1、316 2010 ASHRAEThis paper is based on findings resulting from ASHRAE Research Project RP-1017.ABSTRACTEarlier we demonstrated the effectiveness of multimediaand advanced presentation techniques such as 3D computergraphics, visualization and animation techniques (Akleman2002). The previous paper was
2、intended to serve as a modeland guide for the broad use of these techniques in otherASHRAE publications. However, the 3D Models and Anima-tions that were developed for ASHRAE publications has aunique set of problems that are different from classical 3Dmodeling and animation problems. Our experience
3、with thisproject convinced us that these models and animations cannotbe created without close collaboration between ASHRAE engi-neers and animation specialists. Therefore, in this paper, weexpand the discussion initiated in the first paper by presentingsome of the unique sets of difficulties we have
4、 faced during theprocess using two case studies, modeling and animation, of:(1) Rolling Piston and (2) Twin Screw Compressors.INTRODUCTIONRecently a set of enhancements to the ASHRAE Hand-book (ASHRAE 96) were presented. These enhancementsdemonstrated the effectiveness of multimedia and advancedpres
5、entation techniques such as 3D computer graphics, visu-alization and animation techniques (Akleman 2002). Usingcompressors as the subject, in the ASHRAE Research Project1017-RP, we expanded on the traditional printed materialcontained in Chapter 34 of the 1996 HVAC Systems andEquipment Handbook. Thi
6、s demonstration currently serves asa model and guide for the broader use of these techniques inother ASHRAE publications. The enhanced chapter which iscontained in the CD-ROM version of the Handbook, is used topromote the effectiveness of improved presentation tech-niques, and the value of ASHRAE in
7、formation resources.Our earlier paper gives a general introduction to all theenhancements to the chapter. However, among these enhance-ments, 3D Modeling and Animation warrant a more carefulexamination because they create a special set of problems thatrequire specific solutions with a collaboration
8、betweenASHRAE engineers and animation specialists. In this paper,we discuss the several causes of temporal aliasing problemsand we present a unique set of difficulties we faced during theprocess using two case studies, namely modeling and anima-tion of: (1) Rolling Piston and (2) Twin-Screw Compress
9、ors.BACKGROUND: RECONSTRUCTION ERROR AND TEMPORAL ALIASINGThe motion of many types of compressors is cyclical, i.e.,compressors repeat the same motion again and again rapidlycompressing small batches of gas (so fast it appears to becontinuous). These cyclic motions are the result of the rotationof a
10、xially (or rotationally) symmetric objects which can bedescribed as follows. Formally, an object O is rotationallysymmetric around the rotation axis n with rotation angle ifO = Rn,O where Rn,is a rotational operator that rotatesobject O around the rotation axis n.The angle of rotational symmetry dep
11、ends on the repre-sentation of the shape as well as the coloring and rotation axis.The basic shapes that have rotational symmetry are spheres,cylinders, toroidal shapes, and stars. Figure 1 shows how theshape of the object affects the rotational-symmetry angle.Demonstration of the Use of Multimedia
12、Electronic Information Enhancements for a Chapter Handbook CD-ROM: 3D Modeling and AnimationJeff Haberl, PhD, PE Ergun Akleman, PhDFellow ASHRAEJeff Haberl is a professor in the Department of Architecture and an associate director of the Energy Systems Laboratory at Texas A Table 1 shows the recon-s
13、truction error for different values. In this table, the absolutevalue of the difference between and the rotation angle fromthe last frame to the first frame corresponds to the reconstruc-tion error. For a realistic animation, we want the value of thereconstruction error to be zero. If the value is n
14、ot zero, theviewers will observe a sudden change in speed from the lastframe to the first frame. As is shown in the table in Table 1, thesudden change in speed can be as much as 50% of the speedof animation.The reconstruction error problem can be solved by iden-tifying the minimum number of the fram
15、es that will give seam-less cyclic animation. For seamless animation, the totalrotation after N number of frames must be divisible by both and . In other words, the total rotation must be lcm(,) wherelcm is the least common multiplier of and . Based on thisvalue, we can find that(3)Figure 1 Shape ve
16、rsus rotational angle: An example thatshows how the representation affects therotational-symmetry angle.Figure 2 Color versus rotational angle: An example thatshows how coloring of a shape changes therotational symmetry.Nlcm ,()-= 2010, American Society of Heating, Refrigerating and Air-Conditioning
