Shaft Equations: All of the following equations are general equations; you may need to use modifying...
1
Shaft Equations: Shaft Equations: All of the following equations are general equations; you may need All of the following equations are general equations; you may need to use modifying factors such as: loading factors, pulsating power to use modifying factors such as: loading factors, pulsating power source factors, safety factors, and stress concentration factors. source factors, safety factors, and stress concentration factors. Basic equations in torsion: Basic equations in torsion: Solid round shaft: Solid round shaft: 3 16 D T Hollow round shaft: Hollow round shaft: ) ( 16 4 4 0 0 i D D D T Basic equation in bending: Basic equation in bending: Solid shaft: Solid shaft: 3 32 D M Hollow shaft: Hollow shaft: ) ( 32 4 4 i o o D D D M Combined loading (solid shaft): Combined loading (solid shaft): 2 2 3 max ) 8 ( ) 8 ( 2 T D F M D (18-4) max sheer (18-4) max sheer stress stress † 2 2 3 48 ) 8 ( 4 ' T D F M D (18-5) Von Mises stress (18-5) Von Mises stress † Torsional deflection: Torsional deflection: 4 32 D G L T Radians Radians Factors of Safety: Factors of Safety: n S y all 2 (18-6) Max sheer stress (18-6) Max sheer stress theory theory † n S y ' (18-7) (18-7) Distortion energy Distortion energy † T= torque (lb-in, N-m) T= torque (lb-in, N-m) F= axial load (lb, N) F= axial load (lb, N) Sy= yield strength Sy= yield strength n = factor of safety n = factor of safety = sheer stress (psi, Pa) = sheer stress (psi, Pa) D= diameter of solid shaft (in, m) D= diameter of solid shaft (in, m) D o o = outside diameter of solid shaft (in, m) = outside diameter of solid shaft (in, m) D i = inside diameter of solid shaft (in, m) = inside diameter of solid shaft (in, m) M= bending moment (lb-in, N-m) M= bending moment (lb-in, N-m) L= length of shaft (in, m) L= length of shaft (in, m) G= sheer modulus (psi, Pa) G= sheer modulus (psi, Pa) Use of Shafts Use of Shafts A machine is a device that converts some sort of energy into work. In many machines A machine is a device that converts some sort of energy into work. In many machines transfer of power (energy with respect to time) is needed in order to perform this transfer of power (energy with respect to time) is needed in order to perform this task. Shafts are efficient devices for transferring power and can commonly be found task. Shafts are efficient devices for transferring power and can commonly be found in machines world wide. in machines world wide. Shaft Definitions Shaft Definitions Shaft- Shaft- A rotating member used to transmit power. A rotating member used to transmit power. Axle- Axle- A stationary member used as support for rotating elements such as wheels, idler gears, etc. A stationary member used as support for rotating elements such as wheels, idler gears, etc. Spindle- Spindle- A short shaft or axle (e.g., head-stock spindle of a lathe). A short shaft or axle (e.g., head-stock spindle of a lathe). Stub shaft- Stub shaft- A shaft that is integral with a motor, engine or prime mover and is of a size, shape, and projection A shaft that is integral with a motor, engine or prime mover and is of a size, shape, and projection as to permit easy connection to other shafts as to permit easy connection to other shafts Line shaft- Line shaft- A shaft connected to a prime mover and used to transmit power to one or several machines A shaft connected to a prime mover and used to transmit power to one or several machines Jackshaft- Jackshaft- (Sometimes called countershaft). A short shaft that connects a prime mover with a line shaft or a (Sometimes called countershaft). A short shaft that connects a prime mover with a line shaft or a machine machine Flexible shaft- Flexible shaft- A connector which permits transmission of motion between two members whose axes are at A connector which permits transmission of motion between two members whose axes are at an angle with each other an angle with each other Shapes Shapes Most shafts are round but they can come in many different shapes including square and Most shafts are round but they can come in many different shapes including square and octagonal. Keys and notches can also result in some unique shapes. octagonal. Keys and notches can also result in some unique shapes. Hollow Versus Solid Shafts Hollow Versus Solid Shafts Hollow shafts are lighter than solid shafts of comparable strength but are more Hollow shafts are lighter than solid shafts of comparable strength but are more expensive to manufacture. Thusly hollow shafts are primarily only used when weight is expensive to manufacture. Thusly hollow shafts are primarily only used when weight is critical. For example the propeller shafts on rear wheel drive cars require critical. For example the propeller shafts on rear wheel drive cars require lightweight shafts in order to handle speeds within the operating range of the lightweight shafts in order to handle speeds within the operating range of the vehicle. vehicle. Material Material Processing Processing Tips Tips o To