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International Review of Mechanical Engineering (I.RE.M.E.), Vol. 14, N. 1 ISSN 1970 - 8734 January 2020

Modernization of the Metal Structure of the Grader Working Equipment Mikhail Doudkin, Alina Kim, Andrey Savelyev, Mikhail Zhileikin, Vladimir Gribb, Valeria Mikhailovskaya Abstract – The developed 3D model for determining the limiting states of the metal grader construction and the mathematical model for determining forces arising on the working body and wheels during the operation of the grader allows comparison of the new designs revealed with the traditional grader designs. Moreover, the article allows assessing the stress-strain state of the motor grader, depending on the new design provisions. In the presented work, a comparison of the stress-strain state of the metal structure of the motor grader produced by DORMASH CJSC and the new design, protected by invention patent, was made. The article developed a method for determining external power factors on the working body and the motor grader engine; additionally, their influence on the stress-strain state of the metal structure of the motor grader. This technique allows finding and evaluating the most realistic design positions of the grader, in addition to already adopted. Copyright © 2020 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Auto Grader, 3D Model, Mathematical Model, Stress-Strain State, Calculated Positions of the Auto Grader, Additional Calculated Positions

Resistance to grader movement Resistance to friction of the grader’s knife against the ground Variables of external forces; moments; parameters characterizing the position of the working body (cutting angle, angle of capture, folding angle of the articulated frame, etc.) “White noise” with a mathematical expectation of zero and a variance of one Equivalent stress at the most loaded point of the section Cutting angle

Nomenclature

l

Angle of capture Angle of inclination Dispersion of the roughness of the road surface Length of the track Coefficients characterizing the degree of irregularity of the road profile Adhesion coefficient Rolling resistance coefficient Longitudinal traction coefficient Lateral adhesion coefficient Part of the auto grader weight, falling on the rear truck Part of the auto grader weight, falling on the front axle Folding angle of the frame Normal ground reactions of all wheels of the grader Ordinate of the road profile Time interval for which the car traveled the path Machine speed Cutting resistance Resistance to movement of the ground prism in front of the blade Resistance to movement of the ground up the dump

I.

Introduction

The active development of transport infrastructure, the growth of residential construction, and commercial real estate increase the demand for road construction equipment. The need to improve the design of newly created technology is due to fierce competition from the outside, and the desire to conform to the level of world technical progress. Therefore, the improvement of the construction of road-building machines is an important and urgent task nowadays. The research results and solutions to this issue may be different, for example, the modernization of existing equipment, made according to traditional mounting and assembly schemes or creation and implementation of fundamentally new machines and

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https://doi.org/10.15866/ireme.v14i1.17990

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In general:

equipment with better characteristics. The purpose of the work is the design optimization of the working equipment of auto grader in terms of reducing the load on the metal structure. Most of the inventions are considering: Improved visibility for the operator; Decrease in metal consumption; Simplified management of working bodies; Expansion of functionality; Increased maneuverability; Improved planning capabilities. Well-known research optimization design of bulldozers [2]-[6] describes how a significant effect from a technical point of view and an economic one was achieved, due to the optimal location of the working hinges equipment of the bulldozers. Using the machines which are manufactured according to this methodology proves its effectiveness. The invention presented in this article was carried out by a similar technique. The objective of the invention is to reduce the operational loads on the metalwork equipment. The location of the blade cutting edge is in the same plane passing through the axis of symmetry of the turntable. The location of the hydraulic cylinder axis for the removal of the traction frame is in the same plane. Development of a method for determining external power factors on the working body and the motor grader engine is an important feature in order to prove new grader efficiency. Moreover, the influence of external power factors on the stress-strain state of the metal structure of the motor grader is an essential factor. Section II describes the strength calculation of the auto grader and the calculation of the reactions. The next section shows the main results on modeling the driver, engine, transmission, and wheel using MATLAB program. Moreover, the section describes the behavior of the machine during the impact. Sections IV, V present the main results of modeling design and operation modes.

II.

(1) where is the equivalent stress at the most loaded point of the section, are the variables of external forces, moments, parameters characterizing the position of the working body (cutting angle, angle of capture, folding angle of the articulated frame, etc.). In this case, the goal function is: (2) where is the part of the auto grader weight, falling on the rear truck; is the part of the auto grader weight, falling on the front axle; is the rolling resistance coefficient; is the longitudinal traction coefficient; is the lateral adhesion coefficient; is the angle of capture; is the angle of inclination; is the cutting angle; is the folding angle of the frame; are the normal ground reactions of all the wheels of the grader. The second point of the algorithm is the calculation of the wheel reactions. According to RD 24.220.03-90, the strength calculation of the steel structure of the motor grader is in three design positions. The wheel reactions are obtained from the equilibrium equations of the spatial force system. In this case, it is necessary to write the following equations: (3) (4) (5) When solving equations in the MathCad program, the research results are: After that, it is needed to recount on all wheel reaction . The resulting equations do not take into account the inertia force, because the influence of inertial and static loads is spaced. To confirm this, it is necessary to consider the oscillogram in Fig. 3, obtained during the experiment with the impact of the grader blade into a hard obstacle [8]-[14]. The oscillogram shows that when the grader dumps into an insurmountable obstacle, peak loads reach dynamic loads. Then the process of increasing static loads begins. They do not occur simultaneously, but one after the other. Thus, it is impossible to take into account the effect of static and dynamic loads at a time. It takes into account their influence separately and then chooses which of them is the most dangerous. Inertia force is calculated using the formula:

