These authors contributed equally to this work.
In order to improve the ride comfort of a continuously variable cotton picker, the shift quality of the cotton picker is analysed. Firstly, the transmission principle of the hydrostatic power split continuously variable transmission (CVT) with a single planetary gear set is introduced; secondly, the shift dynamic model of the power train is constructed, and the key models are verified by experiments; finally, the influence law and mechanism of various factors in the shift qualities of a cotton picker are analysed. The results show that the increase in main circuit pressure will reduce the shift quality of the cotton picker; the influence of clutch-charging flow and acceleration rate on the shift quality of the cotton picker can be ignored; with the action time of the clutch delayed in a certain range, the shift impact first decreases slightly, then increases, and finally decreases; the increase in the cotton box weight can slightly improve the shift quality of the cotton picker but is at the cost of consuming more clutch-sliding energy. If different factors are evaluated together, the value of the main circuit pressure and charging flow should not be too large or too small. At the same time, the action time of a clutch to be disengaged should be delayed, and the action time of a clutch to be engaged should be advanced. The conclusions of this study can provide theoretical support for the controller development of a continuously variable cotton picker.
The working condition of the cotton picker is complex, and its working load is not stable (Kazama et al., 2018; Delhom et al., 2019). In recent years, hydrostatic continuously variable transmission (CVT) has been applied in cotton pickers, which can realize constant power output of an engine through load-adaptive control so as to ensure the stability of a working system. However, hydrostatic CVT has low transmission efficiency and high energy consumption, resulting in poor fuel economy. Hydrostatic power split CVT combines the advantages of mechanical CVT and hydrostatic CVT. It has good power performance and fuel economy (İnce and Güler, 2020; Rotella and Cammalleri, 2018; Zeman et al., 2017; Li et al., 2020), making it an ideal transmission system of a cotton picker. Since Fendt presented the first hydrostatic power split CVT for its 926 “Vario” tractor in 1996, this kind of transmission has been gradually applied to various agricultural vehicles (Dam et al., 2020). However, due to the performance limitation of swash plate axial piston units, most of the current hydrostatic power split CVT has to set multiple ranges to limit the energy consumption caused by parasitic power in each range. For example, “Eccom” developed by ZF, “S-Matic” developed by Steyr and “AutoPowr” developed by John Deere all have at least two ranges (Renius and Resch, 2005; Renius, 2020). The introduction of multi-range technology in CVT has brought the problem of power shift, so it is necessary to control the shift quality of agricultural vehicles (Zhu et al., 2016). In order to solve this problem, structural optimization and software optimization are usually used. The way to optimize the structure is to use different planetary gear sets alternately in different ranges, so that the CVT has the same transmission ratio before and after a shift without changing the displacement of a variable pump. This method avoids the operation of swash plate axial piston units in the shift process but only involves the control of wet clutches. Different from structure optimization, the purpose of software optimization is to obtain the best matching law of control parameters of a wet clutch (Iqbal et al., 2015; Yu et al., 2020). Generally speaking, using multiple planetary gear sets alternately can obtain better shift quality, but it leads to complex transmission structure, which is not suitable for cotton pickers. Therefore, a hydrostatic power split CVT with a single planetary gear set for a cotton picker is proposed in this paper. Although the structure of the transmission is simple, it needs to control the variable pump and wet clutch at the same time when shifting. In order to improve the shift quality of the cotton picker, the influence mechanism of various parameters on the shift quality is studied in this paper.
The principle of the CVT is shown in Fig. 1. In the forward direction, the
transmission has a direct range R
Principle of continuously variable cotton picker transmission.
When the transmission works in range R
When the running speed of the cotton picker reaches the required speed of range R
The tractor speed and clutch schedule at the rated engine speed are shown in Table 1.
Clutch/brake schedule of the cotton picker in the forward direction.
