Tooth thickness Dedendum. Addendum. Centre distance Nominal

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Marcus Richards
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1 FORMULAS SPUR GEARS TO FIND:- PCD ØD MODULE No. of TEETH CP ADDENDUM DEDENDUM MODULE No. of TEETH x MOD (mm) (No. of TEETH + ) x MOD (mm) 5.4 MODULE CP π (mm) PCD MODULE (mm) MODULE x π (mm) MODULE (mm) 1.4 x MOD 1.5 x MOD (0.5-1 MOD) (1.5-8 MOD) IMPERIAL No. of TEETH (ins) No. of TEETH + (ins) π CP 5.4 PCD x π (ins) 1 (ins) 1.4 (-4 ) 1.5 (-6 ) CORRECTED TEETH FOR 8-17 TEETH ON REQUEST OR WHERE LISTED Corrected PCD Corrected ØD (No. of Teeth + 1) x MOD [(No. of Teeth + 1) / ] (No. of Teeth + 3) x MOD [(No. of Teeth + 3) / ] Our SPUR GEARS are made to give * Approx. backlash at standard centres. Housing centres should be nominal mm. PCD (A) + PCD (B) FROM NOMINAL CENTRES mm * Depends on pitch INCREASE IN BACKLASH mm Whole depth Addendum + Dedendum Tooth thickness Dedendum Addendum Centre distance Nominal Outside Diameter Whole depth PCD A PCD B CP Root clearance

FORMULAS HELICAL GEARS TO FIND:- MODULE IMPERIAL P.C.D. ØD (NORMAL) MODULE No.

HELIX )< PCD + ( x MOD) (mm) 5.4 MODULE CP (mm) π PCD x COS.

3mm* approx. backlash at standard centres.

of TEETH (ins) x COS. HELIX )< PCD. + π CP 5.4 ( x COS.

dependent on pitch LEFT hand runs with LEFT hand.

2 FORMULAS HELICAL GEARS TO FIND:- MODULE IMPERIAL P.C.D. ØD (NORMAL) MODULE No. of TEETH CP (NORMAL) ADDENDUM Lead No. of TEETH x MOD (mm) COS. HELIX )< PCD + ( x MOD) (mm) 5.4 MODULE CP (mm) π PCD x COS. )< (mm) MODULE MODULE x π (mm) MODULE PCD x π TAN )< Made to give mm* approx. backlash at standard centres. Housing centres should be nominal mm. No. of TEETH (ins) x COS. HELIX )< PCD. + π CP 5.4 ( x COS. )< ) x PCD π (ins) 1 (ins) Where HELIX )< HELIX Angle CROSSED AXIS * dependent on pitch LEFT hand runs with LEFT hand. RIGHT hand runs with RIGHT hand. DRIVER DRIVER DRIVER DRIVER DRIVEN DRIVEN DRIVEN DRIVEN PARALLEL AXIS LEFT hand runs with RIGHT hand. DRIVER General Direction of Force DRIVEN 7. 49

3 LOAD CALCULATIONS SPUR & HELICAL SPUR GEARS, BSI 436 : 19 ALLOWABLE TANGENTIAL LOAD, P.A. Xb factor for strength WEAR Xc factor for wear Xc Z Sc F Y Strength factor lbs. K Z Zone factor Sc* Material rating (surface stress) Sb* Material rating (bending stress) STRENGTH K Pitch factor 0.8 power Xb Y Sb F lbs. F Face width (inches) 5.4 MOD 1N 0.48 lbs Allowable tangential teeth load lbs Torque lbs ins x pcd The lowest of the four values for pinion and wheel gives the gear rating. The normal rating for gears is based on 1 hours/day. HELICAL GEARS, BSI 436 : 19 Xb Xc Y Z Sc* Sb* K F α ALLOWABLE TANGENTIAL LOAD OF HELIX ANGLE, P.A. Factor for Strength Factor for Wear Strength Factor Zone Factor Material Rating (surface stress) Material Rating (bending stress) Pitch Factor 0.8 Power Face Width (inches) Helix Angle 5.4 MOD WEAR * Please refer to Material Strength page for values Xc Z* Sc F K STRENGTH Xb Y* Sb F 1.33 Cos Sec Cos Cosine Sec Secant Torque lbs ins x.113 Torque Nm 1kg 1 lb 1N x Torque Nm Torque lbs Ins.113 lbs. lbs. *for other helix angles multiply Z by 0.75 sec α *for other helix angles multiply Y by 1.33 cos α

4 SPEED FACTORS SPUR & HELICAL Xc FOR WEAR Rpm Xb FOR STRENGTH Rpm RUNNING TIME (hours per day) RUNNING TIME (hours per day)