Theoretical Studies

The strength of the auto grader is calculated according to the design provisions [1], [7]-[12]. The search for additional design positions minimized to finding the maximum of the goal function.

Fig. 1. Fastening scheme of the working equipment of the auto grader: 1-propulsion: 2-underdrive frame: 3-spinal beam: 4-traction frame: 5turn circle: 6-blade: 7-hydraulic cylinders for raising/lowering the traction frame: 9-hydraulic ram traction frame

(6) where is the adhesion coefficient.

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International Review of Mechanical Engineering, Vol. 14, N. 1

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the magnitude force impact, in most cases, is determined by the machine adhesion to the supporting surface. The design calculation in statics does not allow obtaining adequate values of the support surface reactions and adhesion coefficient values. Because at each moment, they are different in direction and magnitude. It depends on many factors, one of which is the road profile. The MATLAB program has a generator unit of a normally distributed random signal, a process called “white noise” is generated (Fig. 4). A system of firstorder differential equations (8) assembled from the blocks, which can be transformed into a second-order differential equation (7) [14]-[16]:

Fig. 2. Estimated scheme of loads application on the motor grader

(7)

(8) Fig. 3. Oscillogram of the impact by the grader blade center into an insurmountable obstacle

(9)

Considering the calculation of the object only in static is insufficient since it characterized low accuracy of the obtained results and the reflected conditions. During calculation in statics, the change in the wheels adhesion coefficient to the ground, tires vibrations, the resonance of the structural elements, the mutual influence of the structural elements, the redistribution of loads under offcenter loading are not taken into account. As an example, the drawback description of such a static calculation is an essential feature. During calculation using the static equations, the soil reaction from the wheel interaction acts along the wheel axis, perpendicular to the support surface, but it is not always the case. Because of the irregularities of the support surface, the contact is different at each moment and it is not always symmetrical. The reaction from this contact acting on the wheels is often not directed along the axis of the wheel and not perpendicular to the supporting surface. Taking into account the shortcomings of the traditional method, the creation of a tool using the MATLAB program simulation is important, which would allow receiving the loads that occur during the entire work, as close as possible to the actual conditions. Objects of modeling: the profile of the support surface, working environmentsoil, machine design, engine, transmission, wheels, “driver”, machine operation modes-transport, technological, and impact. Some of the presented model objects will be described in detail.

(10)

(11) where is the time interval for which the car traveled the path; is the ordinate of the road profile; is the “white noise” with a mathematical expectation of zero and a variance of one; is the machine speed. The solution of differential equations (2) allows obtaining the ordinate values of the support surface profile. Thus, the system (2) has the meaning of a shaping filter, which cuts out the profile following the given coefficients of the initial data of the incoming signal-the white noise. The initial data determining the profile of the roadway: is the dispersion of the roughness of the road surface, l is the length of the track; are coefficients characterizing the degree of irregularity of the road profile [17]-[22].

III. Modeling of Ground Profile The behavior of the machine during the impact depends not only on its rigidity; the application place of

Fig. 4. White noise

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International Review of Mechanical Engineering, Vol. 14, N. 1

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According to the scheme: (12) (13)

(14) Engine and transmission modeling. In order to correctly form the current speed of the car, it is needed to clarify the external characteristics of the engine and transmission ratios. It is necessary to explain why an external engine characteristic is needed when the mismatch between the current speed and the setpoint is determined, and the regulating signal of the PI controller is determined. It is essential to multiply the value of this coefficient by the current value of the engine torque, then get a control signal that goes to the engine. It turns out that the PI controller determines the degree of depression of the gas pedal [24]-[27]. The program provides a block that allows recording the ordinate dependence on the abscissas under the schedule. Thus, the model takes into account the external characteristic of the engine. In addition to the engine, the model takes into account the hydromechanical transmission of the grader. The pump characteristics (the speed moment dependence), the gear ratios of the wheel gearboxes, the gearbox, the main gear, and the balancers are taken into account. There are four gears in the transmission model, and the car initially goes in first gear, depending on speed, which is necessary to maintain the increase in speed. The gearbox control unit receives a current speed signal at any time [28]. Table I explains at what amount of current speed gear changes occur. Switching occurs to upshift and downshift at different speeds; thus, some “dead zone” is obtained, which allows avoiding auto-oscillations. It also took into account transmission pump characteristics and transmission ratios of the wheel gearboxes, because the torque to the front wheels is transmitted through the hydraulic transmission. Wheel modeling. There is always a mismatch between current and given speed since the profile of the support base is not constant in the mathematical model. The resistance that occurs when the wheels interact with the support surface will always be different [29]-[30].

