2024年1月24日发(作者：)

力学的基本概念

对运动，时间和作用力作出科学分析的分支被称为力学，它由静力学和动力学两部分组成。静力学对静止系统进行分析，即在静力学系统中不考虑时间这个因素，而动力学是对随时间变化的系统进行分析。

通过配合表面作用力被传送到机器的各个部件，例如从齿轮传到轴或者是从一个齿轮通过啮合传递到另一个齿轮，从三角皮带传到皮带轮，或者从凸轮传到从动件。由于很多原因，我们必须知道这些力的大小。在边界或啮合表面作用力的分布一定要合理，他们的大小必须在构成配合表面材料的工作极限以内。例如，如果施加在滑动轴承的作用力太大，那么它就会将油膜挤压出来，并且造成金属和金属的接触，使温度过高，使滑动轴承失效。如果作用在齿轮轮齿上的力过大，就会将油膜从齿间挤压出来。这将会导致金属表层的破裂和剥落，噪音增大，运动不精确，直至报废。在力学研究中，我们主要关心力的大小，方向和作用点。

当一些物体连接在一起形成一个组合或者系统时，在两个接触的物体之间作用和反作用的力被称之为约束力。这些力约束各个物体使其处于特有的状态。作用在这个物体系统外部的力叫做外力。

电力，磁力和重力是不需要直接接触就可以施加的力的实例。不是全部但是大多数，与我们有关的力都是通过直接的实际接触或者是机械接触才能产生的。

力是一个矢量。力的要素就是它的大小，它的方向和作用点，一个力的方向包括力的作用线的概念和它的指向。因此，沿着力的作用线，力的方向有正副之分。

沿着两条不重合的平行线作用在一个物体上的两个大小相等、方向相反的作用力不能合并成一个合力。任何作用在一个刚体上的两个力构成一个力偶。力偶臂就是这两个力的作用线之间的垂直距离。

力偶矩也是一个矢量，用M表示，垂直于力偶面；M的方向主要依据右手螺旋定则确定。力矩的大小是力偶臂与其中一个力的大小的乘积。

如果一个刚体满足下列条件，那么它处于平衡状态：

（1）作用在它上面的所有外力的矢量和等于零。

（2）作用在它上面的所有外力对于任何一个轴的力矩之和等于零。

在数学上这两个条件被表示为

F0

M0

所使用的术语“刚体”可以是整台机器，一个机器中几个相互连接的零件，一个单独的零件或者是零件的一部分。隔离体简图是一个从机器中隔离出来的物体的草图或视图，在图中标出所有作用在物体上的力和力矩。通常图中应该包括已知的力和力矩的大小、方向还有其他相关信息。

这样得到的图成为“隔离体简图”，其原因是图中的零件或物体的一部分已经从其余的机械零部件中隔离出来了，其余的机器零部件对它的作用已经用力和力矩代替。对于一个完整的机器零部件隔离体简图，图上所表示出的，作用在其上面的力和力矩是通过与其相邻或相接触零件施加的，是外力。对于一个零件的一部分的隔离体简图作用在切面上的力和力矩都是通过被切掉部分施加的，是内力。

绘制和提交简洁、清晰的隔离体简图是工程交流的核心。这是真实的，因为

他们代表了思考过程的一部分，无论这个过程有没有绘制在图纸上，因为简图的绘制是把思考结果进行交流的唯一方式。无论出现的问题多么简单，你都要养成绘制隔离体简图的习惯。隔离体简图的绘制加速了解决问题的过程，大大的降低了犯错误的机会。

使用隔离体简图的优点总结如下：

（1）对于一个人来说，把词语、想法和观点用物理模型表示是很容易的。

（2）有助于帮助人们观察和理解一个问题的各个方面。

（3）有助于确定解决问题的途径。

（4）有助于发现和数学的关系。

（5）他们的应用易于记录解题的步骤，有助于作出有关简化的假设。

（6）解题所用的方法可以存储，供以后参考。

（7）他们有助于你的记忆，并且易于向其他人解释和表达你的工作。

在分析机器中的力时，我们几乎总是要把机器分离成许多单个的部件来绘制标有作用在各个部件上的力的隔离体简图。许多部件都要通过运动副进行连接。

在任何工程结构中，单个的零件或部件都将受到外力，而这些力是由他们所工作的环境或条件产生的。如果零部件处于平衡状态，那么外力作用的结果就是零，但是这些力共同在这个零部件上施加了一个载荷，这个载荷使这个零部件有变形的趋势，这种趋势是内力相互作用的结果，是在物体内部建立起来的。

把载荷施加到零部件上有许多不同的方法。载荷可以被归为如下几类：

（a） 静载荷是一个逐渐施加的载荷，因此在一个相对很短的时间力就可以达到平衡。

（b） 持续载荷是一个在相当长的时间内持续作用的载荷，例如物体的重力。这种类型的载荷被认为是和静载荷以同样的方式作用着；但是，由于温度和应力的原因，在短时间内加载和持续加载两种情况下，阻力失效有所不同。

