|
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
|
10.0
|
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 M
z
)
|
М
(
ω
e
),
N
·
m
|
147.2
|
176.6
|
191.3
|
181.5
|
157.0
|
117.7
|
63.8
|
0.0
|
-512.1
|
-750.5
|
|
ω
e
,
rad
/
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
|
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
|
123.0
|
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
.
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.
|