Solved: A 16-tooth pinion drives the double-reduction

A certain application requires a ball bearing with the inner ring rotating, with a design life of 25 kh at a speed of 350 rev/min. The radial load is 2.5 kN and an application factor of 1.2 is appropriate. The reliability goal is 0.90. Find the multiple of rating life required, xD, and the catalog rating C10 with which to enter a bearing table. Choose a 02-series deep-groove ball bearing from Table 112, and estimate the reliability in use.

An angular-contact, inner ring rotating, 02-series ball bearing is required for an application in which the life requirement is 40 kh at 520 rev/min. The design radial load is 725 lbf. The application factor is 1.4. The reliability goal is 0.90. Find the multiple of rating life xD required and the catalog rating C10 with which to enter Table 112. Choose a bearing and estimate the existing reliability in service.

The other bearing on the shaft of Prob. 112 is to be a 03-series cylindrical roller bearing with inner ring rotating. For a 2235-lbf radial load, find the catalog rating C10 with which to enter Table 113. The reliability goal is 0.90. Choose a bearing and estimate its reliability in use.

Problems 112 and 113 raise the question of the reliability of the bearing pair on the shaft. Since the combined reliabilities R is R1R2, what is the reliability of the two bearings (probability that either or both will not fail) as a result of your decisions in Probs. 112 and 113? What does this mean in setting reliability goals for each of the bearings of the pair on the shaft?

Combine Probs. 112 and 113 for an overall reliability of R 5 0.90. Reconsider your selections, and meet this overall reliability goal.

A straight (cylindrical) roller bearing is subjected to a radial load of 20 kN. The life is to be 8000 h at a speed of 950 rev/min and exhibit a reliability of 0.95. What basic load rating should be used in selecting the bearing from a catalog of manufacturer 2 in Table 116?

Two ball bearings from different manufacturers are being considered for a certain application. Bearing A has a catalog rating of 2.0 kN based on a catalog rating system of 3 000 hours at

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 116. Assume an application factor of one.

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 116. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2.

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 116. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2.

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 116. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2.

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 116. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2.

For the shaft application defined in Prob. 377, p. 153, the input shaft EG is driven at a constant speed of 191 rev/min. Obtain a Basic Load Rating for a ball bearing at A for a life of 12 kh with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 116.

For the shaft application defined in Prob. 379, p. 153, the input shaft EG is driven at a constant speed of 280 rev/min. Obtain a Basic Load Rating for a cylindrical roller bearing at A for a life of 14 kh with a 98 percent reliability, assuming distribution data from manufacturer 2 in Table 116.

An 02-series single-row deep-groove ball bearing with a 65-mm bore (see Tables 111 and 112 for specifications) is loaded with a 3-kN axial load and a 7-kN radial load. The outer ring rotates at 500 rev/min. (a) Determine the equivalent radial load that will be experienced by this particular bearing. (b) Determine whether this bearing should be expected to carry this load with a 95 percent reliability for 10 kh

An 02-series single-row deep-groove ball bearing with a 30-mm bore (see Tables 111 and 112 for specifications) is loaded with a 2-kN axial load and a 5-kN radial load. The inner ring rotates at 400 rev/min. (a) Determine the equivalent radial load that will be experienced by this particular bearing. (b) Determine the predicted life (in revolutions) that this bearing could be expected to give in this application with a 99 percent reliability.

An 02-series single-row deep-groove ball bearing is to be selected from Table 112 for the application conditions specified in the table. Assume Table 111 is applicable if needed. Specify the smallest bore size from Table 112 that can satisfy these conditions.

An 02-series single-row deep-groove ball bearing is to be selected from Table 112 for the application conditions specified in the table. Assume Table 111 is applicable if needed. Specify the smallest bore size from Table 112 that can satisfy these conditions.

An 02-series single-row deep-groove ball bearing is to be selected from Table 112 for the application conditions specified in the table. Assume Table 111 is applicable if needed. Specify the smallest bore size from Table 112 that can satisfy these conditions.

