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Calculation to the contact strength and oil-film thickness of the involute spur gear
渐开线直齿圆柱齿轮接触强度和油膜厚度计算
Finite element simulation analysis of involute spur gear
渐开线直齿圆柱齿轮有限元仿真分析
Finite Element Analysis of Involute Spur Gear Based on ANSYS
基于ANSYS的渐开线直齿圆柱齿轮有限元分析
This paper introduced a method that how to design the application of involute spur gear with UG/OPEN GRIP,and de- tailedly explained the process that develop a module of involute spur gear with UG/OPEN API. These two kinds of methods for designing parametric models of gears are successfully applied in modeling gear-box of loaders.
本文介绍了使用UG/OPEN GRIP开发渐开线直齿圆柱齿轮应用程序的方法,详细阐明了使用UG/OPEN API实现渐开线直齿圆柱齿轮模块开发的过程,这两种齿轮参数化设计方法在完成装载机变速箱三维设计过程中得到了成功应用。
THe PHYSICAL SIGNIFICANCE OF COINCIDENCE ε_a WHICH IS NOT INTEGER IN INVOLUTE SPUR GEAR DRIVING
渐开线直齿圆柱齿轮传动的重合度εa不为整数时实际物理意义的一点说明
In this paper, we obtained the analytics mathematical model involute spur gear's slide coefficient as following: U1k=(1+i21)(1-tan(α)/tan(α)-ωt) U2k=(1+i21)(1-tan(α)/tan(α)+i21ωt)
本文得到了渐开线直齿轮滑动系数的解析数学模型如下: U1k=(1+i21)(1-tan(α)/tan(α)-ωt) U2k=(1+i21)(1-tan(α)/tan(α)+i21ωt)
introduced
parts,discussed
noncircular
section,and
application
简述粉末冶金成形圆形模径向尺寸设计公式 ,进而讨论截面为非圆曲线时成形模曲线的设计模型 ,并详细描述其在渐开线直齿轮成形模具设计上的应用
The Accurate Solution of Tooth Deflection of Involute Spur Gear Solved by the Conformal Mapping Method
保角映射法精确求解渐开线直齿轮轮齿挠度
The Analytics Model of Involute Spur Gear's Slide Coefficient
渐开线直齿轮滑动系数的解析模型
On Involute Spur Gear Enveloping Worm Drive
渐开线直齿轮包络蜗杆传动
Multilevel Technique for Lubrication Design of Involute Spur Gear Transmission
渐开线齿轮润滑设计的多重网格数值模拟技术
This paper gives an analytical method for calculation of conformal mapping function of the tooth profile of involute gear, The method is simple, and the accuracy of mapping is high,According to this conformal mapping function, the accurate solution of tooth deflection of involute spur gear is given, On the basis of a computer program,influert elements and rule on tooth deflection is analysed,
用解析方法推导出渐开线齿轮实际齿廓（包括渐开线和过渡曲线）的保角映射函数、计算方便,而且映射精度高,应用此映的函数求得斯开线直齿轮轮齿挠度的精确解：编制了计算程序：对影响挠度的因素及其影响规律进行了分析,
Based on the average flow model by Patir and Cheng,it establishes EHL equations and analyzes the pressure and film thickness during a mesh cycle of a pair of involute spur gear. The result presents the influence of roughness on the surface during the mesh cycle.
采用了Patir and cheng的平均流动模型,通过联立求解弹流基本方程组,获得渐开线齿轮啮合过程的油膜压力、膜厚,并分析了啮合过程中表面粗糙度对齿轮传动最小膜厚和压力的影响。
Research of 3D Parametric Design System of Involute Spur Gear Reducer
渐开线圆柱齿轮减速器三维参数化设计系统的研究
The relative sliding ratio formulas of an involute spur gear pair are developed
The influences of relative sliding ratio on the gear wear, friction moment of engagement and elastohydrodynamic lubrication are analyzed
推导了渐开线圆柱齿轮副相对滑动率的计算公式 ,分析了相对滑动率对齿轮磨损、相啮合的摩擦力矩与弹流润滑等问题的影响
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你可能喜欢Chapter 7. Gears
Rapid Design through Virtual and Physical Prototyping
Introduction to Mechanisms
Stephannie Behrens
Gears are machine elements that transmit motion by means of
successively engaging teeth.
