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The Parameterization Design and Motion Analysis for Multi-start ZA Worm Gearing Based on Virtual Processing Jianping SUN, Zhaoping TANG School of Railway Transportation East China Jiao Tong University Nanchang, Jiangxi Province 330013, China Abstract Archimedes worm gears teeth surfaces are comply and their models were usually built approximately in CAD. This article analyses the processing character and formation principle of the Multi-start ZA worm, builds the accurate model and makes the full parametric design. In environment of Pro/E, applying the entire relevance character between virtual assembly and component, simulating reality processes, the worm gear was produced virtually, and its model was built accurately. Furthermore, the generated worm gear and worm were assembled virtually and their motions were simulated and analysed. Keywords: Computer aided design, Parameterization design, Motion analysis, Pro/E, Multi-start ZA worm gearing 1. Introduction Archimedes worm gears teeth surfaces are comply. At present, in the common CAD software, it is general that approximate drawing instead of worm gears really jugged 1 . It is very difficult to draw out its complicated and accurate tooth; in addition to, its match worm is classified for left- handed, right-handed, single-thread and multi-start. Those have increased difficulty to build its model. This paper starts mainly from the processing principle of Archimedes column worm (ZA worm), simulate its produce procedure, and make use of relations function in Pro/E, realize the accurate and parametric model of ZA worm. Furthermore, on the basis, the worm gear was produced virtually, and the generated worm gear and worm were assembled virtually and their motions were and analysed. 2. The train of thought to build model To imitate ZA worm turning process, draw cross section with the size and shape of parameterization worm gear hobs cross section, take Archimedes spiral as trajectory, make use of the “Variable Section Sweep/Cut” function in Pro/E, cut off one slot on the worm blank, then pattern the slot, the multi- start worm gear hob is generated. It is the model difficult points to full parameterize its hands and number of threads. The key point is: firstly, to set up the parameters of hands (right-handed value is 1, the left-handed value is -1) and number of threads, to establish the Archimedes spiral by the way of equation which can change with hands and number of threads. Secondly, while pattern worm slot, it is necessary that designer select the pattern way of “Direction”, and select the worm blanks axis as a reference to establish the first direction, enter the number of threads as number of members in the first direction and enter screw pitch as the spacing pattern members in the first direction. After finished worm gear hob parameterized model, on the basis, the worm model can generate by change parameter. The difference between worm and worm gear hob is that the worm gear hob has blade slot, and its radius is a clearance bigger than that of worm gear. The way which get worm gear model is to adopt the worm gear hob virtual processing. The basic train of thought is: in the virtual environment, to establish separately the worm gear blank and the worm hob, then place respectively them in each coordinate system which accord to the theory geometry assembles relation, make them rotate in each regulation, and do the Boole subtraction operation between them at different engagement position in the motion process, until the worm gear has been produced entire envelope surfaces 2 . 3. Build the relevance parameter From all above the train of thought, it can be known that ZA worm gearings parameterization design and motion analyse need to build those files such as the worm gear hob part, the worm part, the assembly between the worm gear hob and worm hob, and the assembly between the worm gear and worm. In order to realize parameterization design, these files need to parameterize their fundamental dimension. Table 1.The parametric table parameter m (modulus) q ( worm characteristic number) z1 (number of threads) xuan (hands) n (number of turns) value 5 18 3 1.0 4 parameter z2 (worm gear teeth number) hax (addendum factor) cx (bottom clearance factor) alpha (pressure angle) x2 (modification coefficient) value 53 1.0 0.2 20 -0.1 Making use of the parameters and relations function which Pro/E provides, according to the parameter relation between _____________________________ 978-1-4244-5268-2/09/$25.00 2009 IEEE Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. the worm and worm gear, parameters need be set up such as worm and worm gears modulus, worm characteristic number, hands, number of threads, number of turns, as shown in table 1. 