An 02-series single-row deep-groove ball bearing is to be selected from Table 112 for the application conditions specified in the table. Assume Table 111 is applicable if needed. Specify the smallest bore size from Table 112 that can satisfy these conditions.

An 02-series single-row deep-groove ball bearing is to be selected from Table 112 for the application conditions specified in the table. Assume Table 111 is applicable if needed. Specify the smallest bore size from Table 112 that can satisfy these conditions.

The shaft shown in the figure is proposed as a preliminary design for the application defined in Prob. 372, p. 152. The effective centers of the gears for force transmission are shown. The dimensions for the bearing surfaces (indicated with cross markings) have been estimated. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh with a 95 percent reliability in each bearing, assuming distribution data from manufacturer 2 in Table 116. Use an application factor of 1.2. (a) Obtain a Basic Load Rating for a ball bearing at the right end. (b) Use an online bearing catalog to find a specific bearing that satisfies the needed Basic Load Rating and the geometry requirements. If necessary, indicate appropriate adjustments to the dimensions of the bearing surface.

Repeat the requirements of Prob. 1127 for the bearing at the left end of the shaft

The shaft shown in the figure is proposed as a preliminary design for the application defined in Prob. 373, p. 152. The effective centers of the gears for force transmission are shown. The dimensions for the bearing surfaces (indicated with cross markings) have been estimated. The shaft rotates at 900 rev/min, and the desired bearing life is 12 kh with a 98 percent reliability in each bearing, assuming distribution data from manufacturer 2 in Table 116. Use an application factor of 1.2. (a) Obtain a Basic Load Rating for a ball bearing at the right end. (b) Use an online bearing catalog to find a specific bearing that satisfies the needed Basic Load Rating and the geometry requirements. If necessary, indicate appropriate adjustments to the dimensions of the bearing surface.

Repeat the requirements of Prob. 1129 for the bearing at the left end of the shaft.

Shown in the figure is a gear-driven squeeze roll that mates with an idler roll. The roll is designed to exert a normal force of 35 lbf/in of roll length and a pull of 28 lbf/in on the material being processed. The roll speed is 350 rev/min, and a design life of 35 kh is desired. Use an application factor of 1.2, and select a pair of angular-contact 02-series ball bearings from Table 112 to be mounted at 0 and A. Use the same size bearings at both locations and a combined reliability of at least 0.92, assuming distribution data from manufacturer 2 in Table 116.

The figure shown is a geared countershaft with an overhanging pinion at C. Select an angularcontact ball bearing from Table 112 for mounting at O and an 02-series cylindrical roller bearing from Table 113 for mounting at B. The force on gear A is FA 5 600 lbf, and the shaft is to run at a speed of 420 rev/min. Solution of the statics problem gives force of bearings against the shaft at O as RO 5 2387j 1 467k lbf, and at B as RB 5 316j 2 1615k lbf. Specify the bearings required, using an application factor of 1.2, a desired life of 40 kh, and a combined reliability goal of 0.95, assuming distribution data from manufacturer 2 in Table 116.

The figure is a schematic drawing of a countershaft that supports two V-belt pulleys. The countershaft runs at 1500 rev/min and the bearings are to have a life of 60 kh at a combined reliability of 0.98, assuming distribution data from manufacturer 2 in Table 116. The belt tension on the loose side of pulley A is 15 percent of the tension on the tight side. Select deepgroove bearings from Table 112 for use at O and E, using an application factor of unity.

A gear-reduction unit uses the countershaft depicted in the figure. Find the two bearing reactions. The bearings are to be angular-contact ball bearings, having a desired life of 50 kh when used at 300 rev/min. Use 1.2 for the application factor and a reliability goal for the bearing pair of 0.96, assuming distribution data from manufacturer 2 in Table 116. Select the bearings from Table 112.

