1、02FTM2Development and Application ofComputer-Aided Design and ToothContact Analysis of Spiral-Type Gearswith Cylindrical Wormsby: V.I. Goldfarb and E.S. Trubachov, IzhevskState Technical UniversityTECHNICAL PAPERAmerican Gear Manufacturers AssociationDevelopment and Application of Computer-AidedDesi
2、gn and Tooth Contact Analysis of Spiral-TypeGears with Cylindrical WormsV.I. Goldfarb and E.S. Trubachov, Izhevsk State Technical UniversityThestatementsandopinionscontainedhereinarethoseoftheauthorandshouldnotbeconstruedasanofficialactionoropinion of the American Gear Manufacturers Association.Abst
3、ractThepaperpresentsthemethodofstep-by-stepcomputer-aideddesignofspiral-typegearswithworms,whichinvolvesgearschemedesign,geometricalcalculationofagearing,drivedesign,calculationofmachinesettingsandtooth-contactanalysis.Models of operating and machine-tool gearing have been developed, including model
4、s of flank generation and theiractual interaction with account of flank modifications, manufacture and assembly errors, force and temperaturedeformations, and drive element wear as acting in real gearing.Possibilities of CAD-technique application are shown to solve design and manufacture tasks for g
5、earboxes andgear-motors with spiral-type gears.Copyright2002American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, Virginia, 22314October, 2002ISBN: 1-55589-802-5DEVELOPMENT AND APPLICATION OF COMPUTER-AIDED DESIGN AND TOOTH CONTACT ANALYSIS OF SPIRAL-TYPE GEARS WITH CYLINDRIC
6、AL WORMS V.I. Goldfarb and E.S. Trubachov Institute of Mechanics, Izhevsk State Technical University 7, Studenchenskaya str., Izhevsk 426069 Russia Tel/Fax +7 3412 590578 email: goldim.udm.ru Introduction The design process of any kind of gearing is a complex multi-step procedure; and different dire
7、ctions of the design and choice of parameters are possible with respect to many factors: initial requirements to the gear under design, mode of its operation, the applied technique, specific decisions made by a designer, and others. The determinacy level of the design procedure depends on the accumu
8、lated experience of design, manufacture and application of gears, formalized as standards for the calculation and CAD systems. Note that the design procedure is not quite determinate even for the most widespread cylindrical gear with its national and international standards and plenty of various com
9、puter systems, since there are (and obviously, there will be) many unsolved questions related with the strength evaluation, wear resistance, vibration activity, thermal balance, different degrees of manufacturing accuracy, materials of links, lubricants, modes of loading and so on. Lets divide conve
10、ntionally all the variety of gears into two groups depending on the existence or absence of standards (technique stated by law) for the calculation (design) of a gear. The first group is for gears with the worked out standards. Its interesting to note that CAD systems for a gear design may be also d
11、ivided conditionally into two groups depending on the same feature - availability of the standard design technique. The bases of first group CAD systems are standards. All the following computer systems (we name them CAI systems - Computer Aided Investigation) - applied to investigate the correspond
12、ing gearing - are a kind of subordinate ones and intended to solve special research tasks (influence of errors, stress loading, noise and so on) and modernize the basic standard and its corresponding CAD system. The second group of CAD systems are in the essence CAI systems. The gear design is perfo
13、rmed in this case when investigating the range of parameter values. The design experience accumulated under such investigation may be formed as some CAD system which is a component of the CAI system and is mostly the information data base of design references for certain ranges of initial parameters
14、. Spiral-type gears are referred to the second group of gears. They are gears with skew axes with the geometrical features of hypoid type gears but they are related to worm type gears according to the manufacturing technique 1. The remarkable role in the appearance (1954) and development of such gea
15、rs was played by ITW Inc., under the trade name spiroid, and its representatives O.Saari 2, 3 and others W. Nelson 4, 5 and others. Specific features and advantages of this gear are described in a great number of publications the major of which come from Russia lately 6, 7, 8, 9 and others where it
16、has been studied for about 40 years (spiroid gears are young compared with others with the age of several centuries). Nowadays many varieties of this gear are known, some of them are shown in Fig.1, and their effective applications in different technical fields are known to be successful within a bi
17、g range of performance parameters - gear ratio from 4 to 600 in one gear pair and torque from 1 to 50000 Nm and more. The computer system for spiral-type gear design described in this paper is in the essence a CAI system. Construction Fundamentals and Structure of Design Process 1. Any kind of gear
