Source code for gearbox.standards.agma2101._factors
"""Influence factors of AGMA 2001-D04 other than the geometry factors."""
from __future__ import annotations
from math import ceil, log, sqrt
from numpy import interp
from gearbox.models import Gear
from gearbox.transmission import Transmission
def _estimated_quality_number(gear: Gear) -> float:
"""``Q_v`` equivalent to the ISO 1328 single pitch deviation of ``gear``.
Inverts the empirical ``f_pt`` formula of ISO 1328-1 (accuracy grade ``A_v``) and uses
``Q_v = 17 - A_v``, the relation between the ``B`` exponents of AGMA 2101-C95 and
AGMA 2001-D04 (A.3). It is an estimate, not a classification of the standard.
"""
if gear.internal: # negative diameters: d ~ |d_a| + 2 m
root_to_tip_diameter = -gear.tip_diameter + 2 * gear.module
else:
root_to_tip_diameter = gear.tip_diameter - 2 * gear.module
tolerance = gear.tolerances.single_pitch_deviation
accuracy_grade = (
log(abs(tolerance)) - log(0.3 * gear.module + 0.12 * sqrt(root_to_tip_diameter) + 4)
) / 0.3466 + 5
return 17 - ceil(accuracy_grade)
[docs]
def dynamic_factor(transmission: Transmission) -> float:
"""Dynamic factor ``K_v``, AGMA 2001-D04 annex A, formulae (A.1) to (A.3).
``K_v = ((A + sqrt(v_t)) / A)^B`` with ``B = 0.25 (12 - Q_v)^0.667``, ``A = 50 + 56 (1 - B)``
and ``v_t`` the pitch line velocity in ft/min. ``Q_v`` is limited to 5..11 (A.2).
Args:
transmission: The gear pair. ``agma_quality_number`` selects ``Q_v``; if ``None`` the lower
of the values estimated for pinion and wheel is used.
Returns:
The dynamic factor (>= 1).
"""
quality = transmission.agma_quality_number
if quality is None:
quality = min(
_estimated_quality_number(transmission.pinion),
_estimated_quality_number(transmission.wheel),
)
quality = min(max(quality, 5), 11)
b = 0.25 * (12 - quality) ** 0.667
a = 50 + 56 * (1 - b)
velocity_ft_per_min = transmission.pitch_line_velocity * 196.85
return ((a + sqrt(velocity_ft_per_min)) / a) ** b
[docs]
def size_factor(transmission: Transmission) -> float:
"""Size factor ``K_s`` (AGMA 2001-D04, clause 18), interpolated on the module.
Args:
transmission: The gear pair.
Returns:
The size factor.
"""
modules = [5, 6, 8, 12, 20]
factors = [1, 1.05, 1.15, 1.25, 1.40]
module = transmission.pinion.module
if module < 5:
return 1
if module > 20:
return 1.40
return float(interp(module, modules, factors))
[docs]
def load_distribution_factor(transmission: Transmission) -> float:
"""Load distribution factor ``K_m = 1 + C_mc (C_pf C_pm + C_ma C_e)`` (clause 16).
Args:
transmission: The gear pair.
Returns:
The load distribution factor.
"""
p = transmission.pinion
crowning_factors = [1, 0.8]
alignment_improvement = [0.8, 1]
width = transmission.net_face_width
diameter = p.reference_diameter
# AGMA 2001-D04, clause 15.3: F/(10 d) is not taken below 0.05 in equations 39 to 41.
slenderness = max(width / (10 * diameter), 0.05)
if width <= 25:
pinion_proportion = -0.025 + slenderness
elif 25 < width <= 432:
pinion_proportion = slenderness - 0.0375 + 0.000492 * width
else:
pinion_proportion = slenderness - 0.1109 + 0.000815 * width - 0.000000353 * width**2
if p.offset / p.bearing_span < 0.175:
pinion_proportion_modifier = 1
else:
pinion_proportion_modifier = 1.1
a = [2.47e-1, 1.27e-1, 0.675e-1, 0.380e-1]
b = [0.657e-3, 0.622e-3, 0.504e-3, 0.402e-3]
c = [-1.186e-7, -1.69e-7, -1.44e-7, -1.27e-7]
index = int(transmission.gearing_type) - 1
mesh_alignment = a[index] + (b[index] * width) + c[index] * width**2
return 1.0 + crowning_factors[int(p.crowning) - 1] * (
pinion_proportion * pinion_proportion_modifier
+ mesh_alignment * alignment_improvement[int(p.assembly_condition) - 1]
)
[docs]
def rim_thickness_factor(gear: Gear) -> float:
"""Rim thickness factor ``K_B`` of one gear, AGMA 2001-D04 annex B (B.1 and figure B.1).
``m_B = t_R / h_t``; ``K_B = 1`` for ``m_B >= 1.2`` and ``1.6 ln(2.242 / m_B)`` below. For a
gear without a specified rim (solid disc) the radial thickness under the root is
``(d_f - d_shaft) / 2``.
Args:
gear: The gear.
Returns:
The rim thickness factor.
Raises:
ValueError: If the backup ratio is 0.5 or less (needs a special analysis, B.2).
"""
if gear.rim_thickness:
rim_thickness = gear.rim_thickness
else:
rim_thickness = (gear.root_diameter - gear.shaft_diameter) / 2
backup_ratio = rim_thickness / gear.tooth_height
if backup_ratio <= 0.5:
raise ValueError(
f"AGMA 2001 rim thickness factor needs a backup ratio above 0.5, got {backup_ratio:.2f}"
)
if backup_ratio >= 1.2:
return 1.0
return 1.6 * log(2.242 / backup_ratio)