Consider that the speed of each shaft of the planetary gear set satisfies the equation
The rotation speed of the motor and pump meets the following relationship:
It is easy to deduce the transmission ratio in each range as follows:
On this basis, the running speed of the cotton picker in each range can be
obtained according to the following equation:
Substituting Eq. (3) into (4) and considering
Swash plate axial piston units are composed of a variable displacement pump and a constant displacement motor, which is the core speed regulation
component of the hydrostatic power split CVT. The variable displacement pump transforms mechanical energy into pressure energy, while the constant
displacement motor converts pressure energy into mechanical energy. The
pressure, flow, torque and rotation speed of the variable pump meet the
following relations:
Due to the high energy consumption of the hydraulic system, the friction and
leakage of the pump and motor need to be considered (ITI GmbH, 2012):
Since the motor needs to accelerate in reverse when the transmission is
shifting, the dynamic response of the swash plate axial piston units should
be considered in modelling. According to previous studies (Yuan et al.,
2008; ITI GmbH, 2012), the response of a pump displacement-regulating mechanism can be regarded as a second-order system; the response of the motor to pump displacement can be regarded as a second-order system; the response of the electronic control system can be regarded as a first-order system.
Therefore, the swash plate axial piston units can be regarded as a fifth-order system, and its transfer function is as follows:
The relationship between the speed and torque of a standard gear is as follows:
The rotation speed of each shaft of the planetary gear set can be determined by Eq. (1), and the torque of each shaft satisfies the following equation:
The moment of inertia of the gear and shaft is obtained by
The transmission ratio of each gear pair and the equivalent moment of inertia of each shaft are shown in Tables 2 and 3, respectively.
Transmission ratio of each gear pair.
Equivalent moment of inertia of each shaft.
The sliding torque of the wet clutch is calculated as follows (Wang et al.,
2020):
Based on Eqs. (7)–(22), the power-train model of the cotton picker is constructed under
Transmission model of the continuously variable cotton picker.
The swash plate axial piston units used in this study are composed of a variable displacement pump and a fixed displacement motor with the same rated displacement produced by Linde, and its parameters are shown in Table 4. The inlet and outlet of the pump are, respectively, connected with the outlet and inlet of the motor through the hydraulic hose lines, while the inlet and outlet of the charge pump are connected with the oil tank.
Parameters of variable displacement pump and fixed displacement motor.
The step response of the swash plate axial piston units was measured in the author's early research (Wang et al., 2013). The test was carried out in different rotation directions of the motor, and the step amplitude of the displacement ratio is 0.42. The comparison between the test results and the simulation results of the step response is shown in Fig. 3. Obviously, the simulation model constructed in this paper can well simulate the dynamic characteristics of the swash plate axial piston units.
Step response of swash plate axial piston units.
The WF012 wet clutch used in this study is a type of WF series clutch, which was produced by Shanghai Wind Co., Ltd., and its parameters are shown in Table 5. The test bench for testing the WF series clutch is shown in Fig. 4.
Parameters of wet clutch WF012.
Test circuit of wet clutch WF012.
The pressure of the main circuit is set to 4 or 5 MPa through the relief valve, and the maximum charging flow of the clutch is set to 3 or 5 L/min through the speed control valve. During the test, power on or power off the solenoid valve, respectively, to obtain the step pressure response of the clutch when it is engaged or disengaged, as shown in Fig. 5. By comparing the simulation results with the test results, it can be seen that the model constructed in this paper can accurately simulate the variation of clutch pressure with time under the same test conditions.
According to the test results, the rising process of clutch pressure can be divided into two stages I and II: when the clutch works in stage I, the piston starts to move and the clutch pressure depends on the reaction force of return spring; when the clutch works in stage II, the piston moves to the end stop, and the clutch pressure rises rapidly until it reaches the pressure of the main circuit. Similarly, the separation of the clutch can also be divided into the pressure relief process of the clutch and the reset process of the piston, which will not be repeated here.
Pressure response of wet clutch.
There are many factors affecting the shift quality of the cotton picker, including controllable factors and working conditions. The former includes
the pressure of the main circuit, the flow of speed regulating the valve and the action time of clutches C
It should be pointed out that the purpose of this study is to reveal the
influence mechanism of controllable factors and working conditions on the
shift quality of the cotton picker. Therefore, the “peak jerk”, which is widely used in the research of vehicle ride comfort, is used as the
evaluation index of the shift quality of the cotton picker, and its expression is as follows:
The influence of the main circuit pressure on the shift quality of the cotton picker is shown in Fig. 6. It can be seen from the figure that when the main circuit pressure changes between 3 and 5 MPa, its influence on the clutch pressure curve is reflected in two aspects: (1) with the increase in the main circuit pressure, the piston moves faster and the time of the pressure curve staying in stage I decreases. This also directly leads to the formation time of peak acceleration and peak jerk advancing with the increase in the main circuit pressure. (2) With the increase in the main circuit pressure, the slope of the pressure curve increases in stage II, which shortens the sliding time of the clutch friction disc. This also directly leads to the increase in peak acceleration and peak jerk with the increase in the main circuit pressure.