5 ZONE FACTORS SPUR & HELICAL SPUR GEARS, P.A. Z No. of NUMBER OF TEETH ON PINION Teeth in Gear Rack HELICAL GEARS FOR HELIX ANGLE, P.A For other helix angles, multiply zone factor by 0.75 x Sec helix angle NOTE 0.75 x Sec No. of NUMBER OF TEETH ON PINION Teeth in Gear Rack Rack Z

6 STRENGTH FACTORS SPUR & HELICAL HELICAL GEARS WITH HELIX ANGLE, P.A. AND P.A. SPUR GEARS For other helix angles, multiply zone strength by 1.33 x Cos helix angle. NOTE: 1.33 x Cos No. of NO. OF TEETH ON MATING GEAR OR PINION Teeth in Gear Rack Rack The zone factor (Z) is a factor dependent on the total contact between mating teeth and the radii of curvature of the tooth surfaces. Internal Gears - The zone factor for internal gears shall be equal to that for the same combination of external teeth multiplied by:- ( R + 1 ) 0.8 Power RRatio R The Strength Factor (Y) is a factor dependent on the number of teeth in contact, the cantilever strength of an individual tooth, and the distribution of load over the face of the tooth. Internal Gears - The strength factor for the pinion gearing with an internal gear shall be the same as that for a pinion of the same number of teeth gearing with a rack. The strength factor for the internal gear shall be the same as that of a rack gearing with a pinion having the same number of teeth as the actual pinion, multiplied by:- (1 + 3) T where T is the number of teeth in the internal gear Idler Gears The idler gears in which the teeth make contact on one side with the driving gears and on the other with the driven gears, should be calculated on the Y normal basis for wear, but the speed co-efficient used in calculating the load capacity for strength must be half the normal value. Multiple Contact - If a gear makes contact on the same set of flanks with more than one other gear, the equivalent running time per day is to be taken as the sum of those applying to the separate mating gears. GEAR LUBRICATION Given the variety of gear types, service requirements, environmental influences and service temperature ranges, the choice of lubricant is an important factor for the service reliability and service life of the machine concerned. The following are recommended, on the basis of DIN (Selection of Lubricants for Gears):- 1. At peripheral velocities up to v m/s: High-consistency adhesive lubricants are used on large open gears.. At peripheral velocities up to v 4 m/s: Here, splash-lubrication using a soft gear-grease is customary into which the gear wheel dips 3. At peripheral velocities up to v 15 m/s: Here it is oil splash-lubrication which predominates 4. At peripheral velocities above v 15 m/s: In this range, oil spray lubrication is required in most cases

7 FORMULAS BEVEL GEARS TO FIND:- PINION WHEEL PCD PITCH ANGLE (for 90 shaft angle) PITCH ANGLE (for shaft angle <90 ) PITCH ANGLE (for shaft angle > 90 ) n d or n x mod (ins) (mm) n No. of teeth. -1 n Y tan (deg) N -1 sin Σ Y tan N [( + cos Σ n ) ] [ ] Σ SHAFT ANGLE -1 sin (1 Σ) Y tan N cos (1 Σ) n N D or N x mod (ins) (mm) N No. of teeth. Γ 90 Y (deg) Γ Σ Y Γ Σ Y D CONE DISTANCE Ao See Pinion * see note sin Γ * A pitch angle (Σ) greater than 90 indicates an internal gear. Please contact Technical to determine if the gear can be cut. FORMULAS - WORMS & WHEELS TO FIND:- MODULE IMPERIAL ØD TANGENT OF THE LEAD ANGLE CENTRE DISTANCE TO FIND:- MODULE IMPERIAL THROAT Ø (No. of TEETH + ) x MOD (mm) No. of TEETH + (inches) TIP Ø P.C.D. REDUCTION RATIO ( x MODULE) + PCDmm MODULE x No. of STARTS PCD PCD (Worm) + PCD (Wheel) in mm (No. of TEETH + 3) x MOD (mm) No. of TEETH x MOD (mm) No. of TEETH in WHEEL No. of STARTS in WORM PCD (WORM) + PCD (WHEEL) CENTRE DISTANCE + PCD CP x No. of STARTS PCD x π PCD (Worm) + PCD (Wheel) No. of TEETH + 3 (inches) No. of TEETH (inches) Our WORMS and WORMWHEELS are made to give mm backlash at standard centres. Housing centres should be nominal mm

