M =
rails:
WL . This moment gives rise to an auxiliary reaction N between the wheel wall and the side .
2
N = M = WL
E 2E
If N is too large, the wheel will not rotate but only slide. To eliminate this possibility, we must ensure that the driving force on each side of the rail overcomes the frictional resistance in the presence of force N.
W N.f _
W WL f _ _
2 2 2E
nice
E f_
OFFER
where: f is the coefficient of friction between the wheel wall and the rail edge. In calculation
usually take
f 1 1 _ _
7 5
* Calculation characteristics of main girder of crane
The cross-sectional size of the main girder must be large enough to ensure strength and rigidity. In particular, beams need to meet the following requirements for static stiffness and dynamic stiffness:
- The maximum roundness of the bridge girder under the effect of the vehicle weight and the nominal lifting load and the device carrying the object placed in the middle of the girder must not exceed the maximum value.
allowable value: 1 LOT
400
for hand-operated cranes; 1 LOT
500
for single girder overhead crane
machine drive and 1
700
for machine-driven double girder overhead crane.
- For cranes with box girders, the damping oscillation time of the steel structure must be checked under the following conditions:
td _
ln 2 f t
p .
15 s _
Where: f t - the static roundness of the girder at the cross-section between the girders, cm;
δ – logarithmic coefficient of vibration reduction, usually δ = 0.05 ÷ 0.07, depending on beam height;
1 k o
2 m_
p – natural frequency of oscillation of the girder, Hz
p _
here: k o – girder stiffness, kG/cm
m – the measured mass of the girder, kG.s 2 /cm
k 48 EJ_
o L 3
m 17G d Gx _ _
35 g 2 g
Of the above formulas:
E – elastic modulus of beam material, E = 2.1.10 6 kG/cm 2 ; J – moment of inertia of the cross-section between the girders, cm 4 ;
L – girder aperture, cm;
G d – weight of a girder, kg;
G x – car weight; kg
g – acceleration due to gravity, g = 981 cm/s 2 .
* Calculate the transmission axis of the moving mechanism
The transmission shaft of the crane traveling mechanism must be fully calculated with the usual shaft calculations such as preliminary calculation, strength calculation, and fatigue strength calculation. In addition, depending on the working conditions of the transmission shaft, additional checks on torsional stiffness and vibration are required.
- Check the torsion angle of the transmission shaft: because the transmission shaft is very long compared to its diameter, its torsion angle can be very large, especially for slow transmission shafts with large torque. In order to avoid load loss due to deformation when transmitting the torque M x and to avoid causing the crane to shift, the torsion angle of the transmission shaft should not exceed
more than 1
3
over 1 m in length. The total torsion angle of the transmission shaft of length l , m, and
The constant diameter is determined by the formula:
x _ _
M x
G . J p
Where: G - anti-twist modulus;
4 4
Jp - single pole moment of inertia, for solid shafts with diameter d, J p ≈ 0.1d 4 , for hollow shafts with outer diameter d n and inner diameter d t , J p ≈ 0, 1(d n – d t ).
2_
l 2
EJ
m
- Check stability when oscillating: when the transmission shaft rotates quickly, it is easy to lose stability due to oscillation, which is easy to generate resonance phenomenon. The cause of resonance is that the forced angular frequency from the motor is approximately equal to the free oscillation frequency
of the transmission shaft. The natural frequency of the transmission shaft is .
,s -1
. From we have
the critical number of revolutions for a rapidly rotating transmission shaft can be determined;
30 2 EJ _
l2 m _
th _ _
In which: λ - specific vibration parameters of the shaft, depending on the structure connecting the shaft end, taken according to table 2.1;
l – length of transmission shaft, cm; E – modulus of elasticity, kG/cm 2 ;
J – moment of inertia of the shaft section, cm 4 ;
m = G/g. l , kG.s 2 /cm 2 – distributed mass of the transmission shaft where G is the shaft weight, kG; g = 9.81cm/s 2 .
Table 2.1. Specific oscillation parameters of shaft
Shaft end connection structure
|
λ |
|
|
|
3.28 |
|
|
3.18 |
|
|
3.14 |
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The transmission shaft will work stably and safely when the following conditions are satisfied:
n th _
1 , 2
n
n tt _
1 , 2
1 _
n th _
2
Where: n - the number of calculated revolutions of the shaft received from the drive motor; n tt – the actual number of revolutions of the shaft.
For preliminary calculation, the formula can be used:
nth _
1210 d _
l 2
Where: d- shaft diameter, cm;
l - length of the shaft, m.
2.3.2. Rotary Crane
A rotary crane is a boom type crane, placed in a fixed place. The main movements of the crane include lifting and turning. The crane can have a constant or variable reach. In the case of cranes with variable reach, an additional reach change mechanism is available.
Rotary cranes are commonly used for loading and unloading on trucks, railroad cars, in mechanical manufacturing and repair workshops, on construction sites...
According to the structure, there are two types: rotary mast crane and fixed column crane.
a. Rotary column crane
The feature of this type of crane is that the steel structure of the crane rotates in supports fixed on the foundation and to the structure of the building. To save working space, the pillows are often placed close to the wall or close to the fixed columns of the factory. The rotary mast crane has a constant reach (Figure 2.26) for lifting and transporting goods on a circular arc with a radius equal to the reach of the crane. The service area of a rotating mast crane with variable reach (Figure 2.25) is a donut shape limited by the angle of rotation of the crane, the turning radii being the maximum and minimum reach of the crane. This type of crane usually uses the method of changing the reach by traveling on a horizontal boom. Variable reach rotary mast cranes typically use an electric hoist with a traveling mechanism that runs on an I-rail mounted on a boom to perform lifting and lowering movements and varying reach.
