# Determining Optimum Location Places for Clutch Couplings in Hydrostatic and Mechanical Transmissions of Wheeled Tractors

I.O Taran, A.I Bondarenko

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I.O Taran, A.I Bondarenko. Determining Optimum Location Places for Clutch Couplings in Hydrostatic and Mechanical Transmissions of Wheeled Tractors. Mechanics, Materials Science & Engineering Journal, 2017, 7, 10.13140/RG.2.2.35672.90888. [hal-01508632](https://hal.science/hal-01508632)

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# Determining Optimum Location Places for Clutch Couplings in Hydrostatic and Mechanical Transmissions of Wheeled Tractors

Taran I.O.¹,ª, Bondarenko A.I.²

1. Department of Transport Management, National Mining University, Dnipro, Ukraine

2. Department of Automobiles and Tractor Industry, National Technical University "Kharkiv Polytechnic Institute", Kharkiv, Ukraine

a. taran_70@mail.ru

<figure><img src="image_2.png" /></figure>

DOI 10.13140/RG.2.2.35672.90888

**Keywords:** wheeled tractor, hydrostatic and mechanical transmissions, clutch coupling, emergency braking.

**ABSTRACT.** Using a technique of Hooke-Jeeves, constructed partial criteria, and determined generalized criterion in terms of emergency braking of wheeled tractors the paper determines optimum location place for clutch couplings in hydrostatic and mechanical transmissions of wheeled tractors operating by means of "input differential" and "output differential" schemes. Recommendations concerning changes in relative parameter to control hydraulic machines with hydrostatic and mechanical transmission in the process of emergency braking of wheeled tractors to maintain working capacity of transmissions have been formulated.

**Introduction.** Agroindustrial complex is among the most important economic sectors; food safety of any country depends heavily on its level of development and functioning. Constant increase in overall agricultural production and violent annual fluctuations in transport needs are those prerequisites stipulating rural use of wheeled tractors.

Striving for stepless speed variation and moving force and improving ergonomic properties while performing various technological operations have become the key reasons to increase world output of wheeled agricultural tractors with hydrostatic and mechanical transmissions (HSMT).

**Statement of the problem.** Acceleration of wheeled tractors has extremely aggravated the problem of safety maintenance in braking mode. Despite the sufficient popularity of HSMTs in tractor industry current designs of transmissions of the type require further improvement. In the first instance it concerns the following: load reduction on both hydraulic portion and components of mechanical portion in the process of braking as incorrect location place of coupling will result in sharp increase of values of angle velocities of HSMT chains in the process of emergency braking and neglecting rules of changes in parameters to control hydrostatic drive (HSD).

**Analysis of the research and publications.** The problem of positive-displacement hydromachines and HSDs design, development and analysis of HSMTs for both wheeled and crawler tractors, lorries, combines, road-building machines, and mine diesel locomotives is highlighted in papers by world and domestic scientists [1-10]. The majority of the papers proposes structure and design parameters for two-flow HSMTs. They formulate recommendations concerning the choice of service braking and emergency braking implementation technique for wheeled tractors with stepless transmissions; however, authors appeal to their own designing experience only and use heuristic approach [4, 8].

Recently there is a tendency to use standard two-flow HSMTs in agricultural tractors. Range of their application increases as well as in the number of tractor models as in the power to be transmitted. Designs of HSMTs have a tendency to raise power transmitted mechanically and to decrease the number of frictional multidisk clutches. As a result, there is a decrease in the number
of ranges (subranges) and complex mechanical parts [2]. However, the problem of defining optimum clutches location place in HSMTs of wheeled tractors is not covered.

**The problem solving.** Series of perspective tractor schemes have been developed on the basis of the complex statistic analysis of HSMTs [10]. Maximum transmission efficiency is 0.82-0.88 depending upon a scheme. They served as a basis for defining optimum clutches location place in HSMTs. The research was done on the basis of emergency braking of the wheeled tractors case when engine is kinematically broken from the drive wheels in different alternatives of clutch location places: right behind the engine (alternative 1); within mechanical branch of closed circuit of HSMT (alternative 2); within hydraulic branch of closed circuit of HSMT in front of HSD (alternative 3); within hydraulic branch of closed circuit of HSMT behind HSD (alternative 4) (Figures 1 and 2). Emergency braking has been considered as it is the case when release of drive portions and loose portions of clutches (that is power flow break off) takes place. Specifically area of power flow break off effects on values of angular velocities of HSMT chains having certain limitations (angular velocity of satellites gears, shafts of hydromachines etc.).