The gear teeth act like small levers.
Gears may be classified according to the relative position of the
axes of revolution. The axes may be
intersecting,
neither parallel nor intersecting.
Here is a brief list of the common forms.
We will discuss each
in more detail later.
Spur gears
The left pair of gears makes external contact, and the right pair
of gears makes internal contact
Parallel helical gears
Herringbone gears (or double-helical gears)
and pinion (The rack is like a gear whose
axis is at infinity.)
Straight bevel gears
Spiral bevel gears
Crossed-helical gears
Hypoid gears
Worm and wormgear
shows two mating gear teeth,
Tooth profile 1 drives tooth
profile 2 by acting at the instantaneous contact point K.
N1N2 is the common normal of the two profiles.
N1 is the foot of the perpendicular from
O1 to N1N2
N2 is the foot of the perpendicular from
O2 to N1N2.
Figure 7-2 Two gearing tooth profiles
Although the two profiles have different velocities
V1 and V2 at point
K, their velocities along N1N2 are
equal in both magnitude and direction.
Otherwise the two tooth
profiles would separate from each other. Therefore, we have
We notice that the intersection of the tangency
N1N2 and the line of center
O1O2 is point P, and
Thus, the relationship between the angular velocities of the driving
gear to the driven gear, or velocity ratio, of a pair of mating
Point P is very important to the velocity ratio, and it is
called the pitch point. Pitch point divides the line between
the line of centers and its position decides the velocity ratio of the
two teeth. The above expression is the fundamental law of
gear-tooth action.
For a constant velocity ratio, the position of P should remain
unchanged. In this case, the motion transmission between two gears is
equivalent to the motion transmission between two imagined slipless
cylinders with radius R1 and R2 or
diameter D1 and D2. We can get two
circles whose centers are at O1 and
O2, and through pitch point P. These two
circle are termed pitch circles. The velocity ratio is equal to
the inverse ratio of the diameters of pitch circles. This is the
fundamental law of gear-tooth action.
The fundamental law of gear-tooth action may now also be stated
as follow (for gears with fixed center distance)
The common normal to the tooth profiles at the point of contact must
always pass through a fixed point (the pitch point) on the line of
centers (to get a constant velocity ration).
To obtain the expected velocity ratio of two tooth profiles,
the normal line of their profiles must pass through the corresponding
, which is decided by the
velocity ratio. The two profiles which satisfy this requirement
are called conjugate profiles. Sometimes, we simply termed the
tooth profiles which satisfy the fundamental law of gear-tooth
action the conjugate profiles.
Although many tooth shapes are possible for which a mating tooth could
be designed to satisfy the fundamental law, only two are in general
use: the cycloidal and involute profiles. The involute
has important advantages -- it is easy to manufacture and the center
distance between a pair of involute gears can be varied without
changing the .
Thus close
tolerances between shaft locations are not required when using the
involute profile.
The most commonly used conjugate tooth curve
is the involute curve .
The following examples are involute spur gears.
We use the word
involute because the contour of gear teeth curves inward.
Gears have many terminologies, parameters and principles.
One of the
important concepts is the velocity ratio, which is the ratio of
the rotary velocity of the driver gear to that of the driven gears.
The SimDesign file for these gears is simdesign/gear15.30.sim.
The number of teeth in these gears are 15 and 30, respectively.
the 15-tooth gear is the driving gear and the 30-teeth gear is the
driven gear, their velocity ratio is 2.
