The HMCVT adopted a partial moment-speed arithmetic continuous transmission scheme combining “variable displacement pump + quantitative motor” and double row planetary gear pair combination, as shown in Fig. 1 (Bao et al., 2019). The HMCVT consisted of the R gear, the pure hydraulic section H gear, the low speed hydraulic machinery section HM1 gear, high speed hydraulic machinery section HM2 gear. The R gear was the reverse gear. The pure hydraulic section H gear, the hydraulic machinery section HM1 gear and the HM2 gear were forward gears (Xia et al., 2020). The HMCVT used the combination of the clutch and the brake to achieve the shifting and control. The displacement ratio range of the pure hydraulic section H gear was 0–1, the displacement ratio range of the hydraulic machinery section HM1 gear was 1 to -1, and the displacement ratio range of the hydraulic machinery section HM2 gear was -1–1. The pure hydraulic system was composed of a variable displacement pump, a quantitative motor and a fuel supply system; the mechanical power transmission system was composed of a planetary gear pair K1, a planetary gear pair K2, a fixed shaft gear pair i1, the clutches C1, C2 and a brake. The HMCVT can be adapted to a self-propelled cotton picker with a working speed of 0–25 kmh-1.

The HMCVT shift control was controlled by the wet clutch C1, the wet clutch C2, the brake and the variable pump displacement ratio. Table 1 shows the joint site diagram of the wet clutches and the brake during the HMCVT shifting process.

The HMCVT test bench was a special test equipment for the experimental performance tests of key components of agricultural machinery, mainly consisting of the transmission system (Engine 1, Flexible Coupling 3, Quantitative Motor 4, Variable Displacement Pump 5, HMCVT 6, Solenoid Directional Control Valve Assembly 7, Universal Joint Coupling 8, Auxiliary Pump 9), the detection system (Speed Torque Sensor 2, 10, Data Acquisition Instrument 12), the loading equipment (Magnetic Powder Brake 11). The specific structure is shown in Fig. 2.

The HMCVT test bench measurement and control system is shown in Fig. 3a. The HMCVT measurement and control system included a variable pump displacement ratio control zone, the clutches C1, C2 and the brake switch control zones. The system also monitored the transmission input-output speed and the transmission I-axis and II-axis rotational speed. Figure 3b shows the clutch hydraulic oil circuit control system for the visual monitoring of the pressure and flows in the clutch oil circuit (Xiao et al., 2018; Cheng et al., 2006).

The control system adjusted the input voltage signal by the PWM duty ratio to control the variable displacement pump mechanism and change the displacement of the variable displacement pump so as to control the output speed of the quantitative motor. Magnetic powders were used by the magnetic powder brake as a medium to form a magnetic powder chain to transmit the torque when the test bench was energized. The oil pump provided oil to the clutch through a three-phase asynchronous motor. The system adopted the Hall sensor to test shaft speed and acceleration (Xiao et al., 2019; Yang et al., 2018; Cheng et al., 2019).

(1)

Jerk

The jerk was the second-order rate of change of the vehicle speed, obtained from the second order derivation of the travel speed versus time. In the gear shifting process, the transmission component meshing would inevitably produce a shift shock. The jerk expression is: 1J=dadt=d2vdt2=rdd(Meia)Iibdt where, J was the jerk, ms-3; v was the vehicle speed, ms-1; a was the vehicle acceleration, ms-2; rd was the wheel radius, m; Me was the engine torque, Nm; ia, ib was the transmission ratio of the speed transmission and the drive axle; I was the moment of inertia of the associated section of the output shaft.

(2)

Dynamic load coefficient

The dynamic load coefficient was a reflection of the load torque fluctuation, the torque transmitted by the clutch during the gear shifting process of the HMCVT. The dynamic frictional torque was converted to the static frictional torque. 2δ=|TmaxTs| where, δ was the dynamic load coefficient; Tmax was the HMCVT output maximum torque value, Nm; Ts was the HMCVT output steady state torque value, Nm.

(3)

Speed Drop

During the HMCVT gear shifting process, there was no overlap phenomenon in the clutch engagement. When the C1 clutch was disconnected and the C2 clutch was not engaged, the speed of the transmission was provided by the hydraulic drive. Under the load action, the shaft would have a certain speed drop, resulting in the short-term decline of the HMCVT output speed. 3γ=nmin-ns where, γ was the speed drop, rpm; nmin was the output minimum speed value, rpm; ns was the output steady state speed value, rpm.

