A Study of a Variable Compreion Ratio and Diplacement Mechanim Uing Deign of Experiment Methodology Shugang Jiang, Michael H. Smith, Maanobu Takekohi Abtract Due to the ever increaing requirement for engine performance, variable compreion ratio and diplacement are drawing great interet, ince thee feature provide further degree of freedom to optimize engine performance for variou operating condition. Different type of mechanim are ued to realize variable compreion ratio and diplacement. Thee mechanim uually involve relatively complicated mechanical deign compared with conventional engine. While the flexibility in thee mechanim introduce additional engine deign and control poibilitie, it alo increae the challenge for the development and optimization, ince how the geometry of the mechanim affect the engine performance i not traightforward, and building prototype engine of variou mechanical deign parameter take a long time with high cot. Thi paper preent a tudy of a multiple-link mechanim that realize variable compreion ratio and diplacement by varying the piton motion, pecifically the Top Dead Center (TDC) and Bottom Dead Center (BDC) poition relative to the crankhaft. The tudy focue on obtaining deirable behavior for both compreion ratio and diplacement. It i determined a major requirement for the deign of the mechanim i that when the control action change monotonically over it whole range, the compreion ratio and diplacement hould change in oppoite direction monotonically. Thi paper give an approach on how to achieve multiple-link mechanim deign that fulfill thi requirement. Firt, a condition i obtained on how the TDC and BDC poition hould change with repect to the control action to fulfill the deign requirement. Then Deign of Experiment (DoE) methodology i ued for creating et of geometric deign of the mechanim. Kinematic of the mechanim are calculated for each deign and checked againt the condition. Baed on the outcome, a feaible deign i elected and detailed tudy on uch characteritic a piton motion, troke length, combution chamber volume, diplacement, crank angle range of the expanion troke, and compreion ratio i performed. Direction for future work in imulation and teting of the mechanim are given. 1. Introduction Ever increaing requirement for engine performance and tricter exhaut emiion and fuel economy tandard have been driving engine technology advancement. Variable compreion ratio technology ha long been recognized a a method to improve engine fuel economy [1]-[]. A the compreion ratio increae, the engine thermal efficiency increae. However, too high compreion ratio will lead to engine knock. With variable compreion ratio, at low power level the engine operate at a higher compreion ratio to capture the benefit of high fuel efficiency; at high power
level the engine operate at a lower compreion ratio to prevent knock. By continuouly changing the compreion ratio, an engine enable optimum combution efficiency at all engine peed and load condition, realizing better engine performance, lower fuel conumption, and lower exhaut emiion. There are variou approache to realize variable compreion ratio, uch a moving the cylinder head, moving the crankhaft axi, and uing multiple link for connection between piton and crankhaft. While the main purpoe of thee mechanim i to realize variable compreion ratio, they might alo lead to change in many other apect of the engine, uch a piton motion, troke length, charging and dicharging efficiency, and combution procee. Thee characteritic need to be conidered when deigning the variable compreion ratio mechanim and determining it detailed dimenion value. Optimization of related engine control parameter need be performed accordingly a well. Thi paper focue on tudying a multiple-link connecting rod mechanim [4]-[6]. Thi mechanim realize variable compreion ratio by varying the piton motion, pecifically the TDC and BDC poition of the engine. So far major tudie of the multiple-link mechanim have focued on the variable compreion ratio characteritic. However, a good deign of the geometry of the mechanim hould realize not only the deired compreion ratio, but alo advantageou diplacement behavior of the engine. Since higher compreion ratio i ued for low and medium power level, where decreaed diplacement i advantageou, the deired