Environmental Engineering Reference
In-Depth Information
any.speciic.performance.attribute..This.allows.an.in-depth.understanding.
of.the.root.causes.of.its.behavior.and.enables.engineers.to.minimize.the.risk.
of.failure.during.subsequent.assessment.test.on.prototypes.
LMS. Virtual.Lab. provides. several. methods. to. model. the. meshing. of.
gears..The.most.suited.is.the.so-called.
gear contact force
.element..It.is.appli-
cable.to.any.kind.of.gear.system.that.is.spur.or.helical,.external.or.internal..
The. method. also. applies. to. planetary. gears. that. are. often. used. in. wind.
turbines.. In. case. of. the. gear. contact. force,. the. contact. formulation. is. not.
computed. based. on. one-tone. tooth. geometry. interpenetration.. Instead,. it.
is.directly.derived.from.the.global.gear.theory.for.more.eficient.analytical.
solving. and. shorter. calculation. times.. Moreover,. it. takes. into. account. the.
variability. of. the. stiffness,. which. is. due. to. the. proile. of. one. single. tooth.
and. to. the. instantaneous. number. of. meshing. teeth,. according. to. the. Cai.
and.ISO.formulations.
41-44
The.equivalent.meshing.stiffness.between.the.two.gears.is.the.sum.of.the.
contact.stiffness.over.the.number.of.contacting.teeth,.which.varies.in.time.
according.to.the.contact.ratio.
Each.single.tooth.equivalent.stiffness.is.also.varying.during.the.meshing.
time,.since.the.bending.is.bigger.at.the.top.than.at.the.root.of.the.tooth..An.
example.of.the.meshing.stiffness.variation.is.shown.in.Figure 5.13,.assuming.
that.the.contact.ratio.is.2.5,.meaning.the.number.of.contacting.
Teeth.vary.from.two.to.three..The.total.contact.stiffness,.consequently,.has.
a.luctuation.nature.(oscillation.around.a.static.stiffness),.which.introduces.
internal.excitations.to.the.gears.that.could.cause.whining.noises.and.possible.
tooth.separations.under.certain.loading.conditions.
In.Figure 5.13,.the.dependent.variable.is.the.stiffness.and.the.independent.
variable.is.the.meshing.time,.from.0.to.€tz,.where the.total.contact.ratio,.tz.
the.meshing.period.for.a.single.tooth,.and.åtz.the.whole.meshing.period.
View A
Scale 2:1
Measuring stiffness between gear rim
and pinions planetary reducer.
FIGURE 5.13
Measuring.stiffness.variation.
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