Arcabouço Inferior
Lower Housing
SRLN-PRT-SSEM-001
The Project
Helical Gear Pair Project Justification
The choice of helical gear topology for the first stage of this speed reducer is based on the need to combine kinematic precision, high load transmission capacity, and operation with low noise and vibration levels. The pinion-gear pair was designed to reduce the input speed from 1000 RPM to approximately 233 RPM, delivering an effective transmission ratio of i = 4.2941, with an insignificant deviation from the nominal target of 4.3.
The adoption of a helix angle β of 20º and a pressure angle α of 20º ensures a high contact ratio (total contact ratio ε ≈ 2.73). This means that the load is distributed gradually and supported by multiple teeth simultaneously, mitigating mechanical shocks in the meshing (single overload factor KAS = 1.0) and optimizing the system's service life under continuous operation.
From a metallurgical and structural perspective, the selection of 18CrNiMo7-6 (~SAE 4320) alloy steel offers an excellent combination of core toughness (yield strength Sy = 800 MPa) and high surface hardness on the flanks after heat treatment (380 HV). The strength calculations, based on the ISO 6336:1996 standard, attest to the extreme robustness of the design for the 1 kW power rating: the safety factor against contact fatigue (pitting) resulted in SH ≈ 3.44, while the safety factor against tooth root breakage (bending) exceeds the mark of SF > 17. These values ensure not only technical viability but superior operational reliability against catastrophic failures.
Technical Details
Arcabouço Superior
Upper Housing
SRLN-PRT-SSEM-002
Eixo com Chaveta
Keyed Shaft
SRLN-PRT-SSEM-003
Eixo com Engrenagem
Pinion Shaft
SRLN-PRT-SSEM-004
Engrenagem Helicoidal
Helical Gear
SRLN-PRT-SSEM-005
Tampa Menor Furada
Smaller Blind Cover
SRLN-PRT-SSEM-006
Tampa Menor sem Furo
Smaller Open Cover
SRLN-PRT-SSEM-007
Tampa Maior sem Furo
Larger Blind Cover
SRLN-PRT-SSEM-008
Tampa Maior sem Furo
Larger Blind Cover
SRLN-PRT-SSEM-009
Tampa do Visor de Óleo
Oil Sight Cover
SRLN-PRT-SSEM-010
Vihal de Óleção
Oil Sight Glass
SRLN-PRT-SSEM-011
Calculation Memorial
Helical Gear Drive Component Generator
Project output · Total profile shift · Profile shift distribution per Merrit · Torque calculation for specified power and rotational speed
Helical Gear Pair
z₁ = 17 · z₂ = 73 · m = 3.500 mm · β =
20°
Design Check: Positive
Calculation confirms design compatibility.
General Pair Parameters
Gear ratio
i
4.2941
Desired gear ratio
iin
4.3000
Module
m
3.500
mm
Helix angle
β
20.0000
deg
Pressure angle
α
20.0000
deg
Center distance
aw
168.000
mm
Actual center distance
a
167.608
mm
Total profile shift
Σx
0.1129
Circular pitch
p
10.996
mm
Base circular pitch
ptb
10.911
mm
Working pressure angle
αw
20.3866
deg
Transverse pressure angle
αt
21.1728
deg
Working transverse pressure angle
αtw
21.5154
deg
Base helix angle
βb
18.7472
deg
Transverse module
mt
3.725
mm
Transverse circular pitch
pt
11.701
mm
Total contact ratio
ε
2.7306
Transverse contact ratio
εα
1.1754
Overlap ratio (face contact ratio)
εβ
1.5553
Shaft parallelism deviation limit (fx)
fx
0.0140
mm
Shaft parallelism deviation limit (fy)
fy
0.0070
mm
Gear Geometry
| Parameter | Symbol | Gear 1 | Gear 2 | Unit |
|---|---|---|---|---|
| Number of teeth | z | 17 | 73 | — |
| Profile shift coefficient | x | 0.3164 | −0.2036 | — |
| Reference (pitch) diameter | d | 63.319 | 271.897 | mm |
| Tip (outside) diameter | da | 71.128 | 276.066 | mm |
| Root diameter | df | 58.674 | 263.612 | mm |
| Base circle diameter | db | 59.044 | 253.543 | mm |
| Working pitch diameter | dw | 63.467 | 272.533 | mm |
| Face width | b | 60.000 | 50.000 | mm |
| Face width coefficient | br | 0.7897 | 0.1839 | — |
| Addendum coefficient | a* | 0.8000 | 0.8000 | — |
| Dedendum clearance coefficient | c* | 0.1800 | 0.1800 | — |
| Root fillet radius coefficient | rf* | 0.2735 | 0.2735 | — |
| Normal tooth thickness | s | 6.304 | 4.979 | mm |
