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Lecture #10 TYPES OF BELTS and Belt Selection Course Name : DESIGN OF MACHINE ELEMENTS Course Number: MET 214 Types of belts: 1) flat belt 2) V belt drive 3) synchronous belts (timing belts) Flat belt: Simplest type often made from leather or rubber coated fabric. The sheave (pulley) is also flat and smooth, and the driving force is therefore limited by pure friction between the belt and the sheave. Some designers prefer flat belts for delicate machinery because the flat belt will slip if the torque tends to rise to a level high enough to damage the machine. V-belt: The V shape causes the belt to wedge tightly into a groove formed in a pulley, (called a sheave) increasing friction and allowing high torques to be transmitted before slipping occurs. Most V belts have high strength cords positioned at the pitch diameter of the belt cross section to increase the tensile strength of the belt. The cords, made from natural fibers, synthetic strands, or steel, are embedded in a firm rubber compound to provide the flexibility needed to allow the belt to pass around the sheave. Often an outer fabric cover is added to give the belt good durability. Synchronous belt drives Synchronous belts are constructed with ribs or teeth across the underside of the belt. The teeth mate with corresponding grooves in the driving and driven pulleys, called sprockets, providing a position drive without slippage. Therefore, there is a fixed relationship between the speed of the driver and the speed of the driven sprocket. Examples of various types of belts are shown below. Insert diagrams Comparison of V-belts with Flat belts Plain flat belts have been almost entirely replaced by V-belts and timing belts (synchronous belts) due to their inherent drawbacks, such as excessive slippage, high bearing pressure, axial space requirements, and noise. As detailed on a previous slide, a distinction must be made between the outside diameter of the sheave and the pitch diameter of the pitch circle of the sheave. Standard V Belt Cross Sections are shown in the figures below. Insert Images The design of a V belt drive involves specifying 1) the sheave diameters needed to implement a desired speed ratio existing between an input and output shafts of a system, 2) Selecting the belt size and length and number of belts required to transfer the amount of power from one shaft to another required by the application consistent with the shaft to shaft spacing that can exist in a particular application, and 3) selecting a mounting technique for attaching the sheaves to the shafts of the system. As noted in the book by Mott, page 273, several guidelines can be used to initialize a design. 1) if belt speed is less than 1000 ft/min, an alternative drive component such as gear type or chain should be considered. 2) Most commercially available sheaves are cast iron, which should be limited to a belt speed of 6500 ft/min. 3) The angle of wrap on the smaller sheave should be greater than 1200. The design process will be illustrated by example 7-1 page 278 in book by Mott. Example 7-1 Design a V belt drive that has the input sheave on the shaft of an electric motor (normal torque) noted at 50 hp at 1160 rpm full load speed. The drive is to a bucket elevator in a potash plant that is to be used 12 hours (h) daily at approximately 675 rpm. Note: Bucket elevator operates at 675 rpm. Motor provides 50 hp at 1160 rpm. Accordingly pulley system must be designed to reduce speed of motor to match speed of bucket elevator. Procedure: Step 1: Modify the normal rating by the V-belt service factor to produce the design power. The design power is related to the normal by as shown below. Design Power = (normal power)(service factor) The value of the service factor depends on the applications as shown in table provided below. For the example under consideration: Service factor: 1.3 Design power =(1.3)(50)=65 hp Step 2: Select the belt section: Figure 7-9 from the book by Mott is provided below to assist in identifying an appropriate cross section with the design power. To utilize figure 7-9, the following issues need to be noted. 