Proceedings of the 7th World Congress on Mechanical, Chemical, and Material Engineering (MCM'21)
Prague, Czech Republic Virtual Conference – August, 2021
Paper No. ICMIE 121
DOI: 10.11159/icmie21.121

Dynamic Analysis of a Convergence Diagnostic Equipment for
Preventive Maintenance in Light Vehicles
Claudio Cordova1, Fredy Llulluna 2, Juan Sinchi3, David Pachacama4, Darwin Pachacama5
1

Department of Basic Sciences /Escuela Politécnica Nacional
Ladrón de Guevara E11-253, Quito, Ecuador
claudio.cordova@epn.edu.ec
2
Deparament Sustainable Architecture /Universidad Regional Amazónica Ikiam
Parroquia Muyuna, kilómetro 7 vía a Alto Tena. Napo, Ecuador
fredy.llulluna@ikiam.edu.ec
3
Deparament Automotive Engineering / Universidad Politécnica Salesiana
Calle Vieja 12-30 y Elia Liu, Cuenca, Ecuador
jsinchi@ups.edu.ec
4,5
Deparament of Exacts Sciences / Universidad de las Fuerza Armadas ESPE
Av. Gral. Rumiñahui y Av. Ambato, Sangolquí, Ecuador
dppachacama1@espe.edu.ec/dapachacama@espe.edu.ec
Abstract - This research carries out the dynamic analysis of light and semi-light automotive convergence diagnostic equipment, with agross weight of up to three tons. A comparative analysis of the implications and consequences due to positive, negative, and neutral
convergences is carried out. Then the different mechanical and electronic design characteristics of the device to determine theconvergence in the tires. The design of the equipment has three stages: mechanical, electrical, and electronic. The mechanical stagecomprises the structure of the equipment, the electrical stage consisting of the design and construction of a longitudinal motion sensor,
The electronic stage formed by a microcontroller which, once the microprocessor has been programmed, performs the measurement
process based on the variables: relative displacement and potential difference. The elements designed and built are integrated into theequipment, which through a test protocol was evaluated both in empty and under load.
Keywords: dynamic, electromechanical, convergence, automotive, alignment.

1. Introduction
The good mechanical condition of the vehicle, and the correct calibration of each of its parts or systems, ensure good
dynamic response and safety of its occupants. Each year about 1.3 million people on the roads of the world, between 20 and
50 million suffer serious and minor injuries. Traffic accidents are one of the main causes of death in all age groups, and thefirst among people between 15 and 29 years of age (UN, 2019). In addition to economic losses, and psychologicalconsequences of people who have suffered after a car accident. These reasons are enough to understand that developed theautomotive industry over time has put emphasis on energy efficiency, operational functionality, aesthetics, safety, andminimizing the harmful effects to the environment caused as a result of its functioning.
The parameters that reflect a good dynamic response of the vehicle are caster or advance, camber or fall, convergenceor divergence of its tires, the inclination of ball joints, thrust angle, and inclination of the steering axis, among others. [1] In
the present work, convergence alignment is studied in automobiles with a maximum weight of 4000 kg. The misalignmentof convergence of the vehicle is classified as a serious defect in the dynamic behavior of the same according to the guidelinesof the Vehicle Technical Review implemented in our country at the national level, it considers that any defect of the vehicle
classified as serious, must be corrected compulsorily movement in urban districts. These regulations must be complied withfor the annual certificate of good vehicle operation to be issued. The main objective is to design and build a two-part
diagnostic kit, to detect toe misalignment in a vehicle and perform the measurement to correct such a defect. The alignment
equipment is scarce, and the cost is high, the present work is an alternative for local development, with a view to national
industrial development.