resist wear, case-hardening methods such as, nitriding, cyaniding, flame To resist wear, case-hardening methods such as, nitriding, cyaniding, flame and induction hardening can be used. and induction hardening can be used. o Cold-drawn steel bars have better physical properties than hot-rolled bars of Cold-drawn steel bars have better physical properties than hot-rolled bars of similar steels. Cold-drawing causes residual surface stresses that offset similar steels. Cold-drawing causes residual surface stresses that offset higher endurance strength due to hot-rolling. higher endurance strength due to hot-rolling. o Cutting keyways and slots in the shaft may cause warping due to the relief of Cutting keyways and slots in the shaft may cause warping due to the relief of surface stresses. surface stresses. o Peening and other processes that produce surface compressive stresses Peening and other processes that produce surface compressive stresses counteract the effect of fatigue stress. counteract the effect of fatigue stress. Rules of Deflection Rules of Deflection o Deflections should not cause mating gear teeth to Deflections should not cause mating gear teeth to separate more than about .005 in. They should also not separate more than about .005 in. They should also not cause the relative slope of the gear axes to change cause the relative slope of the gear axes to change more than .03 deg. more than .03 deg. o The shaft deflection across a plain bearing must be The shaft deflection across a plain bearing must be small compared to the oil film thickness. small compared to the oil film thickness. o The shaft angular deflection at a ball or roller The shaft angular deflection at a ball or roller bearing should generally not exceed .04 deg. unless the bearing should generally not exceed .04 deg. unless the bearing is self-aligning. bearing is self-aligning. o Rule Of Thumb: Restrict the torsional deflection to 1° Rule Of Thumb: Restrict the torsional deflection to 1° for every 20 diameters of length, sometimes less. for every 20 diameters of length, sometimes less. o Rule Of Thumb: In bending the deflection should be Rule Of Thumb: In bending the deflection should be limited to .01 in. per foot of length between supports. limited to .01 in. per foot of length between supports. General Principles General Principles o Keep shafts short, with bearings close to the applied loads. This will reduce Keep shafts short, with bearings close to the applied loads. This will reduce deflections and bending moments, and increases critical speeds. deflections and bending moments, and increases critical speeds. o Place necessary stress raisers away from highly stressed shaft regions if Place necessary stress raisers away from highly stressed shaft regions if possible. If unavoidable, use generous radii and good surface finishes. possible. If unavoidable, use generous radii and good surface finishes. Consider local surface-strengthening processes (shot-peening or cold- Consider local surface-strengthening processes (shot-peening or cold- rolling). rolling). o Use inexpensive steels for deflection-critical shafts because all steels have Use inexpensive steels for deflection-critical shafts because all steels have essentially the same modulus of elasticity. essentially the same modulus of elasticity. o Early in the design of any given shaft, an estimate is usually made of Early in the design of any given shaft, an estimate is usually made of whether strength or deflection will be the critical factor. A preliminary whether strength or deflection will be the critical factor. A preliminary design is based on that criterion; then, the remaining factor is checked. design is based on that criterion; then, the remaining factor is checked. Common Means of Securing Shafts Common Means of Securing Shafts † o Press and shrink fits Press and shrink fits o Cotter and washer Cotter and washer o Nut and washer Nut and washer o Sleeve Sleeve o Shaft shoulder Shaft shoulder o Ring and groove Ring and groove o Setscrew Setscrew o Split hub or tapered Split hub or tapered two-piece hub two-piece hub o Collar and screw Collar and screw o Pins Pins Common Elements Used To Transfer Torque Common Elements Used To Transfer Torque † o Keys Keys o Splines Splines o Setscrews Setscrews o Pins Pins o Press or shrink fits Press or shrink fits o Tapered fits Tapered fits Keyed Shafts Keyed Shafts www.robotcombat.com www.robotcombat.com www.theadamscompany.com/ www.theadamscompany.com/ shafts.htm shafts.htm REFERENCE: REFERENCE: † † Shigley, Joseph Edward, and Charles R. Shigley, Joseph Edward, and Charles R. Mischke. Mechanical Engineering Design. Mischke. Mechanical Engineering Design. Fifth Edition. Boston: McGraw Hill, 2002. Fifth Edition. Boston: McGraw Hill, 2002. POSTER BY: POSTER BY: AUSTIN HOWARD AUSTIN HOWARD BRADY CALVERT BRADY CALVERT ERIK VAN PATTEN ERIK VAN PATTEN
-
Upload
stewart-miller -
Category
Documents
-
view
212 -
download
0
Transcript of Shaft Equations: All of the following equations are general equations; you may need to use modifying...
