1、附录Kinematics and dynamics of machineryOne princple aim of kinemarics is to creat the designed motions of the subject mechanical parts and then mathematically compute the positions, velocities ,and accelerations ,which those motions will creat on the parts. Since ,for most earthbound mechanical syste
2、ms ,the mass remains essentially constant with time，defining the accelerations as a function of time then also defines the dynamic forces as a function of time. Stress，in turn, will be a function of both applied and inerials forces . since engineering design is charged with creating systems which wi
3、ll not fail during their expected service life，the goal is to keep stresses within acceptable limits for the materials chosen and the environmental conditions encountered. This obvisely requies that all system forces be defined and kept within desired limits. In mechinery , the largest forces encoun
4、tered are often those due to the dynamics of the machine itself. These dynamic forces are proportional to acceletation, which brings us back to kinematics ,the foundation of mechanical design. Very basic and early decisions in the design process invovling kinematics wii prove troublesome and perform
5、 badly. Any mechanical system can be classified according to the number of degree of freedom which it possesses.the systems DOF is equal to the number of independent parameters which are needed to uniquely define its posion in space at any instant of time. A rigid body free to move within a referenc
6、e frame will ,in the general case, have complex motoin, which is simultaneous combination of rotation and translation. In three-dimensional space , there may be rotation about any axis and also simultaneous translation which can be resoled into componention along three axes, in a plane ,or two-dimen
7、tional space ,complex motion becomes a combination of simultaneous along two axes in the plane. For simplicity ,we will limit our present discusstions to the case of planar motion: Pure rotation the body pessesses one point (center of rotation)which has no motion with respect to the stationary frame
8、 of reference. All other points on the body describe arcs about that center. A reference line drawn on the body through the center changes only its angulai orientation.Pure translation all points on the body describe parallel paths. A reference line drawn on the body changes its linear posion but do
9、es not change its angular oriention. Complex motion a simulaneous combination of rotion and translationm . any reference line drawn on the body will change both its linear pisition and its angular orientation. Points on the body will travel non-parallel paths ,and there will be , at every instant ,
10、a center of rotation , which will continuously change location. Linkages are the bacis building blocks of all mechanisms. All common forms of mechanisms cams , gears ,belts , chains are in fact variations of linkages. Linkages are made up of links and kinematic pairs. A link is an (assumed)rigid bod
11、y which possesses at least two or more links (at their nodes), which connection allows some motion, or potential motion，between the connected links. The term lower pair is used ti describe jionts with surface contact , as with a pin surrounded by a hole. The term higher pair is used to describe jion
12、ts with point or line contact ,but if there is any clerance between pin and hole (as there must be for motion ),so-called surface contact in the pin jiont actually becomes line contact , as the pin contacts actually has contact only at discrete points , which are the tops of the surfaces asperities.
13、 The main practical advantage of lower pairs over higher pairs is their better ability to trap lubricant between their envloping surface. This ie especially true for the rotating pin joint. The lubricant is more easily squeezed out of a higher pair .as s result , the pin joint is preferred for low w
14、ear and long life . When designing machinery, we must first do a complete kinematic analysis of our design , in order to obtain information about the acceleration of the moving parts .we next want te use newtons second law to caculate the dynamic forces, but to do so we need to know the masses of al
15、l the moving parts which have these known acceletations. These parts do not exit yet ! as with any design in order to make a first pass at the caculation . we will then have to itnerate to better an better solutions as we generate more information. A first estimate of your parts masses can be obtain
16、ed by assuming some reasonable shapes and size for all the parts and choosing approriate materials. Then caculate the volume of each part and multipy its volume by materials mass density (not weight density ) to obtain a first approximation of its mass . these mass values can then be used in Newtons
17、 equation.How will we know whether our chosen sizes and shapes of links are even acceptable, let alone optimal unfortunately , we will not know untill we have carried the computations all the way through a complete stress and deflection analysis of the parts. It it often the case ,especially with lo
18、ng , thin elements such as shafts or slender links , that the deflections of the parts, redesign them ,and repeat the force ,stress ,and deflection analysis . design is , unavoidably ,an iterative process .It is also worth nothing that ,unlike a static force situation in which a failed design might
19、be fixed by adding more mass to the part to strenthen it ,to do so in a dynamic force situation can have a deleterious effect . more mass with the same acceleration will generate even higher forces and thus higher stresses ! the machine desiger often need to remove mass (in the right places) form pa
20、rts in order to reduce the stesses and deflections due to F=ma, thus the designer needs to have a good understanding of both material properties and stess and deflection analysis to properlyshape and size parts for minimum mass while maximzing the strength and stiffness needed to withstand the dynam
21、ic forces.One of the primary considerations in designing any machine or strucre is that the strength must be sufficiently greater than the stress to assure both safety and reliability. To assure that mechanical parts do not fail in service ,it is necessary to learn why they sometimes do fail. Then w
22、e shall be able to relate the stresses with the strenths to achieve safety .Ideally, in designing any machine element，the engineer should have at his disposal should have been made on speciments having the same heat treatment ,surface roughness ,and size as the element he prosses to design ;and the
23、tests should be made under exactly the same loading conditions as the part will experience in service . this means that ,if the part is to experience a bending and torsion，it should be tested under combined bending and torsion. Such tests will provide very useful and precise information . they tell
24、the engineer what factor of safety to use and what the reliability is for a given service life .whenever such data are available for design purposes，the engineer can be assure that he is doing the best justified if failure of the part may endanger human life ,or if the part is manufactured in suffic
25、iently large quantities. Automobiles and refrigrerators, for example, have very good reliabilities because the parts are made in such large quantities that they can be thoroughly tested in advance of manufacture , the cost of making these is very low when it is divided by the total number of parts m
