Chapter 2 Gear Drive-2
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Transcript of Chapter 2 Gear Drive-2
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Driving gear
Driven gear
Driving gear
1. Force Analysis
2.4 Loading, and Stress on Spur Gear
Fn1
Fn2
Fn1
Ft1
Fr1
c
b
aFn1
Fr1
T1
C
Ft1
Considering
pitch point
Given a pair of standard spur gear with standard center
distance. Assuming Force is exerted on the middle point of
tooth width, ignoring friction force.
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Fn1
Ft1
Fr1
1. Magnitude of force components
2000 20001 2
t1 t2
1 2
T TF F
d d
For the driving gear,
decomposing Fn on pitch point C:
Tangential force
Radial forcer1 t1
tanF F
Normal force t1n
cos
F
F
Torque 3 11
1
9.55 10 N mP
Tn
20001
1
cos
T
d
r2F
Only a normal force Fn acting on the tooth face,
with an invariable direction, always along the
acting line.
Driving
gear
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2. Direction of force components
Tangential forceF
t
Radius Force Fr
Along the tangential line, pointing to
Pointing to the gear center along the center line
Ft1Ft2
Fr1
Fr2
For driving gear: Opposite to the rotational speed
Driving
gear
Driven
gear
For driven gear: Coincident with the rotational speed
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Example
n2
n1
Fr1
Ft1Ft2
n1
n2
Fr2
Ft2
Ft11
2Fr2
Fr1
Front View Side View
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2. Load Calculation Nominal loadt1
n
cos
FF
nc nF KF
K: Load coefficient, K>1
Actual loadLoad coefficient
KAOverload coefficientConsidering the types of engine
and driven machine. Vibration, impact
KKAKVKKb
Power
source
Driven machine
uniform Slight shock Moderate shock Heavy shock
Uniform 1.0 1.25 1.5 1.75
Light
shock 1.1 1.35 1.6 1.85
Moderate
shock1.25 1.5 1.75 2
KA, Table 2-7
Electric motor
or constant-speed gas turbine
Water turbine
or variable-speed driveMulti-cylinder engine
Constant
generator
Fans, conveyor and
pump
Machine tool,
textile machineryRock crusher
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Dynamic load coefficient Kv
Considering the tolerance of gear in mesh,
such as tolerance of tooth profile and deformation of tooth profile
resulting from manufacturing tolerance, et al
Additional loading
Spur gear KV 1.05 ~1.4
Helical gearKV 1.02 ~ 1.2
Precision Kv
Linear speed of pitch circle Kv
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Load-distribution coefficient among teeth K
Loading-distribution coefficient among teeth for bending: KFLoading-distribution coefficient among teeth for contact: KH
For the continuous gear driving, the contact ratio is above 1. The
actual loading on the teeth in mesh is not uniform because of the error
of manufacturing and the different stiffnesswhile engaged.
Gear drive conditions:
1. Material of teeth is steel, or grey iron ;
2. The basic teeth profile meets the requirements of GB/T 1356-2001;
3. Spur gear or helical gear with a helical angle not above 30
.
Table 2-8 Loading distribution coefficient KH and KF
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Table 2-8 Loading distribution coefficient KH and KF
KAFt/b 100N/mm
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Load-distribution coefficient from tooth alignment Kb
1. Inaccurate gear teeth profile
2. Misalignment of shafts carrying gears
3. Elastic deformations of the gear, shafts, bearings, housings, and supportstructures
4. Clearances between the shafts and the gears, the shaft and bearings, or
the bearing and housing
5. Thermal distortion during operation
6. Crowning or end relief of gear teeth
If the intensity of loading on all parts of all teeth in contact at any given
time were uniform, the value of Kb
would be 1.00. But the following
reasons cause misalignment of the teeth on the pinion w.r.t. those on thegear.
Loading-distribution coefficient from tooth alignment for bending: KFb
Loading-distribution coefficient from tooth alignment for contact: KHb
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Considering the arrangement and deformation of shaft seated by a gear
Loading concentration
Bending deflexion of shaft
1. A deflexion of the gear axis, and an unbalanced
loading acting on the teeth.
3. If the shaft can be regarded as a
cantilever, the unbalanced loading will be
more significant.