The worm shaft shown in part a of the figure transmits 1.2 hp at 500 rev/min. A static force analysis gave the results shown in part b of the figure. Bearing A is to be an angular-contact ball bearing selected from Table 112, mounted to take the 555-lbf thrust load. The bearing at B is to take only the radial load, so an 02-series cylindrical roller bearing from Table 113 will be employed. Use an application factor of 1.2, a desired life of 30 kh, and a combined reliability goal of 0.99, assuming distribution data from manufacturer 2 in Table 116. Specify each bearing

In bearings tested at 2000 rev/min with a steady radial load of 18 kN, a set of bearings showed an L10 life of 115 h and an L80 life of 600 h. The basic load rating of this bearing is 39.6 kN. Estimate the Weibull shape factor b and the characteristic life u for a two-parameter model. This manufacturer rates ball bearings at 1 million revolutions.

A 16-tooth pinion drives the double-reduction spur-gear train in the figure. All gears have 25 pressure angles. The pinion rotates ccw at 1200 rev/min and transmits power to the gear train. The shaft has not yet been designed, but the free bodies have been generated. The shaft speeds are 1200 rev/min, 240 rev/min, and 80 rev/min. A bearing study is commencing with a 10-kh life and a gearbox bearing ensemble reliability of 0.99, assuming distribution data from manufacturer 2 in Table 116. An application factor of 1.2 is appropriate. For each shaft, specify a matched pair of 02-series cylindrical roller bearings from Table 113.

Estimate the remaining life in revolutions of an 02-30 mm angular-contact ball bearing already subjected to 200 000 revolutions with a radial load of 18 kN, if it is now to be subjected to a change in load to 30 kN.

The same 02-30 angular-contact ball bearing as in Prob. 1138 is to be subjected to a two-step loading cycle of 4 min with a loading of 18 kN, and one of 6 min with a loading of 30 kN. This cycle is to be repeated until failure. Estimate the total life in revolutions, hours, and loading cycles.

A countershaft is supported by two tapered roller bearings using an indirect mounting. The radial bearing loads are 560 lbf for the left-hand bearing and 1095 for the right-hand bearing. An axial load of 200 lbf is carried by the left bearing. The shaft rotates at 400 rev/min and is to have a desired life of 40 kh. Use an application factor of 1.4 and a combined reliability goal of 0.90, assuming distribution data from manufacturer 1 in Table 116. Using an initial K 5 1.5, find the required radial rating for each bearing. Select the bearings from Fig. 1115.

For the shaft application defined in Prob. 374, p. 152, perform a preliminary specification for tapered roller bearings at C and D. A bearing life of 108 revolutions is desired with a 90 percent combined reliability for the bearing set, assuming distribution data from manufacturer 1 in (a) 3 8 12 9 2 60 T E C A F c b a D B 20 T 16 T 80 T 16 Developed view (b) Developed view 2385 1113 1530 3280 E 8 3 895 417 F c 874 2274 3280 1530 C 6 2 3 613 1314 393 613 1314 657 D b 239 111 A 9 2 1075 502 B a Problem 1137 (a) Drive detail; (b) force analysis on shafts. Forces in pounds; linear dimensions in inches. bud98209_ch11_561-608.indd Page 607 10/28/13 10:52 AM f-494 /204/MH01996/bud98209_disk1of1/0073398209/bud98209_pagefiles 608 Mechanical Engineering Design Table 116. Should the bearings be oriented with direct mounting or indirect mounting for the axial thrust to be carried by the bearing at C? Assuming bearings are available with K 5 1.5, find the required radial rating for each bearing. For this preliminary design, assume an application factor of one.

For the shaft application defined in Prob. 376, p. 153, perform a preliminary specification for tapered roller bearings at A and B. A bearing life of 500 million revolutions is desired with a 90 percent combined reliability for the bearing set, assuming distribution data from manufacturer 1 in Table 116. Should the bearings be oriented with direct mounting or indirect mounting for the axial thrust to be carried by the bearing at A? Assuming bearings are available with K 5 1.5, find the required radial rating for each bearing. For this preliminary design, assume an application factor of one

An outer hub rotates around a stationary shaft, supported by two tapered roller bearings as shown in Fig. 1123. The device is to operate at 250 rev/min, 8 hours per day, 5 days per week, for 5 years, before bearing replacement is necessary. A reliability of 90 percent on each bearing is acceptable. A free body analysis determines the radial force carried by the upper bearing to be 12 kN and the radial force at the lower bearing to be 25 kN. In addition, the outer hub applies a downward force of 5 kN. Assuming bearings are available from manufacturer 1 in Table 116 with K 5 1.5, find the required radial rating for each bearing. Assume an application factor of 1.2.