Other examples of gears
are in simdesign/gear10.30.sim and
simdesign/gear20.30.sim
Figure 7-3 Involute curve
The curve most commonly used for gear-tooth profiles is the involute
of a circle. This involute curve is the path traced by a point
on a line as the line rolls without slipping on the circumference of a
circle. It may also be defined as a path traced by the end of a string
which is originally wrapped on a circle when the string is unwrapped
from the circle. The circle from which the involute is derived is
called the base circle.
In , let line MN roll in the
counterclockwise direction on the circumference of a circle without
When the line has reached the position M'N', its
original point of tangent A has reached the position K,
having traced the involute curve AK during the motion. As the
motion continues, the point A will trace the involute curve
The distance BK is equal to the arc AB, because
link MN rolls without slipping on the circle.
For any instant, the instantaneous center
of the motion of
the line is its point of tangent with the circle.
Note: We have not defined the term instantaneous center
previously. The instantaneous center or instant center
is defined in two ways :
When two bodies have planar relative motion, the instant
center is a point on one body about which the other rotates at the
instant considered.
When two bodies have planar relative motion, the instant center is
the point at which the bodies are relatively at rest at the instant
considered.
The normal at any point of an involute is tangent to the base
circle. Because of the property (2) of the involute curve, the motion of
the point that is tracing the involute is perpendicular to the line at any
instant, and hence the curve traced will also be perpendicular to the
line at any instant.
There is no involute curve within the base circle.
shows some of the terms for gears.
Figure 7-4 Spur Gear
In the following section, we define many of the terms used in the
analysis of spur gears.
Some of the terminology has been defined
previously but we include them here for completeness. (See
(Ham 58) for more details.)
Pitch surface : The surface of the imaginary rolling
cylinder (cone, etc.) that the toothed gear may be considered to
Pitch circle: A right section of the pitch surface.
Addendum circle: A circle bounding the ends of the teeth,
in a right section of the gear.
Root (or dedendum) circle: The circle bounding the spaces
between the teeth, in a right section of the gear.
Addendum: The radial distance between the pitch circle and
the addendum circle.
Dedendum: The radial distance between the pitch circle and
the root circle.
Clearance: The difference between the dedendum of one gear
and the addendum of the mating gear.
Face of a tooth: That part of the tooth surface lying
outside the pitch surface.
of a tooth: The part of the tooth surface lying
inside the pitch surface.
Circular thickness (also called the tooth
thickness) : The thickness of the tooth measured on the pitch
circle. It is the length of an arc and not the length of a straight
Tooth space: The distance between adjacent teeth measured
on the pitch circle.
Backlash: The difference between the circle thickness of
one gear and the tooth space of the mating gear.
Circular pitch
p: The width of a tooth and a space,
measured on the pitch circle.
Diametral pitch
The number of teeth of a gear per
inch of its pitch diameter.
A toothed gear must have an integral number of teeth. The circular
pitch, therefore, equals the pitch circumference divided by the
number of teeth. The diametral pitch is, by definition, the
number of teeth divided by the pitch diameter. That is,
p = circular pitch
P = diametral pitch
N = number of teeth
D = pitch diameter
That is, the product of the diametral pitch and the circular pitch
m: Pitch diameter divided by number of teeth. The
pitch diameter is usually specified in i in the
former case the module is the inverse of diametral pitch.
Fillet : The small radius that connects the profile of a
tooth to the root circle.
Pinion: The smaller of any pair of mating gears. The
larger of the pair is called simply the gear.
Velocity ratio: The ratio of the number of revolutions of
the driving (or input) gear to the number of revolutions of the driven
(or output) gear, in a unit of time.
Pitch point: The point of tangency of the pitch circles of
a pair of mating gears.
Common tangent: The line tangent to the pitch circle at
the pitch point.
Line of action: A line normal to a pair of mating tooth
profiles at their point of contact.
Path of contact: The path traced by the contact point of
a pair of tooth profiles.
Pressure angle :
The angle between the common normal at the point of tooth contact and
the common tangent to the pitch circles. It is also the angle between
the line of action and the common tangent.
