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On the issue of dynamic loading of supporting structures of special wheeled chassis


The paper focuses on a method for assessing the dynamic loading of the frame of a special wheeled chassis when it moves on roads of various categories. Based on the developed finite element model of the frame, we obtained and analyzed full-size patterns of the stress-strain state of the frame and oscillograms of equivalent stresses in the most loaded zones of the frame.

For citation:

Tarichko V.I., Shalupina P.I. On the issue of dynamic loading of supporting structures of special wheeled chassis. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2019;(4):73-83.

A special position in the tactical vehicles (TV) fleet is held by special wheeled chassis and trac­tors (SWCT) intended for installation of mobile ground units and other types of weapons and military equipment (WME). Under heavy-duty operating conditions, high demands are placed on SWCT as a whole and their supporting sys­tems in particular with regard to their strength, durability, and reliability. In this respect, today the SWCT designers are facing a hard task of developing within the shortest terms an arti­cle meeting customer’s requirements. At that, a matter of no small importance is SWCT off- road performance, since accessibility of duty locations can be seriously limited. On the other hand, due to continuous improvement and so­phistication of the WME designs, a necessity is growing for increase of SWCT load-carrying capacity.

Given these conditions, application of mathematical modelling methods for investi­gation into the effect of different factors on the SWCT performance characteristics becomes more topical, allowing to considerably reduce expenses on tests and experimental research of the developed equipment at the engineering de­sign stage.

In this paper we shall consider the issue of assessing stress-strain state (SSS) of SWCT supporting systems (frames), which take up loads when moving over road irregularities and serve as a mounting base for assemblies and units. It is obvious that in case of frame breakdown further operation of SWCT will be impossible; however, under conditions of lim­ited resources it is necessary to maintain an op­timal proportion between the strength, rigidity, and other characteristics and the customer’s requirements. In connection with this, a pref­erable research technique of the SSS of SWCT frames is simulation modelling, which allows to estimate the degree of their dynamic loading with fair accuracy [1].

To begin with, we shall consider a design option of a ladder type frame used in the SWCT of “Voshchina-1” family manufactured by Bry­ansk Automobile Plant, JSC. The frame con­sists of two side rails (1), interconnected by cross-members (2) (Fig. 1), and has a constant cross-section with narrowing in the front part for bumper (6) attachment. The side rails are welded Z-profiles, additionally reinforced by stiffening plates (5) of variable cross-section, intended to increase structural rigidity. Cross-members con­nection to the side rails is basically bolted, with electric riveting additionally applied. Gussets (3) are secured on the cross-members by weld­ed connection.


Fig. 1. General view of the frame:

1 – side rail; 2 – cross-member; 3 – cross-member gusset; 4 – “cutout”; 5 – stiffening plate; 6 – bumper

A specific feature of this frame is a “cut­out” (4) (see Fig. 1), required for accommoda­tion of additional customer’s equipment. The “cutout” (4) is additionally reinforced by rims of the same thickness as the side rail main pro­file. To transfer forces from road to the frame, an independent torsion-bar suspension on lateral arms is applied.

The basic specifications of frame and sus­pension are as follows:


Material.......................................... 10KhSND

Side rail profile................................ Z-shaped

Side rail thickness, mm.................... 8

Profile height, mm........................... 600


Type............................................... Independent, torsionbar, on lateral arms

Compression stroke, mm.................. 130

Recoil stroke, mm............................ 105

Material of torsion bars..................... 45KhN2MFA-Sh-1GP

Material of arms.............................. 30KhGT

Let us consider the technique of simulation modelling applied for assessment of SSS of the frame in question. This technique is based on the finite elements technique (FET), which enables to solve a wide variety of research tasks with frames of virtually any design within the framework of a consistent approach.

At the first stage, an idealised spatial fi­nite element model (FEM) of the suspension was developed, consisting of one-dimensional finite elements (FE). Such FE take into account the material characteristics of suspension elements, their inertial and rigidity parameters, as well as damping parameters for elastic-dissipative ele­ments. Shock absorber non-linear characteris­tic was selected in accordance with the typical characteristic stipulated by the design documen­tation. The wheel-and-tyre assembly and wheel- hub drive with service brakes were considered in the model in the form of a lumped mass element located in a geometrically determined centre of gravity. Its connection to the suspension elements is implemented using a special interpolation ele­ment for mass load distribution. A general view of the idealised suspension model is given in Fig. 2.


Fig. 2. General view of an idealised suspension model:

1 – torsions; 2 – connection of suspension centre of mass to suspension elements; 3 – suspension mass; 4 – shock absorber; 5 – arms

The idealised frame model is a shell one. The position of shells in it corresponds to the arrangement of median surfaces of the sheet el­ements. The idealised model takes into account fastening points of the suspension elements and attachable equipment (cabin, power unit, engine compartment, etc.).