8 LOAD CALCULATIONS BEVELS BEVEL GEARS, BSI 545 : 1949 Xc Z Sc* Sb* K F Xb Y C P Based on 1 hour day. Cone Distance C ALLOWABLE TANGENTIAL LOAD AT PITCH RADIUS factor for wear Zone factor (see chart) Material rating (surface stress) Material rating (bending stress) Pitch factor 0.8 power Face width (inches) for strength Strength factor Cone distance (inches) PCD" of Gear x Sin Pitch Angle of Gear Allowable tangential load at PCR Torque lbs ins x PCD Pitch Angle of Gear 90 Pitch Angle of Pinion Pitch Angle of Pinion tan 1 No. of Teeth Pinion No. of Teeth Gear WEAR Xc Sc Z F C - F x K x x C STRENGTH Xb Sb Y F C - F x P ( 1.1 x C) lbs ( ) lbs. lbs. The lowest of the four values for pinion and wheel gives the gear rating. The normal rating for gears is based on 1 hours/day. hrs per day Approx Total hours life Wear multiply by Strength multiply by Gear torque allowable Tangential Load x PCD Allowable Tangential Load Gear Torque x PCD * Please refer to Material Strength page for values

9 BEVEL GEARS ZONE FACTORS Z maximum ratio 4:1 Gleason No. of NUMBER OF TEETH IN MATING GEAR Teeth in Gear STRENGTH FACTORS Y No. of NUMBER OF TEETH IN MATING GEAR Teeth in Gear SPEED FACTORS Xc FOR WEAR Rpm Xc Rpm Xc Rpm Xc Rpm Xc SPEED FACTORS Xb FOR STRENGTH Rpm Xc Rpm Xc Rpm Xc Rpm Xc

10 LOAD CALCULATIONS WORMS & WHEELS BSI 71 : 1937 TORQUE CAPACITY (based on 1 hour day) Xc factor for wear (see chart) 0.18 Constant value Sc Material rating - surface stress (see tables) Sb Material rating - bending stress (see tables) efw Effective face width of wheel Xb factor for strength 1.8 Constant value M Addendum in inches D Wheel PCD Lr Length at root of wheel teeth in inches Cosα Cosine of lead angle of worm WEAR 0.18 Sc Xc efw D 1.8 lbs. Ins. STRENGTH 1.8Sb Xb Lr M D Cosα L r e fw lbs. ins. Rubbing Feet/Minute Worm pcd x π x RPM 1 efw x Addendum ( Worm O/D Addendum ) x secant lead angle Lr x θ x Worm O/D Cosθ ( x PCD of Worm ) O/D of Worm Note : The lowest of the four values for Worm and Wheel gives the gear rating. Angle θ Cos -1 θ Wear Strength 1/6 1/4 1/ RUNNING TIME (hours per day) Xc and Xb to be divided by factors below for different hrs/day

11 SPEED FACTORS WORMS & WHEELS Xc FOR WEAR RPM of RUBBING SPEED (ft/min) Worm & Wheel Xb FOR STRENGTH RPM Factor RPM Factor RPM Factor RPM Factor

12 BENDING AND SURFACE STRESS FACTORS WORMS & WHEELS Wheel WHEEL Materials Phosphor Bronze Sand Cast A Phosphor Bronze Chill Cast Phosphor Bronze Centrifugally Cast B Cast Iron (Gray) Worm C D E WORM Materials 0.4% Carbon Steel Normalised 0.55% Carbon Steel Normalised Low-carbon CasehardeningSteel 3.5% Nickel Casehardening Steel 5% Nickel Casehardening Steel 3.5% Nickel Chromium Casehardening Steel High Nickel-chrom Casehardening Steel Bending Stress Factor Sb Pounds per Sq. In. 7,000 8,500,000 6,000 Find surface stress factor Sc for wheel, under worm material classification letter A B C D E 900* 0* * 0* 0* * HPC standard wheels use sand cast PB *For standard hardened worms use Sc value for wheels Bending Stress Factor Sb Pounds per Sq. In.,000,000 7,000,000 47,000 47,000 47,000 Find surface stress factor Sc for wheel, under worm material classification letter NOTE: Section E - hardened, ground and polished. HPC Standard Worms Unhardened - Sc Sb 17,000 Hardened - Sc 00 Sb 7,000 * Maximum permissible rubbing speeds, 500 feet per minute. Should not be used except for hand operated gearing. 0 A B C D E

13 EFFICIENCY WORMS & WHEELS Excluding bearing and oil churning losses. Values are based on PB Wheels and case hardened and ground and polished worms lubricated by mineral oil. The efficiency may be improved after the running in period. NOTE: As HPC standard worms are not hardened ground and polished lower efficiency values can be expected. TAN )< Efficiency (%) [ TAN (θ + )< ) ] X θ TAN -1 f )< Lead Angle f Coefficient of friction INPUT TORQUE Output Torque x Ratio Efficiency OUTPUT TORQUE Input Torque x Ratio x Efficiency Coefficients of Friction for Worm Gearing Rubbing Ft. per min. Coefficients of Friction Rubbing Ft. per min. Coefficients of Friction Rubbing Ft. per min. Coefficients of Friction Rubbing Ft. per min. Coefficients of Friction

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