<figure><img src="image_3.png" /><figcaption>Fig. 1. Alternatives to locate clutches within structural HSMT schemes with input differential: a) is alternative 1; b) is alternative 2; c) is alternative 3; d) is alternative 4; 1 is internal combustion engine; 2 is a clutch; 3 is planetary gear set (k is transmission ratio of planetary gear set); 4 is HSD; 5 are wheels; 6 are reduction units (i is transmission ratio of reduction unit).</figcaption></figure>

Optimization problem is solved to determine optimum location place for clutches in HSMT and rules to change relative parameters to control HSD ($e(t)$) in the context of emergency braking exercising a significant influence on operating ability of transmission.

To estimate braking efficiency in the process of optimization it is expedient to use braking path as a factor. It is recommended to estimate trajectory controllability according to deviation of tractor from predetermined trajectory. To estimate performance figures of HSMT it is expedient to use power parameters (working pressure difference in HSD $|\Delta P|_{max}$) and kinematic ones (angular velocity of satellites $|\omega_s|_{max}$, angular velocity of hydraulic pump shaft $|\omega_l|_{max}$ and hydromotor as well as difference between values of angular velocities of driving clutch shaft and driven clutch shaft $|\Delta\omega|_{max}$). Boundary values $|\Delta P|_{max}$, $|\omega_l|_{max}$, and $|\omega_s|_{max}$ depend mainly on design features of HSD; they are listed in specifications of hydromachines being indicated as $P^*$, $\omega_l^*$, and $\omega_s^*$. $P^*$ means
maximum pressure within induction pipe of HSD. Allowable value of angular velocity of satellites does not depend upon transmission parameters. However, it has its own limitation (i.e. 600 rad/s to be $|\omega_s|_{max} \le 600$); it is indicated as $\omega_s^*$. Maximum allowable difference between angular velocities of driving clutch shaft and driven clutch shaft indicating as $\Delta\omega^*$ depends on clutch type, its design parameters etc.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Alternatives to locate clutches in structural schemes of HSMT with output differential (symbols are similar to those in Fig. 1).</figcaption></figure>

Then, if tractor applies the brakes within curved road section (driven wheels are fixed at the level of 5° right after the start of braking process), generalized criterion is

$$ K_{\Sigma}(e(t)) = Z_1 \cdot \left(1 - \frac{S_g(e(t))}{S_g^*}\right) + Z_2 \cdot \left(1 - \frac{\Delta_{\max}(e(t))}{\Delta^*}\right) + Z_3 \cdot \left(1 - \frac{|\Delta P(e(t))|_{\max} + P_p}{P^*}\right) + Z_4 \cdot \left(1 - \frac{|\omega_1(e(t))|_{\max}}{\omega_1^*}\right) + \\ + Z_5 \cdot \left(1 - \frac{|\omega_2(e(t))|_{\max}}{\omega_2^*}\right) + Z_6 \cdot \left(1 - \frac{|\omega_s(e(t))|_{\max}}{\omega_s^*}\right) + Z_7 \cdot \left(1 - \frac{|\Delta\omega(e(t))|_{\max}}{\Delta\omega^*}\right) + Z_{\Delta\omega} \cdot P_{\Delta\omega}(\Delta\omega) + Z_{\Delta V} \cdot P_{\Delta V}(\Delta V), \quad (1) $$

where $Z_i$ and $Z_j$ – are weight coefficients ($Z_i$ is a value before partial criteria, $Z_j$ is a value before penalty functions);

$S_g(e(t))$ and $S_g^*$ – are real value of braking path and its allowable value;

$\Delta_{\max}(e(t))$ – is a value of maximum tractor deviation from predetermined trajectory after full braking;

$\Delta^*$ – is boundary value of deviation of tractor from predetermined trajectory;

$|\Delta P(e(t))|_{\max}$ – is maximum of real value of working pressure difference in HSD;

$P_p$ – is intake pressure; its value is equal to that one produced by delivery pump;

$P^*$ – is allowable pressure value within induction pipe of HSD;
$|\omega_1(e(t))|_{\max}$, $|\omega_2(e(t))|_{\max}$, and $|\omega_s(e(t))|_{\max}$ – are maximums of real value of angular velocity of hydraulic pump shaft, hydraulic motor, and satellites respectively;

$\omega_1^*$, $\omega_2^*$, and $\omega_s^*$ – are allowable values of angular velocity of hydraulic pump shaft, hydraulic motor, and satellites respectively;

$|\Delta\omega(e(t))|_{\max}$ – is maximum of real difference value between angular velocities of driving clutch shaft and driven one;

$\Delta\omega^*$ – is allowable difference value between angular velocities of driving clutch shaft and driven one;

$P_{\Delta\omega}(\Delta\omega)$ – is penalty function reducing generalized criterion value when rotational directions of driving clutch shaft and driven clutch shaft differ;

$P_{\Delta V}(\Delta V)$ – is penalty function reducing generalized criterion value if difference being greater than allowable value between real velocity of tractor V and its ideal velocity $V_e$ (which should be available at the moment relying on e value) is appeared.