The gear-reduction unit shown has a gear that is press fit onto a cylindrical sleeve that rotates around a stationary shaft. The helical gear transmits an axial thrust load T of 250 lbf as shown in the figure. Tangential and radial loads (not shown) are also transmitted through the gear, producing radial ground reaction forces at the bearings of 875 lbf for bearing A and 625 lbf for bearing B. The desired life for each bearing is 90 kh at a speed of 150 rev/min with a 90 percent reliability. The first iteration of the shaft design indicates approximate diameters of 11 8 in at A and 1 in at B. Assuming distribution data from manufacturer 1 in Table 116, select suitable tapered roller bearings from Fig. 1115.

A certain application requires a ball bearing with the inner ring rotating, with a design life of 25 kh at a speed of 350 rev/min. The radial load is 2.5 kN and an application factor of 1.2 is appropriate. The reliability goal is 0.90. Find the multiple of rating life required, \(x_D\), and the catalog rating \(C_10\) with which to enter a bearing table. Choose a 02-series deep-groove ball bearing from Table 11–2, and estimate the reliability in use.

An angular-contact, inner ring rotating, 02-series ball bearing is required for an application in which the life requirement is 40 kh at 520 rev/min. The design radial load is 725 lbf. The application factor is 1.4. The reliability goal is 0.90. Find the multiple of rating life \(x_D\) required and the catalog rating \(C_10\) with which to enter Table 11–2. Choose a bearing and estimate the existing reliability in service.

The other bearing on the shaft of Prob. 11–2 is to be a 03-series cylindrical roller bearing with inner ring rotating. For a 2235-lbf radial load, find the catalog rating \(C_10\) with which to enter Table 11–3. The reliability goal is 0.90. Choose a bearing and estimate its reliability in use.

Problems 11–2 and 11–3 raise the question of the reliability of the bearing pair on the shaft. Since the combined reliabilities R is \(R_1 R_2\), what is the reliability of the two bearings (probability that either or both will not fail) as a result of your decisions in Probs. 11–2 and 11–3? What does this mean in setting reliability goals for each of the bearings of the pair on the shaft?

Combine Probs. 11–2 and 11–3 for an overall reliability of R = 0.90. Reconsider your selections, and meet this overall reliability goal.

A straight (cylindrical) roller bearing is subjected to a radial load of 20 kN. The life is to be 8000 h at a speed of 950 rev/min and exhibit a reliability of 0.95. What basic load rating should be used in selecting the bearing from a catalog of manufacturer 2 in Table 11–6?

Two ball bearings from different manufacturers are being considered for a certain application. Bearing A has a catalog rating of 2.0 kN based on a catalog rating system of 3 000 hours at 500 rev/min. Bearing B has a catalog rating of 7.0 kN based on a catalog that rates at \(10^6\) cycles. For a given application, determine which bearing can carry the larger load.

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-8 2 kN \(10^9\) rev 90%

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-9 800 lbf 12 kh, 350 rev/min 90%

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-10 4 kN 8 kh, 500 rev/min 90%

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-11 650 lbf 5 yrs, 40 h/week, 400 rev/min 95%

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-12 9 kN \(10^8\) rev 99%

For the bearing application specifications given in the table for the assigned problem, determine the Basic Load Rating for a ball bearing with which to enter a bearing catalog of manufacturer 2 in Table 11–6. Assume an application factor of one. Problem Number Radial Load Design Life Desired Reliability 11-13 11 kips 20 kh, 200 rev/min 99%

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2. Problem Number Original Problem, Page Number 11–14* 3–68, 151

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2. Problem Number Original Problem, Page Number 11–15* 3–69, 151

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2. Problem Number Original Problem, Page Number 11–16* 3–70, 151

For the problem specified in the table, build upon the results of the original problem to obtain a Basic Load Rating for a ball bearing at C with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh. Use an application factor of 1.2. Problem Number Original Problem, Page Number 11–17* 3–71, 151

For the shaft application defined in Prob. 3–77, p. 153, the input shaft EG is driven at a constant speed of 191 rev/min. Obtain a Basic Load Rating for a ball bearing at A for a life of 12 kh with a 95 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6.