deign of the multiple-link mechanim i that when the control action change monotonically, the compreion ratio and the diplacement change monotonically in oppoite direction. Thi paper preent an approach to obtain geometric deign of the mechanim that fulfill the requirement mentioned above. Firt a condition i obtained in the format of how the TDC and BDC poition hould change with repect to the control action in order that the mechanim will give the deired behavior. Equation decribing the kinematic of the component in the mechanim are derived. The piton poition can be calculated during the whole revolution of the crankhaft for pecific mechanim dimenion and control action. To obtain geometric deign of the mechanim that atify the condition, Deign of Experiment (DoE) methodology i ued for creating et of geometric parameter, including crank radiu, crank offet, upper link length, lower link dimenion, control link length, control link poition, and control haft length. Piton motion correponding to each parameter et i calculated and the behavior i checked againt the condition. A feaible deign that atifie the condition i elected for further tudy. Such characteritic a detailed piton motion profile, piton velocity and acceleration, crank angle range of the expanion troke, combution chamber volume, diplacement, and compreion ratio are invetigated for the deign. Thee reult erve a a bai for further analyi and optimization of the mechanim geometric deign. The paper i organized a follow: the multiple-link mechanim i decribed and it equation of motion are derived in Section. Section preent the condition on how the TDC and BDC poition hould change with repect to the control action to fulfill the deign requirement for achieving deired compreion ratio and diplacement behavior. In Section 4, a Deign of Experiment (DoE) plan i
etablihed for the mechanim dimenion, and the kinematic of the mechanim are calculated for each deign and checked againt the condition. Further detailed tudy of a deign that atifie the condition i preented in Section 5. Section 6 provide direction for future tudie of the mechanim uing imulation oftware and teting. The lat ection ummarize the paper.. Multiple-link Mechanim Configuration of the multiple-link mechanim i hown in Figure 1. Origin (O) i the crankhaft axi. The crank pin (A) and piton pin (E) are connected by mean of an upper link (DE) and a lower link (ABD). The lower link i alo connected, via a control link (BC), to the eccentric journal of a control haft (SC). When the crankhaft rotate, the lower link revolve around the crankhaft axi and pivot around the crank pin. Meanwhile, motion of the lower link i contrained by the control link. Note the crankhaft (OA), the lower link (AB), the control link (BC), and egment (OC) which can be conidered a ground link, form a four-bar linkage. A a reult, when the crankhaft rotate, the control link act a a rocker and rotate through a limited range of angle around the eccentric journal of the control haft. The connection point (D) of the lower and upper link trace roughly an oval hape and the piton pin (E) undergoe reciprocal motion. The control haft (SC) i upported by the engine block. The ditance between the center of the eccentric journal and the control haft axi i denoted a l, and will be called control haft length in thi tudy. When the angle of the control haft relative to the engine block ( θ ) i changed, the poition of the control link will change, which ubequently tilt the lower link clockwie or counterclockwie and thereby affect the motion of the piton and hift the TDC and BDC poition. Thi lead to change in both the combution chamber volume and the wept volume, and conequently change the compreion ratio. By manipulating the control haft angle θ the engine can realize different compreion ratio for variou operating condition. Note that in order for the multiple-link mechanim to operate a deired, certain contraint need to be atified for it geometric dimenion over the whole range of the control action θ. A major requirement i that the length of link of the four bar linkage (OABC) need to atify the Grahof Condition, which tate that the um of the length of the hortet and longet link need be le than that of the remaining link. Thi contraint need to be verified during deign of the mechanim dimenion.