17、 Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 318 ASHRAE TransactionsUnfortunately, t
18、he value of N fluctuates depending on values and can be very large for relatively-prime and values. An example is shown in the table in Table 2.As seen in Table 2, making larger does not help to createa smaller animation file. Generally speaking, for , the bestchoice is = /3. This choice will create
19、 a cyclic animationusing only three frames. In practice, we use more than threeframes.Temporal AliasingTemporal aliasing may cause the animated object toappear: (1) to rotate slower than the intended speed, (2) torotate in the opposite direction of the intended motion, and(3) to stop. In order to id
20、entify these cases, we will first lookat the relationship between and . Note that since the objectis rotationally symmetric, if /2, the viewer cannotperceive the real motion. For instance, if = n , where n is anyinteger, then the rotationally symmetric object will appear tobe static; in each time st
21、ep, the object will look exactly thesame. The statement = n can be rewritten as(4)where F is the largest integer that is smaller than F andF =1/T is the intended frequency of the rotation. Equation (4)is useful to identify three distinct temporal aliasing cases.Case 1: 1 0.5. In this case, the objec
22、t appears tobe rotating in the opposite direction than the intended motionsdirection.More Than One Rotationally-Symmetric ObjectIn engineering applications, we often need complicated,rotationally symmetric objects that will be constructed as acombination of basic symmetric shapes. This can be descri
23、bedin the following way: if a rotationally symmetric objectconsists of N basic shapes, and each basic shape i has a rota-tional angle i, the combined rotational angle of theconstructed object equals lcm(1, 2, , N) where lcm is theleast common multiplier of 1, 2, , N.If a rotationally symmetric objec
24、t consists of two basicshapes, such as those shown in Figures 1A and 2A, since inboth cases = 30, then the combined also becomes 30. Onthe other hand, if we create a shape combining two basicshapes, such as those shown in Figures 1B and 2B, then thecombined = lcm(45, 60) = 180, which is much larger
25、thaneither of the . If is are relatively-prime, then the combined = 1 2 N, which is a much larger number than therotation angle of any one of the basic components. In suchcases, to avoid reconstruction error, we need to have longeranimations. The only solution in these cases is to slightlychange the
26、 rotational symmetry of each component. We willdiscuss this solution in the following section. CASE STUDIESWe consider two case studies: Rolling piston and twin-screw compressor animations.Case 1: Rolling Piston CompressorFor rolling piston compressors, the figure provided inChapter 34 (ASHRAE 1996)
27、 is shown in Figure 3. In Figure3, it is not easy to understand how the piston is working just bylooking at this figure. This is because most people fail to seethe opposing rotation of the concentric pistons. To understandthis motion, we first created a cardboard model of a rollingpiston to show how
28、 the piston turns. We eventually figured outthat the piston rolls in a counter-clockwise direction while theshaft is rotating clockwise. To animate this, we faced a numberof problems which varied depending on whether we werecreating a pre-computed animation or an interactive anima-tion.The basic que
29、stions were:How can we graphically display the piston motion?How can we graphically display the fluid motion?Table 1. Reconstruction Error versus , , T, NThe Table that Shows the Reconstruction Error for = 30 T NRotation Angle from the Last Frame to the First FrameRecon-struction ErrorPercentageErro
30、r30 13 2.3 2 17 4 4/13=%31 faster30 12 2.5 2 18 6 6/12-%50 faster30 11 2.7 3 8 3 3/11=527 slower30 10 3.0 3 10 0 0/10=%030 9 3.3 3 12 3 3/9=%33 faster30 8 3.7 4 6 2 2/8=%25 slower30 7 4.3 4 9 2 2/7=%29 fasterTable 2. The Tables that Show How Many Frames are Needed to Avoid the Reconstruction Error f
31、or = 30 30 13 3030 12 530 11 3030 10 330 9 1030 8 1530 7 30Nlcm ,()-=-1T-1T- FF 0= 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribu
32、tion, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 319How can we create a small size web-efficient anima-tions?We first created a computer model with correct dimen-sions as shown in Figure 4. One problem was that it le
33、ft sucha small space to display fluid motion. To resolve this problemwe enlarged the gap where the fluid flows. A more importantproblem was that it was impossible to create a small animationfile using the correct dimensions. Since the size of the anima-tion file directly depends on the period of cyc
