Procedia Engineering 150 ( 2016 ) 1131 – 1136

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1877-7058 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of ICIE 2016doi: 10.1016/j.proeng.2016.07.225

ScienceDirect

International Conference on Industrial Engineering, ICIE 2016

Estimation of Screw-Ball Differential on Vehicle Dynamics

A.V. Keller, A.A. Shelepov*, D.I. Istomin South Ural State University, 76, Lenin Avenue, Chelyabinsk, 454080, The Russian Federation

Abstract

The article dwells upon the nonlinear dynamic model of the vehicle 4×4 with a screw-ball differential. The car model is carried out in the software package LMS Imagine.Lab Amesim automated modeling. In this model, we implemented limited slip differentials as their use in cars is promising, enabling simultaneously to improve safety and vehicle patency. Full-scale test "evasive maneuver S=20 m" results of UAZ 3151 confirm the adequacy of the physical behavior of the model. The developed model can be used to evaluate the dynamic properties of the vehicle in different driving modes as well as for the design of new power distribution systems and evaluating drivability. © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of ICIE 2016.

Keywords: the movement of the car model; simulation; limited slip differential; coefficient lock differential; road test.

1. Introduction

For reliable assessment of performance operating ability car and their further optimization of the design stage is necessary to create spatial dynamic models based on differential drive kinematics. An effective tool to solve these problems are software systems automated analysis of body system dynamics. The description of such complexes in the system is a set of typical elements in the library or to create new items. These software packages allow for a mathematical description of the components of the car model on the basis of which constitute the equations of motion and get their numerical solution, as well as visual assessment of the behavior of the car when driving on a virtual test area.

* Corresponding author. Tel.: +7-951-775-7322.

E-mail address: shelepov-aa@mail.ru

© 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of ICIE 2016

1132 A.V. Keller et al. / Procedia Engineering 150 ( 2016 ) 1131 – 1136

Nomenclature

M0 torque at the crown wheel M1 torque moment on trailing shaft M2 torque moment on outrunning shaft M3 frictional torque in differential Kb differential gear blocking factor K*

b differential gear blocking factor kk factor defined by a design of the mechanism

2. Mathematical model of screw-ball differential

In given article is considered creation of dynamic model of transmission of car UAZ-3151 with differentials under characteristics similar screw-ball differential for definition of the basic operational performance of the car in a program complex of the automated modeling. For this purpose in the development environment of LMS Imagine. Lab Amesim have created mathematical model of movement of the car with screw-ball differential (Fig. 1).

In mathematical model parameters of car UAZ-3151 in full weight of 1720 kg with the wheel arrangement 4x4 are realized. The car body represents a solid body to which forces and the movings defined by a power-plant and environment are transferred.

The load curve of the engine presented on Fig. 2, is picked up according to characteristics of the engine established on car UAZ-3151.

The car model consists of the systems shown on fig. 1. The model of brake system was is taken from system of a set of base libraries.

The suspension system in model has been realized same, as at car UAZ-3151 - dependent spring on all wheels. The model spring parts consists of weightless geometrical model of a body and the in large quantities-inertial model set in the form of a set of in large quantities-dimensional equivalents of the basic units of the car.

For the description of work of differentials following mathematical dependences have been used:

3 0/bK M M (1)

The friction moment in differential describe following expression:

3 ( , , )kM f k M (2)

The friction moment in differential depends or on change of a difference of frequencies of rotation drives hafts or semi-axes, or from a difference of the created moments M [1-3, 5-8].

Also under blocking factor Kb* as understand the torque moment relation on trailing shaft to outrunning shaft.

*1 2/bK M M (3)

Between differential gear blocking factors Kb and *bK there is a following dependence:

* (1 ) / (1 )b b bK K K (4)

The model of interaction of the tyre with road with sufficient degree of accuracy describes Pacejka Magic formula which is realised in given model [9].

In the given model following assumptions have been accepted:

1133 A.V. Keller et al. / Procedia Engineering 150 ( 2016 ) 1131 – 1136

The bearing system of the car is presented as absolutely firm body having a longitudinal plane of symmetry, arising deformations in a design of a body as a result of movement in model are not considered; The equations of communications between angular and linear deviations of parts of bearing system and car bridges at fluctuations are linear; Dissipative elements consider energy losses on a friction in transmission mechanisms; Communications of wheels of the car with a basic surface of road are described by the equations considering only elastic sliding (wheels do not come off road) [4, 10, 11]; Communication of wheels with a car body in a vertical plane is considered as rigid, i.e. without elastic properties of a suspension bracket.

Fig. 1. Model of the car with screw-ball differential.

1134 A.V. Keller et al. / Procedia Engineering 150 ( 2016 ) 1131 – 1136

Fig. 2. Load curve of the engine.

3. Testing

For model check laboratory road tests of car UAZ-3151 have been conducted. The given car has been equipped strain gauge system and compact analyzer LMS SCADAS Mobile for registration of the parameters received from strain gauges through running contact. As on the car two three-co-ordinate gauges of linear accelerations have been established.

Strain gauges for measurement have been established on everyone semi-axes the car, inductive gauges of frequencies of rotation as are established on all semi-axes and car drive shafts. The scheme of placing of gauges on the car is presented on fig. 3.

Fig. 3. The layout strain gauge system on the car UAZ-3151: 1-differential gear; 2- semi-axes; 3- drive shafts; 4- transfer gear case; 5- strain gauge; 6-running contact; 7-computer.

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4. Results

Road tests were spent on speeds to 80 km/h, at maneuver performance «evasive maneuver S=20 m» on dry paving asphalt and have received following dependences, on the same schedules results of imitating modeling have been combined also.

According to tests conducted by the car equipped with limited slip differential has performance handling and stability, meet the requirements of para. 4.5 of GOST R 52302-2004.

Fig. 4. Change frequencies rotation wheels.

Fig. 5. Change torque moments on front wheels.

Fig. 6. Change torque moments on rear wheels.

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Fig. 7. lateral acceleration.

5. Conclusion

The received results of experiment testify to adequate physical behavior of model. It is established that the relative error of imitating model in this case does not exceed 15 % that allows to draw a conclusion that the realized model of the car in the given environment of imitating modeling with confidential probability 0,95 well describes investigated processes in the specified limits of a variation of factors.

On the basis of the given model probably method of imitating modeling to estimate operational qualities of a vehicle. The main advantages of methods of imitating modeling are: possibility of the decision of difficult nonlinear mathematical problems, accuracy of received results, possibility of study of concrete technical decisions on product design stages, definition of optimum factors of blocking of differentials for all bridges in aggregate for the purpose of maintenance of operational safety of the car.

Lab Amesim have created mathematical model of movement of the car with screw-ball differential (Fig. 1).

Acknowledgements

Work was performed under financial support of the Federal State Institution "Fund for Assistance to Small Innovative Enterprises in Science and Technology" in the frames of the project «Development of screw-ball differential civilian vehicles under agreement No. 9109GU2/2015 dated 24.12.2015 and OOO . "DAK".

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