Received May 18, 2020, accepted June 26, 2020, date of publication June 30, 2020, date of current version November 9, 2020.
Digital Object Identifier 10.1109/ACCESS.2020.3005915
Study on the Design Method of a New
Hydro-Mechanical Continuously Variable
Transmission System
YU XIA , DONGYE SUN , DATONG QIN , AND WENFENG HOU
State Key Laboratory of Mechanical Transmissions, School of Automotive Engineering, Chongqing University, Chongqing 400044, China
Corresponding author: Dongye Sun (dysun@cqu.edu.cn)
This work was supported in part by the National Natural Science Foundation of China under Grant 51875055, and in part by the National
Key Research and Development Program under Grant 2016YFD0701100.
ABSTRACT A design method for a new power-cycling hydro-mechanical continuously variable transmission (PCHMCVT) system is proposed in this study. The transmission efficiency in this method is
defined to be the design standard. The design target ensures the maintenance of the transmission efficiency
at more than 80% in different driving modes. In this study, the primary structural parameters are first
calculated with respect to the PCHMCVT for the Dongfanghong 1302R tractor, based on the tractor’s
required traction. Moreover, the original transmission structure is improved for the purpose of improving
transmission efficiency in the reverse gear mode through the simulation analysis. Thereafter, according to
the speed requirement of the tractor and the speed ratio continuous condition of PCHMCVT, two gears
and five working modes (four forward modes and one reverse mode) are designed to maintain the tractor
to operate high efficiency at different driving modes. Finally, PCHMCVT has more powerful low-speed
torque-increasing characteristics and vehicle power commutation characteristics based on the simulation
analysis of the tractor’s basic characteristics and then proved the feasibility of PCHMCVT design method.
INDEX TERMS Tractor, hydro-mechanical, continuously variable transmission, transmission efficiency,
design method.
NOMENCLATURE
PCHMCVT
PST
Q
V
v
P/M
PG
Pe
Pi
Po
ne
ni
no
Pe max
Power-cycling hydro-mechanical CVT
Power split transmission
Flow rate [L/min]
Displacement [cm3 ]
Tractor speed [km/h]
Hydraulic variable-displacement pump /
hydraulic fixed-displacement motor [-]
Planetary gear [-]
Rated power of diesel engine [kW]
Input power of the PCHMCVT [kW]
Output power of the PCHMCVT [kW]
Rated speed of diesel engine [r/min]
Input speed of the PCHMCVT [r/min]
Output speed of the PCHMCVT [r/min]
Maximum power of diesel engine [kW]
The associate editor coordinating the review of this manuscript and
approving it for publication was Jenny Mahoney.
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Te max
rd
k
m
f
t
io
ig
irg
ibx
idx
Zx
Bx
Hx
Kx
Fq
Fg
Ff
Fw
Fi
Maximum torque of diesel engine [N·m]
Tires/wheel radius [m]
Planetary gear structure parameter [-]
Vehicle mass [kg]
Rolling resistance coefficient [-]
Time [s]
Final drive speed ratio [-]
PCHMCVT speed ratio [-]
Reverse gear speed ratio of PCHMCVT [-]
xth gear speed ratio [-]
xth reverse gear speed ratio [-]
Number of the ploughshare [-]
Monomer ploughshare width [m]
Ploughing depth [m]
Soil specific resistance [N/cm2 ]
Traction resistance [kN]
Tillage resistance [kN]
Rolling resistance [kN]
Air resistance [kN]
Slope resistance [kN]
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
Acceleration resistance [kN]
Rated traction force of tractor [kN]
Front wheel radius [m]
Rear wheel radius [m]
Pressure difference [bar]
Fj
Feq
Rf
Rr
1p
GREEK LETTERS
ε
εr
Displacement ratio [-]
Displacement ratio at minimum reverse speed ratio
[-]
Displacement ratio at minimum forward gear
speed ratio [-]
Transmission efficiency of PCHMCVT tractor [-]
Reverse gear transmission efficiency of PCHMCVT [-]
Transmission efficiency of the reference vehicle [-]
Efficiency of the P/M [-]
Gear meshing transmission efficiency [-]
Slip efficiency [-]
Traction efficiency [-]
Diesel power reserve factor [-]
Slope [◦ ]
Ground adhesion coefficient [-]
Uneven rate of traction resistance [-]
Frequency of resistance change [-]
Angular acceleration of variable-displacement
pump [-]
Tillage speed [km/h]
εg
ηg
ηrg
ηg0
ηy
ηb
ηδ
ηf
ηµ
α
ϕ
ϑq
λ
ω̇
υ
SUBSCRIPT AND SUPERSCRIPTS
c
s
r
Planetary gear, carrier shaft
Planetary gear, sun shaft
Planetary gear, ring shaft
I. INTRODUCTION
The working environment of agricultural and engineering
vehicles is highly complex. The vehicles are frequently traveling at low-speeds, or standing still, and require increased
output torque to complete specific tasks [1], [2]. These factors render the vehicle more demanding in terms of power
and economy. A continuously variable transmission (CVT)
is an ideal form of transmission, and applying it to tractors
significantly improves the economy of the vehicle [3]–[7].
In addition, the hydrostatic stepless transmission, represented by a hydraulic variable-displacment pump/hydraulic
fixed-displacement motor (P/M), has been widely used
in tractor transmission systems because of their convenient layout, high torque transmission capability, and shock
absorption [8]–[12].
Considering the above, Volpe et al. provided a detailed
optimization procedure and a kinematic analysis of power
split infinitely variable transmissions used in off-road vehicles. With proper optimization, power recirculation can be