Shaft Equations:Shaft Equations:All of the following equations are general equations; you All of the following equations are general equations; you may need to use modifying factors such as: loading factors, may need to use modifying factors such as: loading factors, pulsating power source factors, safety factors, and stress pulsating power source factors, safety factors, and stress concentration factors.concentration factors.
Basic equations in torsion:Basic equations in torsion:Solid round shaft:Solid round shaft:
3
16
D
T
Hollow round shaft:Hollow round shaft:
)(
1644
0
0
iDD
DT
Basic equation in bending:Basic equation in bending:Solid shaft:Solid shaft:
3
32
D
M
Hollow shaft: Hollow shaft:
)(
3244io
o
DD
DM
Combined loading (solid shaft):Combined loading (solid shaft):
22
3max)8()8(
2TDFM
D
(18-4) max sheer(18-4) max sheer stress stress††
22
348)8(
4' TDFM
D
(18-5) Von Mises stress(18-5) Von Mises stress††
Torsional deflection:Torsional deflection:
4
32
DG
LT
RadiansRadiansFactors of Safety:Factors of Safety:
n
Sy
all 2
(18-6) Max sheer stress(18-6) Max sheer stress theory theory††
n
Sy'
(18-7)(18-7) Distortion energyDistortion energy††
T= torque (lb-in, N-m)T= torque (lb-in, N-m)F= axial load (lb, N)F= axial load (lb, N)Sy= yield strengthSy= yield strengthn = factor of safety n = factor of safety = sheer stress (psi, Pa)= sheer stress (psi, Pa)D= diameter of solid shaft (in, m)D= diameter of solid shaft (in, m)DDo o = outside diameter of solid shaft (in, m)= outside diameter of solid shaft (in, m)
DDii= inside diameter of solid shaft (in, m)= inside diameter of solid shaft (in, m)
M= bending moment (lb-in, N-m)M= bending moment (lb-in, N-m)L= length of shaft (in, m)L= length of shaft (in, m)G= sheer modulus (psi, Pa)G= sheer modulus (psi, Pa)
Use of ShaftsUse of ShaftsA machine is a device that converts some sort of energy into work. In many machines transfer of A machine is a device that converts some sort of energy into work. In many machines transfer of power (energy with respect to time) is needed in order to perform this task. Shafts are efficient power (energy with respect to time) is needed in order to perform this task. Shafts are efficient
devices for transferring power and can commonly be found in machines world wide.devices for transferring power and can commonly be found in machines world wide.Shaft DefinitionsShaft Definitions
Shaft- Shaft- A rotating member used to transmit power.A rotating member used to transmit power.Axle- Axle- A stationary member used as support for rotating elements such as wheels, idler gears, etc.A stationary member used as support for rotating elements such as wheels, idler gears, etc.
Spindle- Spindle- A short shaft or axle (e.g., head-stock spindle of a lathe).A short shaft or axle (e.g., head-stock spindle of a lathe).Stub shaft- Stub shaft- A shaft that is integral with a motor, engine or prime mover and is of a size, shape, and A shaft that is integral with a motor, engine or prime mover and is of a size, shape, and
projection as to permit easy connection to other shaftsprojection as to permit easy connection to other shaftsLine shaft- Line shaft- A shaft connected to a prime mover and used to transmit power to one or several A shaft connected to a prime mover and used to transmit power to one or several
machinesmachinesJackshaft- Jackshaft- (Sometimes called countershaft). A short shaft that connects a prime mover with a line (Sometimes called countershaft). A short shaft that connects a prime mover with a line
shaft or a machineshaft or a machineFlexible shaft- Flexible shaft- A connector which permits transmission of motion between two members whose axes A connector which permits transmission of motion between two members whose axes
are at an angle with each otherare at an angle with each otherShapesShapes
Most shafts are round but they can come in many different shapes including square and octagonal. Most shafts are round but they can come in many different shapes including square and octagonal. Keys and notches can also result in some unique shapes.Keys and notches can also result in some unique shapes.
Hollow Versus Solid ShaftsHollow Versus Solid ShaftsHollow shafts are lighter than solid shafts of comparable strength but are more expensive to Hollow shafts are lighter than solid shafts of comparable strength but are more expensive to
manufacture. Thusly hollow shafts are primarily only used when weight is critical. For example the manufacture. Thusly hollow shafts are primarily only used when weight is critical. For example the propeller shafts on rear wheel drive cars require lightweight shafts in order to handle speeds within propeller shafts on rear wheel drive cars require lightweight shafts in order to handle speeds within
the operating range of the vehicle.the operating range of the vehicle.