For discretisation of frame geometry, 3- and 4-node flat FE were used. The FEM of the frame is built with consideration of openings in the side rails for drive shafts and steering system elements. Additionally modelled are the points of suspen­sion fastening to the frame and fastening elements of the attachable equipment. The average FE size in this FEM is 40 mm, with condensation in the areas of possible concentration of stresses. The FE size was selected after preliminary test calcu­lations, performed with successive condensation of grid for the assessment of accuracy of the ob­tained results. As a result, it was possible to signif­icantly reduce final dimensionality of FEM, while preserving the required accuracy of calculations.

Bolted connections between the component parts are modelled by means of special modelling objects, which are an aggregate of one-dimension­al elements. At that, a ‘cobweb’ connection of the bolted joint opening nodes to their centres by ab­solutely rigid elements is done, and then central nodes of the openings are connected by an elastic one-dimensional element having bolt properties. Welded joints in the model are also modelled with the use of special modelling objects and represent elastic connections made from one-dimensional FE and having the properties of the material of the welded parts.

For consideration of heavy equipment mass­es, concentrated-mass FE are applied. Their posi­tions in the model correspond to the weight data sheet of the chassis. Connection of equipment centres of mass to the fastening elements on the frame is implemented by means of one-dimen­sional elements of weight loads distribution. In a real structure, connection of the suspension el­ements to the frame is done using a suspension bracket. To transfer the forces from suspension to frame, absolutely rigid one-dimensional FE are applied in the developed model. The developed FEM contains in total 88,520 nodes and 147,677 elements (Fig. 3).

Fig. 3. FE model of frame and suspension assembly

Correctness of the applied frame and sus­pension FEM is verified by a number of analytical calculations and laboratory researches conducted at the enterprise within the framework of various activities and tests. SWC static position on the ground and different options of jacking the axles were considered test calculations in the static lin­ear layout. As regards the reactions occurring on the axles, the results obtained from the test tasks are generally consistent with the results of ana­lytical calculations and laboratory research with weighing of similar articles.

A determining effect on the loading re­gimes of wheeled vehicles is produced by the road microprofile [2][3]. It determines dynamic loading of the vehicle’s supporting system as a whole and restricts possibilities to use the speed, power, manoeuvrability, and load carrying po­tential to the full advantage. Road irregularities can be determined using power spectral densi­ties S(n), S(ω), which are the functions of spatial frequency n (cycle/m) or cyclic spatial frequen­cy ω = 2πn (rad/m). To generate the heights of irregularities z,an algorithm based on the Rice - Pearson factorisation is used:

where N - number of harmonics;

S(n) - spectral density of road irregularities, m2 / (cycle/m);

n - frequency quantisation interval;

φi - random phase uniformly distributed over the interval [- π, π];

Δs - irregularity spacing, m;

k - harmonic sequential number;

n0 - minimum frequency.

Based on these data, microprofiles of roads of different categories, 500 m in length, were plotted in the form of dependences of irregularity height on path coordinate h(x). SWC movement on roads of the following categories will be considered:

  • asphalt-concrete roads;
  • dirt roads (in satisfactory condition);
  • worn-down cobblestone roads.

Given in Fig. 4 are the examples of mod­elled microprofiles of different road categories.

Fig. 4. Microprofiles of different road categories: a – asphalt-concrete roads; b – dirt roads (in satisfactory condition); c – worn-down cobblestone roads


For dynamic loading assessment, the exter­nal disturbance is rendered in the form of kinemat­ic displacement of the points of wheels contact according to the calculated microprofile parame­ters. For assessment of the effect of speed on the frame SSS, it is proposed to simulate motion at the speeds of 5, 10, and 20 m/s. In so doing, we make the following assumptions:

  • wheel contact with the road is a point contact;
  • the loading characteristics of torsions and shock absorbers are linear, and the coefficients of rigidity and resistance are constant;
  • the tyres are idealised in the form of an elastically damping model with constant coeffi­cients of rigidity and damping;
  • the soil is non-deforming;
  • the selected microprofile is symmetrical relative to the SWC longitudinal axis for the left- and right-hand sides;
  • movement speed during the modelling pe­riod is constant (the effect of longitudinal accel­eration is not taken into account).

In this way, 9 design conditions were gener­ated, the information about which is summarised in a table.


Conditions of SWC movement simulation for frame SSS study


Road category

Movement speed, m/s











Dirt road (in satisfactory condition)








Worn-down cobblestone road






The calculations results are presented in the form of dynamically changing SSS patterns of the frame at simulation of SWC movement over the given road microprofile.