minimized and transmission efficiency can be improved [13].
Linares et al. proposed a type of power-split CVT with
three active shafts and described the relationships between the
195412
design parameters of the transmission. The study was aimed
at proposing a set of concepts that would aid in classifying
and understanding CVT transmissions [14].
Bietresato et al. developed a theoretical model that could
be useful for investigating the performance of ground vehicles
using acceleration tests, and tested the model on three tractors
with different equipment to evaluate the performance of the
tractor based on the average efficiency of the transmission.
The results of the CVT tests indicated that there is a possible
effect in the transmission architecture that takes precedence
over general transmission types [15].
Chen et al. proposed a new type of CVT (W–CVT) with
a significant torque capacity and transmission efficiency, and
verified the kinematic feasibility of the W–CVT through a
kinematic analysis that indicated that the W–CVT can realize
stepless speed regulation under the action of a speed changing
actuator [16].
Macor et al. analyzed the fuel consumption of the
hydro-mechanical power-split transmission based on a city
bus, and reported that the power-split transmission could
reduce the fuel consumption compared to traditional transmissions by controlling the engine operating point to improve
the engine efficiency [17].
Osinenko et al. proposed a new strategy for optimal traction control, that is based on traction parameter estimation
via drive torque feedback. The proposed methodology could
be primarily implemented in farm tractors equipped with
hydraulic or electrical infinitely variable transmissions using
drive torque feedback [18].
Cammalleri and Rotella proposed a novel mathematical
model for the preliminary design of power-split CVTs. The
study aimed to establishing a simple method to address all
possible different constructive solutions and analyze the operation of an existing power-split transmission by identifying
the functional parameters defined in the new model. This
method significantly decreased the numerical calculations
and simplified the analysis process [19], [20].
A study proposed a novel transmission structure, the socalled power-cycling hydro-mechanical continuously variable transmission (PCHMCVT), this transmission structure
possesses the characteristics of both stepless speed regulation
and increased torque at low-speed. Moreover, the speed ratio
can be zero, which is more suitable for agricultural and engineering vehicles [21]. According to the required traction and
the target speed for reference vehicles, the primary parameters of the PCHMCVT were designed in this study. Because
of its great range of speed ratios, the number of gears is significantly decreased compared to conventional tractors, the
space structure is optimized, the weight of the entire vehicle
is decreased, and the transmission efficiency is improved.
II. WORKING PRINCIPLE OF PCHMCVT
A. COMPOSITION STRUCTURE
The PCHMCVT designed in this study adopts input coupled transmission structure, because the angular velocities
of the hydraulic pump-motor system are not constant in an
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
output-coupled transmission system when the input angular
velocities are constant, and the hydraulic unit may not be able
to exert the maximum power if the planetary structure parameters are inappropriately selected. In addition, the hydraulic
system may also exceed the maximum allowable angular
velocities. However, a form of input coupling can satisfy the
requirements of the rated angular velocities of the hydraulic
system, maintain a stable angular velocity, and ensure that the
maximum hydraulic power is obtained as the absolute value
of the displacement ratio ε increases.
The PCHMCVT comprises four primary components: the
hydraulic variable-displacement pump, the hydraulic fixeddisplacement motor, two single planetary gear (PG) trains,
and two wet clutches, as shown in Fig. 1. The hydraulic
transmission is a closed-loop volumetric speed control system
comprising a hydraulic variable-displacement pump and a
hydraulic fixed-displacement motor (PV-MF).
will gradually fall below zero and, therefore, achieve reverse
gear conditions.
III. TRANSMISSION SYSTEM PARAMETER DESIGN
The primary parameters of the PCHMCVT design include
the hydraulic pump-motor system (PV-MF), the maximum
and minimum speed ratios of the transmission system (igmax ,
igmin ), the planetary structure parameter k, and the speed ratio
of the final drive io .
The design goals of the PCHMCVT should be to reduce
the speed ratio of the low-gear to improve the starting acceleration and climbing performance of the vehicle, this should
be done to ensure tire-ground adhesion and high transmission
efficiency (greater than 80%). It can also simultaneously
improve the speed ratio of the high gear to ensure that the
vehicle has better fuel economy [22]. The design flow of
PCHMCVT is shown in Fig. 3.
The reference vehicle for the transmission study is the
Dongfanghong 1302R tractor. The operating characteristics
are presented in Table 1. The speed ratio in this study is
expressed as the output speed divided by the input speed.
