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Contents >> Engineering Mathematics >> Mobile Machines >> Traction Analysis >> One engine transmission >> Example

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

Example: single-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. 5а and in the graphic form – on Fig. 5б.

Ris3_DRAWN.gif

 

Fig. 3. A wheel loader with hydro mechanical transmission

 

Input data

Quantity of engines =1

Traction forсе: Тmin = 0 N,  Тmax = 78400 N,  a step of a traction force increment ΔT= 4900 N

Machine: G = 105000 N,  φ = 0.1

Diesel engine: Mz= 490 N·m, kr= 86887 N, а = 0.0255 N·s 2, b = 0.8535 N·s 2/m, c = 56113 N/m,  F = 801.5 N, zmax= 5.6 mm

Hydraulic torque converter: D = 0.34 m, kп = 0 N·m·s,  М0 = 98.1 N·m,  uen = 0.85

Wheel propeller: rw = 0.75 m, umech = 71.8,  ηmech = 0.9

 

Characteristics of transmission elements

Diesel engine

External characteristic (without considering Mz)

 М(ωe), N·m

 49.05

 58.86

 63.765

 68.67

 68.67

 63.765

 49.05

 29.43

 14.715

  0.00

 ωe, rad/s

115.0

120.3

125.6

136.0

146.5

157.0

167.5

178.0

186.0

192.7

 

Hydraulic torque converter

Pump wheel

104·ρλ1(i), N·s2/m4

 
274.68

 
289.395

 
294.30

 
289.395

 
274.68

 
255.06

 
225.63

 
161.865

 
73.575


-132.435

       i

 0.0

 0.1

 0.2

 0.3

 0.6

 0.7

 0.78

 0.9

 0.95

10.0

 

Turbine wheel

104·ρλ2(i), N·s2/m4


794.61

 
667.08

 
588.60

 
490.50

 
328.635

 
268.794

 
213.858

 
128.511

 
36.788


-132.435

       i

  0.0

  0.1

  0.2

  0.3

  0.6

  0.7

 0.78

  0.9

 0.95

10.0

 

Wheel propeller

Slipping curve

   δ(R), %

 0.0

 10.0

 20.0

 30.0

 40.0

 50.0

 60.0

 70.0

 80.0

100.0

   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=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

 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

  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

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 Ne , kW; the hydraulic torque converter pump wheel power Np , kW; traction power NT , kW; efficiency of the hydraulic torque converter η ; traction efficiency ηT ; fuel consumption Gf , kg/h. These rezults have been presented in Tab.2.

 

       Table 2.

     Т,

    kN

     Ne ,

       kW

     Np ,

       kW

      NT,

         kW

      η ,

      -

     ηT ,

      -

     Gf ,

   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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Last updated: April 30, 2015.