2. Gear is not at the middle of shaft, and a larger
bending load acts on the teeth near bearings.
http://localhost/var/www/apps/conversion/tmp/scratch_10/0808/%E6%9C%BA%E6%A2%B0%E8%AE%BE%E8%AE%A1/%E6%9C%BA%E8%AE%BE56%E5%AD%A6%E6%97%B6/3%E7%AB%A0%EF%BC%8D%E9%BD%BF%E8%BD%AE%E4%BC%A0%E5%8A%A8%E8%AE%BE%E8%AE%A1/t3%EF%BC%8D8p.jpg -
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Stress distribution for torque
Stress distribution for moment
CombinedStress distributionInputting
torque
Shearing deformation of shaft
A larger torque load acts on the teeth
root closer to the inputting component.
Combined deformation
If the gear is located closer to theinputting component, the unbalanced
loading can be more serious.
If the gear is located farther fromthe inputting components, the
unbalanced loading can be less
serious.
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So, if the position of gear is not straddling at the middle of two bearings, it
is necessary to locate the gear far from the inputting end.
vFF v
Example
Which design is better?
The right design is better.
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Table 2-9 Loading distribution coefficient from tooth alignment KH
symmetricalasymm
etrical
Cantile
ver
Formula
Precision grade, under
hardening & tempering
Not examiningwhen assembling
Examining whenassembling
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Table 2-9 Loading distribution coefficient from tooth alignment KH
Precision grade,
under hard surface processing
Not examining
when assembling
Examining when
assembling
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Fig. 2-9 Loading distribution coefficient from tooth alignment KHand KF
Unbalanced loading ->K
Teeth width band working depth h:
1. If band HB, K;
2. Drum-like gear tooth, K.
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3. Stress Analysis of Gear Drive
For gear drive, a normal force acts on the tooth surface. There are two kinds
of stress:
1. Contact stress on tooth surface HFluctuating stress;
Relating to loading, deformation of
contact area and material properties
Unidirectional working condition:
Fluctuating stress or reverse and repeated stress
Bidirectional working condition:
Reverse and repeated stress
Fig. 2-11 Bending stress at the root of tooth
2. Bending stress at the root of tooth F
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(1) Tooth breakage
Bending fatigue
Overload
1. Failure type of gear drive
2-5 Failure Type and Design Principles of Gear Drive
Fatigue breakage is one of the most
important failure types for closed gear drive
Measures to avoid tooth breakage:module;
Fillet radius;
Surface quality;
Material ductility;
Positive-modified gear drive .
1. Crack initiation. Plastic deformation occurs in areas of
stress concentration or discontinuities, such as notches or
inclusions, leading to microscopic cracks.
2. Crack propagation. A smooth crack grows perpendicular
to the maximum tensile stress.3. Fracture. When the crack grows large enough, it causes
sudden fracture.
Sudden fracture for a short time, poor static strength of tooth
(2) F i i i
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(2) Fatigue pitting
Forming process of pitting:
Variable contact force
Fatigue cracks either at or below the surface
Lubrication into cracks
A piece of surface material to break out
Macropitting is categorized as nonprogressive, progressive.
The nonprogressive type consists of pits less than 1 mm diam. in localized areas.
These pits distribute load more evenly by removing high points on the surface. Then
pitting stops after a certain period of service .
Progressive macropitting consists of pits larger than 1 mm diameter that cover a
significant portion of the tooth surface.
A pit with sharp edges
Hardness;
Surface quality;
Equivalent curvature radius;
Viscosity of lubrication.
Measures to relieve fatigue pitting:
(3) S ffi
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(3) Scuffing
Under Heavy duty and high speed
Metal contact, adhesive;
A relative sliding on tooth surfaces;
Oil film breaks because of great friction;
Hard to form oil film
Phenomenon
Scratches form along the sliding direction
Measures to relieve scuffing:
Metal on soft surface is torn along the sliding direction.
Hot Scuffing
The surface oil film is punctured
and adhesion occurs.
Cool Scuffing
Forming process of scuffing
Under Heavy duty and low speed
Hardness;
Surface quality;
Pitch diameter;
Module and whole depth.
(4) W
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(4) Wear
It is one of the most important failure
types for open gear drive.
Measures to relieve wear
Lubrication;Sealing condition;
Gear tooth surface wear involves removal or
displacement of material due to mechanical,
chemical or electrical action.
The three major types of wear are adhesion,
abrasion and polishing.
(5) Pl ti d f ti
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(5) Plastic deformation
Phenomenon
Concave on the pitch circle of driving gear;
Convex on driven gear.
If soft surface,
Metal will flow along the friction direction
Loading and friction is significant
forming process of plastic deformation
Measures to relieve plastic deformation
Hardness;
Viscosity of lubrication;
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2. Design principles of gear drive
Fatigue pitting1. Closed gear drive, soft surface
For the two major failure types: Fatigue breakage and fatigue pitting
While in service
gears should havereliable root strength under bending
fatigue stress andsurface strength under contact fatigue stress
First design the main geometries of gear by HHP ;Then check by FFP.
