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Apply the relations of Prob. 15-7 to Ex. 15-1 and find the Brinell case hardness of the gears for equal allowable load Wt in bending and wear. Check your work by reworking Ex. 15-1 to see if you are correct. How would you go about the heat treatment of the gears?
EXAMPLE 15-1 A pair of identical straight-tooth miter gears listed in a catalog has a diametral pitch of 5 at the large end, 25 teeth, a 1.10-in face width, and a 20° normal pressure angle; the gears are grade 1 steel through-hardened with a core and case hardness of 180 Brinell. The gears are uncrowned and intended for general industrial use. They have a quality number of Qv = 7. It is likely that the application intended will require outboard mounting of the gears. Use a safety factor of 1, a 107 cycle life, and a 0.99 reliability.
- (a) For a speed of 600 rev/min find the power rating of this gearset based on AGMA bending strength.
- (b) For the same conditions as in part (a) find the power rating of this gearset based on AGMA wear strength.
- (c) For a reliability of 0.995, a gear life of 109 revolutions, and a safety factor of SF = SH = 1.5, find the power rating for this gearset using AGMA strengths.
15-7 In straight-bevel gearing, there are some analogs to Eqs. (14-44) and (14-45) pp. 766 and 767, respectively. If we have a pinion core with a hardness of (HB)11 and we try equal power ratings, the transmitted load Wt can be made equal in all four cases. It is possible to find these relations:
| Core | Case | |
| Pinion | (HB)11 | (HB)12 |
| Gear | (HB)21 | (HB)22 |
- (a) For carburized case-hardened gear steel with core AGMA bending strength (sat)G and pinion core strength (sat)P, show that the relationship is
This allows (HB)21 to be related to (HB)11.
- (b) Show that the AGMA contact strength of the gear case (sac)G can be related to the AGMA core bending strength of the pinion core (sat)P by
If factors of safety are applied to the transmitted load Wt, then SH =
- (c) Show that the AGMA contact strength of the gear (sac)G is related to the contact strength of the pinion (sac)P by
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Chapter 15 Solutions
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- The upper half of a compound Epicyclic gearset is shown in Figure, with input shaft I rotating at a constant speed of 700 rpm in a clockwise direction and generating 12 kW input power. The Annulus wheel A2 is coupled to an auxiliary gear N on shaft X and forms a compound wheel with gear O. The Annulus A1 rotates in a counter-clockwise direction at a speed of 5,300 rpm. Calculate the following using this condition: Number of gear teeth:P1 = 30 , A1 = 120P2 = 50 , A2 = 140N = 60 , O = 120 a) The output shaft O (NO), shaft X (NX), and gear ratio speed and direction (n). b) Calculate the speed and direction of output shaft O (NO), shaft X (NX), and gear ratio if Annulus wheel A1 is locked (n). c) The braking torque (Tb) that must be applied to Annulus wheel A1 to keep it stationary (magnitude and direction), assuming gear transmission efficiency of 90%.arrow_forwardProvide the complete step-by-step solution, given data, conversion of units, and sketch for this problem. A turbine at 30,000 rpm is used to drive a reduction gear delivering 3 hp at 3,000rpm. The gears are 20 degrees involute herringbone gears of 28 pitch and 2 1/8 ineffective width. The pinion has 20 teeth with a helix angle of 23 deg. Determine theload normal to the tooth surface. A. 20.4 lbs B. 24.4 lbs C. 28.4 lbs D. 32.4arrow_forwardTwo spur gears transmit 36kW with a velocity ratio of 2:1. The speed of the smaller driving gear is 100rpm. The centre distance between the shafts is to be as near as possible to 920mm. If m=10 and all-21MPa, determine a) Diameter of the shafts b)PCD for each wheel c)Number of teeth on each wheel d) Actual centre distance [ e) Width of the teetharrow_forward
- The top half of a compound Epicyclic gearset is shown in Figure, with input shaft I rotating at a constant speed of 700 rpm in a clockwise direction and generating 12 kW input power. The Annulus wheel A2 isform a compound wheel with gear O and connected to an auxiliary gear N on shaft X. . The Annulus A1 rotates in a counter-clockwise direction at a speed of 5,300 rpm. Calculate the following using this condition: The speed and direction of output shaft O (NO), shaft X (NX) and gear ratio (n). If Annulus wheel A1 is locked calculate the speed and direction of output shaft O (NO), shaft X (NX) and gear ratio (n). The braking torque (Tb) (magnitude and direction) that must be applied to Annulus wheel A1 to hold it stationary, assuming gear transmission efficiency is 90%. Number of gear teeth:P1 = 30 , A1 = 120P2 = 50 , A2 = 140N = 60 , O = 120arrow_forwardpair of 14.5 degree full depth spur gears are used to transmit 20kW between shafts 40 cm apart running at 1440 rp.m and 360 r.p.m respectively. The allowable stress and BHN are 600 MN/m, 160 and 550 MN/mm 140 respectively for the pinion and gear. Find the module, number ot teeth and face width. CheCk tor wear.arrow_forwardA Coniflex, straight-tooth bevel gearset is supported on shafts with centerlines intersecting at a 90° angle. The gear is straddle mounted between closely positioned bearings, and the pinion overhangs its support bearing. The 15-tooth pinion rotates at 900 rpm, driving the 60-tooth gear, which has a di- ametral pitch of 6, pressure angle of 20°, and face width of 1.25 inches. The material for both gears is through-hardened Grade I steel with a hardness of BHN 300 (see Figure). It is desired to have a reliability of 90 percent, a design life of 10° cy- cles, and a governing safety factor of 2.5. Estimate the maximum horsepower that can be transmitted by this gear re- ducer while meeting all of the design specifications given.arrow_forward
- Bearing stress 5. Please provide proper discussion and illustration also complete solution and clear solution please thank you A solid shaft is designed to transmit 50kN @ 1800 rpm to a gear by means of 156 mm long key with square cross-section. The shaft diameter is 35.6mm. What should the cross-section be in mm2 to resist shearing, if the allowable shear stress on the key is 20 MPa?arrow_forward13–31 Shaft a in the figure has a power input of 75 kW at a speed of 1000 rev/min in the counterclockwise direction. The gears have a module of 5 mm and a 20° pressure angle. Gear 3 is an idler.(a) Find the force F3b that gear 3 exerts against shaft b.arrow_forwardA gear train is composed of four helical gears with the three shaft axes in a single plane, as shown in the figure. The gears have a normal pressure angle of 20 and a 30 helix angle. Gear is the driver, and is rotating counterclockwise as viewed from the top. Shaft b is an idler and the transmitted load from gear 2 to gear 3 is 500 Ibf. The gears on shaft b both have a normal diametral pitch of 7 teeth/in and have 54 and 14 teeth, respectively. Find the forces exerted by gears 3 and 4 on shaft barrow_forward
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