（c） 冲击载荷是一个快速被施加的载荷（能源载荷）。震动通常是由冲击载荷引起的，直到震动被消除才能达到平衡，震动通常都是有阻尼力消除的。

（d） 重复载荷是一个被施加并且移动过上千次的载荷。

（e） 疲劳载荷或交变载荷的大小随着时间而改变。

有人注意到上述作用在处于平衡状态的物体上的外力和物体的内力相互作用。因此，如果一个物体受到拉伸或是挤压，例如在横截面上施加一个均匀的外力，那么就会产生均匀的内力，并且这个物体也会受到均匀的应力，这个应力被定义为

loadPstress

areaA因此应力是压缩应力还是拉伸应力取决于载荷的性质，它的单位是牛顿每平方米。

如果一个物体受到轴向载荷的作用，还产生力应力，物体的长度将发生变化。如果物体的原始长度是L，变化后长度增加了L，那么所产生的应变如下

strainchangeinlengthL

originallengthL因此应变衡量了物体的变形程度，它是无量纲，例如它没有单位；他是两个

具有相同单位的数量的比值。

因此，在载荷的作用下材料的变化实际上都是很小的，通常都用应变来表示，其形式是应变106，当它的形式变为时就是微应变。

拉伸应力和应变被认为是正向的。拉缩应力和应变被认为是负向的。因此负应变使长度减小。

如果材料在卸下载荷后恢复到没加载荷是的状态，这种材料是弹性材料。应用于大范围的工程材料，至少部分在负载范围内的弹性，其特点就是产生的变形和所施加的载荷成正比。因此载荷和它们所产生的应变成比例关系，变形和应变成比例关系，这也就意味着当材料是弹性材料时应力和应变成比例。因此胡克定律是

stressstrain

这则定律在一定的范围内适用于铁合金材料，甚至可以以一定的精度用于其他工程材料，如混凝土，木材和有色金属等。

如果材料是弹性的，当卸下载荷时，所产生的变形将完全恢复；不会产生永久变形。

在材料弹性范围内，在胡克定律应用范围内，可表示为

stressconstant

strain这种持续的象征用E来表示，被成为弹性模量或杨氏模量。因此

stressE

strain杨氏模量E在拉伸和压缩是被认为是一样的，对于大多数工程材料其数值都是很高的。特别是钢，E200109Nm2，因而应变通常都是很小的。

在大多数普通工程应用中应变很少超过0.1%。对于任何材料，杨氏模量的精确值都是通过在材料样品上进行标准试验才能确定。

Basic Concepts in Mechanics

The branch of sicientific analysis which deals with motions,time,and forces is

called mechanic and is made up of two parts,statics and s deals with

the analysis of stationary ,those in which time is not a factor,and dynamics

deals with systems which change with time.

Forces are transmitted into machine members through mating ,fron a

gear to a shaft or from one gear through meshing teeth to another gear,from a V belt to

a pulley,or from a cam to a is necessary to know the magnitudes of these

forces for a variety of distribution of the forces at the boundaries or

mating surfaces must be reasonable,and theirintensities must be within the working

limits of the materials composing the example,if theforce operating on a

journal bearing becomes too high,it will squeeze out the oil film and cause

metal-to-metal contact overheating,smd rapid failure od he the forces

between gear teeth are too large,the oil film may be squeezed out from between

could result in flaking and spalling of the metal ,noise,rough motion,and

eventual the study of mechanics we are principallyinterested in determining

the magnitude,direction,and location of the forces.

When a number of bodies are connected togther to form a group or system,the

forces of action and reaction between any two of the cinnecting bodies are called

constraint forces constrain the bodies to behave in a specific

external to this system of bodies are called applied forces.

Electic,magnetic,and gravitational forces are examples of forces that may be

applied without actual physical contact.A great many ,if not most,of the forces eith

which we shall be concerned occur through direct physical or nechanical contact.

Force F is a characteristics of a force are its nagnitude,its direction,and

its point of direction of a force includes the concept of a line,along

which the forfe is directed,and a ,a forceis directed positively or negatively

along a line of action.

Two equal and opposite foeces acting along two noncoincident parallel straifht

lines in abody cannot be combined to obtain a single resultant two such

forces acting on a body constitute a atm of the couple is the perpendicular

distance between their lines of action,and the plane of the couple is the plane

containing the two lines of action.

The moment of a couple is another vector M directed normal to the plane of the

couple;the sense of M is in accordance with the riht-hand rule for

magnitude of the moment is the product of the arm of the couple and the mafnitude of

one of the forces.

A rigid body is in static equilibrium if:

(1) The vector sum of all forces acting upon it is zero.

(2) The sum of the miments of all the foeces acting about any single axis is zero.

Mathematically these two statements are expressed as

F0

M0

The term “rigid body ” as used here may be an entire machine,severral connected

parts of a machine,a single part,or a portion of a part.A free-body diagram is s sketch

or drawing of the body,isolated from the machine,on which the forces and moments

are shown magnitudes and directions as well as other pertinent information.