| Transverse tooth thickness | st | 6.709 | 5.299 | mm |
| Chordal tooth thickness | tc | 5.567 | 4.397 | mm |
| Chordal addendum | ac | 2.891 | 1.284 | mm |
| Base tangent length (span) | W | 27.584 | 101.943 | mm |
| Number of teeth spanned | zw | 3.000 | 10.000 | — |
| Measurement over pins (MOP) | M | 72.988 | 278.835 | mm |
| Pin diameter | dM | 6.000 | 6.000 | mm |
| Helix angle tolerance limit | Fβ | 0.0140 | 0.0150 | mm |
| Total radial composite deviation limit | Fr | 0.0210 | 0.0280 | mm |
| Single pitch deviation limit | fpt | 0.0085 | 0.0090 | mm |
| Base pitch deviation limit | fpb | 0.0080 | 0.0085 | mm |
| Equivalent (virtual) number of teeth | zv | 20.175 | 86.634 | — |
| Virtual reference diameter | dn | 70.612 | 303.218 | mm |
| Virtual tip diameter | dan | 78.421 | 307.387 | mm |
| Virtual base circle diameter | dbn | 66.354 | 284.932 | mm |
| Profile shift without tip narrowing | xz | 0.3037 | −1.5182 | — |
| Profile shift without undercut | xp | −0.3800 | −4.2671 | — |
| Profile shift with permissible undercut | xd | −0.5133 | −4.4004 | — |
| Tip relief (addendum shortening) | k | 0.0009 | 0.0009 | — |
| Tip land thickness coefficient | sa | 0.7996 | 0.9800 | — |
| Tip pressure angle | αa | 33.2250 | 22.2558 | deg |
Loads & Forces
| Parameter | Symbol | Gear 1 | Gear 2 | Unit |
|---|---|---|---|---|
| Power | P | 1.000 | 0.980 | kW |
| Rotational speed | n | 1000.00 | 232.88 | rpm |
| Torque | T | 9.549 | 40.186 | N·m |
| Efficiency | η | 0.980 | — | — |
| Radial force (separating) | Fr | 118.630 | — | N |
| Tangential force (transmitted) | Ft | 300.923 | — | N |
| Axial (thrust) force | Fa | −109.527 | — | N |
| Normal (resultant) force | Fn | 341.635 | — | N |
| Pitch line velocity | v | 3.315 | — | m/s |
| Resonance speed | nE | 119,379.991 | — | rpm |
Material — 18CrNiMo7-6 (~SAE 4320)
Ultimate tensile strength
Su
1150
MPa
Yield strength
Sy
800
MPa
Young's modulus
E
206,000
MPa
Poisson's ratio
μ
0.300
Allowable bending stress (fatigue)
σFlim
460.0
MPa
Allowable contact stress (fatigue)
σHlim
1500.0
MPa
Core hardness
JHV
210
HV
Surface (flank) hardness
—
380
HV
Reference load cycles — bending
NFlim
3×10⁶
Reference load cycles — contact
NHlim
5×10⁷
S-N curve exponent — bending
qF
6.0
S-N curve exponent — contact
qH
10.0
Heat treatment type
type
4
Additional Load Factors
| Factor | Symbol | Gear 1 | Gear 2 |
|---|---|---|---|
| Application factor | KA | 1.200 | — |
| Dynamic factor | KHv | 1.078 | 1.078 |
| Face load factor | KHβ | 3.281 | 2.541 |
| Transverse load factor | KHα | 2.120 | 2.120 |
| Single overload factor | KAS | 1.000 | — |
Contact Factors
| Factor | Symbol | Gear 1 | Gear 2 |
|---|---|---|---|
| Elasticity factor | ZE | 189.812 | — |
| Zone factor | ZH | 2.351 | — |
| Contact ratio factor | Zε | 0.922 | — |
| Single pair tooth contact factor | ZB | 1.000 | 1.000 |
| Life (durability) factor | ZN | 1.000 | 1.000 |
| Lubricant factor | ZL | 0.967 | — |
| Surface roughness factor | ZR | 1.000 | — |
| Velocity factor | Zv | 0.973 | — |
| Helix angle factor | Zβ | 0.969 | — |
| Size factor | ZX | 1.000 | 1.000 |
| Work hardening factor | ZW | 1.000 | — |
Bending Factors
| Factor | Symbol | Gear 1 | Gear 2 |
|---|---|---|---|
| Tooth form factor | YFa | 1.930 | 1.982 |
| Stress correction factor | YSa | 2.065 | 1.988 |
| Ground root factor | YSag | 1.000 | 1.000 |
| Helix angle factor | Yβ | 0.833 | — |
| Contact ratio factor | Yε | 0.822 | — |
| Alternating bending factor | YA | 1.000 | 1.000 |
| Manufacturing technology factor | YT | 1.000 | 1.000 |
| Life (durability) factor | YN | 1.000 | 1.000 |
| Notch sensitivity factor | Yδ | 1.281 | 1.258 |
| Size factor | YX | 1.000 | 1.000 |
| Root surface condition factor | YR | 1.000 | — |
Results — Safety Factors
SH
Pitting resistance safety factor
3.447
/
3.447
SF
Tooth bending safety factor
20.534
/
17.895
SHst
Static contact safety factor
3.598
/
3.598
SFst
Static bending safety factor
40.081
/
35.568
