HYDROSTATIC TRANSMISSIONS
10.4 HYDROSTATIC TRANSMISSION DYNAMIC ANALYSISDYNAMIC ANALYSIS
10.4.2 Final Comments on the Soil Bin Example
The analysis shown has made many simplifying assumptions. As indicated earlier, it is usually desirable to simplify as much as possible initially and then add complexity as the problem demands. Altering viscous drag to Coulomb friction would be a sensible modification in this design. The goal of the design was to provide a soil bin that could be used for tillage research, yet no tool force was incorporated in the design. The designer should introduce this tool force for a period after the bin reaches constant velocity and should observe how much the velocity drops as the tool engages. In a different context, it might be necessary to include the dynamics of the swash plate control in the pump. Likewise in a system where the load was much less massive, it would be necessary to include the moment of inertia of the motor as well as the load.
It was shown inChapter 8that volumetric efficiency improves with pump
270 HYDROSTATIC TRANSMISSIONS
0 5 10 15 20 25 30 35
0 2 4 6 8 10 12 14
TIME s
DISPLACEMENT m
Figure 10.7
: Simulated soil bin drive using flexible hoses, position vs.time.
-1.0E+07 -8.0E+06 -6.0E+06 -4.0E+06 -2.0E+06 0.0E+00 2.0E+06 4.0E+06 6.0E+06 8.0E+06
0 2 4 6 8 10 12 14
TIME s
PRESSURE Pa
Figure 10.8
: Simulated soil bin drive using rigid pipe, pressure vs.time.
0 1 2 3 4 5
0 2 4 6 8 10 12 14
TIME s
VELOCITY m/s
1 2
1 DESIRED VELOCITY 2 SIMULATED VELOCITY
Figure 10.9
: Simulated soil bin drive using rigid pipe, velocity vs.time.
0 5 10 15 20 25 30 35
0 2 4 6 8 10 12 14
TIME s
DISPLACEMENT m
Figure 10.10
: Simulated soil bin drive using rigid pipe, position vs.time.
272 HYDROSTATIC TRANSMISSIONS We also indicated that the backlash in the gearbox would be ignored. In a system like the soil bin, only the forward motion dynamics are of concern, so gearbox backlash would have little or no effect. In a system that moves forward and backwards, e.g. a positioning system, the gearbox backlash effect would have to be incorporated. Another feature that might be im-portant would be elasticity in the drive components between the motor and the bin. Simulation is always a compromise between accuracy of prediction and cost.
There is one feature of the design that should be noted by the reader.
A brief discussion of the relation between torque and speed of an induction motor was given. The analysis then proceeded as if the prime mover speed was invariant and that the prime mover could both produce and absorb torque. This may not be far from true for an induction motor, but may be far from true for an internal combustion engine. If the prime mover is to provide system braking, the speed vs. torque characteristics for such operation must be determined, otherwise a potentially damaging overshoot could occur.
PROBLEMS
10.1 The two rear drive sprockets on a crawler tractor are powered with variable displacement hydraulic motors through a reduction gear set.
The motors are driven by a single hydraulic pump with equal flow to each motor.
Determine the highest and lowest sprocket speeds, nsl and nsh, that will occur as the motor displacement advances from Dml to Dmh. Determine the tractor drawbar pull, Fd, and the tractor power, P , that will be produced with the values for motor displacement Dml
and Dmh, and the other values given in the table.
Characteristics of a hydrostatic transmission for a crawler tractor
Characteristic Size Units
Pump displacement, Dp 38 mL/rev
Pump speed, np 1250 rpm
Pump volumetric efficiency, ηvp
96 %
Outlet pressure, ps 23 MPa
Motor displacement, low, Dml 230 mL/rev Motor displacement, high,
Dmh
550 mL/rev
Motor volumetric efficiency, ηvm
96 %
Motor mechanical efficiency, ηmm
97 %
Motor discharge pressure, pr 230 kPa Gear ratio, N = nm/ns 4.3:1
Sprocket effective rolling ra-dius, r
377 mm
10.2 The two rear drive sprockets on a crawler tractor are powered with variable displacement hydraulic motors through a reduction gear set.
The motors are driven by a single hydraulic pump with equal flow to each motor.
Determine the highest and lowest sprocket speeds, nsl and nsh, that will occur as the motor displacement advances from Dml to Dmh. Determine the tractor dozer blade force, Fz, and the tractor power, P , that will be produced with the values for motor displacement Dml
and Dmh, and the other values given in the table.
274 HYDROSTATIC TRANSMISSIONS Characteristics of a hydrostatic transmission for a crawler tractor
Characteristic Size Units
Pump displacement, Dp 40 mL/rev
Pump speed, np 1200 rpm
Pump volumetric efficiency, ηvp
97 %
Outlet pressure, ps 23.5 MPa
Motor displacement low, Dml 220 mL/rev Motor displacement high,
Dmh
570 mL/rev
Motor volumetric efficiency, ηvm
97 %
Motor mechanical efficiency, ηmm
96 %
Motor discharge pressure, pr 240 kPa Gear ratio, N = nm/ns 4.5:1
Sprocket effective rolling ra-dius, r
375 mm
10.3 The drive sprockets on a crawler tractor are powered with hydraulic motors through a reduction gear set.
Determine the required motor displacement, Dm, to produce the given dozer force, Fz, and drawbar force, Fd. Determine the required motor flow, Q, to produce the given tractor speed, ˙x.
Characteristics of a hydrostatic transmission for a crawler tractor
Characteristic Size Units
Motor overall efficiency, ηom 93 % Motor mechanical efficiency,
ηmm
95 %
Motor inlet pressure, p1 28.5 MPa
Motor return pressure, p2 300 kPa
Gear ratio, N = nm/ns 4.1:1 Sprocket effective rolling
ra-dius, r
373 mm
Drawbar force, Fd 15 kN
Dozer force, Fz 17 kN
Tractor speed, ˙x 5.1 km/h
REFERENCES
1. Lambeck, R. P., 1983, Hydraulic Pumps and Motors: Selection and Application for Hydraulic Power Control Systems, Marcel Dekker, Inc., New York, NY.
2. Steenhoek, L., Smith, R. J., Akers, A., and Chen, J., 1993, ”Sim-ulation and Validation of a Mathematical Model of a Hydrostatic Transmission”, New Achievements in Fluid Power Engineering (’93 ICFP), pp. 396-403.
3. Chapman, S. J., 1998, Electrical Machinery fundamentals, WCB/McGraw- Hill, Boston, MA.