MaterialMaterial ProcessingProcessing TipsTips
o To resist wear, case-hardening methods such as, nitriding, cyaniding, flame and induction To resist wear, case-hardening methods such as, nitriding, cyaniding, flame and induction hardening can be used.hardening can be used.
o Cold-drawn steel bars have better physical properties than hot-rolled bars of similar steels. Cold-drawn steel bars have better physical properties than hot-rolled bars of similar steels. Cold-drawing causes residual surface stresses that offset higher endurance strength due to Cold-drawing causes residual surface stresses that offset higher endurance strength due to hot-rolling.hot-rolling.
o Cutting keyways and slots in the shaft may cause warping due to the relief of surface Cutting keyways and slots in the shaft may cause warping due to the relief of surface stresses.stresses.
o Peening and other processes that produce surface compressive stresses counteract the Peening and other processes that produce surface compressive stresses counteract the effect of fatigue stress.effect of fatigue stress.
Rules of DeflectionRules of Deflection
o Deflections should not cause mating gear teeth to separate more Deflections should not cause mating gear teeth to separate more than about .005 in. They should also not cause the relative slope than about .005 in. They should also not cause the relative slope of the gear axes to change more than .03 deg.of the gear axes to change more than .03 deg.
o The shaft deflection across a plain bearing must be small The shaft deflection across a plain bearing must be small compared to the oil film thickness.compared to the oil film thickness.
o The shaft angular deflection at a ball or roller bearing should The shaft angular deflection at a ball or roller bearing should generally not exceed .04 deg. unless the bearing is self-aligning.generally not exceed .04 deg. unless the bearing is self-aligning.
o Rule Of Thumb: Restrict the torsional deflection to 1° for every 20 Rule Of Thumb: Restrict the torsional deflection to 1° for every 20 diameters of length, sometimes less.diameters of length, sometimes less.
o Rule Of Thumb: In bending the deflection should be limited to .01 Rule Of Thumb: In bending the deflection should be limited to .01 in. per foot of length between supports.in. per foot of length between supports.
General PrinciplesGeneral Principles
o Keep shafts short, with bearings close to the applied loads. This will reduce deflections and Keep shafts short, with bearings close to the applied loads. This will reduce deflections and bending moments, and increases critical speeds.bending moments, and increases critical speeds.
o Place necessary stress raisers away from highly stressed shaft regions if possible. If Place necessary stress raisers away from highly stressed shaft regions if possible. If unavoidable, use generous radii and good surface finishes. Consider local surface-unavoidable, use generous radii and good surface finishes. Consider local surface-strengthening processes (shot-peening or cold-rolling).strengthening processes (shot-peening or cold-rolling).
o Use inexpensive steels for deflection-critical shafts because all steels have essentially the Use inexpensive steels for deflection-critical shafts because all steels have essentially the same modulus of elasticity.same modulus of elasticity.
o Early in the design of any given shaft, an estimate is usually made of whether strength or Early in the design of any given shaft, an estimate is usually made of whether strength or deflection will be the critical factor. A preliminary design is based on that criterion; then, the deflection will be the critical factor. A preliminary design is based on that criterion; then, the remaining factor is checked.remaining factor is checked.
Common Means of Securing ShaftsCommon Means of Securing Shafts††
o Press and shrink fitsPress and shrink fits
o Cotter and washerCotter and washer
o Nut and washerNut and washer
o SleeveSleeve
o Shaft shoulderShaft shoulder
o Ring and grooveRing and groove
o SetscrewSetscrew
o Split hub or tapered two-Split hub or tapered two-piece hubpiece hub
o Collar and screwCollar and screw
o PinsPins
Common Elements Used To Transfer TorqueCommon Elements Used To Transfer Torque††
o KeysKeys
o SplinesSplines
o SetscrewsSetscrews
o PinsPins
o Press or shrink fitsPress or shrink fits
o Tapered fitsTapered fits
Keyed ShaftsKeyed Shafts
www.robotcombat.comwww.robotcombat.com
www.theadamscompany.com/ shafts.htm www.theadamscompany.com/ shafts.htm
REFERENCE:REFERENCE:
† † Shigley, Joseph Edward, and Charles R. Mischke. Shigley, Joseph Edward, and Charles R. Mischke. Mechanical Engineering Design. Fifth Edition. Mechanical Engineering Design. Fifth Edition. Boston: McGraw Hill, 2002.Boston: McGraw Hill, 2002.
POSTER BY:POSTER BY:
AUSTIN HOWARDAUSTIN HOWARD
BRADY CALVERTBRADY CALVERT
ERIK VAN PATTENERIK VAN PATTEN
