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Traction analysis of hydro mechanical transmissions - Example: single-motor transmission

Example: s ingle-motor transmission.

Let's consider as an example a wheel loader with hydro mechanical transmission (Fig. 3). Input data and zero approach are presented in the tabulated form on Fig. 4, and results of calculation in the tabulated form – on Fig. 5 а and in the graphic form – on Fig. 5 б .

Fig. 3. A wheel loader with hydro mechanical transmission

Input data

Quantity of engines =1

Traction for се : Т min = 0 N, Т max = 78400 N,  a step of a traction force increment Δ T = 4900 N

Machine : G = 105000 N, φ = 0.1

Diesel engine : M z = 490 N·m, k r = 86887 N, а = 0.0255 N·s 2 , b = 0.8535 N·s 2 /m, c = 56113 N/m, F = 801.5 N, z max = 5.6 mm

Hydraulic torque converter : D = 0.34 m, k п = 0 N·m·s, М 0 = 98.1 N·m, u en = 0.85

Wheel propeller : r w = 0.75 m, u mech = 71.8, η mech = 0.9

Characteristics of transmission elements

Diesel engine

External characteristic (without considering M z )

 М ( ω e ), N·m 49.05 58.86 63.765 68.67 68.67 63.765 49.05 29.43 14.715 0 ω e , rad/s 115 120.3 125.6 136 146.5 157 167.5 178 186 192.7

Hydraulic torque converter

Pump wheel

 10 4 · ρλ 1 ( i ), N·s 2 /m 4 274.68 289.395 294.3 289.395 274.68 255.06 225.63 161.865 73.575 -132.435 i 0 0.1 0.2 0.3 0.6 0.7 0.78 0.9 0.95 10

Turbine wheel

 10 4 · ρλ 2 ( i ), N·s 2 /m 4 794.61 667.08 588.6 490.5 328.635 268.794 213.858 128.511 36.788 -132.435 i 0 0.1 0.2 0.3 0.6 0.7 0.78 0.9 0.95 10

Wheel propeller

Slipping curve

 δ ( R ), % 0 10 20 30 40 50 60 70 80 100 R , kN 9.32 53.955 68.67 73.575 78.48 80.933 83.385 86.328 88.29 89.271

Zero approach

( at Т = Т min )

 ω e , rad / s z , mm M с , N · m i , – ω p , rad / s ω t , rad / s М t , N · m R , kN δ , % v , m / s 185.0 2.22 212.9 0.95 218.0 207.0 109.6 10.5 0.0 2.16

Fig. 4. Input data and zero approach

Results of traction analysis of single-motor transmission

Table 1.

 Т , kN ω e , rad / s z , mm M с , N · m i , – ω p , rad / s ω t , rad / s М t , N · m R , kN δ , % v , m / s 0.0 183 . 6 2.13 322.8 0.936 216.0 202.1 121.8 10.5 0.26 2.11 4.9 181 . 7 1.46 385.5 0.919 213.8 196.4 178.7 15.4 1.36 2.02 9.8 179.7 0.78 448.1 0.901 211.4 190.4 235.7 20.3 2.46 1.94 14.7 178.1 0.27 496.3 0.855 209.6 179.1 292.6 25.2 3.56 1.80 19.6 170.3 0.00 534.3 0.785 200.4 157.4 349.5 30.1 4.66 1.57 24.5 161.4 0.00 548.2 0.694 189.8 131.8 406.4 35.0 5.76 1.30 29.4 156.9 0.00 554.3 0.601 184.7 111.0 463.4 39.9 6.86 1.08 34.3 155.8 0.00 554.8 0.517 183.3 94.7 520.3 44.8 7.96 0.91 39.2 154.7 0.00 555.3 0.430 182.1 78.3 577.2 49.7 9.05 0.74 44.1 153.6 0.00 555.8 0.341 180.8 61.6 634.2 54.6 10.47 0.58 49.0 152.8 0.00 556.2 0.274 179.8 49.3 691.1 59.5 13.80 0.44 53.9 152.3 0.00 556.4 0.227 179.2 40.6 748.0 64.4 17.13 0.35 58.8 152.2 0.00 556.5 0.178 179.1 31.9 805.0 69.3 21.40 0.26 63.7 152.8 0.00 556.2 0.130 179.8 23.3 861.9 74.2 31.40 0.17 68.6 153.5 0.00 555.9 0.090 180.6 16.3 918.8 79.1 42.80 0.10 73.5 154.5 0.00 555.4 0.064 181.7 11.6 975.8 84.0 62.33 0.05 78.4 155.4 0.00 555.0 0.039 182.9 7.1 1032.7 88.9 94.00 0.004

Except for calculation of main parameters entering into the equations (1), for each value of traction force T, kN , the program calculates some additional values: the engine power N e , kW ; the hydraulic torque converter pump wheel power N p , kW ; traction power N T , kW ; efficiency of the hydraulic torque converter η ; traction efficiency η T ; fuel consumption G f , kg/h . These rezults have been presented in Tab.2.

Table 2.

 Т , kN N e , kW N p , kW N T , kW η , - η T , - G f , kg / h 0.0 59.3 41.3 0.0 0.60 0.00 16.8 4.9 70.0 52.2 9.9 0.67 0.19 19.2 9.8 80.5 62.9 19.1 0.71 0.30 21.8 14.7 88.3 70.9 26.6 0.74 0.37 23.8 19.6 91.0 74.3 30.7 0.74 0.41 23.0 24.5 88.4 72.6 31.8 0.74 0.44 21.9 29.4 86.9 71.6 31.8 0.72 0.44 21.3 34.3 86.4 71.1 31.3 0.69 0.44 21.2 39.2 85.9 70.8 29.2 0.64 0.41 21.0 44.1 85.4 70.3 25.4 0.56 0.36 20.9 49.0 85.0 70.0 21.8 0.49 0.31 20.8 53.9 84.7 69.8 19.0 0.44 0.27 20.7 58.8 84.7 69.7 15.4 0.37 0.22 20.7 63.7 85.0 69.9 10.7 0.29 0.15 20.8 68.6 85.3 70.2 6.7 0.21 0.095 20.9 73.5 85.7 70.6 3.4 0.16 0.05 21.0 78.4 86.2 71.0 0.4 0.10 0.005 21.1

а

Fig. 5. Results of calculation of the traction characteristic of a wheel loader

а – table form, b – graphic form.

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