1) Design hp appears on the horizontal axis 2) Speed of faster shaft appears on vertical axis. 3) To identify an appropriate cross section for an application, the design power is located on the horizontal axis. After locating the design power level on the X axis, move vertically until the speed of the faster shaft is incurred. Cross section is determined from the region of the figure containing the operating point , i.e. operating point = (X coordinate, Y coordinate) = (H.P., speed of faster shaft) For the design power of 65 hp and the input (faster) speed of 1160 rpm, the cross section recommended from the graph is a size 5V belt. Q: Given a particular design power, why does recommend cross section decrease as speed increases? i.e. @ (65 hp, 110 rpm)-> 8V @(65 hp, 500 rpm)-> 5V @(65 hp, 4000 rpm)-> 3Vx Step 3: Compute the nominal speed ratio mw n A 1160 1.72 nB 675 Step 4: Compute diameter of drive sheave to produce a belt speed of Vb=4000 ft/min vb Dn .262 Dn 12 where vb belt speed ft/min D diameter of sheave in inches n speed of rotation of sheave in rpm Rearranging for D DA 124000 13.17inches 12vb nA 3.141160 Step 5: Select trait sizes for the input sheave and compute the desired size of the output sheave. In order to utilize stock components, a few iterations involving different diameter combinations may needed to be performed until a ratio of stock diameters produces a ratio very nearly equal to the speed ratio calculated from the shaft speeds. The degree of mismatch that is acceptable depends on the application. Table 7-3 from the book by Mott has been provided to illustrate the process of searching for stock components to produce an acceptable speed ratio. nA DA nB DB nA DB 1.72 nB DA From previous step DA = 13.17 inches Estimate DB = (1.72)(13.17) = 22.65 As is evident from table 7-3 below DA = 12.4 and DB = 21.1 Step 6: Determine the rated power (for the belt size selected previously) using figures 710, 7-11 or 7-12 repeated below for convenience. The figures provided below identify the power handling capability of a single belt. Utilizing the design power and power rating of a belt along with some correction factors to be discussed later will enable the designer to specify the member of belts required for an application. Figure 7-10 is used with 3V belts. Figure 7-11 is used with 5V belts and figure 7-12 is used with 8V belts. Images 7-10 and 7-11 Figure 7-12 and Figure 7-13 Viewing graph 7-11 for the small sheave pitch diameter of 12.4 at 1160 rpm. The rated power using the solid curve for 1160 rpm is 26.4 hp. The dotted curve lying immediately above the solid curve is an additional horse power added rating that can be added to the basic power rating. A given belt can carry a greater power as the speed ratio increases, up to a ratio of approximately 3.38. Figure 7-13 is a plot of the data for power to be added to the basic rating as a function of speed ratio for 5 V belts. For a speed ratio of 1.72 at 1160 rpm, the added power is 1.15 Actual rated power of belt = 26.4 +1.15 =27.55 hp Step 7: Specify a trail center distance. The trial distance is an estimate so that the design process can proceed. To assist in specifying a 1st estimate on center distance, use the relationship provided below. D2 C 3D2 D1 21.1 C 321.1 12.4 21.1in C 100.5in In the interest of conserving space, assume C = 24.0 in. Step 8: Compute the required belt length using the equation provided below. 2 D2 D1 L 2C 1.57D2 D1 4C L D D1 2(24.0) + 1.57(21.1 + 12.4) + 2 4C 2 = 101.4 in Step 9: Select a standard belt length from table 7-2 provided below that is close to the length calculated in the previous step and compute the resulting center distance using the procedure defined below. Use the values of D1 and D2 and the length L of the belt you are going to use in the equations provided below to calculate the center to center spacing necessary for use with the belt length chosen. 1) To find center to center separation, first calculate the following quantity B 4L 6.28D2 D1 2) Calculate center to center spacing using the following formula. B B 2 32D2 D1 C 16 2 Step 9 continued: L = 100.0 in → = 189.6 → = 23.3 Step 10: compute the angle of wrap of the belt around the sheaves from the following equations. D D1 1 1800 2 sin 1 2 2C D D1 2 1800 2 sin 1 2 2C 1 = 158 Q: Is θ1 or θ2 associated with the larger diameter pulley and why? Step 11: Determine the correction factors from figures 7-14 and 7-15 provided below. = 0.94 = 0.96 Step 12: Compute the corrected rated power per belt and the number of belts required to carry the design power: Corrected power = = 24.86ℎ Number of belts = 65/24.86 = 2.61 belts → 3 Summary of design Input: Electric motor, 50.0 hp at 1160 rpm Service factor: 1.3 Design power: 65.hp Belt: 5V cross section, 100 in length, 3 belts Sheaves: Driver, 12.4 in pitch diameter, 3 grooves, 5V. Driven, 21.1 in pitch diameter, 3 grooves, 5V Actual output speed: 682 rpm