34、lic animation, toreduce the size of the animation file, we made the period of theanimation as small as possible while avoiding a reconstructionerror. Unfortunately, based on the correct dimensions, theperiod of the cyclic animation turned out to be high.The source of the problem was that there were
35、twomotions in the rolling piston animation (inner and outer circle-rotations), and the periods of these two motions were rela-tively prime. To resolve this, we noted that we can change and by changing the radius of the inner and outer circles. Byplaying the values of and , we were able to drasticall
36、yreduce the size of the animation. Although the resulting modelwas not technically correct, the resulting animation workedfaster, downloaded faster and gave a better idea about themotion of pistons in a rolling piston compressor. Selectedframes of the resulting animation are shown in Figure 5.Note t
37、hat Figure 5 also shows flow animation. To improvethe quality of the visualization of rolling piston compressors,we used a flow animation method developed earlier byAkleman (2000, 2002). Rolling piston compressors use aroller mounted on the eccentric axis of a shaft with a singlevane or blade suitab
38、ly positioned in the non-rotating cylindri-cal housing, generally called the cylinder block. This bladereciprocates in the slot machined in the cylinder block. Thisreciprocating motion is caused by the eccentricity of themoving roller directly below the blade that repeatedly lifts theblade. In order
39、 to create a rolling piston animation, we devel-oped a simple texture-mapped 3D model for the compressorand animated the cylinders. We then rendered this animationusing a parallel projection technique to include flow anima-tion. The flow animation, which is used to give the illusion ofthe gas flow i
40、n the compression, was created separately. Thesetwo animations were then combined using a compositingprogram (Brinkman 1999).Case 2: Twin-Screw CompressorDue to their complex 3D motions, the working principlesof twin-screw compressors need to be visualized with 3Dperspective projection. The Chapter
41、34 figures related to thesecompressors were drawn using static perspective projection toshow rotating and translating parts (ASHRAE 1996). Unfor-tunately, these static images provide little insight into howthese parts move during the compression process. Forinstance, the figure provided in Chapter 3
42、4 for twin-screwcompressors is shown in Figure 6. Unfortunately, it is not easyto understand the 3D structure of the compressor just by look-ing at this figure, and without an understanding of the exact 3Dstructure, it is difficult to understand how the compressorworks.Fortunately, we had a simple m
43、odel of this particularcompressor with a transparent casing that was obtained by atrade fair. Figure 7 shows a photograph of this simplifiedFigure 3 Rolling piston diagram.Figure 4 A computer-generated model of a rolling pistonwith correct dimensions. 2010, American Society of Heating, Refrigerating
44、 and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. 320 ASHRAE Transac
45、tionsmodel of a twin-screw compressor with a transparent casing.By viewing this model, we discovered that the number of theblades in the two screws were not the same. Another problemwas understanding how the compressor worked. To under-stand the air motion, we dropped small candies into this modelan
46、d observed how the candies travel through the twin screws.By tracing the individual candy motion, we eventually deter-mined that the air did not rotate inside of the twin-screw cham-bers. Instead, we observed that each pocket of air followed anear linear path from the inlet to the outlet. Note that
47、to create engineering animations, it is some-times unnecessary to use computer technology. In the ease ofthe transparent model of the twin-screw compressor, it waspossible to use stop-motion animation of an existing 3Dmodel. Figure 8 shows nine frames of stop-motion animationof a twin-screw compress
48、or model.To represent these compressors with an animation, we firstdeveloped high-quality, three-dimensional computer modelsusing a commercial software package (Boardman 2001). Wethen produced animations showing the dynamic operation ofthese compressors and the compressor components usingphoto-reali
49、stically rendered animation images. An example ofa photo-realistically rendered 3D animation image frame isshown in Figure 9. These 3D image frames provide “picture-quality,” solid-looking dynamic representations of the criticalFigure 5 Selected (every 4th) frames of a rolling piston animation. The numbers below indicate the frame number. The wholeanimation consists of 32 frames. Note that the piston rolls clockwise.Figure
