Machine Design 3(2+1)

LESSON 20 SELECTION OF BELTS

Following is the procedure for selection of a flat belt:

1.      Select suitable belt material

Two types of belts are generally available – HI-SPEED duck belting and FORT duck belting. Specified transmission capacities of these two types, for an angle of contact of 180°and belt velocity of 5.08 m/s, is as follows:

Type of Belt                                         Transmission Capacity/ Power Rating (R)

HI-SPEED                                                             0.012 kW / mm width / ply

FORT                                                                     0.015 kW / mm width / ply

2.      Assume belt velocity and calculate diameters of pulleys

Optimum value of belt velocity lies between 15 m/s to 25 m/s. Assume any value for belt velocity, within this range and calculate diameter of the smaller (driving) pulley using the following relationship:

where,       v = velocity of belt

            N₁ = input speed (rpm) of smaller pulley

Diameter of larger pulley (D) can be calculated, for required velocity ratio i.e. for required output speed (N₂), using the following relationship:

N1d = N2D

3.      Calculate design power

For design purpose, maximum power transmitted by the belt is obtained by multiplying the required power (P) by a load correction factor (K_load). Value of K_load can be taken from Table 20.1. Also, Power transmission capacity of belts (Step 1) is based on angle of contact of 180°. But in actual conditions, angle of contact varies depending upon diameters of pulleys and centre distance. If angle of contact is less than 180°, there is additional tension in the belt. This is taken care of, by multiplying the required power to be transmitted by angle of contact factor, K_a.. Value of K_a can be taken from Table 20.2. Design power of the belt is thus given by,

Table 20.1 Load Correction Factor, K_load

Type of Load		Kload
Normal Load		1.0
Steady Load	(light machine tools, fans, centrifugal pumps, conveyors etc.)	1.2
Intermittent Load	(compressors, blowers, heavy-duty fans, line shafts, reciprocating pumps, heavy-duty machines etc.)	1.3
Shock Load	(hammers, grinders, rolling mills, vacuum pumps etc.)	1.5

Table 20.2 Angle of Contact Factor, K_a

Angle of Contact (as)	120°	130°	140°	150°	160°	170°	180°	190°	200°	210°
Angle of Contact Factor, Ka	1.33	1.26	1.19	1.13	1.08	1.04	1.00	0.97	0.94	0.91

4.      Determine corrected power rating

Power transmission capacity of belts (Step 1) is based on belt velocity of 5.08 m/s. But in actual conditions, belts run at different speeds. For different velocity, corrected power rating is obtained as follows:

where, R is Power Transmission Capacity or Rating of belt and v is actual belt velocity.

5.      Calculate the product of width and number of plies by dividing maximum power to be transmitted by corrected power rating.

6.      Select suitable width and number of plies

Suitable width and number of plies can now be selected from the catalogue so that the desired product is obtained. Table 20.3 gives standard width thickness and number of plies for rubber belts.

Table 20.3 Rubber Belt Data

No. of Plies	Thickness (mm)	Belt Width (mm)
3	3.9	25, 32, 40, 50, 63, 71
4	5.2	40, 50, 63, 71, 80, 90, 100, 112, 125, 140
5	6.5	71, 80, 90, 100, 112, 125, 140, 160
6	7.8	112, 125, 140, 160, 180, 200, 224, 250
7	9.1	160, 180, 200, 224, 250, 280, 315
8	10.4	224, 250, 280, 315, 355, 400, 450, 500

7.         Calculate desired length of belt and specify all the dimensions.

     

20.2   Selection of V-Belts

V-belts are also selected from the manufacturer’s catalogue. Following is the procedure for selection of a flat belt:

1.      Select suitable V-belt section

Five types of standard V-belt sections are available. Dimensions of these are given in Table 20.4. Refer figure 20.1 for basic dimensions of the trapezoidal section of V-belt.

