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

Example: double-motor transmission

As example we’ll lead calculation of the traction characteristic of a double-motor scraper with hydro mechanical transmission by power of 1000 kW with capacity of a ladle 16 м 3 (see Fig. 8) on the first transfer. Input data and zero approach are presented in the tabulated form on Fig. 9, and results of calculation of the scraper traction characteristic on the first transfer in tabulated form – on Fig. 10 а and in the graphic form – on Fig. 10 b . As results of calculation have shown, in operating modes of two motor branches of transmission there is no synchronism. The executed calculations have allowed estimating the actual contribution of each branch to the realized traction power of the machine and to execute deeper analysis of transmission with the purpose of a choice of its optimum variant.

Fig. 8.  The scheme of double-motor hydro mechanical transmission of self-propelled scraper

Input data

Quantity of engines = 2

Traction forсе: Т min = 0 N, Т max = 240000 N, a step of a traction force increment ΔT = 10000 N .

Machine : G = 441500 N, φ = 0.07

I branch of transmission

Diesel engine 1 : M z = 1138 N·m, k r = 437673 N, а = 0.0059 N·s 2 , b = 0.7583 N·s 2 /m, c = 60135 N/m, F = 287.4 N, z max = 2.6 mm

Hydraulic torque converter 1 : D = 0.47 m, k п = 1.128 N·m·s, М 0 = 2.943 N·m, u en = 1.00

Wheel propeller : 1 : r w = 1.03 м , u mech = 84.35, η mech = 0.893

II branch of transmission

Diesel engine 2 : M z = 1138 N·m, k r = 437673 N, а = 0.0059 N·s 2 , b = 0.7583 N·s 2 /m, c = 60135 N/m, F = 287.4 N, z max = 2.6 mm

Hydraulic torque converter 2 : D = 0.47 m, k п = 1.579 N·m·s, М 0 = 129.5 N·m, u en = 1.00

Wheel propeller : 2 : r w = 1.03 m, u mech = 84.35, η mech = 0.893

Characteristics of transmission elements

Histogram of distribution of traction forсе

( number of intervals = 12):

 Т , kN 10 30 50 70 90 110 130 150 170 190 210 230 Frequency 0.02 0.08 0.15 0.2 0.27 0.16 0.07 0.025 0.016 0.005 0.003 0.001

Diesel engine 1

External characteristic (without considering M z )

 М ( ω e ), N · m 147.2 176.6 191.3 181.5 157 117.7 63.8 0 -512.1 -750.5 ω e , rad / s 94 115 136 157 178 199 221 238 243 499

Dependence of fuel consumption on angular speed

 Consumption, kg/h 3 2 .0 66.0 1 8.0 ω e , rad / s 94 .0 221. 0 2 3 8 .0

Hydraulic torque converter 1

Pump wheel

 10 4 · ρλ 1 ( i ), N · s 2 / m 4 1 2 3 .0 116 . 6 99 . 3 85 . 8 63 . 3 54 . 4 0 .0 -63 . 3 -100 . 1 -1 22 . 6 i 0.0 0. 6 0. 8 0. 85 0. 9 0. 92 1 . 0 1 . 1 1 . 2 5 10 0 .0

Turbine wheel

 10 4 · ρλ 2 ( i ), N · s 2 / m 4 369 . 7 154 . 1 95 . 7 80 . 8 59 . 4 51 . 2 0 . 0 -63 . 3 -100 . 1 -1 22 . 6 i 0.0 0. 6 0. 8 0. 85 0. 9 0. 92 1 . 0 1 . 1 1 . 2 5 10 0 .0

Wheel propeller 1

Slipping curve

 δ ( R ), % 0 .0 3 . 2 5 . 6 7 . 8 11 . 4 16 . 9 25 . 3 37 . 8 55 . 8 100 . 0 R , kN 17 . 0 75 . 8 95 . 5 105 . 3 115 . 1 124 .9 1 3 4 . 7 144 . 5 154 .3 173 . 9