26、anufactrued. You can now appreciate the following four design categories :(1)failure of the part would endanger human life ,or the part ismade in extremely large quantities ;consequently, an elaborate testingprogram is justified during design .(2)the part is made in large enough quantities so that a
27、 moderate serues of tests is feasible.(3)The part is made in such small quantities that testing is not justified at all ; or the design must be completed so rapidlly that there is not enough time for testing.(4) The part has already been designed, manufactured, and tested and found to be unsatisfact
28、ory. Analysis is required to understand why the part is unsatisfactory and what to do to improve it. It is with the last three categories that we shall be mostly concerned.this means that the designer will usually have only published values of yield strenth , ultimate strength,and percentage elongat
29、ion . with this meager information the engieer is expected to design against static and dynamic loads, biaxial and triaxial stress states , high and low temperatures，and large and small parts! The data usually available for design have been obtained from the simple tension test ,where the load was a
30、pplied gradually and the strain given time to develop. Yet these same data must be used in designing parts with complicated dynamic loads applied thousands of times per minute. No wonder machine parts sometimes fail. To sum up, the fundamental problem of the designer is to use the simple tension tes
31、t data and relate them to the strength of the part ，regardless of the stress or the loading situation. It is possible for two metal to have exactly the same strength and hardness, yet one of these metals may have a supeior ability to aborb overloads, because of the property called ductility. Dutilit
32、y is measured by the percentage elongation which occurs in the material at frature. The usual divding line between ductility and brittleness is 5 percent elongation. Amaterial having less than 5percent elongation at fracture is said to bebrittle， while one having more is said to be ductile. The elon
33、gation of a material is usuallu measured over 50mm gauge length，siece this id not a measure of the actual strain, another method of determining ductility is sometimes used . after the speciman has been fractured, measurements are made of the area of the cross section at the fracture. Ductility can t
34、hen be expressed as the percentage reduction in cross sectional area.The characteristic of a ductile material which permits it to aborb largeoverloads is an additional safety factot in design. Ductility is also important because it is a measure of that property of a material which permits it to be c
35、old-worked .such operations as bending and drawing are metal-processing operations which require ductile materials. When a materals is to be selected to resist wear ， erosion ,or plastic deformaton, hardness is generally the most important property. Several methods of hardness testing are available,
36、 depending upon which particular property is most desired. The four hardness numbers in greatest use are the Brinell， Rockwell，Vickers, and Knoop. Most hardness-testing systems employ a standard load which is applied to a ball or pyramid in contact with the material to be tested. The hardness is an
37、easy property to measure , because the test is nondestructive and test specimens are not required . usually the test can be conducted directly on actual machine element . Virtually all machines contain shafts. The most common shape for shafts is circular and the cross section can be either solid or
38、hollow hollow shafts can result in weight savings). Rectangular shafts are sometimes used, as in screw driver bladers ,socket wrenches and control knob stem.A shaft must have adequate torsional strength to transmit torque and not be over stressed. If must also be torsionally stiff enough so that one
39、 mounted component does not deviate excessively from its original angular position relative to a second component mounted on the same shaft. Generally speaking，the angle of twist should not exceed one degree in a shaft length equal to 20 diameters.Shafts are mounted in bearing and transmit power thr
40、ough such device as gears, pulleys,cams and clutches. These devices introduce forces which attempt to bend the shaft;hence, tha shaft must be rigid enough to prevent overloading of the supporting bearings ,in general, the bending deflection of a shaft should not exceed 0.01 in per ft of length betwe
41、en bearing supports.In addition .the shaft must be able to sustain a combination of bending and torsional loads. Thus an equivalent load must be considered which takes into account both torsion and bending . also ,the allowable stress must contain a factor of safety which includes fatigue, since tor
42、sional and bending stress reversals occur.For fiameters less than 3 in ,the usual shaft material is cold-rolled steel containing about 0.4 percent carbon. Shafts ate either cold-rolled or forged in sizes from 3in. to 5 in. for sizes above 5 in. shafts are forged and machined to size ， plastic shafts
43、 are widely used for light load applications . one advantage of using plastic is safty in electrical applications, since plastic is a poor confuctor of electricity.Components such as gears and pulleys are mounted on shafts by means of key. The design of the key and the corresponding keyway in the sh
44、aft must be properly evaluated. For example, stress concentrations occur in shafts due to keyways ,and the material removed to form the keyway further weakens the shaft.If shafts are run at critical speeds , severe vibrations can occur which can seriously damage a machine .it is important to know th
45、e magnitude of these critical speeds so that they can be avoided. As a general rule of thumb ,the difference between the operating speed and the critical speed should be at least 20 percent.Many shafts are supported by three or more bearings, which means that the problem is statically indeterminate
46、text on strenth of materials give methods of soving such problems. The design effort should be in keeping with the economics of a given situation , for example , if one line shaft supported by three or more bearings id needed , it probably would be cheaper to make conservative assumptions as to mom
47、ents and design it as though it were determinate . the extra cost of an oversize shaft may be less than the extra cost of an elaborate design analysis.Another important aspect of shaft design is the method of directly connecting one shaft to another , this is accomplished by devices such as rigid an
48、d flexiable couplings. A coupling is a device for connecting the ends of adjacent shafts. In machine construction , couplings are used to effect a semipermanent connection between adjacent rotating shafts , the connection is permanent in the sense that it is not meant to be broken during the useful
49、life of the machine , but it can be broken and restored in an emergency or when worn parts are replaced.There are several types of shaft couplings, their characteristics depend on the purpose for which they are used , if an exceptionally long shaft is required in a manufacturing plant or a propeller shaft on a ship , it is made in sections that are coupled together with rigid couplings. A common type of rigid couplin