Table 20.4 Dimensions of V-belt Sections

Section	A	B	C	D	E
Pitch Width, wp (mm)	11	14	19	27	32
Nominal Top Width, w (mm)	13	17	22	32	38
Nominal Thickness, t (mm)	8	11	14	19	23
Recommended Velocity (m/s)	25	25	25	30	30
Recommended Power Range (kW)	0.4 - 4.0	1.5 - 15	10 - 70	35 - 150	70 – 260
Recommended Minimum Pitch Diameter of Pulley (mm)	125	200	315	500	630

2.      Determine diameters of pulleys

Recommended diameter of smaller pulley (d) can be taken from table 20.4 for selected cross-section. Diameter of larger pulley (D) can be calculated, for required velocity ratio i.e. for given input speed (N₁) and required output speed (N₂), using the following relationship:

N₁d = N₂D

3.      Calculate design power

For design purpose, maximum power transmitted by the belt is obtained by multiplying the required power (P) by service factor (K_s). Value of K_s can be taken between 1 and 2, depending upon the service conditions i.e. light, medium, heavy or extra-heavy duty, type of driver and driven machinery and operational hours.

P_design = K_s X P

4.      Determine Pitch Length and Centre Distance

Calculate length of the belt from its relation with d, D and C. Select the nearest standard value of belt pitch length from table 20.5. Calculate exact centre distance, C from the relation again.

Table 20.5 Belt Pitch Lengths & Pitch Length Correction Factor

Belt Pitch Length (mm)					Pitch Length  Correction Factor, Klength
Belt Cross-section
A	B	C	D	E
630					0.80
	930				0.81
700		1560	2740		0.82
	1000				0.83
790		1760			0.84
	1100				0.85
890			3130		0.86
	1210	1950	3330		0.87
990					0.88
1100	1370	2190	3730	4660	0.90
		2340			0.91
	1560	2490	4080	5040	0.92
1250					0.93
		2720	4620	5420	0.94
	1760	2800			0.95
1430		3080		6100	0.96
	1950		5400		0.97
1550		3310			0.98
1640	2180	3520		6850	0.99
1750	2300		6100		1.00
1940	2500	4060		7650	1.02
			6840		1.03
2050	2700				1.04
2200	2850	4600	7620	9150	1.05
2300					1.06
			8410	9950	1.07
2480	3200	5380			1.08
2570			9140	10710	1.09
2700	3600				1.10
		6100			1.11
2910			10700	12230	1.12
3080	4060				1.13
3290		6860		13750	1.14
	4430				1.15
3540	4820	7600	12200		1.16
	5000		13700	15280	1.17
	5370				1.18
	6070		15200	16800	1.19
		9100			1.20
		10700			1.21

Table 20.6 Angle of Contact Factor, K_a

 

	Angle of Contact on Smaller Pulley, as	Angle of Contact Factor, Ka
0.00	180	1.00
0.05	177	0.99
0.10	174	0.99
0.15	171	0.98
0.20	169	0.97
0.25	166	0.97
0.30	163	0.96
0.35	160	0.95
0.40	157	0.94
0.45	154	0.93
0.50	151	0.93
0.55	148	0.92
0.60	145	0.91
0.65	142	0.90
0.70	139	0.89
0.75	136	0.88
0.80	133	0.87
0.85	130	0.86
0.90	127	0.85
0.95	123	0.83
1.00	120	0.82

 

 

5.      Determine corrected power rating

Power transmission capacity / rating (R) for a single V-belt, for different types of cross-sections, can be taken from manufacturer’s catalogue. Corrected power rating is obtained by multiplying the power rating by Pitch Length Correction Factor (K_length) and Angle of Contact Factor, K_a as follows:

Values of K_length and K_a can be taken from table 20.5 and table 20.6 respectively.

6.      Determine the number of belts required

Required number of belts is determined by dividing the design power with corrected power rating for one belt.

 

References

1. Design of Machine Elements by VB Bhandari

2. Fundamentals of Machine Component Design by R.C. Juvinall & K.M. Marshek

3. Mechanical Engineering Design by J.E. Shigley

4. Analysis and Design of Machine Elements by V.K. Jadon

5. Design of Machine Elements by C.S. Sharma & K. Purohit

6. Machine Design by R.S. Khurmi