Diesel engine 2

External characteristic (without considering M z )

 М ( ω e ), N · m 147 . 2 17 6. 6 191 . 3 181 . 5 15 7.0 117 . 7 63 . 8 0 .0 -5 1 2 . 1 -75 0. 5 ω e , rad / s 94 .0 1 1 5 . 0 1 3 6 .0 1 57 .0 1 78 . 0 1 99 .0 221 . 0 23 8.0 243 .0 4 9 9 . 0

Dependence of fuel consumption on angular speed

 Consumption, kg/h 3 2 .0 66.0 1 8.0 ω e , rad / s 94 .0 221. 0 2 3 8 .0

Hydraulic torque converter 2

Pump wheel

 10 4 · ρλ 1 ( i ), N·s 2 /m 4 123 116.6 99.3 85.8 63.3 54.4 0.0 -63.3 -100.1 -122.6 i 0 0. 6 0. 8 0. 85 0. 9 0. 92 1 . 0 1 . 1 1 . 2 5 10 0 .0

Turbine wheel

 10 4 · ρλ 2 ( i ), N·s 2 /m 4 369 . 7 154 . 1 95 . 7 80 . 8 59 . 4 51 . 2 0 . 0 -63 . 3 -100 . 1 -1 22 . 6 i 0.0 0. 6 0. 8 0. 85 0. 9 0. 92 1 . 0 1 . 1 1 . 2 5 10 0 .0

Wheel propeller 2

Slipping curve

 δ ( R ), % 0 .0 2 . 5 4 . 5 6 . 6 10 . 3 16 . 5 27 . 0 43 . 9 70 . 2 100 . 0 R , kN 13 . 9 53 . 2 72 . 8 82 .6 92 . 4 102 . 2 112 . 0 121 . 8 131 . 6 13 8. 5

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 231.8 1 . 49 485 . 1 0.95 21 0 . 8 20 0 .0 456 . 2 33 . 3 5 1 . 3 2. 40 230.0 1.12 676.9 0.96 209.0 200.0 348.3 25.51 1.5 2.40