A. TRACTOR KINEMATICS ANALYSIS
Tractors are mainly used for farm work and road transport.
The resistance load is different under different working conditions [23]. Fig. 4 is the force analysis diagram of the rearwheel drive tractor under the traction operation.
The balanced relationship between driving force Fd and
various resistances can be derived from Fig. 4.
Fd = Ff + Fw + Fi + Fj + Fg .
FIGURE 1. Schematic of PCHMCVT.
The hydraulic P/M as the transmission component can
perform both positive and negative stepless speeds regulation,
therefore, two single PG trains and two wet clutches are
employed to achieve power-cycling in the PCHMCVT.
B. WORKING PRINCIPLE
The power flow diagram of the PCHMCVT is shown in Fig. 2,
where ‘‘+’’ and ‘‘−’’ indicate the rotational direction of the
components, and ‘‘ ⊕’’ and ‘‘ ’’ indicate the torque direction. The relative variable rate of the hydraulic variable pump
about its displacement is ε. Assuming the same displacement
as the P/M:
ε=
Qp
Qp
=
Qm
Qp max
(1)
In the PCHMCVT, controlling the displacement ratio ε can
reduce the speed ratio of the entire system to zero. In this case,
power is always available in the power-cycling path, and can
effectively prevent an engine flameout condition because of
an excessively great external resistance. If the displacement
ratio ε is continuously reduced, the speed ratio of the system
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(2)
where the driving force Fd represents the soil reaction force
of the driving wheel parallel to the ground; the tillage resistance Fg indicates the component of the traction resistance Fq
in the horizontal direction (As α is small, the vertical component Fg tan α is ignored.).
When the tractor is under working conditions, the resistance is primarily caused by the force of the soil on the farm
tool; therefore,
X
Fx max = Fg = Zx Bx Hx Kx
(3)
According to the selected farm tool model: Zx = 5, Bx =
0.35m, Hx = 0.25m, and Kx = 7N /cm2 .
Therefore, the traction resistance, Fg = 30.625kN .
The traction resistance of a tractor is typically variable as
the operating environment changes over time and location.
Therefore, we typically use the sine curve to represent the
functional relationship between the traction resistance and
time:
Fq = Fg + Fg × 0.5ϑq sin(λt)
(4)
Therefore, the rated traction force of tractor Feq is:
Feq = Fq max = (1.1 ∼ 1.2)Fg
(5)
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
FIGURE 2. Power flow diagram of PCHMCVT: (a): ε > 0; (b): ε < 0.
TABLE 1. Operating characteristics of reference tractor.
FIGURE 4. Schematic diagram of force analysis during tractor traction
operation.
Therefore, by using eq. (6), the following can be calculated: Pe = 95.883kW .
The rated power of the selected diesel engine is 110 kW,
which can satisfy the traction resistance and tractor working
demand.
When the tractor is under transport conditions, the
P speed
is low, as shown in Fig. 5; therefore, the resistance Fx max
overcome by the tractor is approximately:
X
Fx max = mgf cos αmax + mg sin αmax
(7)
FIGURE 3. Design flow chart of PCHMCVT.
In conventional tractor designs, the engine power is usually
determined by the rated traction:
Pe =
0.7335Feq × υ × ηδ
.
9.8 × 270 × ηf × ηµ
where ηδ = 0.8, ηf = 0.7, and ηµ = 0.85.
195414
(6)
In addition, the driving force Ft generated by the tractor needs
to be greater than the resistance overcome on the slope road
and less than the ground adhesion Fϕ to prevent the vehicle
from skidding:
X
Te max
Fx max ≤ Ft =
≤ Fϕ = ϕmg cos α
(8)
ig min io rd
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
TABLE 2. Basic parameters of P/M form SAUER-DANFOSS.
Assume that in the case of the maximum flow of the
variable pump, the pump efficiency ηM = 0.95, and
from Table 1 the maximum output power of the selected
diesel engine Pe max = 120kW , according to information
obtained from the SAUER-DANFOSS company for 90-series
hydraulic products 1Pmax = 480bar [25]. Therefore,
QM max ≥ 142.5L/ min .
FIGURE 5. Schematic diagram of tractor kinematics during transport
conditions.
Meanwhile, the grade ability and starting capability of the
designed PCHMCVT tractor are better than the reference
vehicle, therefore:
Te max
Te max
· η0 .
· ηg ≥ 0
ig min ib1 io
ig min i0b1 i0o g
(9)
where, ηg = 0.8 and ηg0 = 0.85. From eqs. (7), (8), (9)
and Table 1 it can be calculated that ig ib1 io ≥ 0.2574.
Typically, the speed ratio of the final drive of the original
vehicle remains unchanged when designing the transmission
system; therefore,
ig ib1 ≤ 0.2574.
(10)
B. HYDRAULIC PUMP-MOTOR SELECTION
The selection of the hydraulic pump-motor should first satisfy
the normal operation of the system, and then consider the
primary performance parameters (speed, torque, pressure,
displacement, and efficiency) of the hydraulic pump-motor
system with respect to service life, cost performance, and
adaptability [24]. As the fixed-displacement motor is connected to the engine in the PCHMCVT, according to the characteristics of the hydraulic components, it should be satisfied:
PM max =
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QM max 1pmax
≥ Pe max .
600ηM
(11)
(12)
As the variable-displacement pump is connected to the
sun gear in the PCHMCVT, the output torque of the
variable-displacement pump should be satisfied:

Tr
Ts · k

 Tq max = (G · f + Fg ) · rd =
=
i0
i0
(13)
(T
− Ip ω̇) · k

 Tq max ≤ p max
i0
where, Tq max represents the maximum traction resistance
torque, IP represents the moment of inertia of variabledisplacement pump; therefore,
Tp max − Ip · ω̇ ≥ 335.1N · m.
(14)
Considering the cost performance and size for this study
we selected the 055 series variable-displacement pump and
fixed-displacement motor system, as presented in Table 2.
C. DETERMINATION OF MAXIMUM AND MINIMUM
SPEED RATIOS OF TRANSMISSION SYSTEM
Eq. (14) defines the single PG train:


 ns + knr − (1 + k)nc = 0
Ms : Mr : Mc = 1 : k : −(1 + k)


Ps + Pr + Pc = 0
(15)
According to Fig. 2 power flow conditions, the following
is obtained:
When ε > 0, and power transmits through the PG1 train:

ni = nc1 = nm




 ns1 = np
nm
(16)
=ε
iy =


n

p


Pc1 = Pi + Pm
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
FIGURE 6. Relationship between system efficiency, system speed ratio, system pressure, and input speed when ε > 0.
FIGURE 7. Relationship between system efficiency, system speed ratio, system pressure, and input speed when ε < 0.
Therefore, the overall speed ratio and efficiency of the
PCHMCVT are:
no
(1 + k1 )ε − 1
=
ni
k1 · ε
(1 + k1 )ε − 1
ηg =
(1 + k1 )ε − ηy
ig =
(17)
(18)
Similarly, when ε < 0 and the power transmits through the
PG2 train:

ni = nr2 = nm




 ns2 = np
nm
(19)
iy =
=ε


np



Pr2 = Pi + Pm
Specifically,
no
k2 · ε + 1
=
ni
(1 + k2 )ε
k2 ε + 1
ηg =
k 2 ε + ηy
ig =
(20)
(21)
According to eqs. (17) and (20), the maximum speed ratio
of the system igmax = 1 is known and the speed ratio of the
PCHMCVT system can be smaller than zero by controlling
the value of the displacement ratio ε. Therefore, the PCHMCVT can continuously achieve reverse gear conditions.
195416
Similarly, according to eqs. (15)–(21), the efficiency of
the PCHMCVT is ηg = 0 when the overall speed ratio of
PCHMCVT is ig = 0. The system has no external output
power, and the output power of the engine is all in the cycling
path at this time. Therefore, the torque of the output shaft
constantly increases, and the PCHMCVT gains low-speed
increased-torque characteristics.
The primary factors influencing the efficiency of the
hydraulic components are the displacement ratio ε, pressure
difference 1p, and input speed ni [26]. When the planetary
gear structure parameter k = 4, the relationship between the
system efficiency, system speed ratio, working pressure, and
input speed are as shown in Figs. 6 and 7.
In Fig. 6, when ε > 0, the minimal speed ratio igmin = 0.6,
the maximum speed ratio igmax = 1, and the efficiency of
the PCHMCVT can exceed 75%; this means that the system
always works in the ideal range. Similarly, in Fig. 7, when
ε < 0, the minimal speed ratio igmin = 0.2 and the maximum
speed ratio igmax = 0.6. Combining the above conditions,
the minimum and maximum speed ratios of the PCHMCVT
are 0.2 and 1, respectively. According to eq. (10), the 1st gear
speed ratio ib1 = 0.2574 when igmax = 1.
IV. REVERSE GEAR DESIGN
In the PCHMCVT, the speed ratio of the transmission system
can be smaller than zero because of the value of the displacement ratio ε being controlled. Therefore, the transmission
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
FIGURE 8. Power flow diagram of reverse gear condition: (a): ε > 0; (b): ε < 0.
FIGURE 9. Comparison between the PCHMCVT before improvement and power split transmission (PST) on efficiency
(ni = 2300rpm, 1p = 420bar ): (a): ε > 0; (b): ε < 0.
system can achieve reverse gear conditions. However, under
reverse gear conditions, all the input power transmits through
the hydraulic path, part of the power is output through the ring
gear (the planet carrier), and the remaining power is returned
to the input shaft. The power flow is shown in Fig. 8.
As the PCHMCVT belongs to the C–I closed planetary
transmission structure, based on previous research results and
mathematical models [21], the results shown in Fig. 9 can be
obtained.
Fig. 9 clearly demonstrates that the efficiency of the system
is relatively low when the reverse gear is operating. The
reason is that the bulk of the transmission power transmits
through the low-efficiency hydraulic components and subsequently returns to the input shaft through the planetary
gear train. Therefore, we have attempted to modify a reverse
gear pair with a speed ratio of −1 at the gear shifting device
to achieve reverse gear. Therefore, when ε > 0, for the
PG1 train,