For the shaft application defined in Prob. 3–79, p. 153, the input shaft EG is driven at a constant speed of 280 rev/min. Obtain a Basic Load Rating for a cylindrical roller bearing at A for a life of 14 kh with a 98 percent reliability, assuming distribution data from manufacturer 2 in Table 11–6.

An 02-series single-row deep-groove ball bearing with a 65-mm bore (see Tables 11–1 and 11–2 for specifications) is loaded with a 3-kN axial load and a 7-kN radial load. The outer ring rotates at 500 rev/min. (a) Determine the equivalent radial load that will be experienced by this particular bearing. (b) Determine whether this bearing should be expected to carry this load with a 95 percent reliability for 10 kh.

An 02-series single-row deep-groove ball bearing with a 30-mm bore (see Tables 11–1 and 11–2 for specifications) is loaded with a 2-kN axial load and a 5-kN radial load. The inner ring rotates at 400 rev/min. (a) Determine the equivalent radial load that will be experienced by this particular bearing. (b) Determine the predicted life (in revolutions) that this bearing could be expected to give in this application with a 99 percent reliability.

An 02-series single-row deep-groove ball bearing is to be selected from Table 11–2 for the application conditions specified in the table. Assume Table 11–1 is applicable if needed. Specify the smallest bore size from Table 11–2 that can satisfy these conditions. Problem Number Radial Load Axial Load Design Life Ring Rotating Desired Reliability 11-22 8 kN 0 kN \(10^9\) rev Inner 90%

An 02-series single-row deep-groove ball bearing is to be selected from Table 11–2 for the application conditions specified in the table. Assume Table 11–1 is applicable if needed. Specify the smallest bore size from Table 11–2 that can satisfy these conditions. Problem Number Radial Load Axial Load Design Life Ring Rotating Desired Reliability 11-23 8 kN 2 kN 10 kh, 400 rev/min Inner 99%

An 02-series single-row deep-groove ball bearing is to be selected from Table 11–2 for the application conditions specified in the table. Assume Table 11–1 is applicable if needed. Specify the smallest bore size from Table 11–2 that can satisfy these conditions. Problem Number Radial Load Axial Load Design Life Ring Rotating Desired Reliability 11-24 8 kN 3 kN \(10^8\) rev Outer 90%

An 02-series single-row deep-groove ball bearing is to be selected from Table 11–2 for the application conditions specified in the table. Assume Table 11–1 is applicable if needed. Specify the smallest bore size from Table 11–2 that can satisfy these conditions. Problem Number Radial Load Axial Load Design Life Ring Rotating Desired Reliability 11-23 10 kN 5 kN 12 kh, 300 rev/min Inner 95%

An 02-series single-row deep-groove ball bearing is to be selected from Table 11–2 for the application conditions specified in the table. Assume Table 11–1 is applicable if needed. Specify the smallest bore size from Table 11–2 that can satisfy these conditions. Problem Number Radial Load Axial Load Design Life Ring Rotating Desired Reliability 11-26 9 kN 3 kN \(10^8\) rev Outer 99%

The shaft shown in the figure is proposed as a preliminary design for the application defined in Prob. 3–72, p. 152. The effective centers of the gears for force transmission are shown. The dimensions for the bearing surfaces (indicated with cross markings) have been estimated. The shaft rotates at 1200 rev/min, and the desired bearing life is 15 kh with a 95 percent reliability in each bearing, assuming distribution data from manufacturer 2 in Table 11–6. Use an application factor of 1.2. (a) Obtain a Basic Load Rating for a ball bearing at the right end. (b) Use an online bearing catalog to find a specific bearing that satisfies the needed Basic Load Rating and the geometry requirements. If necessary, indicate appropriate adjustments to the dimensions of the bearing surface.