Examples of the calculations results in the form of stress fields are given in Fig. 5. Having an­alysed the quoted data (see Fig. 5), one may con­clude that the most stressed zones during SWCT movement are as follows:

  • suspension bracket of the right-hand wheel of the first axle;
  • front part of the cutout on both sides of the frame;
  • suspension bracket of the right-hand wheel of the third axle.

Fig. 5. Patterns of stress-strain state of the frame under simulation of movement over selected microprofile (deformations scale 1:1): а – asphalt-concrete road, ϑ = 5 m/s, t = 47 s, s = 235 m; b – dirt road (in satisfactory condition), ϑ = 5 m/s, t = 63.2 s, s = 316 m

For expediency of the analysis we shall pres­ent the calculations results in the form of oscillo­grams of dynamic stress changes (Fig. 6) in the said frame zones. The obtained stress values are calcu­lated in accordance with the maximum-distortion (energy) theory.


Fig. 6 (beginning). Oscillograms of dynamic stress changes under simulation of SWC movement as per selected conditions: а – condition I, a (zone 2); b – condition I, b (zone 2); c – condition I, c (zone 2)



Fig. 6 (end). Oscillograms of dynamic stress changes under simulation of SWC movement as per selected conditions: d – condition II, a (zone 1); e – condition II, b (zone 1); f – condition II, c (zone 1);



selected conditions:
d – condition II, a (zone 1); e – condition II, b (zone 1); f – condition II, c (zone 1); g – condition III, a (zone 3); h – condition III, b (zone 3); i – condition III, c (zone 3)

It is seen from Fig. 6 that of all the conditions considered, the highest dynamic stresses occur in zone 3, i. e., fastening of the suspension bracket of the right-hand wheel of the third axle when moving at a speed of 20 m/s on a worn-down cobblestone road. It should be pointed out that in reality such conditions of movement are highly unlikely, but it can be considered for the analysis purposes within the framework of the discussed topic. In evaluation of the obtained results, one will notice significantly higher dynamic loading of the frame during SWC movement on roads that are in poor condition. Thus, dynamic stresses in the frame during SWC move­ment on a worn-down cobblestone road are on the average by 26 % and 32.5 % higher as compared with movement on a dirt and asphalt-concrete road, respectively.

Comparing the results as per conditions of SWC movement at different speeds on roads of the same category, we may conclude that the SWC movement speed, too, has a certain effect on dy­namic loading of the frame. The most considerable difference can be noticed when comparing the results as per conditions of movement at the speeds of 5 and 20 m/s: on the average, stress difference under those conditions is about 20.. .25 %. When comparing the results as per the conditions with movement speeds of 10 and 20 m/s, the difference is not so evident, lying within 9.11 %.

Despite high labour input required to prepare models for simulation modelling, the described ap­proach is justified from the viewpoint of the width of research spectrum where it can be used. For in­stance, at the present time SWCT are ever more fre­quently applied in self-propelled artillery systems for defence needs in the capacity of a process platform.

In the course of intended operation and application of such articles, stresses of various nature occur, in­cluding dynamic and shock ones. Taking them into consideration becomes crucially important when de­signing not only transitional elements (the so-called superframes, providing transfer of forces from the facility directly to the SWCT frame), but also the SWCT supporting structures proper. In this respect, the FEM of the frame and the approach applied, as shown in the paper, can on the whole be regarded as the basic ones. In case of various upgrade activities they can also be used for investigation into resist­ance of articles to external factors as concerns vi­bration strength and vibration resistance, as well as for a more detailed research of the effects of moving vehicle speed on the supporting structure SSS with regard to the occurring linear accelerations.

While on the subject of assessing dynamic loading of the supporting structures of vehicles, we shall also mention the techniques known in the field of rail transport [4][5], based on application of the methods of modelling the dynamics of multibody systems [6], in which the bodies can be assumed to be both absolutely solid and elastic. Generalisation of approaches described in those papers for the as­sessment of supporting systems of the motor trans­port will allow to have a deeper insight into the is­sues touched upon in this paper, but this is a matter of future research.


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About the Authors

V. I. Tarichko
Bryansk Automobile Plant, Joint Stock Company
Russian Federation

Tarichko Vadim Igorevich – Candidate of Engineering Sciences, Deputy General Director, Chief Designer. Science research interests: dynamic processes of power machines, wheeled vehicles and special transport equipment.


P. I. Shalupina
Bryansk Automobile Plant, Joint Stock Company
Russian Federation

Shalupina Pavel Igorevich – Head of the Design Bureau of Calculations and Reliability. Science research Interests: dynamics and strength of land vehicles.



For citation:

Tarichko V.I., Shalupina P.I. On the issue of dynamic loading of supporting structures of special wheeled chassis. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2019;(4):73-83.

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