Fig. 9. Input data and zero approach

Results of traction analysis of double-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 0.0 231.6 229.5 1.46 1.11 522.9 681.2 0.966 0.975 231.6 229.5 223.8 223.7 243.6 178.5 17.8 13.1 0.00 0.00 2.73 9.8 230.7 228.5 1.30 0.96 593.6 750.4 0.956 0.965 230.7 228.5 220.6 220.5 311.1 245.1 22.7 17.9 0.32 0.25 2.69 19.6 229.7 227.5 1.15 0.82 665.3 818.5 0.946 0.955 229.7 227.5 217.3 217.4 379.5 310.6 27.8 22.7 0.59 0.55 2.64 29.4 228.7 226.4 0.99 0.67 737.1 886.4 0.936 0.945 228.7 226.4 214.0 214.0 448.1 376.1 32.8 27.5 0.87 0.85 2.59 39.2 227.6 225.3 0.84 0.53 808.6 954.4 0.925 0.935 227.6 225.3 210.6 210.7 516.6 441.6 37.8 32.3 1.14 1.15 2.54 49.1 226.6 224.1 0.69 0.37 875.5 1027.1 0.913 0.924 226.6 224.1 206.9 207.0 580.3 511.9 42.4 37.4 1.40 1.47 2.49 58.9 225.5 222.9 0.55 0.22 944.3 1098.4 0.897 0.909 225.5 222.9 202.2 202.5 645.8 580.4 47.2 42.4 1.66 1.78 2.43 68.7 224.3 221.6 0.39 0.07 1015.5 1165.8 0.880 0.892 224.3 221.6 197.4 197.7 714.6 645.5 52.3 47.2 1.93 2.08 2.36 78.5 222.7 218.0 0.20 0.00 1107.0 1207.9 0.858 0.876 222.7 218.0 191.0 191.0 803.2 691.0 58.7 50.5 2.29 2.29 2.28 88.3 220.5 210.5 0.00 0.00 1201.9 1226.2 0.821 0.857 220.5 210.5 181.0 180.5 908.3 719.9 66.4 52.6 2.71 2.42 2.15 98.1 214.0 201.4 0.00 0.00 1217.7 1248.5 0.772 0.818 214.0 201.4 165.2 164.7 995.2 767.0 72.8 56.1 3.06 2.77 1.95 107.9 211.5 197.1 0.00 0.00 1223.7 1258.0 0.733 0.783 211.5 197.1 155.0 154.3 1078.5 817.7 78.9 59.8 3.60 3.16 1.82 117.7 209.4 195.0 0.00 0.00 1228.8 1261.9 0.699 0.747 209.4 195.0 146.4 145.6 1146.9 883.3 83.9 64.6 4.20 3.67 1.71 127.5 207.3 192.8 0.00 0.00 1234.0 1265.9 0.664 0.710 207.3 192.8 137.7 136.8 1215.4 948.8 88.9 69.4 4.81 4.18 1.60 137.3 205.2 190.7 0.00 0.00 1239.2 1269.9 0.628 0.671 205.2 190.7 128.8 128.0 1284.7 1013.5 93.9 74.1 5.42 4.83 1.49 147.2 203.6 188.8 0.00 0.00 1243.1 1273.5 0.592 0.634 203.6 188.8 120.6 119.6 1358.6 1073.7 99.3 78.5 6.50 5.77 1.38 157.0 203.4 187.2 0.00 0.00 1243.6 1276.5 0.564 0.603 203.4 187.2 114.7 112.9 1444.5 1121.7 105.6 82.0 8.01 6.52 1.29 166.8 203.2 186.9 0.00 0.00 1244.0 1277.0 0.540 0.577 203.2 186.9 109.8 107.8 1515.0 1185.3 110.8 86.7 9.87 8.17 1.21 176.6 203.1 186.7 0.00 0.00 1244.4 1277.3 0.517 0.551 203.1 186.7 105.1 102.9 1583.5 1250.8 115.8 91.5 11.9 9.95 1.13 186.4 202.9 186.6 0.00 0.00 1244.8 1277.6 0.494 0.526 202.9 186.6 100.3 98.0 1653.0 1315.3 120.9 96.2 14.7 12.7 1.04 196.2 202.8 186.4 0.00 0.00 1245.2 1277.9 0.471 0.500 202.8 186.4 95.5 93.2 1722.0 1380.3 125.9 100.9 17.9 15.8 0.96 206.0 202.6 186.3 0.00 0.00 1245.6 1278.2 0.447 0.474 202.6 186.3 90.6 88.3 1792.2 1444.0 131.1 105.6 22.3 20.3 0.86 215.8 202.5 186.1 0.00 0.00 1246.0 1278.5 0.424 0.449 202.5 186.1 85.8 83.5 1861.9 1508.4 136.2 110.3 27.3 25.3 0.76 225.6 202.3 185.9 0.00 0.00 1246.4 1278.8 0.400 0.424 202.3 185.9 80.9 78.7 1933.1 1571.2 141.4 114.9 33.9 32.2 0.65 235.4 202.1 185.8 0.00 0.00 1246.8 1279.1 0.376 0.398 202.1 185.8 75.9 73.9 2003.6 1634.6 146.5 119.5 41.8 40.2 0.54

Except for calculation of main parameters entering into the equations (10), for each value of traction force T, kN , the program calculates some additional values: powers of engines N e1,2 , kW ; powers of hydraulic torque converters pump wheels N p1,2 , kW ; traction power N T , kW ; efficiencies of hydraulic torque converters η 1,2 ; traction efficiency η T ; fuel consumptions G f1,2 , kg/h . These rezults have been presented in Tab.2.

Table 2.

