Modul 04 Spur Gear Design using AGMA

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Modul 04 Spur Gear Design using AGMA
IntroductionsSegment 1
3 MS3111 Elemen Mesin MAK © 2021
Teknik Mesin - FTMD ITB
and Calculation Methods for Involute Spur and
Helical Gear Teeth
Basic Concept
≥
≥ ,
Fundamental Formula Bending Stress

where for U.S. customary units (SI units), is the tangential transmitted load, lbf (N)
0 is the overload factor
is the dynamic factor
is the size factor
is the transverse diametral pitch
is the face width of the narrower member, in (mm)
is the load-distribution factor
is the rim-thickness factor
is the geometry factor for bending strength (which includes root fillet
stress-concentration factor ) is the transverse metric module
Factor of Safety Bending Stress
Metric unit:

where for U.S. customary units (SI units), is the allowable bending stress, lbf/in2 (N/mm2)
is the stress cycle factor for bending stress
are the temperature factors
are the reliability factors
is the AGMA factor of safety, a stress ratio =

Metric unit:

where , 0, , , , , , are the same terms as previous.
= 0 1

For U.S. customary units (SI units), the additional terms are:
is an elastic coefficient,
is the surface condition factor
1 is the pitch diameter of the pinion, in (mm)
is the geometry factor for pitting resistance
Factor of Safety Pitting resistance (contact Stress)
Metric unit:

where for U.S. customary units (SI units), is the allowable contact stress, lbf/in2 (N/mm2)
is the stress cycle life factor
are the hardness ratio factors for pitting resistance
are the temperature factors
are the reliability factors
is the AGMA factor of safety, a stress ratio
, =
Un-crowned GearsCrowned Gears
2
Crowning is the removal of a slight amount of the tooth from the center on out to the reach edge, making the tooth surface slightly convex. This method allows the gear to maintain contact in the central region of the tooth and permits avoidance of edge contact. Crowning should not be larger than necessary as it will reduce the tooth contact area, thus weakening the gears strength. End relief is the chamfering of both ends of tooth surface.
Crowning of Gear
Formula for Bending Stress
Formula for Wear
=

Transmitted Load,
Metric unit:
= 60000
where: Wt = transmitted load, kN H = power, kW d = gear diameter, mm n = speed, rev/min
=

US Customary unit:
where: Wt = transmitted load, lbf H = power, hp V = pitch-line velocity, ft/min
Overload factors: 0 The overload factor K0 is intended to make allowance for all externally applied loads in excess of the nominal tangential load in a particular application. These factors are established after considerable field experience in a particular application.
=

Dynamic factor: Dynamic factors are used to account for inaccuracies in the manufacture and meshing of gear teeth in action. Transmission error is defined as the departure from uniform angular velocity of the gear pair. Some of the effects that produce transmission error are:
• Inaccuracies produced in the generation of the tooth profile; these include errors in tooth spacing, profile lead, and runout
• Vibration of the tooth during meshing due to the tooth stiffness
• Magnitude of the pitch-line velocity
• Dynamic unbalance of the rotating members
• Wear and permanent deformation of contacting portions of the teeth
• Gear shaft misalignment and the linear and angular deflection of the shaft
• Tooth friction
=

Transmission accuracy level number: Quality number
• 3 – 7: most commercial-quality gears • 8 – 12: precision quality gears
=

where:
The maximum velocity*):
=
Dynamic factor:
Figure 14–9 Dynamic factor . The equations to these curves
Dynamic factor:
Size factor: The size factor reflects nonuniformity of material properties due to size. It depends upon
• Tooth size • Diameter of part • Ratio of tooth size to diameter of part • Face width • Area of stress pattern • Ratio of case depth to tooth size • Hardenability and heat treatment
= 1
= 1
= 1.192

Metric unit:
Lewis Form Factor: Y
Transverse Diametral Pitch,
= =
Face width of the narrower member,
For Spur Gear: For Helical Gear:
Face width, F
Load-distribution factor: The load-distribution factor modified the stress equations to reflect nonuniform distribution of load across the line of contact. The ideal is to locate the gear “midspan” between two bearings at the zero slope place when the load is applied. However, this is not always possible. The following procedure is applicable to
• Net face width to pinion pitch diameter ratio F/d ≤ 2
• Gear elements mounted between the bearings
• Face widths up to 40 in
• Contact, when loaded, across the full width of the narrowest member
=

The load-distribution factor modified the stress equations to reflect nonuniform distribution of load across the line of contact. The ideal is to locate the gear “midspan” between two bearings at the zero-slope place when the load is applied. However, this is not always possible. The following procedure is applicable to: • Net face width to pinion pitch diameter ratio Τ ≤ 2 • Gear elements mounted between the bearings • Face widths up to 40 in • Contact, when loaded, across the full width of the narrowest member
Load-distribution factor: = = 1 + +
=

The load-distribution factor under these conditions is currently given by
the face load distribution factor,
Load-distribution factor: =

Figure 14–10 Definition of distances S and S1 used in evaluating Cpm
Table 14–9 Empirical Constants A, B, and C for Eq. (14–34), Face Width F in Inches∗
Load-distribution factor: =

