INTRODUCTION
The winches were vertical axis winch type machines, widely used in mines to extract minerals and water, which initially had a drum at the top of the axis, and in its lower part the rod or rods to which the chivalry that moved it. Later they went on to use electrical energy to move a horizontal drum and to be on top of a tower. Today this name is used to refer to winches in many parts of Latin America (Carcamo, 1996; Menéndez, 2010 and Rojas & Delgado, 2015).
At present, a winch is a drum that contains a steel wire wound, supported by a base, which is fixed on a fixed surface, or on a vehicle. It is used to drag loads, or, in the case of vehicles and tractors, as an aid to cross terrain difficulties, or to move large weights in a controlled manner (Carcamo, 1996; McKee, 2011; Oltean et al., 2012; Paez and Gómez, 2017).
The Manuel Fajardo Rivero factory provides casting and repair services for centrifugal pumps and mill masses for sugar mills. So it has a machining workshop divided into three main areas, where all parts that come out of the casting process are finished, but it is also used to maintain the equipment that is there.
The pieces that are subjected to the machining processes have large dimensions and weight and need to be moved through the different areas of the workshop, according to the technological sequence to be followed. This action is carried out by lifting, using hoisting equipment (bridge cranes) and towing through a trolley driven by a winch.
However, several of the structural elements that make up the winch have presented failures as a result of continued operation and the deficit of a maintenance plan for it, which is reduced to corrective maintenance, for presenting 40 years of exploitation. In addition to that, the transmission from the electric motor to the reducer is by chain, with a transmission ratio that is one to one, with high rotation frequencies (1,750 min-1). Another factor that affects the occurrence of failures of some elements of the winch structure is corrosion. All this has caused superficial fatigue and pitting, as a source of failure in the elements of transmission of force and power (star wheel, chain, keyway and transmission shaft) of this machine tool. Because by working it without a casing, in a highly corrosive environment (dust, humidity, as well as the small particles that are lost as a result of the manufacture of parts), its deterioration is accelerated, threatening the longevity of the chain and the rest of the transmission elements. This has been referred to by authors as Dobrovolki et al., 1968; Niemann, 1973 and Reshetov, 1975.
The aforementioned has also caused strong vibrations that affected the fixings of the reducer in its chassis and in the bearings. Another element that has been affected is the steel cable, which suffers from crushing causing fatigue. The fundamental causes of this failure are the diameter of the drum and the lack of grooves in it, for good winding.
All this has caused continuous interruptions during the production process of the machining workshop. For this reason, the objective of the present work was to determine the redesigning parameters of the winch structural elements for load traction. Appropriate calculations were carried out to eliminate the chain transmission and connect, directly a gear reducer to the electric motor that generates the torque. That provides as advantages the high performance, great duration and reliability of operation, constancy in the transmission ratio by absence of skating (Dobrovolki et al., 1968 and Reshetov, 1975). The task was carried out using reverse engineering, which is a method that allows knowing the basic geometric and constructive parameters, for its subsequent reconstruction and / or evaluation of the load capacity (González, 1999 and González & Marrero, 2008).
METHODS
The research was carried out at Manuel Fajardo Rivero Factory in Manzanillo Municipality, Granma Province, Cuba. It is located on Paquito Rosales Avenue km 1 and belongs to the company of Industrial Technical Services (ZETI), of the AZCUBA Business Group.
Calculation Methodology
To determine the redesign parameters of the structural elements of the winch gear transmission for load traction, the methodological recommendations were followed for certain calculations presented by Sokolov & Usov, 1976; Faires, 1980; Deutschman Aaron & Michels Walter, 1985, García de la Figal, 1985 and Mott, 2006b).
Electric Motor
Motor power
Torsional torque (
Determination of the Torsional Moment in Shafts II, III, IV and V
Considering the transmission of the frequency of rotation of the motor to the reducer is direct; that is, by metallic coupling (flexible coupling), then the transmission ratio (i1) and the efficiency (ɳ1) between the metallic coupling of the electric motor and the reducer are equal to one. Taking this into account, the following parameters are determined.
Expression 2 was used to determine the torque in shafts II, III, IV and V.
where:
Nx |
- is the power in the shaft to be calculated (Nm s-1) |
nx |
- is the frequency of rotation in the shaft to calculate (s-1) |
However, to obtain this parameter it is necessary to know the power (Nx) and the rotation frequency (nx) in each shaft II. Then the power and frequency of rotation in each shaft were calculated using Equations 3 and 4.