(4)

Weighted Acceleration RMS

The weighted acceleration root mean square value (ams) can characterize the acceleration characteristics during the gear shifting process. It is also an important parameter reflecting the comfort level of the human body. When ams<0.315, the subjective feeling was not uncomfortable; when 0.315<ams<0.63, the subjective feeling of the human body was somewhat uncomfortable; when 0.8<ams<1.6, the subjective feeling was uncomfortable when 1.25<ams<2.5, the human subjective feeling was very uncomfortable. 4ams=∫t1t2a2(t)dttsts=t2-t1 where a was the instantaneous acceleration, ms-2; t1, t2 was the start time and end time of gear shifting, s; ts was the gear shifting time, s.

(5)

Frictional Work

During the HMCVT gear shifting process, the wet clutch changing from the disengaged state to the engaged state made its main and driven parts undergo a frictional phase. The work consumed in the process is known as the frictional work, and its expression is: 5Wf=∫t0ttPfdt=∫t0ttTf|Δw|dt where, Wf was the clutch frictional work, J; Pf was the clutch frictional work rate, kW; Tf was the clutch torque, Nm; t0, tt was the start time and end time of friction.

(1)

Engine speed and load torque

When the load torque changed, the engine speed, torque and output power would also change accordingly. 6Tt=9550Pen where, Tt was the engine output torque, Nm; Pe was the engine effective power, kW; n was the engine speed, rpm.

(2)

Influence of clutch oil pressure on transmission torque

7Tc=sign Δwμp0AvZcsign Δw=-1,Δw<01,Δw≥0 where, Tc was the torque transmitted by the clutch, Nm; μ was the dynamic friction factor; p0 was the oil pressure in the hydraulic cylinder, MPa; Av was the spool drive cavity area, m2; Zc was the clutch characteristic parameter.

It can be seen from Eq. (7) that when the clutch characteristic parameters were constant, the torque transmitted by the clutch was related to the clutch oil pressure. The greater the clutch oil pressure, the greater the torque transmitted; conversely, the smaller the torque transmitted by the clutch.

(3)

Influence of flow control valve on clutch system

8Q=CdAv2(p0-pvo)ρ where, Q was the flow into the hydraulic cylinder, Lmin-1; Cd was the solenoid valve port flow coefficient; pvo was the solenoid valve outlet pressure, MPa; ρ was the oil density.

It can be seen from Eq. (8) that the clutch flow was related to the pressure and the flow coefficient. The flow control valve controlled the size of the valve port to affect the flow entering the clutch, thus affecting the coupling speed of the clutch.

(4)

Influence of displacement ratio on gear shifting process

According to the structural design parameters of the HMCVT, the hydraulic mechanical HM1 gear and the hydraulic machine HM2 gear realized the gear shifting process when the displacement ratio was -1 point. The maximum transmission ratio values of the hydraulic machine HM1 section and the hydraulic machine HM2 section are shown in Table 2 below.

The HMCVT had different transmission ratios before and after the shift, resulting in the speed fluctuation during the gear shifting process. The change of the transmission ratio can be realized by the variable pump-quantitative motor displacement ratio.

The HMCV shifting time was the duration required from the front gear steady state to the rear gear steady state. The total shifting time was: 9t=t3+t4+t5+t6+t7 where, t3 was the clutch disengagement time, s; t4 was the clutch empty time, s; t5 was the clutch selection time, s; t6 was the clutch shifting time, s; t7 was the clutch engagement time, s.

The HMCVT shifting time was a complex and dynamic process, mainly depending on the clutch oil circuit pressure, the oil circuit flow and the oil-filled volume. When the clutch oil pressure and the oil circuit flow were large, the clutch engagement time was shorter, and vice versa. The clutch oil pressure and the flow control valve were important operating parameters of the HMCVT gear shifting process. The value of the shifting time indirectly affected the smoothness of the HMCVT gear shifting process. 10t=VKqμ2Δp where, V was the the oil-filled volume, m3; Kq was the oil-filled flow coefficient; μ was the oil density, Kgm-3; Δp was the pressure difference between the return spring and the oil-filled pressure, MPa.