Influence of the main circuit pressure on the shift quality of the cotton picker.
The influence of clutch-charging flow on the shift quality of the cotton picker is shown in Fig. 7. It can be seen from the figure that when the charging flow changes between 3 and 7 L/min, its influence on the clutch pressure curve is mainly reflected in the movement time of the piston. With the increase in the charging flow, the time of the pressure curve staying in stage I decreases. Although the charging flow affects the clutch engagement speed, it has little effect on the slope of the pressure curve in stage II, so that the peak acceleration and peak jerk do not change significantly with the charging flow. However, the influence of charging flow on piston moving speed is related to the flow range. If the charging flow is further reduced, the piston movement time will be increased and the power will be interrupted eventually.
Influence of charging flow on the shift quality of the cotton picker.
Influence of clutch separation time on the shift quality of the cotton picker.
The influence of the separation time of clutch C
Influence of clutch engagement time on the shift quality of the cotton picker.
Influence of acceleration rate on the shift quality of the cotton picker.
Influence of cotton box weight on the shift quality of the cotton picker.
The influence of the engagement time of clutch C
The influence of acceleration rate on the shift quality of the cotton picker is shown in Fig. 10. It can be seen from the figure that when the acceleration
rate changes between 5.48 and 16.44 cm
The influence of cotton box weight on the shift quality of the cotton picker is shown in Fig. 11. It can be seen from the figure that when the weight of the
cotton box changes between 0 and 2.5 t, the heavier the cotton box is, the more strongly the inertia of the cotton picker suppresses the speed fluctuation, and the smaller the peak value of the acceleration and jerk of the cotton
picker are. However, correspondingly, with the increase in the cotton box weight, the sliding work of clutch C
Simulation scheme based on the L9(3
Considering that the working conditions of the cotton picker are uncertain and uncontrollable, the key to the optimization of shift quality is to determine
the best combination of parameters under each working condition. Let the
acceleration rate be 5.48, 8.22, 10.96, 13.7 and 16.44 cm
Optimized shift quality of the cotton picker.
In this study, the transmission system of a cotton picker equipped with hydrostatic power split CVT was analysed, and its mathematical model was
established. The influence law and mechanism of various factors in the shift quality of the cotton picker were discussed, and the following conclusions were
drawn.
Overly high pressure of the main circuit can aggravate the shift impact level and reduce the shift quality of the cotton picker. The effect of clutch action time on the shift quality of the cotton picker is not monotonous. Whether it is clutch C In the range given in this study, the influence of clutch-charging flow and acceleration rate on the shift quality of the cotton picker is not
significant. With the increase in the cotton box weight, the shift quality of the cotton picker is slightly improved, but this is at the cost of increasing
the sliding work of the clutch and consuming more sliding friction energy, which will shorten the service life of the clutch. If different factors are evaluated together, the optimal combination of
parameters under different working conditions is main circuit pressure 4 MPa, charging flow 5 L/min, clutch separation time 0.5 s and clutch engagement time Through parameter optimization, the peak jerk of the cotton picker under
different working conditions can be limited within 8–12 m/s
All the data used in this paper can be obtained by request from the corresponding author.
GW proposed the concept of this paper. WC, ZX and YZ worked together to complete the simulation work. GW and YW wrote the paper. ZX and MX edited and verified all the formulas and pictures used in this paper.
The authors declare that they have no conflict of interest.
The authors thank the reviewers for their valuable comments and Copernicus Publications for their language and typesetting services.
This research has been supported by the Shandong Provincial Natural Science Foundation (grant no. ZR2020QE163), the Key Technology Research and Development Program of Shandong (grant no. 2018GNC112008) and the Shandong Provincial Agricultural Machinery Research and Development Program (grant no. 2017YF026).
This paper was edited by Dario Richiedei and reviewed by two anonymous referees.