The diagram so obtained is called “free” because the part or portion of the body has

been freed from the remaining machine elements and their effects have been replaced

by forces and the free-body diagram is of an entire machine part,the forces

shown on it are the external forces (applied forces) and miments exerted by adjoining

or connected the diagran is a portion of a part,the forces and moments acting

on the cut portion are the internal forces and moments exerted by the part that has

been cut away.

The construction and presentation of clear and nearly drawn free-body diagrams

represent the heart of engineeting is true because they represent a

part of the thinking process,whether they ate actually placed on paper or not,and

because the constuction of these diagrans is the only way the results of thinking can

be cimmunicated ti should acquire the habit og draqong free-body

diagrams no matter how simple the problem may appear to uction of the

diagrams speeds up the problem-solving process and greatly decreses the chances of

making mistakes.

The advantages of using free-body diagrams can be summarized as follows:

(1) They make it easy for one to translate words and thoughts and ideas into

physical models.

(2) They assist in seeing and understanding all facets of a problem.

(3) They help in planning the attack on the problem.

(4) They make mathematical relations easier to see or find.

(5) Their ude makes it rasy to keep track of one’s progress and helps in making

simplifying assumption.

(6) The methods used in the solution may be stored for future reference.

(7) They assidt your memory and make it easier to explain and present your

work to others.

In analyzing the forces in machines we shall amost always need to separate the

machine into its individual component and cinsteuct free-body diagrams showing

the forces thet act upon each of these parts will be cinnected to

each other by kinematic pairs.

In any engineering structure the individual components will be subjected to

external forces arising from the service conditions or environment in which the

component the component or member is in equilibrium,the resultant of the

external forces will be zero but,nevertheless,they together place a load on the

member which tends to deform that member and which must be reacted by internal

forces set up within the material.

There are a number of different ways in which load can be applied to a

may be classified with respect to time:

(a) A static load is a gradually applied load for which equilibrium is reached in a

relatively short time.

(b) A sustained load is a load that is constant over a long period od time,such as

the weight of a type of load is treated in the same manner as a

static load;however,for some materials and cinditions of temperature and

stress,the resistance to failure may be different under short time loading and

under sustained loading.

(c) An impact load is a rapidly applied load (an energy load).Vibration normally

results from an impact load ,and equilibrium is not established until the

vibration is eliminated,usually by natural damping forces.

(d) A reprated load is a load that is applied and temoved many thousands of

times.

(e) A fatigue or alternating load is a load whose magnitude and sign are changed

with time.

It has been noted above that external force applied to a body in equilibrum is

reacted by internal forces set up within the ,therefore,a bar is subjected to a

uniform tension or a force,which is unifoemly applied across the

cross-section,then the internal forces set up ate also distributed uniformly and the bar

is said to be subjected to a uniform normal stress,the stress being defined as

loadPstress

areaAStress

 may thus be compressive or tensile depending on the nature of the

loaad and wil be measured in units of newtons per square meter

Nm2 or

multiples of this.

If a bar is subjected to an axial load, and hence a stress, the var will change in

length. If the bar has an originallength L and changes in length by an amount

L, the

strain produced is defined as follows:

strainchangeinlengthL

originallengthLStrain is thus a measure of the deformation of the material and is

non-dimensional, i.e. it has no units; it is simply a ratio of two quantities with the

same unit.

Since, in practice, the extensions of materials under load are very small, it is

often convenient to measure the strains in the form of strain

106, i.e.

microstrain,when the symbol used becomes

.

Tensile stresses and strains are cinsidered positive in sense. Compressive stresses

and strains are considered negative in sense. Thus a negative strain produces a

decrease in length.

A material is said to be elastic if it returns to its original, unloaded dimensions

when load is removed. A particular form of elasticity which applies to a large range of

engineering materials, at least over part of their load range, produces deformations

which are proportional to the loads producing them. Since loads ate proportional to

the stresses they produce and deformations are proportional to the strains, this also

implies that, whilst materials are elastic, stress is proportional to strain. Hooke’s law

therefore states that

stressstrain

This law is obeyed within certain limits by most ferrous alloys and it can even be

assumed to apply to other engineering materials such as concrete, timber and

non-ferrous alloys with reasonable accuracy.

Whilst a material is elastic the deformation produced by any load will be

completely recovered when the load is removed; ther is no permanent deformation.

Within the elastic limits of materials, i.e. within the limits in which Hooke’s law

applies, ut has been shown that

stressconstant

strainThis constant is given the symbol E and termed the modulus of elasticity or

Young’s modulus. Thus

stressE (2.5)

strainYoung’smodulus E is generally assumed to be the same in tension or

compression and for most engineering materials has a high numerical value. Typically,

E200109Nm2 for steel, so that it will be oberved from Eq.(2.5) that strains are

normally very small.

In most common engineering applications strains rarely exceed 0.1%. The actual

value of Young’s modulus for any material is normally determined by carrying out a

standard test on a specimen of the material.