Vitaliy Statsenko Scientific supervisor DSc. Leonid Bondarenko

 ANALITICALY FINDING OF

COEFFICIENT OF FRICTION FOR FLANGES

(АНАЛІТИЧНЕ ЗНАХОДЖЕННЯ КОЕФІЦІЕНТУ ТЕРТЯ РЕБОРД)

Known [1] that the resistance movement of the mechanism of movement of friction on a straight line segment path defined by the formula:

Wtr = G + Gk ∙ μd +2 fD ∙ Kp

where G and Gk - the weight of cargo by weight and the crane or trolley; D and d - diameter of the wheel and his neck; f - coefficient of rolling friction; Kp - coefficient which takes into account the friction wheel hubs and rebords; μ - coefficient of friction bearings , brought to the pin wheel.

Figure 1. Dependence of deviation angle ψ longitudinal axis of the wheel from the axis of the rails1-adjusted coefficient of rolling friction KK3a axis and;2 - the same respect in KK3b 3 - the total value of rolling friction coefficient is given KPC, which falls on the sliding friction rim surface of the rails; 3’, 3” - normative coefficient of friction bearings for the flat and rounded surface.

0 1

1

2

3

3 " 3 '

2 3 4 5

V

C , 8

Ê ,

Ê ê

ç à

, Ê ê

ç â

, Ê ê

ç ,

ì ì

0 , 3 5

0 , 3 0

0 , 2 5

0 , 2 0

0 , 1 5

0 , 1 0

0 , 0 5

0

(І)where ψ - angle from the axis of the rails;

V = ωR = πnR - Circular speed wheel rim; n - rotational speed; R - radius of the

wheel. (4)

Efforts PKB which falls on the lines of bK that glides

(5) 

Power of friction (6)

where η - coefficient of friction between wheel and rail.

Find the power of conventional friction coefficient of sliding friction KK3b.

(7).

After similar calculations for the axis a, perpendicular to the axis of b implies an

(8)

(9)

(10)

The formula for determining the coefficient of friction bearings, which

accounted for sliding along an axis that coincides with the transverse axis of the

rails (11)

The total coefficient of friction bearings, which accounted for as a result of twisting

the wheel slip at an angle ψ(12)

Size a and b in the case of equal values of elastic modul and Poisson's ratio node wheels and rails are determined by the expressions [3]

(15)

Experimental value of the resistance movement of friction at Kp = 1 and the current value of Kr,

(13)

But given the value of coefficient of friction bearings

(14)

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

0 1 2 3 4 5 0

0 , 2

0 , 4

0 , 6

0 , 8

1 , 0

1 , 2

1 , 4

1 , 6

1 , 8

2 , 0

1

1 '

4

2 '

2

4 ' 5 ' 5

C , 8 .

W ò

ð ,

W å

ð ,

W ê

ç ,

H

N ê

â ,

N ê

à ,

ê Â ò

Fig.2. Dependence of deviation angle ψ longitudinal axis of the wheel axis rails1 - total experimental values of resistance movement WTP, which includes the friction surface sliding on rails, 2 - component, which accounted for only friction of flange; WEP; 1@, 2@ - size, similar 1 and 2 with linear contact; 4,5 - power that is on a sliding WK3 at contact lines and point ; 4’, 5’ - same with linear contact

We find values of resistance movement from the friction of the normative method WTP that component, which falls on the sliding friction wheels on rails WK3 surface due to a distortion angle.

Calculations of conduct for wheel diameter = 250 mm unit with a static load P = 40 kN of linear and point contacts for crane trolley connected by flexible cable (Kp = 2) and d = 50mm; f = 0,4, f = 0, 3 - rounded and flat (B = 45 mm) head rails, if η = 0,1; μ = 0,15.

1. Factor that takes into account the friction of wheels on rail rebord consists of two main components: direct and friction rebordy component of sliding friction wheel rim on the back rails due to mismatch longitudinal axis with the axis of the wheel rails.

2. A component of sliding friction on the rim rail depends on the angle discrepancy axis rails and wheels and such at ψ = 3 ° is about 12% of the total value of point contacts - about 10% linear

Thank you for your attention.