 Т , kN N e 1 , kW N p 1 , kW N e 2 , kW N p 2 , kW N T , kW η 1 - η 2 - η T - G f1 , kg / h G f2 , kg / h 0.0 121.2 60.0 156.4 43.6 0.0 0.91 0.92 0.00 36.0 42.1 9.8 137.0 76.3 171.6 59.6 26.3 0.90 0.91 0.19 38.7 44.9 19.6 152.9 92.7 186.3 75.2 51.8 0.89 0.90 0.31 41.5 47.8 29.4 168.7 109.0 200.9 90.6 76.2 0.88 0.89 0.38 44.4 50.7 39.2 184.2 125.1 215.2 105.8 99.7 0.87 0.88 0.43 47.4 53.8 49.1 198.5 140.0 230.4 122.0 122.1 0.86 0.87 0.47 50.3 57.3 58.9 213.1 155.0 244.9 137.7 142.9 0.84 0.85 0.49 53.4 60.8 68.7 227.9 170.6 258.5 152.3 162.3 0.83 0.84 0.50 56.7 64.2 78.5 246.7 190.1 263.5 160.3 178.8 0.81 0.82 0.51 61.2 65.2 88.3 265.1 209.7 258.3 161.1 189.8 0.78 0.81 0.51 65.9 63.2 98.1 260.7 208.5 251.6 161.5 191.7 0.79 0.78 0.52 64.1 60.8 107.9 259.0 207.9 248.1 161.2 196.7 0.80 0.78 0.53 63.5 59.6 117.7 257.5 207.5 246.2 160.9 201.6 0.81 0.80 0.55 62.9 59.0 127.5 256.0 206.9 244.3 160.6 204.1 0.81 0.81 0.56 62.3 58.5 137.3 254.5 206.4 242.3 160.3 204.2 0.80 0.81 0.56 61.8 57.9 147.2 253.2 205.9 240.6 159.8 202.5 0.80 0.80 0.55 61.3 57.4 157.0 253.1 205.9 239.1 159.5 202.1 0.81 0.79 0.55 61.3 56.9 166.8 253.0 205.8 238.8 159.5 201.5 0.81 0.80 0.55 61.2 56.9 176.6 252.9 205.8 238.7 159.5 199.7 0.81 0.81 0.55 61.2 56.8 186.4 252.8 205.7 238.5 159.4 194.6 0.81 0.81 0.53 61.2 56.8 196.2 252.6 205.7 238.4 159.4 187.8 0.80 0.81 0.52 61.1 56.7 206.0 252.5 205.6 238.2 159.4 177.1 0.79 0.80 0.49 61.1 56.7 215.8 252.4 205.6 238.1 159.3 164.3 0.78 0.79 0.45 61.0 56.7 225.6 252.3 205.6 237.9 159.3 147.1 0.76 0.78 0.40 61.0 56.6 235.4 252.2 205.5 237.8 159.2 127.1 0.74 0.76 0.35 60.9 56.6

Average values of base parameters of transmission

Full power: 476.00 kW

General useful power: 315.94 kW

Traction power: 162.63 kW

Traction efficiency: 0.4914

General efficiency of machine: 0.6638

Fuel consumption of the 1-st engine 57.85 kg/h,

Fuel consumption of the 2-nd engine 59.69 kg/h,

а

Fig. 10. Results of calculation of the traction characteristic of a scraper on the first transfer

а – table form, b – graphic form.

Considering a random character of loadings acting on working bodies of digging-transport, road and other mobile machines, often it is necessary to spend a traction calculation of hydro mechanical transmissions in view of non-uniform distribution of traction forces. For this purpose it is necessary to give histogram y ( T ) of distribution of traction force T and according to probability theory to define from the formula

(11)

average values of traction and general useful power, traction efficiency, hour fuel consumption and some other variables, depending on a traction force T. After this an average specific fuel consumption equal to relation of the summary average fuel consumption to the general useful power and describing a fuel economy of engine(s) is defined.

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