Rim-thickness factor: When the rim thickness is not sufficient to provide full support for the tooth root, the location of bending fatigue failure may be through the gear rim rather than at the tooth fillet.
=

Bending-strength geometry factor,
The AGMA factor J employs a modified value of the Lewis form factor, also denoted by Y; a fatigue stress-concentration factor Kf ; and a tooth load-sharing ratio mN . The resulting equation for for spur and helical gears is
=

It is important to note that the form factor in this Eq is not the Lewis factor at all. The value of Y here is obtained from calculations within AGMA 908-B89, and is often based on the highest point of single-tooth contact.
Bending-strength geometry factor: J =

AGMA 908-B89 Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth
=

=

=

=

=

Gear bending endurance strength equation or bending factor of safety
Bending strength: The values for gear bending strength, designated here as , are to be found in Figs. 14–2, 14–3, and 14–4, and in Tables 14–3 and 14–4. Since gear strengths are not identified with other strengths such as Sut , Se, or Sy as used elsewhere in this book, their use should be restricted to gear problems.
When two-way (reversed) loading occurs, as with idler gears, AGMA recommends using 70 percent of values. This is equivalent to Τ1 0.70 = . as a value of . The recommendation falls between the value of = 1.33 for a Goodman failure locus and = 1.66 for a Gerber failure locus.
=

Figure 14–2 Allowable bending stress number for through- hardened steels.
Bending strength:
Bending strength: =
Nitrided through-hardened steel gears
Figure 14–3 Allowable bending stress number for nitrided through- hardened steel gears
= 0.569 + 83.8
Bending strength: =

Figure 14–4 Allowable bending stress numbers for nitriding steel gears St .
nitriding steel gears

=
ANSI/AGMA 2001--D04 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth
Stress-cycle factors: The AGMA strengths are based on 107 load cycles applied. The purpose of the load cycle factors YN and ZN is to modify the gear strength for lives other than 107 cycles. • Note that for 107 cycles YN = ZN = 1 on each graph. • Note also that the equations for YN and ZN change on either side of 107
cycles. For life goals slightly higher than 107 cycles, the mating gear may be experiencing fewer than 107 cycles and the equations for (YN )P and (YN)G
can be different.
=
Stress-cycle factors: =
Figure 14–14 Repeatedly applied bending strength stress-cycle factor .
Bending Safety Factor,
= Τ
The ANSI/AGMA standards 2001-D04 and 2101-D04 contain a safety factors: • guarding against bending fatigue failure and • guarding against pitting failure.
=

Temperature factor:
For oil or gear-blank temperatures up to 250°F (120°C), use KT = Y = 1.0. For higher temperatures, the factor should be greater than unity. Heat exchangers may be used to ensure that operating temperatures are considerably below this value, as is desirable for the lubricant.
=1 For T < 120 °C ( 250 °F)
=
Reliability factor:
The reliability factor accounts for the effect of the statistical distributions of material fatigue failures.
=
= 0

Τ1 2
Elastic coefficient: Values of Cp may be computed directly from Eq. (14–13) or obtained from Table 14–8.
=
Transmitted Load,
Metric unit:
= 60000
where: Wt = transmitted load, kN H = power, kW d = gear diameter, mm n = speed, rev/min
= 33000

US Customary unit: where: Wt = transmitted load, lbf H = power, hp V = pitch-line velocity, ft/min
=
Overload factors: 0 The overload factor K0 is intended to make allowance for all externally applied loads in excess of the nominal tangential load in a particular application. These factors are established after considerable field experience in a particular application.
=
Dynamic factor: Dynamic factors are used to account for inaccuracies in the manufacture and meshing of gear teeth in action. Transmission error is defined as the departure from uniform angular velocity of the gear pair. Some of the effects that produce transmission error are:
• Inaccuracies produced in the generation of the tooth profile; these include errors in tooth spacing, profile lead, and runout
• Vibration of the tooth during meshing due to the tooth stiffness
• Magnitude of the pitch-line velocity
• Dynamic unbalance of the rotating members
• Wear and permanent deformation of contacting portions of the teeth
• Gear shaft misalignment and the linear and angular deflection of the shaft
• Tooth friction
Transmission accuracy level number: Quality number
• 3 – 7: most commercial-quality gears • 8 – 12: precision quality gears
=
where:
The maximum velocity*):
=
Dynamic factor: =