18、may have the following sequence of CAD creation: - the construction fundamentals and the structure of design process are formed; - methods of task solution at separate stages with account of the designed gear features are chosen and developed; - the structure of system and its software is worked out
19、. Lets open some principle aspects of this sequence. The construction fundamentals of the design process are also obvious enough: - accurate division of the statements of the design tasks, independent and variable groups, input and output parameters, dependent and independent on given design require
20、ments; this principle allows to focus the design purpose and construct informational bonds; - separation (decomposing) of the design process into stages with corresponding subsets of input and output parameters, which allows to eliminate unacceptable variants at primary stages and accelerate the pro
21、cess of choosing the required design solution; - setting of the order of parameter definition at each stage depending on the problem statement and design requirements. Lets discuss briefly another principle item connected with the statement of the design task. The preferable variant of the statement
22、 is the following: (),p fg p Pg G= (1) where p - are the values of gear parameters, P - is the area of possible p, g - are criteria of gear quality evaluation (technical requirements), G - is the area of possible values g. The sense of (1) is obvious: values of gear parameters are determined for giv
23、en values of technical requirements by means of some functional f. As the functional f is difficult, and more often impossible to create for most of gears including spiral-type, the design task is solved as g = y(p) - for the chosen set of initial parameters p the criteria g are found by means of th
24、e functional y to analyze the quality of the design solution. The design process is in this case the iterative one and implies the sequential approximation of the set p to the required (optimal) one according to given design requirements g. 2. The structure of gear design process may be largely pres
25、ented as the following sequence of stages (Fig.2): - synthesis of ideal gearing; - manufacturing synthesis of gearing; - evaluation of deformation mode of a gear; - analysis of tooth contact in a real gear; - prediction (evolutionary) of gear state; The feedbacks shown in Fig.2 emphasize the iterati
26、ve character of the design process. The information exchange between stages proceeds here via some controlling area Georgiev A.K, Goldfarb V.I., Goldfarb V.I., Goldfarb V.I. Nesmelov I.P. Russkikh A.G., (Russia) (Russia) Truba chov E.S. Patent RU 208396, Patent RU 806935 (Russia) Patent USA 3768326
27、Patent RU 2101582 and 7 Other Countries Fig.1. Different kinds of spiral-type gears Saari O.E. Saari O.E. Georgiev A.K. (USA) (USA) (Russia) Patent USA 2696125 Patent USA 2954704 Patent RU 186240, Patent USA 3289489 where the information concerning initial requirements to the gear under design and a
28、lso data from the primary standard base and reference standardized base are accumulated. Lets consider each of the pointed stages in more details. 2.1. The synthesis of ideal gearing is obviously the first design stage when the main geometrical and evaluation gear parameters are determined. This sta
29、ge (Fig.3) is also decomposed into the following separate steps with independent input and output parameters: - synthesis of gear scheme; - calculation of parameters which define the geometry of the worm (pinion) and wheel; - simulation of gearing geometry and kinematics; - calculation of forces, ef
30、ficiency and load capacity of the gear. Fig.2. Structure of gear design process Fig.3. Structure of ideal (conjugate) gearing synthesisSYNTHESIS OF IDEAL GEARING , 1,8 0,9 2SYNTHESIS OF GEAR SCHEME CALCULATION OF WORM AND GEARWHEEL GEOMETRYMODELING OF GEOMETRY AND KINEMATICS OF GEARING CALCULATION O
31、F FORCES, EFFIECIENCY, LOAD CAPACITY aw, , 1, u12, B1, b1, da1, mx, R, L, de2, di2, , vS, vr1(2), red., T2, , 0 0,3 DESIGN TASK INITIALREQUIREMENTS, PROTOTYPESBASE,REFERENCE BASESYNTHESIS OF IDEAL GEARING MANUFACTURING SYNTHESIS MODELING OF GEAR MODE OF DEFORMATION (LOAD TCA)PREDICTION OF GEAR STATE
32、 CONTROLLINGMODULE Fig.4. Structure of manufacturing synthesis Input parameters for the synthesis of gear scheme are center distance (aw), interaxial angle (), parameters which define the geometry and the position of the primary initial surface of the worm 10, 11, 12. Evaluation parameters of the ge
33、ar scheme are its overall dimensions, type of gearing, relative position of links, realization possibilities. The next stage is the calculation of worm and gearwheel geometry that is the definition of the axial module of worm threads; kind of worm threads screw surface, shape and dimensions of gear