1


 Mm = Mp ·
εηy
(22)
Mo = Mr1



Pm = Pi + Pc1
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In addition, PCHMCVT is in the reverse gear mode,
according to the eq. (17), the eq. (23) can be obtained;
therefore:
1 − (1 + k1 )ε
irg = −ig =
(23)
k1 · ε
From eqs. (22) and (23), the following can be obtained:
(1 + k1 )εηy − ηy
ηrg =
(24)
(1 + k1 )εηy + 1
We can then build the models shown in Fig. 10.
Similarly, when ε < 0, for the PG2 train:
(
Mo = Mc2
(25)
Pm = Pi + Pr2
In addition, PCHMCVT is in the reverse gear mode,
according to the eq. (20), the eq. (26) can be obtained;
therefore,
k2 ε + 1
irg = −ig = −
(26)
(1 + k2 )ε
From eqs. (25) and (26), the following can be obtained:
k2 εηy + ηy
ηrg =
(27)
k2 εηy − 1
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
FIGURE 10. Relationship between system efficiency, system speed ratio, system pressure, and input speed under reverse gear
conditions when ε > 0.
FIGURE 11. Relationship between system efficiency, system speed ratio, system pressure, and input speed under reverse gear
conditions when ε < 0.
We can then build the models shown in Fig. 11.
The efficiency of the transmission system remains low
when the reverse gear is operating (Fig. 10 and 11). As the
power flow has not changed, the bulk of the transmission
power still transmits through the low-efficiency hydraulic
components, and an increased reverse gear is required to
allow the P/M to work in an efficient range (0.2 ≤ ε ≤ 1
and −1 ≤ ε ≤ −0.2 ). In addition, this type of sun gear has a
significant effect on the service life of the components and is
not suitable for vehicular applications. Therefore, it is necessary to implement the improvements shown in Fig. 12 for the
reverse gear conditions of the PCHMCVT.
Fig. 12 illustrates that in the designed reverse gear condition, the brake is engaged and the clutch3 is separated. At this
time, the planet carrier of the planetary gear train is fixed,
the planet wheel changes the angular speed direction as an
idler, the sun gear as the driving wheel inputs power, and the
ring gear as the driven wheel outputs power, thereby realizing
the reverse gear condition of the vehicle.
As there is no power cycle in the reverse gear condition,
the output power of the diesel engine transmit through the
P/M, sun gear and ring gear in turn.
Therefore,
ηrg = ηy .ηb
195418
(28)
FIGURE 12. Power flow diagram of PCHMCVT after improvement.
The reverse gear transmission efficiency of PCHMCVT
after improvement is shown in Fig. 13.
It is worth noting that the reverse gear can only be achieved
with PG1 when the brake is engaged; PG2 cannot realize the
negative gear ratio.
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
In the reverse gear condition, the brake is engaged and the
clutch3 is separated, and the planetary carrier speed nc = 0.
According to the eq. (15) the speed ratio of planetary gear
train can be expressed as
nr1
1
no
=
=−
ni
ns1
k1
The following can be obtained from eq. (30):
1
irg min io = εr · −
· io ≤ 0.0124
k1
(33)
(34)
Hence,
−
(
V. DETERMINATION OF PLANETARY GEAR STRUCTURE
PARAMETERS
The planetary gear structure parameter k determines the size
of the planetary gear train. When 4/3 ≤ k ≤ 4, the planetary gear train is more compact and easier to install [27].
Simultaneously, it can be found from calculations using
eqs. (18)–(21) that, as the value of k increases, the efficiency
of the PCHMCVT also increases.
Similarly, in the design of the PCHMCVT reverse gear,
it is necessary to ensure that the power performance of the
PCHMCVT reverse gear is better than that of the reference
vehicle. Therefore,
Te max
Te max
· ηg ≥ 0
· ηg0
irg min io
ird min i0o
(29)
irg min io ≤ 0.0124
(30)
Hence,
In addition, to ensure the continuity of the designed
PCHMCVT, the planetary gear structure parameter k should
satisfy the displacement ratios ε of the P/M, which are equal
when the PCHMCVT is at the absolute value of the minimum
reverse speed ratio irg min and the minimum speed ratio of
the system forward gear ig min . According to the eq. (17),
the eq. (31) can be obtained:

 irg min = ig min
1
(31)
 εr = εg =
1 + k − ig min k
The reverse gear can only be achieved with PG1, when the
brake is engaged and displacement ratio ε > 0. Therefore,
the minimum speed ratio of the system drive conditions is
jg min = 0.6.
Hence,
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(35)
And finally,
FIGURE 13. Reverse gear transmission efficiency of PCHMCVT after
improvement.
1
εr = εg =
1 + k1 − 0.6k1
1
≤ 0.2638
k1 + 0.4k12
(32)
1.8 ≤ k1 ≤ 4
4/3 ≤ k2 ≤ 4
(36)
VI. TRANSMISSION GEAR DESIGN
As the tractor is the reference vehicle in this study, it can
be classified into working conditions (0–18km/h) and transportation conditions (12–30km/h) [23]. The design principles
proposed in this study require the designed PCHMCVT to
achieve continuous speed ratios and that the power is not
interrupted. Therefore, it should have the same system speed
ratios before and after the shift.
Therefore,
(1 + k1 )ε − 1
k2 · ε + 1
· ib1 =
· ib2
(37)
k1 · ε
(1 + k2 ) · ε
When the tractor is under working conditions, as in
section 3.3, it has been observed that the 1st gear ratio
ib1 = 0.2574. At this time, the clutch 1 is closed and
power transmits through the PG1 train. Therefore, the change
process of the displacement ratio and the system speed ratio
are ε(0.385 → +1) and ig (0.6ib1 → ib1 ), respectively.
Simultaneously, from eq. (37), it can be concluded that
the 2nd gear ratio ib2 = 1.287. The clutch 2 is closed
and power transmits through the PG2 train. The change
process of displacement ratio and the system speed ratio
are ε(− 13 → −1) and ig (0.2ib2 → 0.6ib2 ), respectively.
In the third mode, because of the continuous speed ratio
during the mode switching process, ib3 = ib2 = 1.287,
and the clutch 1 is closed and power transmits through
the PG1 train. The change process of the displacement
ratio and the system speed ratio is ε(0.385 → +1) and
ig (0.6ib2 → ib2 ), respectively.
The tractor speed in each mode can be calculated using
eq. (38), and the result is summarized in Table 3.
v
(38)
ne =
0.377rd · ig · ibx · io
As can be seen in Table 3, the maximum speed of the tractor
under working condition is 18.15km/h. Therefore, only two
gears (ib1 = 0.2574, ib2 = ib3 = 1.287) are required to
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
TABLE 3. Mode switching process of PCHMCVT under working conditions.
TABLE 4. Control process of tractor under transports condition.
TABLE 5. Control process of tractor under reversing condition.
satisfy the tractor speed requirement under working condition
(0–18km/h). In addition, the speed ratio is continuous and the
transmission efficiency is always greater than 80%, the speed
ratio change range of the PCHMCVT is:
ig max
1
=
=5
ig min
0.2
(39)
Therefore, the speed ratio change range of the PCHMCVT is
greater than the power-split transmission in tractors.
The displacement ratio ε changes rapidly during mode
switching (1+ → − 13 , −1 → 0.385) (refer to Tab. 3).
However, this type of variation can be eliminated as there is
clutch separation and engagement during the mode switching,
therefore, the clutch slip process will mitigate the negative
effect of this variation.
Under transport conditions, because the tractor is moving
at a certain speed, it no longer requires the characteristics
of the PCHMCVT. Therefore, the control method of the
power-split transmission can be used. This eliminates the
variation of the P/M displacement ratio, and also ensures
high transmission efficiency. The displacement ratio ε = +1
when the tractor is switched from working conditions to transport conditions. The control process at this time is presented
in Table 4.
Under the reversing conditions, the brake and the
clutch3 are engaged, and PG1 is used to realize the reversing.
The control process at this time is as shown in Table 5.
In addition, the displacement ratio ε − 0.2, at which point
the system speed ratio is zero, and the tractor speed is zero
195420
under driving conditions. The displacement ratio decreases
from 0.2 to 0, which then gradually increases from 0 to
0.2 when the tractor requires reversing; however, this process
is less efficient (0–74.9 %).
According to the above analysis, the primary structural
parameters of the designed PCHMCVT are shown in Table. 6.
VII. DISCUSSION AND RESULTS
According to the primary design parameters (Tab. 6), this
section analyzes the stepless speed regulation characteristics,
torque characteristics, power splitting characteristics and efficiency characteristics of the tractor, and verifies the feasibility
of the proposed design method.
A. STEPLESS SPEED REGULATION CHARACTERISTICS
By introducing the primary design parameters (Tab. 6) into
eqs. (17), (20), (38), the characteristic curve of the tractor
speed with the hydraulic system displacement ratio can be
obtained, as shown in Fig. 14.
It can be seen from the figure that the displacement ratio
of the power split transmission (PST) can be continuously
changed under the same structural parameters, and mainly
use hydraulic system inefficient ranges with displacement
