Compensation modification of plastic gear tooth profile considering meshing deformation
Mingyong LIU1(), Yaole SONG1, Xinguang HAN1, Jun HU1, Chunai YAN2
. Hubei Agricultural Machinery Engineering Research and Design Institute, Hubei University of Technology, Wuhan 430068, China . Intelligent Manufacturing Institute, Wuchang Institute of Technology, Wuhan 430065, China
The plastic gear is widely used in agricultural equipment, electronic products, aircraft, and other fields because of its light weight, corrosion resistance, and self-lubrication ability. However, it has a limited range of working conditions due to the low modulus and thermal deformation of the material, especially in high-speed and heavy-duty situations. A compensation modification method (CMM) is proposed in this paper to restrain the heat production of the plastic gear tooth surface by considering the meshing deformation, and the corresponding modification formulas are derived. Improving the position of the maximum contact pressure (CP) and the relative sliding velocity (RSV) of the tooth surface resulted in a 30% lower steady-state temperature rise of the modified plastic gear tooth surface than that of the unmodified plastic gear. Meanwhile, the temperature rise of plastic gear with CMM is reduced by 19% compared with the traditional modification of removal material. Then, the influences of modification index and the segment number of modification on the meshing characteristics of plastic gear with CMM are discussed, such as maximum CP and steady-state temperature rise, RSV, transmission error, meshing angle, and contact ratio. A smaller segment number and modification index are beneficial to reduce the temperature rise of plastic gear with CMM. Finally, an experiment is carried out to verify the theoretical analysis model.
Fig.1 Meshing diagram of spur gear pair. TSCA: tooth side clearance amount.
Fig.2 Schematic of the compensation modification method.
A
B
C
n
γ
ε0
66.688
66.455
0.001
1.607
0.9
1
Tab.1 Characteristic parameters of POM material
Parameter
Unit
Specification
Number of teeth, z1,z2
–
20,30
Module, m
mm
3.5
Tooth width, W
mm
20
Modification coefficient, x1,x2
mm
0.6293,0.6854
Normal pressure angle, αn
°
20
Tab.2 Basic parameters of plastic gear pair
Fig.3 Finite element analysis model of plastic gear. POM: Polyoxymethylene.
Fig.4 Flowchart of numerical calculation.
Fig.5 Variation of meshing deformation of polyoxymethylene (POM) gear with unmodified tooth profile. (a) Meshing deformation of unmodified plastic gears. (b) Tooth side clearance of gear pair. CMM: compensation modification method.
Fig.6 Compensation modification curve under different modification parameters. L(θ) curves under different (a) num and (b) β.
Fig.7 Variation of meshing characteristic parameters of POM gear along the line of action: (a) meshing process of unit code; (b) meshing relative sliding speed; (c) contact pressure of tooth profile; (d) instantaneous frictional heat flux density.
Fig.8 Contact pressure distribution of tooth surface under different modification methods: (a) standard involute; (b) compensation modification method (CMM; num = 2, k = 0, and β = 1.5); (c) traditional modification method (β = 1.2); (d) traditional modification method (β = 1.5).
Fig.9 Relative sliding velocity of tooth surface under different modification methods: (a) standard involute; (b) compensation modification method (CMM; num = 2, k = 0, and β = 1.5); (c) traditional modification method (β = 1.2); (d) traditional modification method (β = 1.5).
Fig.10 (a–d) Temperature field of pinion under different modification methods. (a) Original involute profile.
Fig.11 Influences of adjustment number (num) on the meshing performance of polyoxymethylene gear: (a) meshing tooth profile, (b) gear pair transmission, (c) working pressure angle, and (d) contract ratio. β = 1.5.
Fig.12 Influence of modification index (β) on the meshing performance of polyoxymethylene gear: (a) meshing tooth profile, (b) gear pair transmission, (c) working pressure angle, and (d) contract ratio. num = 2.
Fig.13 Test scheme of polyoxymethylene (POM) gear.
Fig.14 Comparison of theoretical temperature rise and experimental results of polyoxymethylene gear.
Fig.15 Comparison of tooth surface meshing paths of polyoxymethylene gears: (a) experimental data and (b) theoretical analysis.
Fig.16 Comparison of temperature field between standard tooth profile and compensated modified tooth profile. (a) Experimental temperature of compensation modification method (CMM). (b) Temperature of CMM and standard profile.
Abbreviations
CMM
Compensation modification method
CP
Contact pressure
IFHF
Instantaneous frictional heat flux
POM
Polyoxymethylene
RSV
Relative sliding velocity
TSCA
Tooth side clearance amount
Variables
A
Initial yield stress
A1, B1, etc.
Position corresponding to θ on the pinion
B
Hardening coefficient
C
Sensitivity coefficient of strain rate
e
Groove thickness
k1,k2
Meshing stiffness of pinion and wheel, respectively
L0
Modification constant
n
Hardening index
num
Segment number of modifications
M2
Torque of wheel
r
Radius of circle
s
Tooth thickness
T
Temperature
t
Time
u
Friction coefficient
v
Relative sliding speed
xp
x-coordinate of the center point on the tooth profile
yp
y-coordinate of the center point on the tooth profile
z
Number of teeth
α
Pressure angle
αn
Normal pressure angle
β
Modification index
σ
Equivalent stress
σy
Yield stress
Equivalent plastic strain rate
Equivalent plastic reference strain rate
θ
Expansion angle
δ
Meshing deformation
ζ
Working pressure angle peak-to-peak value
ε
Equivalent strain
εα
Contact ratio
γ
Temperature softening parameters
ξ
Thermal energy conversion coefficient
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