Figure 2.25: Variable reach rotary mast crane
Small rotary mast cranes usually use a hand-pulled chain hoist and the rotary mechanism is also hand-operated or without a rotary mechanism. In the absence of a rotating mechanism, the crane can be rotated by the worker acting directly on the lifting object or the rope tied at the tip of the boom.
The rotary mechanism that drives the machine of a rotating crane is usually located outside of the crane and transmits the force by means of gear drives (Figure 2.26) or by friction between the cable and the ring mounted on the pole (Figure 2.27).
Figure 2.26: Rotary mast crane with constant reach
1- upper and lower support pillows; 2- lifting mechanism; 3- stiff bracing; 4- hoist for lifting objects; 5- need; 6- rotary mechanism
The lifting mechanism of the rotary mast crane is a reversible electric winch and can be mounted on the crane's steel structure or placed outside the crane.
Figure 2.27: Cable-driven rotary mechanism
1- electric motor; 2- gear box; 3- rotation on the column;
4- mourning; 5- cable
The supports of the rotating column crane must be placed concentrically in the vertical direction because if there is a large deviation, the rotational resistance moment will be very large. The upper support is usually a bearing and the lower one is a blocking bearing. This structure allows to determine the reactions at the supports easily according to the static diagram. These reactions can be determined analytically or graphically.
If the lifting mechanism is placed on the steel structure of the crane (Figure 2.28, a), then the external forces acting on the structure causing the reaction at the support are the weight of the lifting object Q and the weight of the steel structure and other factors. mechanism G, whose sum of forces is R. Since R and the supporting reactions A and B must intersect at a point, the reaction at the support at support B must lie on the line BO with O being the intersection point. difference between the directions of action of R and HA . Analyzing force R in the above directions, we get HA and B. Continuing to analyze force B in horizontal and vertical direction, we get VB and HB (see Figure 2.28, a). It is easy to see that the horizontal reactions HA and H Bequal and opposite direction when the total force R acts in the vertical direction.
Figure 2.28: Diagram of rotating column crane
a) Lifting mechanism mounted on the crane; b) Lifting mechanism located outside the crane
In the case that the lifting mechanism is located outside the crane, specifically the lifting cable is squeezed through the cable diverter pulley placed above the crane (this pulley can also rotate with the crane), the external force creates reactions at the bearings. are G, Q, S where S is the tension of
lifting cable (Figure 2.28, b). In this case the total force R = G + Q + S acting
used at an angle from the vertical. Analyze R into HA and B with HA acting in the horizontal direction and B acting in the BO direction and continue to analyze B into H B and VB as shown in Figure 2.28, b. Here the horizontal reactions HA and HB are opposite but not equal.
By analytical method we can also easily determine the reactions. Above
Figure 2.28 diagram, a we have:
M A Rc H B h 0__
M B Rc H A h 0 _
y R V B 0 __
So:
H A H B
Rc _
H
and V REMOVED
= R = Q + WO
The upper support bearing is subjected to horizontal forces, so it is usually a bearing. This bearing can use sliding friction (Figure 2.29, a) or rolling friction (Figure 2.29, b). The drive housing is rigidly attached to the wall or load-bearing structure of the factory.
In order to compensate for the deviation caused by the installation of the outer housing, the bearing usually uses a self-contained ball bearing type
choose.
The upper drive is calculated with the reaction HA . The column head is flexural and calculated for
sections aa and bb with bending moments M a-a = HA A .m and M b-b = HA A .n (Figure 2.29).
Figure 2.29: Top support of a rotary mast crane
a) Sliding bearings; b) Roller bearing
The outer shell of the upper drive is a welded cast construction. The welded structure of the bearing housing (Figure 2.30) includes 2 bases connected to the bearing part of the factory by bolt 3, angle steel bars 1 and 5 have one end welded to base 2, and the other end welded to the upper bearing housing 4. The internal force in the angle steel bars 1, 5 and the reaction at bolts 3 depends on the position of the boom i.e. rotation angle θ of the crane.
Figure 2.30: Upper bearing structure
In fact, angle steel bars 1 and 5 are rigidly connected to base 2 and shell 4 to form a super-static system, but we can consider them to be connected, bars 1 and 5 are only subjected to compressive tension and can easily calculate internal forces. of rods 1, 5 under the action of reaction HA at a position of the rod. The maximum reaction used to calculate the bolt at B is determined by taking the moment at A and the reaction H' A at a position perpendicular to OA (Figure 2.30). So the force to calculate
bolt is
P H ' A . lo _
The lower bearing of the crane is subjected to the horizontal reaction H B and the vertical reaction V, so it includes thrust bearings (Figure 2.31). Commonly used type of rolling bearing (Figure 2.31, b)
than. Bearings usually use self-aligning ball bearings, and the seat of the bearing is also spherical so as not to affect the working process of the bearing. In addition, the spherical support of the bearing has a radius such that its center coincides with the center of the self-aligning sphere on the bearing (Figure 2.31, b). Since the rotational speed of the crane is very slow, the bearings and thrust bearings are calculated with the static load by the reactions H B and V B . The end of the column is subjected to bending and compression and is calculated for sections aa and bb.
Figure 2.31: Lower backrest of rotary column crane:
a) Sliding bearings; b) Roller bearing
Calculation of lifting mechanism, rotating mechanism, mechanism for changing the reach by moving the cart on the horizontal boom and the steel structure of the crane is nothing special.
b. Fixed column crane
Figure 2.32: Fixed mast crane with variable reach