24-05-2014, 10:37 AM
Effects of flank deviation on load distributions for helical gear
Effects of flank deviation.pdf (Size: 1.04 MB / Downloads: 32)
Abstract
Flank deviation is one of the important factors that greatly affect helical gear strength. A qualitative analysis is performed using finite
element method (FEM) for the effects of flank deviation on load distributions for helical gear based on ANSI/AGMA ISO 1328-1 (stan-
dard for cylindrical gears - ISO System of Accuracy - Part 1: Definitions and Allowable Values of Deviations Relevant to Corresponding
Flanks of Gear Teeth). To analyze the effects of flank deviation, tooth contact analysis (TCA) is developed and load distributions of heli-
cal gears with flank deviation are presented. Load distributions in contact lines are derived and compared to each other under grade 5 and
7 after taking five types of flank deviation, including single pitch deviation, profile form deviation, profile slope deviation and helix form
deviation as well as helix slope deviation, into account. It is found that the effects of individual flank deviation on load distribution have
the superposition property. Flank crowning and tip relief corrections must be carefully regarded in the design process because of the ef-
fects of flank deviation on load distributions.
Introduction
Flank deviation is one of the factors that greatly affect gear
strength. After many studies, Semba Seiso [1] thought that the
gear strength calculation equation in every country is still not
precise enough; the main reason for this is that the effect of
flank deviation is not fully considered. He thought the stan-
dard of gear accuracy should be calculated based on the ef-
fects of various errors on noise and strength instead of the size
of various errors processed in various ways. Therefore, some
scholars [2] have put forward the concept of functional equi-
valence among the same gear accuracy. The study of gear
errors is usually performed through experiments. For example,
Velex and Ajmi [3] studied the relationship of the carrying
capacity of gears between different errors and transmission
ratios, and they pointed out that it is difficult to avoid the ap-
pearance of contact stress concentration because of manufac-
turing error, installation error, elastic deformation, etc.
Brief description of gear flank deviation
Several types of individual flank deviations are provided in
standard ANSI/AGMA ISO 1328-1. They are single pitch
deviation, profile form deviation, profile slope deviation, helix
form deviation and helix slope deviation. Other types of inte-
grated flank deviations can be combined by these individual
types. The gear accuracy used in industrial production is main-
ly from grade 5 to 9. It is difficult to study the deviations be-
cause of their complex micro-geometry. Therefore, previous
studies [17] are mainly laboratory-based. The effect of devia-
tions is greatly influenced by processing and laboratory stud-
ies cannot accurately obtain the required gear flank deviation.
However, they provide an effective way to study flank devia-
tions and more accurate flank deviations can be found by nu-
merical method. There are some references [18, 19] that have
recently introduced related research in this area, but the devia-
tion types concerned are not comprehensive.
Single pitch deviation fpt
The single pitch deviation is defined as the algebraic differ-
ence of actual pitch and theoretical pitch on the circle that is
close to the central of gear height at the end plane. In this
study, the single pitch deviation is obtained by offsetting an
equal distance to the theoretical profile flank, and it does not
involve other types of individual deviations because of the
equal offset.
Among all combinations of deviations, the single pitch de-
viation may not be considered when it is both “+” or both “-”
in the two gears because of the equal theoretical profiles. Here,
in Case A and Case B, the most unfavorable situations to the
load distribution are studied, as shown in Table 4. The two
cases with single pitch deviation are shown in Fig. 4. The
wheel is at the upper position and the pinion is below.
Profile slope deviation fHα
Profile slope deviation always appears with single pitch de-
viation. In order to study profile slope deviation independently,
it should be kept at the same pitch circle when building mod-
els with profile slope deviation. The combinations of single
tooth pair profile slope deviation are shown in Table 5.
The load distribution curves of tooth pair 2 in Cases A and
B and tooth pair 1 in Cases C and D are basically parallel.
Because there are no deviations on these tooth pairs, the load
distributions between the two teeth pairs experiences rela-
tively small changes, though these curves does not coincide.
The load distribution curves of tooth pair 1 in Cases A and B
and tooth pair 2 in Cases C and D have an obvious intersec-
tion point close to the pitch circle caused by the same pitch
circle when building model. The load distributions with pro-
file slope deviation are shown in Figs. 10 and 11.
CONCLUSION
The above studies show that flank deviations have great ef-
fects on helical gear load distribution, and the following con-
clusions can be drawn:
(1) The load increasing amplitude under grade 7 is twice
that under grade 5 when considering the effects of flank devia-
tions. A lower load will induce a larger effect by flank devia-
tions though there is only a small deformation in contact areas.
(2) The effect of single pitch deviation on the load distribu-
tion is not in the axial direction, but mainly in a different tooth.
There is little effect of load distribution affected by profile
form deviation and helix form deviation while it is affected by
profile slope deviation and helix slope deviation.
(3) For equal loads, the effect of single pitch deviation on
load distribution along the direction of tooth width is overall
larger or smaller, while there is a larger effect by the helix
deviations. Form deviation can lead to great changes of load
distribution along the direction of tooth width, while it is less
affected by helix deviations.