ratio −0.4 to 0.4, because in the PST, the closer the displacement ratio is to 0, the less power is passed through the
hydraulic path, and the overall efficiency of the system is
higher. Contrary to PST, the PCHMCVT mainly uses the
hydraulic system efficient ranges with displacement ratio
−1 to −0.4 and 0.4 to 1. Although some efficiency is
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
TABLE 6. Primary design parameters of the PCHMCVT.
TABLE 7. Parameter value of engine bench test. Note: 1. Idle speed is 650r/min 2 . Maximum empty car speed is 2600r/min.
the actual curve of the engine fitted by experimental data
(Tab. 7) interpolation is significantly different from the ideal
curve (Fig.15).
FIGURE 14. Characteristic curve of stepless speed regulation of PCHMCVT.
sacrificed, the figure clearly demonstrates that PCHMCVT
has less working mode than PST under the requirement of
tractor speed (30km/h). It is worth noting that to ensure that
the system speed ratio is continuous, the displacement ratio
of PCHMCVT cannot be continuously changed. There is a
step in the displacement ratio of the hydraulic system during
the mode switching, but this problem can be solved or even
eliminated by the control of the clutch.
FIGURE 15. Ideal/actual engine operating curve.
Hence, it is necessary to rely on the power transmission
device to expand the engine working curve in order to satisfy
the torque requirements of tractor
Te =
B. TORQUE CHARACTERISTICS
The ideal power unit should maintain the maximum power
output of the system during the operation of the tractor.
According to the engine parameters (Tab. 1) and the eq. (40),
the ideal engine operating curve can be obtained. However,
VOLUME 8, 2020
9550Pe
ne
(40)
In PCHMCVT, the torque characteristic is expressed by the
o
torque ratio K = M
Mi . According to the schematic diagram
of power flow (Fig. 2), we can derive the torque ratio of each
mode.
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
When the system is in F1 mode, because of the cycle power
Mc = M1 + Mm ,
Mo
k1 ε
K=
=
(41)
Mi
[(1 + k1 )ε − ηy ] · ib1
Similarly, the F2 mode is:
Mo
(1 + k2 )ε
K=
=
(42)
Mi
(k2 ε + ηy ) · ib2
The F3 mode is:
Mo
k1 ε
K=
=
(43)
Mi
[(1 + k1 )ε − ηy ] · ib2
Because the F4 mode uses the PST working mode,
K=
(k22 + k2 )ηy
Mo
= 2
Mi
(k2 · ηy + k2 ε + ε) · ib2
(44)
According to eq. (38) and the derived torque ratio
eqs. (41)–(44), the relationship between the torque ratio of
each mode and the tractor speed can be obtained (Fig. 16).
FIGURE 17. Torque characteristics PCHMCVT in each mode.
C. POWER SPLIT CHARACTERISTICS
In PCHMCVT, the power split characteristics is expressed
by the distribution ratio S = Ps /Pt . Ps represents the input
power of the hydraulic path (the output power of the sun
gear); Pt represents the total input power of PCHMCVT
(excluding power loss); according to the schematic diagram
of power flow (Fig. 2), we can derive the distribution ratio of
each mode, as shown in Fig. 18.
FIGURE 16. Torque ratio K of PCHMCVT.
The figure shows that the lower the tractor speed,
the greater the torque ratio of PCHMCVT. When the vehicle
starts, the engine is in idle state (ne = 650rpm), and the maximum torque ratio is 6.37, which improves the starting performance of the vehicle. When the vehicle suddenly encounters
obstacles and the engine has reached the maximum speed
(ne = 2600rpm), the maximum torque ratio of PCHMCVT
is 13.11, which greatly improves the ability of the tractor to
get rid of obstacles. This design is more conform to the actual
working situation of the tractor.
According to the previous point of view, when the actual
output torque of the engine is expanded by PCHMCVT,
Fig. 17 can be obtained from Fig. 15 and Fig. 16.
It can be seen from the figure that the actual output torque
of the tractor after PCHMCVT expansion encloses the ideal
engine working curve in the commonly used low speed working section (0–12 km/h). Although the output torque after
expansion is slightly reduced when the vehicle speed is high,
the tractor has a lower demand for output torque. Therefore,
the PCHMCVT designed in this paper can satisfy the torque
requirements of the tractor.
195422
FIGURE 18. Distribution ratio S of PCHMCVT.
When the system is in F1 mode, because of the cycle power
Pt = Pi + Pm = Pc ,
Ps
Ps1
ns1 Ms1
1
S=
=
=
=
(45)
Pt
Pc1
nc1 Mc1
(1 + k1 )ε
Similarly, the F2 mode is:
Ps
Ps2
ns2 Ms2
1
S=
=
=
=
(46)
Pt
Pr2
nr2 Mr2
k2 ε
The F3 mode is:
Ps
Ps1
ns1 Ms1
1
S=
=
=
=
(47)
Pt
Pc1
nc1 Mc1
(1 + k1 )ε
As the F4 mode uses the PST working mode,
Ps
Ps2
Ps2
1
S=
=
=
=
(48)
Pt
Po
Pc2
1 + k2 ε
The improved D1 mode is pure hydraulic mode S = 1
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Y. Xia et al.: Study on the Design Method of a New Hydro-Mechanical Continuously Variable Transmission System
Transmission systems always have power cycling due to
the structural characteristics of the PCHMCVT. Although
some efficiency is sacrificed, a wider speed ratio width and
low-speed increased-torque characteristics are obtained. The
distribution ratio reflects the working state of each mode