Note: Hereinafter to determine the values of (Mt3), (Mt4) and (Mt5), it will be necessary to determine the power and frequency of rotation in the corresponding shafts.
In the case of shaft II, the power (N2) was determined using Equation 3.
where:
Nmotor |
- is the power of the electric motor |
ηeng |
- is the efficiency of the gears |
η2coj |
- is the efficiency of the bearings |
Shaft II rotation frequency (n2): was determined by Equation 4.
To determine this rotation frequency, the transmission ratio U1 in Shaft II is presented as unknown. So it was determined through Equation 5.
where:
Z1 |
- is the number of teeth of the gear of the Shaft II |
Z2 |
- is the number of teeth of the gear of the Shaft III |
Note: to determine the values of the moments in the rest of the shafts, the same procedure described above will be used.
Calculation of the Total Gear Ratio of the Reducer
The gear ratio of the reducer (ir): was calculated using Equation 6.
Calculation of the Total Efficiency of the Gear Unit
Reducer efficiency (nr): was calculated using Equation 7.
Note: The maximum value of the transmission efficiency ntrans (0.90-0.98) is taken for being in an oil bath.
Strength Calculation on Flexible Metal Coupling Bolts
The shear stress (τ) was determined by Equation 8.
where:
Mt1 |
- is the torque at the motor output (Nm) |
d |
- is the diameter of the bolts (mm) |
C |
- is the number of bolts in the coupling |
Dbc |
- is the radius of the bolt circle (mm) |
π |
- is the universal constant |
The design shear stress
Drum Calculation
To perform the kinematic calculations related to the drum, such as translation speed (Vc), and rotation speed (Vr), it is necessary to know the drum's outer diameter (Dt = 600 mm) and its inner diameter (Di = 550 mm). So:
The carriage travel speed (Vc) was calculated using Equation 10.
The drum rotation speed (ɳt) was determined by clearing it from Equation 11.
where:
Dt |
- is the external diameter of the drum |
Vc |
- the speed of translation of the car |
π |
- is the universal constant |
So: solving for the rotation speed ɳt, we get Equation 12.
During winch work, the steel cable is to be wound on the drum (Figure 1). So in order to wind up the cable on the drum satisfactorily, without being affected by crushing, the drum has to be grooved to accommodate and guide the cable, therefore:
The steel cable selected to pull the load on the proposed winch is of the hemp core type and its properties are shown in Table 2.
Cable Properties | ||
---|---|---|
Type of cable | Hemp core | |
Cable diameter | 12 mm | |
Length | First section | 60 m |
Second section | 120 m |
Since the cable is 12 mm, the depth of the groove will be equal to half the diameter of the cable, or 6 mm, and the pitch between grooves will be 13 mm.
Then, the perimeter of the drum (P) or the length of the cable to be wound or wrapped in one turn of the drum was determined by Expression 13.
The number of turns or grooves of the drum (Ke): was determined by Equation 14.
The length of the threaded part (l) was determined by Expression 15.
As the drum must comply with the fact that, while winding one cable branch, the other branch must be unwrapped, the threaded part will be double to the right and the other to the left.
So, the total length of the drum (lt) was determined by Expression 16.
Bearing Selection
For the selection of bearings, the procedure referred by Mott (2006a) was used.
The duration of the design (Ld) was calculated by Equation 17.
The basic dynamic load capacity (C) was determined using Equation 18.
where:
Pd |
- is the given design load in pounds |
Ld |
- design duration in hours |
k |
- is equal to 3 for being the ball bearings |
Once the above parameters have been determined, the bearing with the most appropriate dimensions is selected, identified already a set of bearings with the referred basic dynamic load capacity.
Selecting the ball bearing to be used, the bearing with the data of the ball bearing is chosen. For this, the catalog proposed by Mott (2006a) will be used
Static Analysis of Drum and Chassis
The static analysis of the drum and the chassis has been carried out with computer-aided engineering techniques, by means of the finite element analysis software SolidWork (2014), performing the following operations: pre-processing, allocation of materials, establishment of applied forces, meshing and obtaining results regarding deformations, displacements (mm) and von Mises stress (MPa).