Penalty function $P_{\Delta\omega}(\Delta\omega)$ is defined as follows

$$P_{\Delta\omega}(\Delta\omega) = \begin{cases} 1 - \frac{|\Delta\omega(e(t))|_{\max}}{\Delta\omega^{**}}, & \text{if } \omega_{z1} \cdot \omega_{z2} < 0 \text{ and } \|\omega_{z1}\| - \|\omega_{z2}\| > \Delta\omega^{**}; \\ 0, & \text{if } \omega_{z1} \cdot \omega_{z2} < 0 \text{ and } \|\omega_{z1}\| - \|\omega_{z2}\| \le \Delta\omega^{**} \text{ or } \omega_{z1} \cdot \omega_{z2} \ge 0, \end{cases} \quad (2)$$

where $\Delta\omega^{**}$ – is difference value between angular velocities of driving clutch shaft and driven clutch shaft being compensated at the expense of damping fluid properties and discharges to HSD;

$\omega_{z1}, \omega_{z2}$ – are angular velocity of driving clutch shaft and driven clutch shaft.

Penalty function $P_{\Delta V}(\Delta V)$ is defined as follows

$$P_{\Delta V}(\Delta V) = \begin{cases} 1 - \frac{|V_e - V|}{\Delta V}, & \text{if } |V_e - V| > \Delta V; \\ 0, & \text{if } |V_e - V| \le \Delta V, \end{cases} \quad (3)$$

where $\Delta V$ – is allowable difference between real tractor velocity V and $V_e$ velocity, which should be available at the moment relying on e value.

Value of weight coefficient is very important for generalized criterion value. Considering that partial criteria are equivalent and vary within almost comparable ranges, values of all weight coefficients are taken equal to 1/7. Expediency of such choice has also been confirmed by basic research. Rule of $e(t)$ variation in the process of emergency braking is perfect when $K_s(e(t))$ is maximally close to 1.

In turn, penalty functions $P_{\Delta\omega}(\Delta\omega)$, $P_{\Delta V}(\Delta V)$ are equivalent and vary within comparable ranges; however when $\Delta\omega$ and $\Delta V$ are out of allowable range it is proposed to take values of all weight coefficients as equal to $10^5$ before penalty functions. Thus, while determining $\Delta\omega$ and $\Delta V$ within
determined range effect on a value of generalized criterion is equal to zero
($Z_{\Delta\omega} \cdot P_{\Delta\omega}(\Delta\omega) + Z_{\Delta V} \cdot P_{\Delta V}(\Delta V) = 10^5 \cdot 0 + 10^5 \cdot 0 = 0$); and in the process of leaving a range a value
of penalty function together with weight coefficient experiences jump-type decrease. In this context
a value of generalized criterion is decreased as well.

While determining *e*, error is 0.01 (in the braking process, simulation interval was taken as 0.005 sec and determination of *e* optimum value took place; its correction was performed within the next stage). In this context not maximum but current values of indices were substituted into numerators of expression (1). That made it possible to obtain new $K_{\Sigma}(e(t))_{ti}$ values after each 0.005 sec and finally optimum rule of $e(t)$ change. However, value $K_{\Sigma}(e(t))$ from expression (1) is more informative as it takes into consideration not current values but maximum ones from the whole braking process; that is why obtained “optimum rule of $e(t)$ change for the given braking case” was given not maximum $K_{\Sigma}(e(t))_{ti\max}$ value from the whole obtained set $K_{\Sigma}(e(t))_{ti}$, but $K_{\Sigma}(e(t))$ involving maximum values of factors which had been determined after full stop of tractor as complete situation concerning changes in each parameter during braking process was available.

Optimization process is limited by consideration of tractor braking from the velocity of 60 km/h on a road surface with dry asphalt and snow.

In the process of emergency braking when kinematic separation of engine from driving wheels takes place, operating ability of transmission is possible if only correct area of power stream breakage is selected to be correct area of engine separation from driving wheels. As a result of optimization problem (1) – (3) solution involving Hooke-Jeeves technique it has been determined that from the viewpoint of braking process dynamics and generalized criterion values clutching in HSMD is:

* in terms of input differential it is recommended to locate it either behind engine or within hydraulic branch of closed HSMD circuit before HSD (neither alternative has evident advantage);

* in terms of output differential it is preferable to locate clutch within hydraulic branch of closed HSMD circuit before HSD, another alternative being less advantageous is its location within mechanical branch of closed circuit. If the requirements cannot be met (depending upon design features) it is located behind the engine.