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Convergence is measured in degrees and the measurement is performed from the rearmost of the rim to the height of the
cube and most forward point. The difference between the two measurements determines the toe-in value that indicates what,
precisely, the type of toe-in of the wheels. The angle between the plane that contains the lateral faces of the rim and thevertical plane concerning the ground (horizontal). This camber or fall angle in sports cars can measure up to 5 °, inmotorcycles it can reach 50 °. [3] For four-wheel vehicles, the camber angle can be understood as follows: if the planes
containing the pair of fronts (or rear) tires are parallel to each other and perpendicular to the ground, the camber is said to be
zero. The planes containing the pair of fronts (or rear) tires intersect upward from the horizontal floor, forming an acute angle
with each other, the camber angle is said to be negative, and its magnitude is the number of degrees the camber deviates aplane containing the lateral face of the rim for the vertical plane for the ground. If the planes containing the pair of fronts (orrear) tires intersect below the horizontal floor, forming an acute angle with each other, the camber angle is said to be positive,
and its magnitude is the number of degrees the plane deviates. It contains the lateral face of the tire for the vertical plane to
the ground. [4]If the planes containing the pair of fronts (or rear) tires intersect towards the front of the vehicle, forming an acute angle
between them, the vehicle tires are said to have positive toe-in and their magnitude is given by the difference between thefront and rear parts of the pair of front tires (or the pair of rear tires), in other words. When the front of the wheels is closer
to each other than their respective backs, these wheels are said to be convergent. When the front parts of the wheels arefurther apart than their respective rear parts, this pair of wheels is said to diverge or to be divergent. [4] [5]2. Convergence and Its Effects
The torque or torque of the torque transmitted from the engine to the wheels of the vehicle, allowing the rotation of thetires and drive the vehicle. In Figure 1, the torque shown 𝐹⃗ , −𝐹⃗ , friction forcé 𝑓⃗𝑟 between the tire and the ground and the
movement of the axis of the tire (vehicle movement) with speed 𝑣⃗.

Fig. 1: Race Cars Vehicle Dynamics. [4]The force −𝐹⃗ and the component 𝐹⃗ , cancels out with friction force𝑓⃗𝑟 between the wheel and the floor, then the force𝐹⃗ is the cause of the relative movement of the wheel with respect to the floor, thus, the axis of the wheel will move withrespect to the floor with speed 𝑣⃗. Considering that the wheel axis is subject to the chassis of the vehicle, then its movement
relative to the floor is the movement of the vehicle relative to the floor. The friction force between the wheel and the floor
can change with the type of tire, the type of floor, the weight of the vehicle, the inflation pressure, the tire wear. If the friction
force fails to nullify the force −𝐹⃗ of the pair, then the tire starts to slide or skid decreasing mobility of the drive shaft, whichconnects the forward motion of the vehicle relative to the floor. [6]This section presents the concepts and definitions of convergence; null, positive and negative, and their repercussions,vital when designing and building a convergence diagnostic team. All the diagrams presented illustrate the movement of thefront left tire, bearing in mind that the movement of the front right rim is symmetrical to the left rim concerning the vehicle's
advance line. Figure 2a illustrates the movement of wheel A, so it rotates with angular velocity w, advancing towards thefront of the vehicle, driven by the engine M. The centerline I of the rim is superimposed on line R, by the one that moves thevehicle forward. Then the degree of toe-in of the tire is said to be zero or zero. [7] Under these conditions, if the tire treads

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and turns on a sheet of paper lying on the ground and if there is no friction between the sheet and the ground, the sheet ofpaper moves in the H direction, aligned with the centerline I of the rim. The paper does not suffer any lateral deviation. The
vehicle moves in the forward direction even if the driver takes their hands off the wheels.

