Study on the Optimization Model of a Flexible Transmission

Table 5

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Conditions							Lw	d1
Power to be transmitted (kW)	P	4.1231				1	590	50
Rotation speed of small pulley (r/min)	n1	2418.055				2	610	56
Rotation speed of large pulley/small sprocket (r/min)	n2(n3)	1521.2				3	630	63
Rotation speed of large sprocket (r/min)	n4	760.6				4	640	71
Total ratio	i	3.179141467				5	660	80
Chain pitch (mm)	p	12.7				6	670	90
Variables			Order number			7	690	100
The diameter of small pulley (mm)	d1	71	4			8	710	112
The pitch length of belt (mm)	Lw	590	1			9	730	125
Number of belts	Z	2				10	750	140
Number of teeth on drive sprocket	Z1	19
Number of teeth on driven sprocket	Z2	38
Chain length (pitches)	L	89
Design process of belt drive
The diameter of large pulley (mm)	d2	112.8595221
Belt drive ratio	i1	1.589570734
Pulley center distance (mm)	a	149.12835
Arc of contact (degrees)	β	163.86411
Arc of contact factor	c1	0.961199222
	m	1.26E-11	-1.07E-07	3.63E-04	6.41E-01
Length correction factor c3	c3	0.82
Power rating of a single belt (kW)	Pr	2.88
Belt safety factor	c2	1.102750606
Belt speed	Vb	8.98924335
Design process of chain drive
Speed of small sprocket (r/min)	n2(n3)	1521.2
Chain drive ratio	i2	2
Chain mass/metre (kg/m)		0.7
Chain axial breaking force (N)		17800
Application Factor	f1	1.7
Tooth Factor	f2=19/Z1	1
Power selection (kW)	Q	7.00927
Sprocket centre diatance (mm)	C	382.2478846
Small sprocket diameter (mm)	d3	77.15927953
large sprocket diameter (mm)	d4	153.7914829
Tip diameter of large sprocket	da	155.7967461
Chain Velocity (m/s)	v	6.117759333
load due to power transmitted (N)	F1	1145.725031
load due to centripetal acceleration	F2	26.19888548
Total chain load	F	1171.923916
Chain safety factor	c2_	15.18869933
Belt constraints:
1.safety factor should exceed 1.1
g1(x)=1.1-c2<=0	g1	-0.002750606
2.Speed of Belt <=50m/s
g2(x)=pid1n/60000-50<=0	g2	-41.01075647
3.number of belt <=10
g3(x)=Z-10<=0	g3	-8
4.Center distance 0.7(dwg+dwk)<a<2(dwg+dwk)
g4(x)=0.7(dwg+dwk)-a<=0	g4	-20.42668454
g5(x)=a-2(dwg+dwk)<=0	g5	-218.5906942
5.50=<d<=140,590=<Lw<=3550
g6(x)=d1-140<=0	g6	-69
g7(x)=50-d1<=0	g7	-21
g8(x)=Lw-3550<=0	g8	-2960
g9(x)=590-Lw<=0	g9	0
Chain constraints:
1.Center distance should be within the range 30-50 times the chain pitch
g10(x)=C-50p <= 0	g10	-252.7521154
g11(x)=30p-C <= 0	g11	-1.247884581
2. Number of teeth on the drive sprocket should be at least 19 and number of teeth on driven sprocket should be less than 114.
g12(x)=19-Z1 <= 0	g12	0
g13(x)=Z2-114 <= 0	g13	-76
g14(x)=Z1-Z2 <= 0	g14	-19
3. Sum of teeth not less than 50
g15(x)=50-(Z1+Z2) <=0	g15	-7
4.Safety factor should be greater than 8
g16(x)=8-c2_ <=0	g16	-7.18869933
Objective function
Space Volume of Belt Drive	V1	761759.69
Space Volume of Chain Drive	V2	551128.31
Total volume	V	1312888