Use of optimization theory in the process of basic research made it possible to determine that each HSMD scheme has its own optimum rule of changes in relative parameters of HSD control in terms of emergency braking of wheeled tractors with stepless HSMDs when kinematic separation of engine from driving wheels takes place. Braking process when values of control parameters correspond to changes in real velocity of tractor is the closest to optimum one. The analysis of the proposed rule in comparison with optimum one (for the schemes considered) has proved that difference in values of generalized criteria is not more than 6.9%.

It has been identified that in case of emergency braking of tractor in terms of kinematic disconnection of engine from driving wheels changes of HSD control parameters to improve operating ability of HSMD should be performed automatically meeting the requirements of real tractor velocity changes. Moreover, application of the rules allows a driver stopping emergency braking at any stage and continuing movement or acceleration of tractor to execute the manoeuvre without any negative consequences; that will make it possible to improve sufficiently traffic safety level.

The implementation technique is permitted to be used in terms of service braking: kinematic disconnection of engine from driving wheels is maintained and rule of brake pedal pressing may be in any form without time limits, however a driver will have extra stress which cannot favour his intensive and long-term employability. As a rule, the technique is not applied as service one in the context of current tractors with HSMT.
If in terms of emergency braking when kinematic disconnection of engine from driving wheels it is
technically impossible to change parameters to control HSD according to changes in real tractor
velocity (as it is connected with considerable complication of transmission control system)
following requirements shall be subject to compulsory implementation:

* braking of tractor lasts up to full stop;

* parameters of HSD control while braking remains invariable; moreover, they correspond to the value they had at the initial braking stage;

* when full stop of a tractor takes place, HSMT control system should provide automatically changes in HSD control parameters to be in accordance with zero velocity of tractor movement.

**Summary.** It has been proved that in the process of emergency braking when kinematic disconnection of engine from driving wheels takes place, operating ability of transmission is maintain if only correct area of power stream breakage has been chosen, i.e. correct area of disconnection of engine from driving wheels. The optimization problem solution has helped determine that from the viewpoint of braking process dynamics and generalized criterion values, it is recommended to locate HSMT clutch with input differential either behind engine or within hydraulic branch of short circuit in front of HSD (neither alternative is advantageous); in the context of HSMT with output differential it is preferable to locate clutch within hydraulic branch of closed circuit behind HSD.

It has been determined that in case of emergency braking of tractor when engine is disconnected
from driving wheels, changes in parameter values to control HSD to maintain operating ability of
HSMT should be performed automatically meeting changes in real tractor velocity. Use of the
recommendations helps a driver stops emergency braking at any stage without any negative
consequences and continues movement or acceleration of tractor to execute the maneuver; that will
make it possible to improve sufficiently traffic safety level.

References

[1] Bondarenko, A.I. (2015) Scientific Basis of the Theory of Vehicles Braking With Stepless Hydrostatic Mechanical Transmissions // Austrian Journal of Technical and Natural Sciences, «East West» Association for Advanced Studies and Higher Education GmbH. Vienna (Austria). – # 1 – 2. – Pp. 124 – 127.

[2] Bondarenko, A.I. (2014), Samorodov, V.B. Features of Power Flow Distribution in a Closed Circuit of Hydrostatic Mechanical Transmissions // Zbior Raportow Naukowych. Wykonane na Materiałach Miedzynarodowej Naukowo-Praktycznej Konferencji «Inżynieria i Technologia. Osiągnięć, Projekty Hipotezę», 29 – 30 December 2014, Krakow, Poland / Sp. z o.o. «Diamond Trading Tour». – Warszawa: Wydawca: Sp. z o.o. «Diamond Trading Tour», 2014. – Pp. 59 – 70.

[3] Bondarenko, A.I. (2014), Mittsel, M.O., Kozhushko, A.P. Laboratory Stand for Research of the Workflow in Hydrostatic Mechanical Transmissions // Materials of the IX International Research and Practice Conference «European Science and Technology», 24 – 25 December 2014, Munich, Germany / «Strategic Studies Institute». – Munich: «Strategic Studies Institute», 2014. – Vol. II. – Pp. 289 – 295.

[4] Bondarenko, A.I. (2015) Dynamics of the braking process wheeled tractors with hydrovolumetric-mechanical transmission: Monograph. – Kharkiv: published by «Fedorko». – 220 pp.

[5] Samorodov, V.B., Taran, I.A. (2012) Analysis of the distribution power flow considering the efficiency of hydraulic continuously variable two-flow hydrovolumetric-mechanical transmission with differential output // The bulletin of the National Technical University "KhPI". – Vol. 64. – Pp. 3 – 8.
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[7] Taran, I.O. (2013) System of integral stochastic criteria for transmissions of transport vehicles // Naukoviy visnyk Khersons’koi derzhavnoi mors’koi akademii. – Kherson: Kherson state maritime academy. – # 2 (9). – Pp. 277 – 283.

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