Figure 14–9 Dynamic factor . The equations to these curves
Dynamic factor: =

Size factor: The size factor reflects nonuniformity of material properties due to size. It depends upon
• Tooth size • Diameter of part • Ratio of tooth size to diameter of part • Face width • Area of stress pattern • Ratio of case depth to tooth size • Hardenability and heat treatment
= 1 = 1
Lewis Form Factor: Y
Load-distribution factor: The load-distribution factor modified the stress equations to reflect nonuniform distribution of load across the line of contact. The ideal is to locate the gear “midspan” between two bearings at the zero slope place when the load is applied. However, this is not always possible. The following procedure is applicable to
• Net face width to pinion pitch diameter ratio F/d ≤ 2
• Gear elements mounted between the bearings
• Face widths up to 40 in
• Contact, when loaded, across the full width of the narrowest member
=
Load-distribution factor:
The load-distribution factor modified the stress equations to reflect nonuniform distribution of load across the line of contact. The ideal is to locate the gear “midspan” between two bearings at the zero-slope place when the load is applied. However, this is not always possible. The following procedure is applicable to: • Net face width to pinion pitch diameter ratio Τ ≤ 2 • Gear elements mounted between the bearings • Face widths up to 40 in • Contact, when loaded, across the full width of the narrowest member
=
The load-distribution factor under these conditions is currently given by
the face load distribution factor,
=
Figure 14–10 Definition of distances S and S1 used in evaluating Cpm
Table 14–9 Empirical Constants A, B, and C for Eq. (14–34), Face Width F in Inches∗
=

Pitch diameter of Pinion,
=
Face width of the narrower member,
Face width, F
=
Surface Condition Factor, =

Τ
The surface condition factor or is used only in the pitting resistance equation. It depends on:
• Surface finish as affected by, but not limited to, cutting, shaving, lapping, grinding, shot-peening
• Residual stress • Plastic effects (work hardening)
Standard surface conditions for gear teeth have not yet been established. When a detrimental surface finish effect is known to exist, AGMA specifies
a value of greater than unity. For now: = . .
Surface-Strength Geometry factor: =

Τ
The factor is also called the pitting-resistance geometry factor by AGMA.
=
The load-sharing ratio,
The load-sharing ratio is equal to the face width divided by the minimum total length of the lines of contact. This factor depends on:
• the transverse contact ratio , • the face-contact ratio , • the effects of any profile modifications, and • the tooth deflection.
=
For spur gears: = 0
where: is the axial pitch is the face width.
The load-sharing ratio,
For helical gears having a face-contact ratio > 2.0, a conservative approximation is given by the equation: =
0.95
= cos where is the normal circular pitch.
= + 2 − 2 Τ1 2
+ + 2 − 2 Τ1 2
− + sin
= cos
where and are the pitch radii and and the base-circle radii of the pinion and gear, respectively
where is the normal base pitch and is the length of the line of action in the transverse plane.
GEAR CONTACT ENDURANCE STRENGTH EQUATION OR WEAR FACTOR OF SAFETY
, =
, = The allowable contact stress,
The values for the allowable contact stress, designated here as , are to be found in Fig. 14–5 and Tables 14–5, 14–6, and 14–7. AGMA allowable stress numbers (strengths) for bending and contact stress are for:
• Unidirectional loading • 10 million stress cycles (107 cycles) • 99 percent reliability
, = The allowable contact stress,
Figure 14–5 Contact-fatigue strength at 107 cycles and 0.99 reliability for through-hardened steel gears.
through-hardened steel gears.
A ll o
A ll o
Stress-cycle factors:
The AGMA strengths are based on 107 load cycles applied. The purpose of the load cycle factors YN and ZN is to modify the gear strength for lives other than 107 cycles.
• Note that for 107 cycles YN = ZN = 1 on each graph. • Note also that the equations for YN and ZN change on either side of 107
cycles. For life goals slightly higher than 107 cycles, the mating gear may be experiencing fewer than 107 cycles and the equations for (YN )P and (YN)G
can be different.
, =
Stress-cycle factors: , =
Hardness-ratio factor: The pinion generally has a smaller number of teeth than the gear and consequently is subjected to more cycles of contact stress. If both the pinion and the gear are through-hardened, then a uniform surface strength can be obtained by making the pinion harder than the gear. A similar effect can be obtained when a surface-hardened pinion is mated with a through hardened gear. The hardness-ratio factor CH is used only for the gear.
= 1.0 + − 1.0
, =
− 8.29 10−3
, =
Hardness-ratio factor: When surface-hardened pinions with hardness of 48 Rockwell C scale (Rockwell C 48) or harder are run with through-hardened gears (180–400 Brinell), a work hardening occurs. The factor is a function of pinion surface finish and the mating gear hardness.
= 1.0 + 450 − where: ′ = 0.0075 exp −0.0112 and is the surface finish of the pinion expressed as root-mean-square
roughness in in.
, =
, =
Pitting Safety Factor,
= Τ
The ANSI/AGMA standards 2001-D04 and 2101-D04 contain a safety factors: • guarding against bending fatigue failure and • guarding against pitting failure.
=

Τ1 2
Temperature factor:
For oil or gear-blank temperatures up to 250°F (120°C), use KT = Y = 1.0. For higher temperatures, the factor should be greater than unity. Heat exchangers may be used to ensure that operating temperatures are considerably below this value, as is desirable for the lubricant.
=1 For T < 120 °C ( 250 °F)
, =
Reliability factor:
The reliability factor accounts for the effect of the statistical distributions of material fatigue failures.
, =
Thank You Lecturers
Institut Teknologi Bandung
Modul 04 Spur Gear Design using AGMA

Modul 04 Spur Gear Design using AGMA

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