Fig. 2: Null convergence (a), negative convergence (b), positive convergence

Negative convergence or divergence occurs when the movement of the left front wheel A (the orientation of the rightfront wheel is symmetrical to the left, concerning the line R), so that it rotates with angular velocity w, driven by the motor
M with the centerline I of the wheel angle θ deviated one in the anti-clockwise, to the line direction R in which the vehicle
moves forward, 2a. Then it is understood that the convergence of the tire is negative and different from zero.
The positive convergence or just convergence is observed in the movement of the left front wheel A. The orientation of
the right front wheel is symmetrical to the left relative to the line R by advancing the vehicle, it rotates with angular velocity
w, driven by the motor M. The centerline I of the wheel is offset by an angle θ in the clockwise direction, concerning thedirection line R in which the vehicle is moving forward. It is then said that convergence of the rim is positive and different
from zero, Figure 1c. Positive convergence is commonly referred to simply as convergence.
2.1. Displacements Generated By Misalignment
When the vehicle is forced to advance on a line other than the centerline of the rim, with its tires in a positive or negative
toe-in condition, large forces are generated on the tire pivot, which is the axis around which they are oriented. On the other
hand, the movement of the vehicle along the line of advance is difficult, this opposition to moving along the line of advanceis greater the degree of misalignment. This proportionality is not a linear relationship.
The convergence alignment values different from zero, also generate forces concentrated at the edges of the tires(especially the inner edges), causing rapid wear thereof. A convergence nonzero in the rear wheels in addition to the rapid
wear of the tire can change the angle of the motor thrust. The convergence alignment values are positive or negative and canbe corrected by adjusting the threaded ends that connect the rim to the rod. [9]An indicator of the convergence value is the value of the smallest angle formed between the vehicle's line of advanceand the center line of the rim, which at most, rarely reaches a value of two degrees, therefore, its adjustment does not It canbe done by relying on the direct perception of the eye but requires a precision instrument. This detail justifies the objectiveof working on the design and construction of a convergence diagnostic equipment that allows correcting the misalignment
defect of automotive tires.

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3. Methodology
The cases of convergence positive, null, and negative toe-in respectively for the same left front tire of the car. In allcases, the vehicle is forced to move in the same direction R, even though in cases: a), c), its tires deviate from the directionof advance as shown by the centerline I of the tire. In all cases the wheel rotates with an angular velocity, wy magnitude
perpendicular to the plane of relative rotation, then, if the rim in its movement, treads friction to a sheet of paper which in⃗⃗ different in each case as shown in thisturn slides frictionless relative to the floor, it is displaced by drag in the direction 𝐻⃗⃗ can be decomposed into its Cartesian components: 𝐻⃗⃗𝑥 , 𝐻⃗⃗𝑦 . In all the cases shown, thefigure 3. Each displacement 𝐻⃗⃗𝑦 occur in the same direction, so these cannot be used as indicators of the different forms of convergencedisplacements 𝐻⃗⃗𝑥 generate the difference between the different cases of convergencealignment, however, the lateral displacements 𝐻⃗⃗𝑥 to the left, a nullalignment, like this: a positive convergence produces a lateral displacement of the paper sheet 𝐻⃗⃗𝑥 and a negative convergence produces a lateral displacement 𝐻⃗⃗𝑥 towards theconvergence produces a null displacement 𝐻⃗⃗
right of the sheet of paper. It is for this reason that the lateral displacements 𝐻𝑥 of the sheet of paper constitute in themselvesadequate indicators of the different cases of convergence alignment.
The movement of the sheet dragged by the wheels is 2-dimensional, its movement is said to have two degrees of⃗⃗𝑦 . of the blade does not provide information on the different forms of
freedom. On the other hand since the displacement 𝐻alignment, it can be blocked and information on the convergence alignment of the rim is not lost. Consequently, to have the⃗⃗𝑦 . In this sense, it is said that a degree of freedom of theinformation of convergence of the rim, to skip the displacement 𝐻
movement of the blade has been restricted, resulting in that, to determine the different forms of convergence, only the lateral⃗⃗𝑥 of the blade dragged by the rim through friction must be carefully observed.
displacement 𝐻