34、wheel blank part. The most time-consuming step is simulation of conjugate (ideal) gearing geometry and kinematics. The major task at this step is modeling of enveloping process during which one calculates coordinates of points of contact lines, coordinates of tooth flank points, radii of curvatures
35、of surfaces at normal cross-sections, kinematic characteristics of the gearing sliding and rolling speeds, rate of contact points motion along surfaces enveloping each other. The important information concerning geometry (length and location of contact lines, length and location of gearing area, ove
36、rlap ratio, reduced radii of curvature) and kinematics of gearing is obtained. The pointed characteristics now give the idea of possibilities of the gear and, therefore, the quality of the initial set of parameters. The first and the major analysis of gearwheel tooth geometry is also performed at th
37、is stage the presence of tooth undercut and other types of interference, the presence of tooth wedging out at tooth point, the value of the transient area at tooth root. The final step of the first stage is the definition of important performance characteristics of the gear for ideal gearing forces,
38、 efficiency, and load capacity the allowable value of loading torque. Basically, the first stage completes the design of an ideal gear. Iterations here are concerned with such selection of gear parameters that it is realizable and its evaluation characteristics correspond to the initial task of the
39、design. In a number of cases this stage is enough to regard the gear designed and to start its manufacture, testing and application. The following stages give more complete representation of the gear; adjust it to real capabilities of manufacture and loading. 2.2. The task of manufacture synthesis (
40、Fig. 4) has two statements: a) to calculate cutting tool parameters, their position and motion when processing (lets call these parameters setting parameters) when the ideal conjugate flanks are generated; b) to choose setting parameters, providing such surface modification that the desired MANUFACT
41、URING SYNTHESIS SYNTHESIS OF MACHINE-TOOL GEARING ACCORDING TO LOCAL CONDITIONS TOOTH MODIFICATION FIELDS VALUES OF SETTING PARAMETERS METHODS OF MODIFICATION profile modification longitudinal modification method A worm or (and) hob method B settings for variation: aw, , da1, R,L, mx, z1 worm profil
42、e hob profile REQUIREMENTS TO CONTACT PATTERN GEOMETRY OF IDEAL GEARING tooth contact and the given sensitivity of the gear to different errors and deformations could be achieved. For the first statement the task is in many respects implemented even at the stage of synthesis of ideal conjugate geari
43、ng (the first of the pointed above stages), since setting parameters for gearwheel tooth processing repeat in principle the analogous parameters for the gearing of worm and gearwheel. In this case at the stage of manufacturing synthesis the hob imitating the worm or another cutting tool is designed,
44、 for instance, the fly cutter with the edges repeating the screw surface of the worm. The initial requirements to solve the task of manufacturing synthesis within the second statement may be: given position, shape and dimensions of the contact pattern or the instant contact area at the chosen gearin
45、g phase. The value of the necessary profile and longitudinal modification of gearwheel teeth (worm threads) may also be assigned here. These requirements are possible to be met by modifying both the worm thread surface (as it is done in 13) and the gearwheel flanks 14, 15. As a rule, the value of co
46、ntact pattern localization can be controlled by changing the relation of profile curvatures of the worm and cutting tool. The necessary modification in longitudinal direction of gearwheel teeth (worm threads) may be achieved by introducing the difference between the shape of pitch surfaces of the wo
47、rm and cutting tool: for example, by applying the worm with cylindrical (bevel) pitch surface and cutting tool with globoid one, or otherwise, the worm should be barrel-shaped and the cutting tool cylindrical (bevel). The rest setting parameters here remain identical to corresponding parameters of t
48、he ideal conjugate gearing. In general case, however, all the setting parameters may be changed, namely: the distance and angle between axes of the cutting tool and the gearwheel, pitch, diameter and profile angles of the cutting tool, gear ratio and processing feed. The criterion of the correct cho
49、ice of setting parameters is always the fulfillment of all the pointed above initial requirements, their specific implementation are dimensions and location of contact ellipse, calculated according to the reduced radii of flank curvatures, and the values of modifications both in the vicinity of the given calculated point and for the whole modified flank. 2.3. The task of deformation mode evaluation (Fig.5) also consists of two parts: solution of the task for: a) gearing elements and b) for the rest gea
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