Repeat the requirements of Prob. 11–27 for the bearing at the left end of the shaft.

The shaft shown in the figure is proposed as a preliminary design for the application defined in Prob. 3–73, p. 152. The effective centers of the gears for force transmission are shown. The dimensions for the bearing surfaces (indicated with cross markings) have been estimated. The shaft rotates at 900 rev/min, and the desired bearing life is 12 kh with a 98 percent reliability in each bearing, assuming distribution data from manufacturer 2 in Table 11–6. Use an application factor of 1.2. (a) Obtain a Basic Load Rating for a ball bearing at the right end. (b) Use an online bearing catalog to find a specific bearing that satisfies the needed Basic Load Rating and the geometry requirements. If necessary, indicate appropriate adjustments to the dimensions of the bearing surface.

Repeat the requirements of Prob. 11–29 for the bearing at the left end of the shaft.

Shown in the figure is a gear-driven squeeze roll that mates with an idler roll. The roll is designed to exert a normal force of 35 lbf/in of roll length and a pull of 28 lbf/in on the material being processed. The roll speed is 350 rev/min, and a design life of 35 kh is desired. Use an application factor of 1.2, and select a pair of angular-contact 02-series ball bearings from Table 11–2 to be mounted at 0 and A. Use the same size bearings at both locations and a combined reliability of at least 0.92, assuming distribution data from manufacturer 2 in Table 11–6.

The figure shown is a geared countershaft with an overhanging pinion at C. Select an angular contact ball bearing from Table 11-2 for mounting at O and an 02-series cylindrical roller bearing from Table 11-3 for mounting at B. The force on gear A is \(F_A=600 \mathrm{lbf}\), and the shaft is to run at a speed of 420 rev/min. Solution of the statics problem gives force of bearings against the shaft at O as \(\mathbf{R}_O=-387 \mathbf{j}+467 \mathbf{k} \mathrm{lbf}\), and at B as \(\mathbf{R}_B=316 \mathbf{j}-1615 \mathbf{k}\) lbf. Specify the bearings required, using an application factor of 1.2, a desired life of 40 kh, and a combined reliability goal of 0.95, assuming distribution data from manufacturer 2 in Table 11-6.

The figure is a schematic drawing of a countershaft that supports two V-belt pulleys. The countershaft runs at 1500 rev/min and the bearings are to have a life of 60 kh at a combined reliability of 0.98, assuming distribution data from manufacturer 2 in Table 11–6. The belt tension on the loose side of pulley A is 15 percent of the tension on the tight side. Select deep groove bearings from Table 11–2 for use at O and E, using an application factor of unity.

A gear-reduction unit uses the countershaft depicted in the figure. Find the two bearing reactions. The bearings are to be angular-contact ball bearings, having a desired life of 50 kh when used at 300 rev/min. Use 1.2 for the application factor and a reliability goal for the bearing pair of 0.96, assuming distribution data from manufacturer 2 in Table 11–6. Select the bearings from Table 11–2.

The worm shaft shown in part a of the figure transmits 1.2 hp at 500 rev/min. A static force analysis gave the results shown in part b of the figure. Bearing A is to be an angular-contact ball bearing selected from Table 11–2, mounted to take the 555-lbf thrust load. The bearing at B is to take only the radial load, so an 02-series cylindrical roller bearing from Table 11–3 will be employed. Use an application factor of 1.2, a desired life of 30 kh, and a combined reliability goal of 0.99, assuming distribution data from manufacturer 2 in Table 11–6. Specify each bearing.

In bearings tested at 2000 rev/min with a steady radial load of 18 kN, a set of bearings showed an \(L_10\) life of 115 h and an \(L_80\) life of 600 h. The basic load rating of this bearing is 39.6 kN. Estimate the Weibull shape factor b and the characteristic life \(\theta\) for a two-parameter model. This manufacturer rates ball bearings at 1 million revolutions.