Fatigue breakage2. Closed gear drive, hard surface
First design the main geometries of gear by FFP;
Then check by HHP.
3. Open gear drive
Only by the principles of bending fatigue strength,
without contact fatigue strength check.
Increasing the module by 10% for the negative influence of wear.
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Transmission Types Failure types Design PrinciplesSmall, or medium
power
Soft surface pitting
Fatigue root breakage
Contact fatigue strength
Bending fatigue strength
Hard surface Fatigue root breakage
pitting
Bending fatigue strength
Contact fatigue strength
Great power orheavy duty
High speed pittingFatigue root breakage
Hot scuffing
Contact fatigue strengthBending fatigue strength
Strength on hot scuffing
Low speed pitting
Fatigue root breakage
Cool scuffing
Plastic deformation
Contact fatigue strength
Bending fatigue strength
Strength on cool scuffing
Static strength
Table 2-10 Design principles of closed gear drive
2 6 M i l d H T f G D i
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2-6 Materials and Heat Treatments for Gear Drive
1. Requirements on materials
(1)hard surface, to resist wear, pitting and deformation,
(2)High ductility of gear hub, to resist bending fatigue breakage;
(3)Low price, and commercially available.
2. Common materialsSteelis the best material to manufacturing a gear.
Proper heat treatment is needed to improve the
materials performance.
Metallic
material
#45Medium carbon
alloy steel
Low carbon
alloy steel
Most commonly used
Cast
iron
35SiMn, 40MnB, 40Cr, et al
20Cr, 20CrMnTi, et al
ZG310-570, ZG340-640, et al
HT350, QT600-3, et al
Non-
metallic
material
Plastic, textolite, et al
Forged
steel
Criteria of material choice
Working condition, Load
pattern, Economical efficiency,
Manufacturing method, et al
Cast
steel
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3. Heat treatment
Hardening
& tempering
Normalizing
Casehardening
Carburizing
Nitriding
Softsurface
Hard
surface
It is applicable for medium carbon steel or medium carbon
alloy steel, such as 45, 40Cr, 35SiMn et al. After H&T process, the
tooth surface is soft, with a good property for finishing cutting.
It can be used to reduce internal stress, refine grain, improvemechanical properties and machinability. Normalizing medium
carbon steel can be used under a light duty working condition.
Normalizing cast steel is available for a gear with large diameter.
It is applicable for medium carbon steel or medium carbon
alloy steel, such as 45, 40Cr. To produce a high hardness in the
surface layer of gear teeth. To provide surface hardness values
from 50-64 HRC.
It is applicable for low carbon steel or low carbon alloy steel,
such as 20, 20Cr. Carburizing produces surface hardness in the
range of 55-64 HRC. It results in some of the highest strengths in
common use for gear.
Nitriding produces a very hard but very thin case. Nitriding
should be avoided when overloading or shock can be experienced,
because the case is not sufficiently strong or well supported toresist such load. It is applicable for 38CrMoAl.
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2. Case hardening, caburizing and nitriding can produce very hard surfaces,
which can improve the load capacity of gear drive, but require grinding process.
So it is often applicable for the compact structure.
1. Hardening & tempering and normalizing can produce a soft surface, HB 350,
which is valid for common gear drive.
Attentionif teeth of the gear and the pinion are both soft surface, the pinion
hardness should be 20~40HB higher than the gear. That is because the contact
cyclic number of the pinions teeth root is much greater than the gears.
4. Features of heat treatments
Table 2-11 Gear Material and heat treatment
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Table 2-11 Gear Material and heat treatment
N.Normalizing;
H.T.Hardening &
Tempering;
T.H.Through Hardening;
C.H.Case Hardening;
CA.Carburizing;
NI.Nitriding.
BUltimate strength
sYield strength
-1Bending fatigue
strength
Mate
rialHT HB B
(Mpa)s(Mpa)
-1(Mpa)
N.
H.T.
N.H.T.
T.H.
C.H.
H.T.
H.T.
T.H.
C.H.
CA.
NI.
CA.
Mechanical Properties
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Homework-7
Question A closed spur gear drive for speed reduction;
Speed ratio i=3;
pair of mating spur gear, m=2.5;
z1=32, n1=970r/min;
Transmission power P=10kW;
Try to calculate the tangential force Ft and the radialforce F
r
on the pinion and gear.