figure 11.5

if the power transmitted by the belt transmission is p (kw) and the belt speed is V (m/s), then the effective tension f (n) is

f=f1-f2=1000p/v (11.1)

it can be seen from the above formula that within the range of transmission capacity, the size of F is related to the transmitted power P and the belt speed v. When the transmission power increases, the effective tension of the belt, that is, the difference between the tension on both sides of the belt, also increases correspondingly. This change in the tension on both sides of the belt actually reflects the change in the friction on the contact surface of the belt and the belt covered filter material technology 1, which is directly controlled by several foreign companies. When there is a slip trend, the friction reaches the limit value. At this time, the relationship between F1 and F2 can be expressed by the following formula:

where e is the bottom of the natural logarithm

μ-- Friction coefficient between belt and pulley

α-- Wrap angle on pulley

q-- mass per meter of belt length, kg/m

by combining equations 11.1 and 11.2, the tight side tension F1 and the loose side tension F2 are

2 The tension generated by centrifugal force

when the belt moves in a circular motion around the main and driven wheels, centrifugal force will be generated, which makes the belt subject to centrifugal tension of the same size everywhere in the whole length. As shown in Figure 11.6, take a small segment of band DL, and the corresponding wrap angle is d α， The pulley radius is r, and the balance formula between the centrifugal force dfnc on the micro segment DL and the centrifugal tension FC is

when D α Very small, sin (D α/2)≈d α/2

then the centrifugal tension of the belt fc=qv2

figure 11.6

stress analysis of the belt in 2 belt transmission

1 Tight side tensile stress σ 1 and loose edge tensile stress σ 2

σ 1=F1/A， σ 2=f2/a (11.6)

Where a -- the cross-sectional area of the belt

2. Tensile stress caused by centrifugal force

σ C=fc/a=qv2/a (11.7)

visible centrifugal stress σ C is proportional to Q and V2. Therefore, when designing high-speed belt transmission, thin and light transmission belt should be used; When designing general belt transmission, the belt speed should not be too high

3. Bending stress σ B

when the belt bypasses the main and driven wheels, bending deformation will produce bending stress σ b. The bending stress of the belt is obtained from the formula of material mechanics

σ B=ey/r (11.8)

where e -- elastic modulus of belt material

y-- the distance from the neutral layer to the outermost layer; Flat belt y=h/2 (H is the thickness of the belt), V belt y=ha (see table 11.2)

r-- radius of curvature, flat belt r= (d+h)/2, V belt r=dd/2 (see table 11.2). When the diameters of the two pulleys are different, the bending stress of the belt on the small belt cupping experimental machine is relatively simple

the distribution of the above three stresses along the belt length is shown in Figure 11.7. The small and medium-sized pulley in the figure is the driving pulley, and the maximum stress occurs at the place where the tight edge enters the small pulley (point B in the figure), and its value is (11.9)

figure 11.7

3 elastic sliding and slipping

1 Elastic sliding

because the belt is an elastomer, it will inevitably produce elastic deformation after being stressed. When the transmission works, the elastic deformation is also different because of the different tension between the tight side and the loose side. Referring to figure 11.8, when the belt wraps around the driving wheel from point B, the tension on the belt is, and the speed of the belt is equal to the speed of the pulley surface. When the belt is transferred from point B to point C, the tension of the belt is reduced from to, so the tensile elastic deformation of the belt is also gradually reduced, which is equivalent to that the belt is gradually shortened and slides along the wheel surface, so that the speed of the belt lags behind the peripheral speed of the driving wheel, so relative sliding must occur between the two. The same phenomenon occurs on the driven wheel, but the situation is just the opposite. At point E, the belt and the pulley have the same speed, but when the belt turns from point e to point F, the belt is not shortened, but elongated, so that the speed of the belt is higher than that of the pulley. This kind of sliding between the belt and the pulley caused by the elastic deformation of the belt is called elastic sliding

figure 11.8

elastic sliding will cause the following consequences: ① the peripheral speed of the driven wheel is lower than that of the driving wheel; ② Reduce transmission efficiency; ③ Cause wear of the belt; ④ Heating increases the temperature of the belt

in belt transmission, due to friction, the two sides of the belt are stretched and deformed to varying degrees. Friction is necessary for this kind of transmission, so elastic sliding is also inevitable

due to the influence of elastic sliding, the peripheral speed V2 of the driven wheel is lower than the peripheral speed V1 of the driving wheel, and its relative reduction rate is called the sliding rate ε： (11.10)

where N1, N2 -- rotational speed of driving and driven wheels (r/min)

d1, D2 -- datum diameter of driving and driven wheels (mm)

slip ratio ε The value of is related to the size of elastic sliding, that is, it is related to factors such as the material and force of the belt. Therefore, accurate values cannot be obtained, so belt transmission cannot obtain accurate transmission ratio. The slip rate of belt drive is generally 1% - 2%, which can be ignored in rough calculation

2. Slip

under normal circumstances, the elastic sliding of the belt does not occur on the whole contact arc. The contact arc can be divided into two parts: the one with relative sliding (sliding arc) and the one without relative sliding (static arc). The central angles corresponding to the opening and closing of the two large arcs are called sliding angles respectively α` And static angle α``。 The static arc is always located at the beginning of the main and driven wheels on the belt winding (as shown in Figure 11.8)

when the load is not transmitted, the sliding angle is zero. With the increase of load, the sliding angle α` Gradually increase, while the static angle α`` Gradually decrease. When sliding angle α` Increase to pulley wrap angle α At 1 o'clock, the limit state is reached, and the effective tension of the belt transmission reaches the maximum value. Our experimental machine mainly tests the bearing capacity of material mechanics and starts to slip. Due to the wrap angle on the big wheel α 2 is always greater than the wrap angle on the small wheel α 1. Therefore, slip always occurs on the small pulley first

slipping will cause serious wear of the belt, and the movement of the belt is in an unstable state, resulting in transmission failure

elastic sliding and slipping cannot be confused. Slipping is the overall sliding of the belt on the pulley caused by overload, which should be avoided in work. When the transmission is suddenly overloaded, slipping can play the role of overload protection to avoid damage to other parts. (end)

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