RESULTS AND DISCUSSION
Determined the parameters for the design of the structural elements of the winch transmission for load traction, the following results were obtained. Table 3 shows the values of the torques, powers, rotation frequency as well as the transmission ratio in the five reduction gear shafts.
Torque on drive shafts |
Powers |
Rotation frequency (s-1) | Transmission ratio between conjugated gear pairs (Dimensionless) |
---|---|---|---|
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- |
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Total Gear Ratio of the Reducer
The total transmission ratio of the reducer (ir), was determined through mathematical expression 6. Obtaining a result of 153.846.
Total Reducer Efficiency
The efficiency of the reducer (nr) is equal to 0.87 and was determined using Equation 7.
Bolt Strength of Flexible Metal Coupling
The values of real shear stress (τ) and design (τD) were calculated using Equations 8 and 9. The magnitudes obtained are equal to 5.1·10-5 MPa and 67.7 Mpa, respectively. With this result the condition is fulfilled that the real shear stress is less than the design shear stress τ ≤ τD, therefore, the bolts in the flexible coupling resist.
Selection of Ball Bearing
For the selection of the ball bearing to be used, it was necessary to determine the design duration (Ld) with a value of 15,792,000 min-1 and the basic dynamic load capacity (C) which is 19,845.87 lb.
Material Allocation
When presenting the model as a rigid solid, a material was assigned to the part, so that it would give its results as close to reality as possible, such as ASTM A36 Steel, and its physical properties were as follows (Table 5).
Applied Loads
Fixed holdings were applied to the drum in each section where the cable is to be wound, simulating that it is wound on it, in addition, bearing-type supports were applied to each end of the shaft where the drum is supported (Figure 1).
In the case of the chassis, a remote mass load was applied to simulate the conditions of the torque. It was where the coupling between the motor and the reducer is located, where the torque has a value of 5.4597 N·m and the loads of the weight of the system were also taken into account. These are the most critical conditions of it. This has fixed restrictions, which are located where the chassis will be embedded (Figure 2).
Von Mises Voltages for Drum and Chassis Stress State
This is the most suitable failure theory for ductile and uniform materials (tensile strength approximately equal to compressive strength), and whose shear strength is less than tensile strength. This theory basically consists of determining the so-called effective von Mises stress, after having determined the stress state of the worst hit point (Norton, 2011).
As shown in Figure 3, the maximum stress values (9.46 MPa) will be accumulated in the entire section of the shaft where the gear and bearing is coupled, and the minimum stress values in the sections where the cable is wound. So in that place is where the breakage of the piece can occur. The maximum values of stresses do not exceed the elastic limit of the material, therefore, the deformations will not be permanent. This can be corroborated when analyzing the safety factor; it has a value of 26, which can be considered acceptable.
Applying the finite element method to the structure by determining the von Mises stresses, loads were applied to the sections where the motor, reducer and drum are located. It was obtained that the maximum stresses to which the structure will be subjected are equal to 75.6 MPa, located in one of the embedment of the structure, which is not a significant value compared to the elastic limit of the material (250,000 MPa), therefore, the structure will withstand the loads to which it is subjected (Figure 4).
Displacement
In Figure 5 it can be seen that the maximum displacements are in the area where the gear is coupled and then, the bearing with a maximum displacement of 0.008513 mm. In that area is where the greatest amount of stresses are found, for which the displacements will be maximum due to the torsional torque generated there, which is 669,104 Nm. The point where the minimum stress values are located is in the sections of the drum where the cable will be wound.
Security Factor
As shown in Figure 6 the safety factor is 26 for the drum and 3.6 for the chassis. This value obtained by the software takes into account the ratio of the value of the limit voltage (in this case the value of the yield stress of the material) and the von Mises stresses. As this value is greater than 1, it can be expressed that the maximum internal stresses in the parts resulting from the acting loads do not exceed the elastic limit, so the deformations will not be permanent.
CONCLUSIONS
The parameters for the redesign of the winch structural elements for load traction were determined.
With the new gear transmission, better efficiency (0.87) was achieved in the winch transmission ratio.
The results of the analysis using the finite element method showed that the maximum stress values did not exceed the elastic limit of the material (250 N mm-2), so there will be no permanent deformations in the assembly, with a safety factor of 3.6 for the chassis and 26 for the drum.
They managed to eliminate vibrations and also the environmental noise caused by it.