Fig. 3: Degrees of freedom on the wheels

El The study of the movement of the sheet of paper, displaced by friction by the rim and its lateral sliding on the smoothhorizontal floor, is the focus of attention to investigate and quantify the different effects that occur in the convergencealignment, and constitutes the conceptual basis for the development of diagnostic equipment for convergence and can be
abstracted as follows. The sheet of paper can be replaced by a steel plate, with one of its faces rough and the other smooth,this characteristic can be obtained by adhering a mechanical anti-friction system to the lower face of the plate. Once its⃗⃗𝑥 , perpendicular to the line of advance, will
movement is restricted in the vehicle's line of advance, its lateral displacement 𝐻
give information about the convergence alignment. In fact, building such a mechanism is possible and constitutes an essential
first element of our alignment team. The second essential element is to solve the problem of quantization of the lateral

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movement of the steel deck, taking into account the value of lateral displacement is very small relative to the forward travel⃗⃗𝑥 | is a millimeterof the vehicle. Simple calculations show that the accuracy of the transverse displacement measurement | 𝐻or smaller in magnitude.

3.1 Desarrollo De Equipo A Nivel Conceptual
Mechanical stage in its conceptual level, coupled the idea of the paper sheet by the tire tread, with one side rubbing
against the rim and the other sliding without friction relative to the floor. The mechanical stage highlights three sections: themechanical section 1.1 Simulates the fixed ground floor. The mechanical section 1.2 idealizes smooth, between the lower
face of the paper sheet and the floor. The mechanical section 1.3 idealizes the movement of the sheet relative to ground,smooth on its lower face and roughened on its upper face.
The conceptual level of the electrical stage of the equipment requires an element that can transform a displacement
vector into an associated voltage measurement, this type of element, Figure 6 is shown, represented by a transformer block,with an input variable the displacement and an output variable such as the associated voltage, called (according to Soria,2013) an open-loop system. We call this element a motion sensor. The conceptual level of the electronic stage is outlined infigure 4. A system is required that allows obtaining a set of data, processing it, managing it, and proceeding to display it..

Acquisition
Data processing
Calculation Variables
Presentation of results
Fig. 4: Diagram of the convergence system

3.2. Development of the convergence alignment device⃗⃗𝑦 . of the displacement. does not differentiate the different
Mechanical stage, basic development. The component 𝐻⃗⃗𝑥 , Figure 4a illustrates the blocking of thetypes of convergence, its restriction does not affect the value of the indicator 𝐻⃗⃗
longitudinal movement 𝐻𝑦 of section 1.3 concerning section 1.1. However, its transverse rectilinear motion Hx is free. In

this figure: section 1.1 is anchored to the floor; the intermediate section 1.2 formed by a surface distribution of antifriction
spheres allow a frictionless movement of 1.3 concerning section 1.1; The "V" shaped channels made in the sidebars ofsections 1.1 and 1.3 prevent their relative longitudinal displacement; The arrow at the top of Figure 5 is the vehicle's direction⃗⃗𝑥 ., is proportional to the value of the convergence defect,
R of advance. The value of transverse displacement 𝐻

Fig. 5: Mechanical and electronic diagram

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Electrical stage, basic development, constitutes the step from the ideas shown in figure 4b to the concrete ideas shownin figure 4, where the transformer block is constituted by a movable cursor potentiometer B, free to move between its ends
A, D.
Electronic stage, basic development, can be seen in figure 10, in it, three sub-stages are seen: A, B, C. In stage A, theinput voltage for the RV1 motion sensor is conditioned, and its signal output enters the microcontroller, in this stage B, themicrocontroller must achieve the measurement system and process it, it must calculate variables involved in the convergencephenomenon, and then in stage C display them on the screen, figure 6.

Table 6: Microcontroller Diagram

2.4. Mechanical Design of the Structure
El The overall design of the assembly can be seen in figure 11. The sections and their corresponding elements are Meshshaped support structure, ribbed crossbars, reciprocating elastic mechanism, movement sensor, mechanical waxer, safety
pillars, vertical movement blockers. Mobile elements: layette rectilinear, transverse , 49 bearing areas , 19mm diameter andfinally top cover.

