Power transmission. Components used to transmit power: gears, belt, clutch and brakes. Gear (Stresses) act on the tooth Lewis formula and AGMA

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1 Power transmission Components used to transmit power: gears, belt, clutch and brakes. Failure Types Gear (Stresses) Bending: resulted from bending stress.

1 1 Power transmission Components used to transmit power: gears, belt, clutch and brakes. Failure Types Gear (Stresses) Bending: resulted from bending stress. t act on the tooth Lewis formula and AGMA Pitting: Scoring: resulted from surface stress Repetition of high contact stresses resulted from insufficiency of lubrication M 6F h I / c bt t Basic Formula: 2 Where: F t : tangential force h: dend + add b: face width t : tooth thickness

2 2 Assumptions 1. The full load is applied to the tip of a single tooth 2. The radial component is negligible 3. The load distributes uniformly across the full face width 4. Forces which are due to tooth sliding friction are negligible 5. Stress concentration in the tooth fillet is negligible English Unit Metric unit

3 Example 1: 3 A 19 tooth is made of 300 Bhn steel. The gear is shaped by hobbing. This spur Gear Pinion transmit 15 hp at a pinion speed of 360 rpm to a 77 tooth of the same material gear. The face width is 1.7 in, pressure angle = 20 0 and P = 6 in -1. a. Using Lewis formula, calculate the stresses due to bending of the pinion and gear. In reality 1. The load is applied at the pitch circle 2. Contact Ratio: The load is shared by 1.4 to 1.8 tooth 3. Manufacturing accuracy 4. Stress concentration at the base of the tooth 5. Degree of shock loading 6. Accuracy and rigidity of the mounting 7. Moment of inertia and attached rotating members J: spur gear geometry factor

4 Kv: velocity or dynamic factor 4

5 English Unit A: B: C: D: E: 78 V Highest Precision, shaved and ground 78 78 V High precision, shaved and ground 78 50 V 50 Precision, shaved and ground 1200 V 1200 Hobs, shaping cutters 600

5 5 English Unit A: B: C: D: E: 78 V Highest Precision, shaved and ground V High precision, shaved and ground V 50 Precision, shaved and ground 1200 V 1200 Hobs, shaping cutters 600 V 600 Hobs from cutter Note: V in ft/min SI Unit A: B: C: 5.56 V Highest Precision, shaved and ground V High precision, shaved and ground V Precision, shaved and ground 3.56

6 D: E: 6.1 V 6.1 Hobs, shaping cutters 3.05 V 3.05 Hobs from cutter 6 Note: V in m/s Hobbing Process Ko: Overload correction factor Km: Overload correction factor

7 7 Example A 19 tooth is made of 300 Bhn steel. The gear is shaped by hobbing. This spur Gear Pinion transmit 15 hp at a pinion speed of 360 rpm to a 77 tooth of the same material gear. The face width is 1.7 in, pressure angle = 20 0 and P = 6 in -1. b. Using Eq , calculate the stresses due to bending.

Fatigue Strength 8 S n : standard R. R. Moore endurance limit CL: load factor = 1.0 for bending loads CG: gradient factor = 1.0 for P > 5 and 0.85 <= 5 Cs: surface factor from Figure 8.13.

8 Fatigue Strength 8 S n : standard R. R. Moore endurance limit CL: load factor = 1.0 for bending loads CG: gradient factor = 1.0 for P > 5 and 0.85 <= 5 Cs: surface factor from Figure if not mentioned, assume the surface is machined kr: reliability factor, CR, Table 15.3 kt: temperature factor, CT, For steel gears use kt = 1.0 (assumption T < 160 o F) 620 k t 400 T for ( T > 160 o F) kms: mean stress factor (1.0 for idler gear subjected to two-way bending) and 1.4 (for input and output gear: one way bending)

9 Alternating and mean bending stresses 9 Based on idler gear (two-way bending) will produce Ft P a KvKoKm bj 0 For other gear (one-way bending gear) m ( Ft / 2) P a KvKoK bj ( Ft / 2) P m KvKoK bj m m To check whether the gear will have infinite life Example a m 1 S S n A 19 tooth is made of 300 Bhn steel. The gear is shaped by hobbing. This spur Gear Pinion transmit 15 hp at a pinion speed of 360 rpm to a 77 tooth of the same material gear. The face width is 1.7 in, pressure angle = 20 0 and P = 6 in -1. ut

10 c. Determine whether the gear will have infinite. If yes, determine the factor safety against infinite life. Possible Surface deterioration i. Abrasive wear: presence of foreign particles ii.

10 10 c. Determine whether the gear will have infinite. If yes, determine the factor safety against infinite life. Possible Surface deterioration i. Abrasive wear: presence of foreign particles ii. Scoring: when inadequate lubrication at high speed iii. Pitting and spalling: contact between surfaces. Failure i) and ii) can be eliminated with proper care. Therefore, failure iii) has to be taken into account during design. Therefore, the surface stresses: H C P Ft bd I p K v K o K m C P = elastic coefficient

11 11 If the pinion and gear are made of different material CP P g E P I E sin cos R I 2 R 1 Where R is the ration of gear and pinion diameters sin cos R I 2 R 1 d G R d P G = Poisson Ration (Table C-1) E = Modulus of Elasticity (Table C-1)

12 Surface Fatigue Strength 12 Life Factor (CLI) Reliability Factor (CR)

13 13 Safety 1.1 to 1.5 is sufficient Example A 19 tooth is made of 300 Bhn steel. The gear is shaped by hobbing. This spur Gear Pinion transmit 15 hp at a pinion speed of 360 rpm to a 77 tooth of the same material gear. The face width is 1.7 in, pressure angle = 20 0 and P = 6 in -1. d) Calculate the safety factor of the surface stress against fatigue surface stress. Design Based Problem Your task is design a pair of gear with the following design specification. Power to be transferred W = 2 hp Rotational speed of the input gear n= 500 rpm Pressure angle = 20 deg Gear will rotate in both directions Gear is been hobbed Gear material is Carbon Steel with Bhn = 150 Design Objective - To get the smallest gear diameter - To reduce the speed by 1.25 Start your estimation with P = 24 pitch gear

14 Example 1: 14 A 19 tooth is made of 300 Bhn steel. The gear is shaped by hobbing. This spur Gear Pinion transmit 15 hp at a pinion speed of 360 rpm to a 77 tooth of the same material gear. The face width is 1.7 in, pressure angle = 20 0 and P = 6 in -1. a) Using Lewis formula, calculate the stresses due to bending of the pinion and gear. Using Eq , calculate the stresses due to bending. b) Using Eq , calculate the stresses due to bending with light shock power to moderate shock machinery. The mounting is assumed to be less rigid. c) Determine whether the gear will have infinite. If yes, determine the factor safety against infinite life. d) Calculate the safety factor of the surface stress against fatigue surface stress.

Lecture 13 BEVEL GEARS

Lecture 13 BEVEL GEARS CONTENTS 1. Bevel gear geometry and terminology 2. Bevel gear force analysis 3. Bending stress analysis 4. Contact stress analysis 5. Permissible bending fatigue stress 6. Permissible