A 16-tooth pinion drives the double-reduction spur-gear train in the figure. All gears have \(25^{\circ}\) pressure angles. The pinion rotates ccw at 1200 rev/min and transmits power to the gear train. The shaft has not yet been designed, but the free bodies have been generated. The shaft speeds are 1200 rev/min, 240 rev/min, and 80 rev/min. A bearing study is commencing with a 10-kh life and a gearbox bearing ensemble reliability of 0.99, assuming distribution data from manufacturer 2 in Table 11–6. An application factor of 1.2 is appropriate. For each shaft, specify a matched pair of 02-series cylindrical roller bearings from Table 11–3.

Estimate the remaining life in revolutions of an 02-30 mm angular-contact ball bearing already subjected to 200 000 revolutions with a radial load of 18 kN, if it is now to be subjected to a change in load to 30 kN.

The same 02-30 angular-contact ball bearing as in Prob. 11–38 is to be subjected to a two-step loading cycle of 4 min with a loading of 18 kN, and one of 6 min with a loading of 30 kN. This cycle is to be repeated until failure. Estimate the total life in revolutions, hours, and loading cycles.

A countershaft is supported by two tapered roller bearings using an indirect mounting. The radial bearing loads are 560 lbf for the left-hand bearing and 1095 for the right-hand bearing. An axial load of 200 lbf is carried by the left bearing. The shaft rotates at 400 rev/min and is to have a desired life of 40 kh. Use an application factor of 1.4 and a combined reliability goal of 0.90, assuming distribution data from manufacturer 1 in Table 11–6. Using an initial K = 1.5, find the required radial rating for each bearing. Select the bearings from Fig. 11–15.

For the shaft application defined in Prob. 3–74, p. 152, perform a preliminary specification for tapered roller bearings at C and D. A bearing life of \(10^8\) revolutions is desired with a 90 percent combined reliability for the bearing set, assuming distribution data from manufacturer 1 in Table 11–6. Should the bearings be oriented with direct mounting or indirect mounting for the axial thrust to be carried by the bearing at C? Assuming bearings are available with K = 1.5, find the required radial rating for each bearing. For this preliminary design, assume an application factor of one.

For the shaft application defined in Prob. 3–76, p. 153, perform a preliminary specification for tapered roller bearings at A and B. A bearing life of 500 million revolutions is desired with a 90 percent combined reliability for the bearing set, assuming distribution data from manufacturer 1 in Table 11–6. Should the bearings be oriented with direct mounting or indirect mounting for the axial thrust to be carried by the bearing at A? Assuming bearings are available with K = 1.5, find the required radial rating for each bearing. For this preliminary design, assume an application factor of one.

An outer hub rotates around a stationary shaft, supported by two tapered roller bearings as shown in Fig. 11–23. The device is to operate at 250 rev/min, 8 hours per day, 5 days per week, for 5 years, before bearing replacement is necessary. A reliability of 90 percent on each bearing is acceptable. A free body analysis determines the radial force carried by the upper bearing to be 12 kN and the radial force at the lower bearing to be 25 kN. In addition, the outer hub applies a downward force of 5 kN. Assuming bearings are available from manufacturer 1 in Table 11–6 with K = 1.5, find the required radial rating for each bearing. Assume an application factor of 1.2.

The gear-reduction unit shown has a gear that is press fit onto a cylindrical sleeve that rotates around a stationary shaft. The helical gear transmits an axial thrust load T of 250 lbf as shown in the figure. Tangential and radial loads (not shown) are also transmitted through the gear, producing radial ground reaction forces at the bearings of 875 lbf for bearing A and 625 lbf for bearing B. The desired life for each bearing is 90 kh at a speed of 150 rev/min with a 90 percent reliability. The first iteration of the shaft design indicates approximate diameters of \(1\frac{1]{8}\) in at A and 1 in at B. Assuming distribution data from manufacturer 1 in Table 11–6, select suitable tapered roller bearings from Fig. 11–15.