Fig: 7. Schemes of the structure of the convergence alienation device

Between the support elements of antifriction surface composed of rails antifriction observed using spheres bearing, at
the top the mechanical section 1.3, movable with respect to section 1.1 is observed. In mechanical sections: bottom 1.1, 1.3
and higher, are installed the respective components associated mechanical. The assembled equipment including its upper

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platform can be seen in figure 3.33. The platform can be observed as threaded screws T required to lift and place the upper
platform easily.

3. Tests of Operation of the Equipment
Once the equipment was assembled with all its sections: mechanical, electrical, electronic, including its control box
attached to the work site, the equipment was tested under no load. Figure 8a shows the connection of the card's USB cable,with an extension to the work computer. When the power cable was connected from the computer's USB 2.0 port, 15m longto the Arduino card port, Keypad shield as can be seen in figure 8b, then the card was activated.

Fig. 5: Mechanical and electronic diagram

Performance tests are conducted with loaded and unloaded, then to verify proper operation of your computer comparedwith a comparison team teams Center Technical Review vehicle is performed. LRTV gave a reading of 2m / km. It should
be noted that the maximum permissible values for this defect are +6.99 m / Km for a positive convergence, and - 6.99 m /Km for a negative convergence, then the convergence diagnosis is typified as valid and the Vehicle Review is approved. The
details of this test are in the public domain on the Internet. The tests carried out so far show that the equipment has sufficientvertical and transverse mechanical resistance, to the passage of light and medium-heavy vehicles of up to three tons of grossweight. The cost of the equipment is very important and the cost blocks must be determined: direct costs, indirect costs. The
direct costs consider the prices of the materials of each set of pieces and the price of specific works that must be carried out
on them, such as: raw material, cuts, bends, machining, perforations, welds. In a second block of direct costs, the acquisitionof inputs such as: drills, cutting and grinding discs, antioxidant, paints, dye thinner is considered. A third block costs are

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considered indirect costs such as: water, electricity, rent, payment operator. Table 3.1, shown in summary the total cost perteam which amounts to USD 2480, value obtained to the sum of direct costs and indirect production equipment.

4. Conclusion
The alignment condition of zero convergence is ideal for the smooth running of a vehicle when it is in full load operation.
If the vehicle is off in terms of convergence with positive values or greater than or equal negative to 7, it is considered aserious malfunction of the same, a situation that requires prompt restraint, which is to leave the tires at the minimum degreeof convergence, or a value very close to this, in any case with convergence less than 7 in absolute value.
The deviation of the centerline of the tire from the vehicle's line of advance, which is outside the design limit of thevehicle, causes failure in the direction in which the vehicle is moving and is considered a defect of the vehicle. Since thecenterline of the rim from the front line of the advance can be offset to the right or the left, it results in positive convergenceand negative convergence.
Contribute to the change in the country's productive matrix, generating technology to manufacture this type of equipment
locally, and with it, improve the technological level in automotive workshops nationwide, making them more competitive.
It is the way the National Polytechnic School, offering technological solutions to social problems cited as concrete. It is
recommended that the construction of precision elements be supervised by the author, since the lack of elements of judgmentof the technical staff, undermines construction details and on several occasions the costs are implicit and affect the qualityof the product.
Measure the degree of misalignment is equivalent to saying, a diagnosis of convergence in the automotive. With thehelp of the same equipment, it is possible to correct the convergence defect until reaching the permissible values, typified by
the Vehicle Technical Review
We can calculate and conclude that the minimum safety margin in terms of the maximum load of our equipment, about
the weight of the heaviest known vehicles is 40% and concerning the lightest, it is 90% and for the load that The equipment
must support when working with vehicles of average weight 1000Kg, it is 33% of the total load. These results give us
assurance as to the mechanical stability of the team, even in extreme operating conditions.
Through the simulation process, it is required to verify that the stresses generated in the structure of the alignment
equipment, which were previously calculated analytically, do not exceed the yield strength of the material. SAP 2000
software was used for this analysis. Simulating that the loads are applied.

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