4. To build the precise and parameterization model for ZA worm gear hob According to all above train of thought, firstly, designer need to cut off one slot on worm gear hob blank, as shown in Fig. 1 (a), then take worm gear hob blank axis as direction, pattern the slot which has generated just a moment ago, and add array relation: taking the number of threads as number of members and taking screw pitch as the spacing pattern members, as shown in Fig. 1 (b). (a) (b) Figure 1.Worm hob with a slot (a) and after pattern (b) (m=5, q=18, n=4, z1=3, left-handed) Adopting the Program module which is embedded in Pro/E Wildfire 2.0, the consumer can edit program according to design intention, design program, and can drive it size-fully and parametrically. According to systematic hint, consumer import the different design variable, the worm gear hob can be generated to satisfy consumers demand, as shown in Fig. 2. Figure 2.The worm hob which parameter has changed (m=2.5, q=11.2, n=6, z1=2, right-handed) 5. Establish the datum of virtual processing and assembly 5.1 Establish the datum in assembly file In Pro/E, those files are entire relevance between component and assembly. In order to realize the relative motion between worm gear hob and worm gear in the assembly, designer must establish separately the corresponding datum point and datum axis in component and assembly files, and parameterize these data, as shown in Fig. 3. Every component can be assembled with the help of these data. If parameters are changed, the worm gear hob and worm gear will rotate relatively according to given transmission ratio. Figure 3.The needed datum in virtual assembly The included angle is generally 90 degrees between two shafts of worm gearings component in space. In assembly, designer must establish separately the two necessary datum axes which crisscrossed mutually and datum points for place the worm gear hob and worm gear to assembly, and parameterize these data. In assembly, besides necessary parameters which have be stated before such as modulus, tooth number, the revolution angle parameter is also necessary to drive worm gear hob and worm gear revolution. The parameter is set up as jiao, initial value is 0. Finally it is necessary to input relations as follows: $d3=(m*q/2)*cos(jiao) /* x-coordinate of alignment point for worm gear hob $d4=(m*q/2)*sin(jiao) /* y-coordinate of alignment point for worm gear hob d5=m*pi*z1*n/2 /* z-coordinate of alignment point for worm gear hob d2=m*pi*z1*n/2 /*z-coordinate of alignment central point APNT0 for worm motion simulation, both x-coordinate and y- coordinate are 0 /*the worm and worm gear hobs alignment axis is through point APNT0 and vertical to ASM_FRONT /* the coordinate system ACS0 translates to APNT0 $d7=-m*(q+z2+2*x2)/2 /* the alignment datum central point APNT2s y-coordinate in the coordinate system ACS0 for the worm gear blank simulation d8=m*pi*z1*n/2 /* the alignment datum central point APNT2s z-coordinate in the coordinate system ACS0 for the worm gear blank simulation /* the worm gears alignment axis is through APNT2 and vertical to ASM_RIGHT /*the coordinate system translates to APNT2 for the worm gear simulation, taking the x axis positive direction of default coordinate system as its z axis positive direction, and its y axis Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. positive direction is the same as that in default coordinate system $d9=m*z2/2*cos(jiao*z1/z2) /*the worm gear alignment datum points x-coordinate in the worm gear simulation coordinate system $d10=m*z2/2*sin(jiao*z1/z2) /*the worm gear alignment datum points y-coordinate in the worm gear simulation coordinate system 5.2 Establish the needed datum in each part file for virtual processing and assembly To build a datum point on reference circle of the worm gear hob, align the hob axis with the hob datum axis which has been set up in assembly file while place it to assembly, align the datum point on the hob reference circle with corresponding datum point which has been set up in assembly file, because the datum point has been parameterized in assembly file, so the designer can realize to revolve the hob round their each alignment axis. Then it is necessary to make use of the relations function and input relations for the datum point as follows: d69=m*q/2 /*x-coordinate of alignment datum point for worm gear hob d71=m*pi*z1*n/2 /* z-coordinate of alignment datum point for worm gear hob Using same method, the worm gear blank is built. To be convenient to the after assembly, while the designer build model, he must pay attention to the worm gear blanks axis direction and the distance with coordinate system according to assembly relation, and build the necessary date to assemble and simulate, input relations as follows: D74=m*(q+x2*2)/2 /* z-coordinate of alignment datum point for worm gear blank 6. Virtual processing and assembly While place the components to assemble, designer need to align separately the worm axis, worm gear blank axis, the datum point on the worms reference circle and the datum point on the worm gear blanks reference circle with their corresponding axis or datum point which have been set up in assembly file. Because the datum points have been parameterized in assembly file, the designer can realize to revolve the worm and the worm gear blank round their each alignment axis by change the parameter. Making use of the “Tools--Parameters” function, changing the value of parameter “jiao” (the interval angle is smaller, the effect of worm gear is cut is better), the model can be regenerated. Making use of the “Edit--Component