Base circle :An imaginary circle used in involute gearing
to generate the involutes that form the tooth profiles.
lists the standard tooth system
for spur gears.
Table 7-1 Standard tooth systems for spur gears
lists the commonly used diametral pitches.
Coarse pitch
Fine pitch
Table 7-2 Commonly used diametral pitches
Instead of using the theoretical pitch circle as an index of tooth size, the base circle, which is a more fundamental circle,
can be used. The result is called the base pitch
pb, and it is related to the circular pitch p
by the equation
shows two meshing gears contacting at
point K1 and K2.
Figure 7-5 Two
meshing gears
To get a correct meshing, the distance of
K1K2 on gear 1 should be the same as the
distance of K1K2 on gear 2. As
K1K2 on both gears are equal to the base pitch of their gears, respectively. Hence
To satisfy the above equation, the pair of meshing gears must satisfy the
following condition:
Gear trains consist of two or more gears for the purpose of
transmitting motion from one axis to another. Ordinary gear
trains have axes, relative to the frame, for all gears comprising
the train.
shows a simple
ordinary train in which there is only one gear for each axis. In
a compound ordinary train is
seen to be one in which two or more gears may rotate about a single
Figure 7-6 Ordinary gear trains
We know that the velocity ratio of a pair of gears is the
inverse proportion of the diameters of their , and the diameter of the pitch circle equals to the number
of teeth divided by the . Also,
we know that it is necessary for the to mating gears to have the same
diametral pitch so that to satisfy the condition of correct
meshing. Thus, we infer that the velocity ratio of a pair of
gears is the inverse ratio of their number of teeth.
For the ordinary gear trains in , we have
These equations can be combined to give the velocity ratio of the
first gear in the train to the last gear:
The tooth number in the numerator are those of the driven gears,
and the tooth numbers in the denominator belong to the driver
Gear 2 and 3 both drive and are, in turn, driven. Thus, they are
called idler gears.
Since their tooth numbers cancel, idler
gears do not affect the magnitude of the input-output ratio, but they
do change the directions of rotation. Note the directional arrows in
the figure. Idler gears can also constitute a saving of space and
money (If gear 1 and 4 meshes directly across a long center distance,
will be much larger.)
There are two ways to determine the direction of the rotary
direction. The first way is to label arrows for each gear as in Figure 7-6. The second way is to multiple
mth power of "-1" to the general velocity ratio. Where
m is the number of pairs of
gears ( gear pairs
do not change the rotary direction). However, the second method cannot
be applied to the spatial gear trains.
Thus, it is not difficult to get the velocity ratio of the gear train
Planetary gear trains, also referred to as epicyclic gear
trains, are those in which one or more gears orbit about the
central axis of the train. Thus, they differ from an ordinary train by
having a moving axis or axes.
basic arrangement that is functional by itself or when used as a part
of a more complex system.
Gear 1 is called a sun gear , gear
2 is a planet, link H is an arm, or planet
Figure 7-8 Planetary gear trains
To determine the
of the planetary gear trains is slightly more complex an
analysis than that required for . We will follow the procedure:
Invert the planetary gear train mechanism by imagining the
application a rotary motion with an angular velocity of H to the
mechanism.
Let's analyse the motion before and after the inversion
Table 7-3 Inversion of planetary gear trains.
Note: H is the rotary
velocity of gear i in the imagined mechanism.
Notice that in the imagined mechanism, the
H is stationary and functions as a frame. No axis of gear moves any
more. Hence, the imagined mechanism is an .
Apply the equation of
of the ordinary
gear trains to the imagined mechanism. We get
Take the planetary gearing train in
as an example.
Suppose N1 = 36, N2 = 18, 1 = 0, 2 = 30.
the value of N?
With the application of the velocity ratio equation for the planetary
gearing trains, we have the following equation:
From the equation and the given conditions, we can get the answer:瀏覽人數 線上:11&本日:19本月:3428 累計:12675系統維護