of PCHMCVT. By controlling the displacement ratio of the
hydraulic system, the power ratio can be reasonably distributed to improve the transmission efficiency.
D. EFFICIENCY CHARACTERISTICS
According to eqs. (17)–(21) and the primary structural
parameter (Tab. 6), the efficiency curve of each mode for
PCHMCVT can be obtained by simulation and calculation,
as shown in Fig. 19.
changing the power transmission direction. This improvement is unique. As the PCHMCVT possesses a greater
speed ratio change range (igmax /igmin = 5) than power-split
transmission (PST) (igmax /igmin = 2.5) under variation range
of displacement ratio (from -1 to +1). Therefore, only two
gears (ib1 , ib2 = ib3 ) and five working modes (four forward
modes and one reverse mode) need to be designed to satisfy
the speed requirements of the tractor under different operating conditions. This design reduces the number of gears,
and allows the engine to operate in a wider range, thereby
improving the dynamic and economy performance of the
vehicle. Through simulation and calculation, PCHMCVT can
achieve continuous change of speed ratio without power interruption, and has more powerful low-speed torque increasing
characteristics and vehicle power commutation characteristics (There is no gear switching during vehicle forward
and reverse conversion process). Although the transmission
efficiency of PCHMCVT is not optimal, it can still maintain
high efficiency operation and has a wider speed ratio width
compared to PST (displacement ratio from −1 to 1). The
results demonstrate that the PCHMCVT structure can satisfy
the requirements of tractor, and thus proves the feasibility of
PCHMCVT design method.
REFERENCES
FIGURE 19. Efficiency of each mode for the PCHMCVT.
This figure illustrates that the transmission efficiency of
PCHMCVT is slightly lower than that of PST, but it remains
within the high efficiency range. Although some efficiency is
sacrificed, the speed ratio width of PCHMCVT is increased
(displacement ratio from -1 to +1). Under the premise of
meeting the tractor speed requirements, PCHMCVT has
fewer modes of operation compare with PST, meaning fewer
clutch switching processes.
In summary, in order to verify the feasibility of
PCHMCVT, this section has verified from speed regulation
characteristics, torque characteristics, power split characteristics and efficiency characteristics. The simulation
results show that the designed PCHMCVT can satisfy the
requirements of the tractor.
VIII. CONCLUSION
In this study, a design method regarding a new PCHMCVT is proposed. The primary structural parameters of the
PCHMCVT are calculated based on the required traction
of the reference tractor under the premise that the transmission efficiency remains greater than 80%. During the
design process, it was observed that the reverse gear mode
was less efficient, therefore, improvements were made to the
original transmission structure of the PCHMCVT to improve
the transmission efficiency in the reverse gear mode by
VOLUME 8, 2020
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YU XIA was born in Chongqing, China, in 1988.
He received the M.S. degree in agricultural mechanization engineering from Yunnan Agricultural
University, in 2013. He is currently pursuing
the Ph.D. degree in vehicle engineering with
Chongqing University.
His research interests include vehicle power
transmission, mechanical transmission, and new
type power transmission design.
195424
DONGYE SUN was born in Changchun, Jilin,
China, in 1967. He received the Ph.D. degree
in construction machinery from the Jilin University of Technology, in 1996. He is currently a
Professor with the School of automotive Engineering, Chongqing University, and the Director of the State Key Laboratory of Mechanical Transmissions, Vehicle Research Institute.
His current research interests include vehicle power transmission and control, and High
performance powertrain design and control.
DATONG QIN received the B.S., M.S., and
Ph.D. degrees in mechanical engineering from
Chongqing University, Chongqing, China, in 1982,
1984, and 1993, respectively.
In 1989, he was a joint Ph.D. Student with
Tohoku University, Sendai, Japan. He is currently a Professor with the State Key Laboratory
of Mechanical Transmissions and the School of
Automotive Engineering, Chongqing University.
He has conducted more than 60 projects and
has published more than 200 peer-reviewed journal articles and conference proceedings. His research interests include control and application
of mechanical transmission and vehicle power transmission. He was a
recipient of the Changjiang Scholars Program of China and the two first
prizes of provincial-level scientific and technological progress awards,
in 2008 and 2010.
WENFENG HOU was born in Guangdong,
China, in 1997. He received the B.S. degree in
vehicle engineering from Chongqing University,
Chongqing, China, in 2018, where he is currently
pursuing the M.S. degree in vehicle engineering.
His research interests include design and control
of electric drive system of electric vehicle.
VOLUME 8, 2020