The HMCVT shifting time had an important influence on the jerk, dynamic load coefficient, speed drop, frictional work and weighted acceleration RMS. However, the HMCVT gear shifting time cannot decouple the clutch oil pressure and the oil circuit flow, so the gear shifting time was not used as the influencing factor.

In summary, according to the HMCVT characteristics and operating parameters, five factors were selected in this test: engine speed, clutch oil pressure, flow control valve flow, load torque, displacement ratio.

The test was carried out at the Hydraulic Transmission Laboratory of Shihezi University in China. The test process was mainly conducted on the HMCVT test bench made by the research team. The HMCVT test bench parameters are shown in Table 3.

According to the theoretical analysis and pre-experiment of the HMCVT system, the influencing factors and the level ranges were determined as: engine output speed, 900–2200 rpm; clutch oil pressure, 3.4–5 MPa; flow control valve flow, 3–5 Lmin-1; load Torque, 60–180 Nm; displacement ratio, 0.8–1.

Considering the complexity of the HMCVT gear shifting process, the quadratic orthogonal rotation combination design scheme was used to study the influences of engine speed, clutch oil pressure, flow control valve, load torque, displacement ratio on the jerk, dynamic load, speed drop, and frictional work, as well as the weighted acceleration RMS. The multi-objective parameters were optimized. The experiment was arranged according to five factors and three levels. The factor level coding is shown in Table 4.

To ensure the good shift smoothness of the HMCVT, the shifting parameters were optimized based on the objectives of low jerk, low dynamic load coefficient, low speed drop and low weighted acceleration RMS. The optimization was carried out through the Optimization-Numerical module in the data processing software of Design-Expert 10. The objective function and constraints were: 16min⁡Y1min⁡Y2min⁡Y3min⁡Y4Y5[-1,1]X1∈[-1,1]X2∈[-1,1]X3∈[-1,1]X4∈[-1,1]X5∈[-1,1] The optimal combination zone of influencing factors was obtained after the optimization. Selected by Design-Expert 10, the optimal combination of parameters was as follows: the engine speed was 901.35 rpm, the clutch oil pressure was 3.52 MPa, the flow control valve was 4.9 Lmin-1, the load was 130.48 Nm, the displacement ratio was -0.93. In this case, the jerk was 4.84, the dynamic load coefficient was 15.35, the weighted acceleration RMS was 0.45, the speed drop was 21.291 rpm and the frictional work was 1001.01 J.

It can be seen from the optimized combination area that under the optimal parameters, the impact of the gear shifting process was within the acceptable range of the human body. The engine speed of the minimum optimization target was close to the lowest level of experimental factors, the clutch oil pressure was also close to the lowest level while the flow control valve was close to the highest level of experimental factors. Therefore, the values of the engine speed and the clutch oil pressure should be low and the value of the flow control valve should be high during the gear shifting process so that the gear shifting process can be smoother. The displacement ratio should be shifted in advance to minimize all evaluation indexes during the gear shifting process.

According to the test results above, the test was verified under the low jerk, low dynamic load coefficient, low speed drop, low weighted acceleration RMS and low frictional work. Test conditions: the engine output speed was 900 rpm, the clutch oil pressure was 3.5 MPa, the flow speed control valve was 4.9 Lmin-1, the load torque was 130 Nm, and the displacement ratio was -0.93. At 15 s, the hydraulic machinery HM1 was shifted to the hydraulic machinery HM2. As shown in Fig. 14a, the test jerk was 5.04 ms-3; the test weighted acceleration RMS was 0.467. As shown in Fig. 14b, the test speed drop was 20.32 rpm; the test clutch main and driven shaft angular speed difference was 3.62 rads-1. As shown in Fig. 14c, the test dynamic load coefficient was 12.16. Tests showed that in the initial stage of shifting, the jerk, the weighted acceleration RMS, the HMCVT output speed, and the HMCVT output torque all fluctuated sharply. After the gear shifting process was completed, the cutch main and driven shaft angular speed difference was 0. The jerk and the weighted acceleration RMS decreased while the HMCVT output speed and the torque were relatively stable.