Operations--Cut Out” function, and cut the blank, then, in worm gear part files, designer edit the definition of the cut out id which has got just a moment ago, and change its attribute from subordinate to independent, ensure that the cut couldnt change follow the after change of the parameter value. To repeat all above step, until all worm gear slots are entirely and homogeneously cut off by the worm gear hob, as Fig.4 shows. To change the parameters of the worm and the worm gear blank, the different worm gear can be generated, as Fig.5 shows. Figure 4.The virtual processing and finished worm gear (m=5, q=18, n=4, z1=3, z2=53, left-handed) Figure 5.To assemble the worm gear with hob (m=5, q=18, n=4, z1=3, z2=53, left-handed) 7. Virtual assembly simulation and motion analysis of worm gearing 7. 1 Virtual assembly and motion simulation Replacing the worm gear hob, taking the worm as a component to place, worm gear is assembled with worm in the pin connection way. When the pin connections assemble, the simulated motion corresponding alignment axis and datum point must be chosen respectively, as Fig.6 shows. Figure 6.Define assemble connection After finished the component placement, the designer can add corresponding drive for them by the mechanism module, and simulate the motion. To choose “Applications--mechanism”, the designer can enter the mechanism module; click the button of “Define Servo Motors”, new built respectively “ServoMotor1” and “ServoMotor2”. In the “Type” label, to set up“Joint Axis” by choose respectively alignment axis which have defined when Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. Downloaded on May 28,2010 at 05:07:00 UTC from IEEE Xplore. Restrictions apply. assemble the worm gear with the worm, “Motion Type” is to “Rotation”, the designer need to pay attention to motion direction of the two electric motors. In “profile option card, the ServoMotor1s “Specification” need to be defined as “Velocity”, the “Magnitude” as the “Constant”, and its “A” as 360 multiply with worms threads number and divide worm gears teeth number. Hover ServoMotor2s “A” is set up as 360, to ensure that the engaging movement can satisfy the transmission ratio need between the worm gear and worm. The designer clicks the button of “Run an Analysis”, new built “AnalysisDefinition1”. In dialog boxs “preferences” option card, to set up “Start time”, “End time”, “Frame count” and “Frame rate”, expect that “End time” is the worm gear teeth number, the others are default. 7.2 Analyse the motion simulation There are some types that may be measured in mechanism module, such as “Position”, “Velocity”, “Acceleration”, “Connect Reaction”, “Net Load” etc. Analysing relative motion between the worm gear and the worm, designer must chose their each corresponding assembly coordinate system; ensure that coordinate system can not revolve following worm drive. To click the button of “Generate measure result of analyses”, new built measures from Measure1 to Measure4, and choose the “Graph measurement separately”, click the button of “Graph selected measures for results sets” in dialog box, measure values can be exported by the graph and the data. It is perceptual intuition and accurate, as Fig.7 and Fig.8 shows. Figure 7.Positions Y component graph and data of an index circle point on worm gear (up) or worm (down) Figure 8.Velocitys Y component graph and data of an index circle point on worm gear (up) or worm (down) In mechanism module, to click the button of “Replay previously run analyses”, In dialog boxs “interference option card , dynamic interference condition among every component can be detected; to click “Play current result set” -- “Capture” , the computer can record the animation to MPEG(export the film of mpg file format). From all above the output graph of motion simulation, there are following three points can be seen. (1)The worm gear and worm Positions Y component change in the way of the sine or cosine regular, so does velocitys Y component. It is identical with actual law which they do circling motion while they run. (2)The worm gear Positions Y component range is from - 132.5 to 132.5 mm. The worm Positions Y component range is from -45 to 45 mm. The worm gear velocitys Y component range is from -47.1238 to 47.1238 mm/s. The worm velocitys Y component range is from -282.743 to 282.743 mm/s. they are consistent with their theory value. (3)The worm gears Y component has 3 sine waves, and the worms Y component has 53 sine waves. It is identical with actual transmission ratio law while the worm gear and worm engage. It can be seen from all above that all emulation results and their theory calculation values are identical, also does their realities. References 1 CHEN Min-jie, LAI Zhen-hua, LI Zhi-ming. “Precise Modeling of Archimedes Worm in the Environment of UG”, Journal of Hubei University of Technology,2006,21(3):152156. 2 Tan Xin. “Research on the Digital Modeling Theory and Simulation Methods of Planar Double-Enveloping Toroid Worm Gear Drive”, Wuhan: Wuhan University of Technology,2003,6: 1722 Authorized licensed use limited to: CHINA UNIVERSITY OF MINING AND TECHNOLOGY. 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