Fig. 5. Real profile at the filter output

Driver modeling. The driver in the model performs two functions: turns the steering wheel and presses the pedal to maintain the desired speed. The speed that the machine will maintain must present the program code. There is a mismatch between the set speed and the current speed of the machine. The current speed is formed due to the interaction of the wheels with the support profile, taking into account the resistance forces. After the finding of the current mismatch, the PI controller finds the coefficient, which increases or decreases the speed, and it happens in each unit with a specified step [23]. The second function of the driver turn the steering wheel for a curved motion. The value of the rotation angle is set for the front wheels. It is also possible to specify at what point in time the rotation will occur, and with what intensity the steering wheel should be turned. After specifying the angle of rotation, these data enter the block, which describes the geometric characteristics of the rotation of the machine front wheels. The program sets the imaginary rotation "middle wheel", it is indicated in Fig. 7. By geometric dependencies in the block, this rotation angle is calculated by the rotation angle of the real front wheels.

Fig. 6. The law of steering turn

is the angle at which the resultant interaction reaction of the wheel with the support base is located. The program splits the deformable part of the wheel into sectors with an angle . On each side of the sector, the overlap is determined and the equivalent angle is calculated by the formula.

Gear shift Speed km/h

Fig. 7. The scheme for calculating the geometric parameters of the front wheels rotation of the grader

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1→2 6,7

TABLE I GEAR CHANGES 2→1 2→3 3→2 4,8 12 9

3→4 17

4→3 14

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It is important to project the tangential and radial components on the coordinate axes and get reactions on the wheels.

IV. Modeling Design Figures 8 and 9 show the visualization of the machine design. The machine is the collection of absolutely rigid, non-deformable bodies connected by hinges. Each hinge contains the coordinate axes and centers of mass of the bodies, also described by their coordinates. The definition of the relative position of the structural elements is the location description of all these coordinate axes relative to the base coordinate system. In addition to the coordinates for each body, the inertia tensor and mass are specified. The program provides a block that allows it to record the dependence of the ordinates on the abscissas following the schedule. Thus, the model takes into account the external characteristic of the engine. In addition to the engine, the model takes into account the hydromechanical transmission of the grader.

V.

Fig. 10. A sequence diagram of the change in time of the shock force

In the form of a function, the change of impact force overtime was recorded. The first conclusion: the car movement process was modeled to take into account the processes which are not taken into account during static calculations: the change in the wheel friction coefficient during movement, the redistribution of loads under offcenter loading, etc. Then the results obtained from the mathematical model reactions on the car wheels apply to the finite element model and calculate the real stressstrain state of the motor grader. The strength of the metal grader is determined by calculation. According to RD 24.220.03-90, the motor grader parameters is calculated according to the main, random and emergency loads. Currently, there are three provisions [1]: - Estimated position 1: the front axle is hung and rests on the edge of the ditch, the rear wheels are stalled, and the work finishes on a cross slope with angle λ. - Estimated position 2: hitting the edge of the blade, pushed to the side, on an insurmountable obstacle. - Estimated position 3: grader in transport mode, there are vertical and horizontal loads from the mass of the nodes. Since the calculation method was developed a long time ago, some features were not taken into account, namely: every year companies of road-building machines offer more efficient and universal machines. Motor graders began to have greater maneuverability, and the range of soil development categories increased by highquality hydraulic systems, powerful engines, the availability of all-wheel drive, and ease of operation. Nowadays, motor graders are exploited more intensively and in more aggressive environment. Therefore, a calculation that includes the aboveestimated positions cannot reflect all possible loads acting on the motor grader. Thus, at any position, an unrecorded load may appear, which will affect the quality of operation and also durability. Therefore, it is necessary to include in the calculation additional design provisions, the analysis of which will give a complete picture of the stress-strain state at any position of the grader. The article presents the calculated position in Fig. 1, 3: a motor grader in transport mode, at a speed of 10 km/h, hit the edge of the dump on an insurmountable and rigid obstacle. It is precisely this position that chosen because it is often realized in life, for example, when the motor grader is passed from site to site and because in such a situation dangerous stresses arise that lead to the destruction of the metal structure. The calculation of the model at the described position will be finished

Modeling Modes of Operation

In order to simulate the technological mode of operation, the forces arising on the heap during “slaughter” are mathematically set: (15) where is the cutting resistance; is the resistance to movement of the ground prism in front of the blade; is the resistance to movement of the ground up the dump; is the resistance to grader movement; is the resistance to friction of the grader’s knife against the ground. To simulate the situation of the grader blade impact into an insurmountable obstacle, second law of Newton formula, written in...