6Bevel GearsAre used to transmit rotary motion between intersecting shaftsTeeth are formed on conical surfaces, the teeth could be straight or spiral.
7Worm GearsAre used for transmitting motion between non parallel and non transmitting shafts, Depending on the number of teeth engaged called single or double. Worm gear mostly used when speed ratio is quiet high, 3 or more
8Nomenclature Smaller Gear is Pinion and Larger one is the gear In most application the pinion is the driver, This reduces speed but it increases torque.
10pitch circle, theoretical circle upon which all calculation is based p, Circular pitch, p the distance from one teeth to the next, along the pitch circle. p=πd/Nm, module=d/N pitch circle/number of teethp= πmP, Diametral Pitch P=N/dpP= π
11Angle Φ has the values of 20 or 25 degrees. Angle 14 Angle Φ has the values of 20 or 25 degrees. Angle 14.5 have been also used.Gear profile is constructed from the base circle. Then additional clearance are given.
12How Gear Profile is constructed A1B1=A1A0, A2B2=2 A1A0 , etc
13Standard Gear Teeth Item 20o full depth 20o Stub 25o full depth Addendum a1/P0.8/PDedendum1.25/PClearance f0.25/P0.2/PWorking depth2/P1.6/PWhole depth2.25/P1.8/PTooth thickness1.571/PFace width9/P<b<13/P
15Planetary Gear train You can get high torque ratio in a smaller space There are two inputs to the planetary gears, RPM of sun and Ring, The out put is the speed of the arm.
16Example of planetary Gear train Gear 1, sun , RPM 1200, Number of teeth 20,Planet Gear , Number of teeth 30Ring Gear, Rotates RPM 120, and teeth of 80,¼ horse power, find the speed of the arm and torque on the ring.Alternatively you may have Certain Out put Torque requirements
17Transmitted LoadWith a pair of gears or gear sets, Power is transmitted by the force developed between contacting Teeth
18These forces have to be corrected for dynamic effects , we discuss later, considering AGMA factors d in, RPM rev./min, V in/secd in, n rpm, V fpmToque lb-inV fpmT= N.m, V m/s, F Newton
19Some Useful Relations F=33000hp/V V fpm English system Metric System KW=(FV)/1000=Tn/9549F newton, V m/s, n rpm, T, N.mhp= FV/745.7=Tn/7121
20Bending Strength of the a Gear Tooth Earlier Stress Analysis of the Gear Tooth was based onA full load is applied to the tip of a single toothThe radial load is negligibleThe load is uniform across the widthNeglect frictional forcesThe stress concentration is negligibleThis equation does not consider stress concentration, dynamic effects, etc.
21Design for the Bending Strength of a Gear Tooth: The AGMA Method U.S. CustomarySI unitsBending stress at the root of the toothTransmitted tangential loadOverload factorVelocity factorDiameteral pitch, PFace widthMetric modueSize factorMounting factorGeometry factor
22Your stress should not exceed allowable stress Allowable bending stressBending StrengthLife factorTemperature factorReliability factor
23Overload Factor - KoThere are comprehensive charts available with application factors. These encapsulate the load on the driven machine.Power sources think of hand driving bike wheel. Finger on spokes continuously – uniform load; hand driving tire – 3 times per cycle requires higher value of instantaneous force; hand driving tire – 1 time per cycle require even higher instantaneous value of force.Lifts with high lifting speeds have dynamic effects (oscillation on elastic rope/chain) which cause overload
24Dynamic Factor - KvE – A: are different manufacturing operations with increasing levels of precisionE: Form cutters used on milling machines cut teeth then index gearD: shaping cutters - Fellows gear shaper uses a vertically oscillating ram that is forced radially inward to the tooth depth and then rotated with gear to form teethC , B: have finishing methods applied to keep tooth form precise honing or grinding where gear is run meshed with and abrasive substance; shaving is designed to remove fine chips from the surfaceA: kept to tight tolerancesEven with steady loads tooth impact can cause shock loadingImpact strength depends on quality of the gear and the speed ofgear teeth (pitch line velocity)-Gears are classified with respect to manufacturing tolerances:-Qv 3 – 7, commercial quality-Qv 8 – 12, precision-Graphs are available which chart Kv for different quality factors
25Load Distribution Factor - Km Ideally your face width should be less than your pinion diameterValues up to 1.5 Dp are not too bad but the value should definitely be less than 2DpIdeally face-width times Pitch (b*P) should be between 9 and 12.Initial estimate of fP = 11 can be used.-Failure greatly depends on how load is distributed across face-Accurate mounting helps ensure even distribution-For larger face widths even distribution is difficult to attain-Note formula depends on face width which has to be estimated for initial iteration-Form goal: b < Dp; 6 < b*P < 16
26Reliability Factor - KR -Adjusts for reliability other than 99%- KR = – ln (1-R) 0.5 < R <0.99- KR = 0.50 – ln (1-R) < R <
27AGMA Geometry Factor - J Updated Lewis Form Factor includes effect of stress concentration at filletDifferent charts for different pressure anglesAvailable for Precision Gears where we can assume load sharing (upper curves)HPSTC – highest point of single tooth contactAccount for meshing gear and load sharing (contact ratio > 1)Single tooth contact conservative assumption (bottom curve)J = ln N (20 degree)J = ln N (25 degree)Formula allow J to be programmed – quicker iteration to solution
28Bending Strength No. – St, Fatigue bending strength Quality Grade varies between 0 – 3 depending on how closely quality items like surface hardness, core hardness, etc. are controlled0 – indicates no control1 – good quality (modest control)2 – premium quality (close control)3 (super quality) – absolute control-Tabulated Data similar to fatigue strength-Range given because value depends on Grade-Based on life of 107 cycles and 99% reliability
29St – Analytical Estimate Hb – Brinnell HardnessWe have seen earlier in the semester that HB is related to Su and subsequently to SeAnalytical formula allow you to quickly modify design for iterative solution-Through hardened steel gears-Different charts for different manufacturing methods-Grade 1 – good qualitySt = 77.3 HB + 12,800-Grade 2 – premium qualitySt = 102 HB + 16,400
30Bending Strength Life Factor- KL -Adjusts for life goals other than 107 cycles-Fatigue effects vary with material properties and surface finishes-KL = N N>3E6rpm reach 3 million cycles in 1 day of serviceAnalytic formulas help with iterative nature of gearing solutions
31Example: A conveyor drive involving heavy-shock torsional loading is operated by an electric motor, the speed ratio is 1:2 and the pinion has Diameteral pitch P=10 in-1, and number of teeth N=18 and face width of b=1.5 in. The gear has Brinnel hardness of 300 Bhn. Find the maximum horspower that can be transmitted, using AGMA formula.