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Contents >> Engineering Mathematics >> Mobile Machines >> Traction Analysis >> Two engines transmission >> Example

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 м3 (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. 10а and in the graphic form – on Fig. 10b. 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: Тmin = 0 N, Тmax = 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: Mz= 1138 N·m, kr= 437673 N, а = 0.0059 N·s2, b = 0.7583 N·s2/m, c = 60135 N/m, F = 287.4 N, zmax= 2.6 mm

Hydraulic torque converter 1: D = 0.47 m, kп = 1.128 N·m·s, М0 = 2.943 N·m, uen= 1.00

Wheel propeller: 1: rw = 1.03 м, umech = 84.35, ηmech = 0.893

II branch of transmission

Diesel engine 2: Mz= 1138 N·m, kr= 437673 N, а = 0.0059 N·s2, b = 0.7583 N·s2/m, c = 60135 N/m, F = 287.4 N, zmax= 2.6 mm

Hydraulic torque converter 2: D = 0.47 m, kп = 1.579 N·m·s, М0 = 129.5 N·m, uen = 1.00

Wheel propeller: 2: rw = 1.03 m, umech = 84.35, ηmech = 0.893

 

Characteristics of transmission elements

Histogram of distribution of traction forсе

(number of intervals = 12):

    Т, kN

10.0

30.0

50.0

70.0

90.0

110.0

130.0

150.0

170.0

190.0

210.0

230.0

Frequency

0.02

0.08

0.15

0.20

0.27

0.16

0.07

0.025

0.016

0.005

0.003

0.001

 

Diesel engine 1

External characteristic (without considering Mz)

М (ωe), N·m

147.2

176.6

191.3

181.5

157.0

117.7

 63.8

  0.0

-512.1

-750.5

ωerad/s

 94.0

115.0

136.0

157.0

178.0

199.0

221.0

238.0

243.0

499.0

    

Dependence of fuel consumption on angular speed

Consumption, kg/h

 32.0

 66.0

 18.0

   ωerad/s

 94.0

221.0

238.0

 

Hydraulic torque converter 1

Pump wheel

104·ρλ1(i),

N·s 2/m4

123.0

116.6

 99.3

 85.8

 63.3

 54.4

  0.0

-63.3

-100.1

-122.6

i

  0.0

  0.6

  0.8

 0.85

  0.9

 0.92

  1.0

  1.1

 1.25

100.0

 

Turbine wheel

104·ρλ2(i),

N·s 2/m4

369.7

154.1

 95.7

 80.8

 59.4

 51.2

 0.0

-63.3

-100.1

-122.6

  i

  0.0

  0.6

  0.8

  0.85

  0.9

  0.92

 1.0

  1.1

 1.25

100.0

 

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

134.7

144.5

154.3

173.9

 

Diesel engine 2

External characteristic (without considering Mz)

М (ωe), N·m

147.2

176.6

191.3

181.5

157.0

117.7

 63.8

  0.0

-512.1

-750.5

ωerad/s

 94.0

115.0

136.0

157.0

178.0

199.0

221.0

238.0

243.0

499.0

 

Dependence of fuel consumption on angular speed

Consumption, kg/h

 32.0

 66.0

 18.0

ωerad/s

 94.0

221.0

238.0

 

Hydraulic torque converter 2

Pump wheel

104·ρλ1(i),

N·s2/m4

123.0

116.6

  99.3

  85.8

63.3

54.4

  0.0

-63.3

-100.1

-122.6

  i

  0.0

  0.6

  0.8

 0.85

  0.9

 0.92

  1.0

  1.1

 1.25

100.0

 

Turbine wheel

104·ρλ2(i),

N·s2/m4

369.7

154.1

 95.7

 80.8

 59.4

 51.2

 0.0

-63.3

-100.1

-122.6

i

  0.0

  0.6

  0.8

  0.85

  0.9

  0.92

 1.0

  1.1

 1.25

100.0

 

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

138.5

 

Zero approach

 (at Т= Тmin)

  ωe

 rad/s

    z ,

  mm

   Mс ,

  N·m

    i ,

    –

   ωp

 rad/s

   ωt

rad/s

  Мt ,

  N·m

   R,

  kN

   δ ,

   %

    v ,

   m/s

 231.8

 1.49

 485.1

 0.95

 210.8

 200.0

 456.2

 33.35

  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

  ωe

 rad/s

    z ,

  mm

   Mс ,

  N·m

    i ,

    –

   ωp

 rad/s

ωt,

 rad/s

  Мt ,

  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 Ne1,2 , kW; powers of hydraulic torque converters pump wheels Np1,2 , kW; traction power NT , kW; efficiencies of hydraulic torque converters η1,2 ; traction efficiency ηT ; fuel consumptions Gf1,2 , kg/h. These rezults have been presented in Tab.2.

 

     Table 2.

Т,

kN

 Ne1,    

  kW

  Np1 ,

   kW

  Ne2 ,

    kW

  Np2 ,

   kW

  NT ,

   kW

  η1

   -

  η2

   -

 ηT

  -

 Gf1 ,

kg/h

 Gf2 ,

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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