Figure 1 Multiple-link Mechanim The equation governing the motion of the multiple-link mechanim are derived a follow. In Figure 1, denote the poition of the control haft axi (S) a ( X S, Y S ). The poition of control link point (C) i then: X = X + l coθ (1) Y C C S S = Y + l inθ () Note for the four bar linkage (OABC), we have: OA + AB = OC + CB () Rewrite equation () and define a new vector a: = ( X, Y ) = OA OC = CB AB (4) Since OA and OC are known at each crank angle θ 1 and control haft angle θ, can be calculated and we have X l coθ (5) From equation (4) we alo have Y = 1 1 X c = l1 1 Y c inθ (6)
X Y = l θ θ (7) co l co in l in = l θ θ (8) By eliminating θ from equation (7) and (8), we obtain l l + X + Y (9) X coθ + Y inθ = l Define the right hand ide of equation (9) a m, we have the olution a (10) 1 Y 1 ± m θ = tan co X X + Y The two olution of θ correpond to the two mode of aembly for the four bar linkage (OABC), which are ymmetric about line OC. The olution for Figure 1 i: (11) 1 Y 1 + m θ = tan co X X + Y Subequently, θ can be calculated from equation (8) a: 1 l inθ Y (1) θ = π in l Since OB = OC + CB, the poition of B can be calculated a: X X l coθ B = C + (1) Y = Y l inθ (14) C B + Thu, the motion of the four bar linkage (OABC) i determined. The motion of point (D) can be calculated by making ue of the lower link dimenion. Note: 1 l + l4 l (15) 5 θ = 4 θ co ll4 the Poition of (D) can be obtained from OD = OA + AD a: X D = l1 coθ1 + l4 coθ (16) 4 Y D = l + θ (17) 1 inθ1 l4 in Latly, the poition of the piton pin (E) can be obtained. Denote the crank offet a δ, then 1 δ X (18) θ = 6 co D l6 and ubequently from 4 OE = OD + DE, the piton pin poition i obtained a: Y = Y l inθ (19) 6 6 E D + Thu, with the geometric dimenion of the multiple-link mechanim known, we can calculate the motion of each component for the whole crank haft revolution, given the control haft angle. In thi tudy the piton motion i the focu. With the piton motion profile calculated for the crank angle ( θ 1 ) range from 0 to 60, we can obtain the TDC and BDC poition and their correponding crank angle. We can alo calculate the velocity and acceleration of the piton, the troke length, the crank
angle range of the expanion troke, the diplacement, the combution chamber volume, and the compreion ratio.. Multiple-link Mechanim Deign Criterion The main purpoe of the multiple-link mechanim i to realize variable compreion ratio. However, becaue the mechanim realize thi feature by changing the piton motion, it may lead to change in the troke length, and conequently the diplacement, a well. When compreion ratio and diplacement change, variou characteritic of the engine, uch a the charging and dicharging procee, volumetric efficiency, combution proce and efficiency, and power output all can change. When deigning a multiple-link mechanim, all thee influence need to be conidered. Since compreion ratio and troke length (and diplacement) are ultimately determined by the geometry of the mechanim, thi paper focue on finding an approach to obtain the geometric dimenion that give advantageou compreion ratio and diplacement behavior. Thi i the bai for further deign and optimization of the mechanim. A dicued before, when engine load decreae, compreion ratio hould increae to capture the benefit of higher fuel efficiency; while for a decreaed engine load demand, a decreaed diplacement i advantageou, ince for decreaed diplacement and troke length, the pumping lo and frictional lo are reduced. With variable diplacement, le throttling of the intake air will be needed to take care of the load variation. Thi i a deired property for the engine. From the above dicuion, we can ee that a deired deign of the multiple-link mechanim i that when the control action change monotonically, the compreion ratio and the diplacement hould change monotonically in oppoite direction. Denote compreion ratio a ε and diplacement a V note they are both function of the control haft angle θ then for the whole range of θ, we want to have either Scenario I: dε ( θ ) (0) < 0 dθ dvd ( θ ) (1) > 0 dθ or Scenario II: dε ( θ ) () > 0 dθ dvd ( θ ) () < 0 dθ Let u invetigate Scenario I. Denote the combution chamber volume a V c, which i alo a function of θ. Becaue Vd ( ) ( θ ) (4) ε θ = 1 + Vc ( θ ) we have d
dvd dv (5) c Vc Vd dε dθ dθ = dθ Vc To atify (0), we need dvd dvc Vc Vd dθ < (6) dθ From (1) and (6), it i obviou that we mut have dvc ( θ ) (7) > 0 dθ That i, to achieve lower compreion ratio when θ increae, both Vd and V c need to increae. Regarding change of TDC and BDC poition, denote the poition of TDC a Y TDC and that of BDC a Y BDC, which are function of θ. Since 1 (8) Vd = π d ( YTDC YBDC ) 4 where d i the cylinder bore diameter, we have dv d 1 dytdc dy (9) BDC = πd dθ 4 dθ dθ Alo note the change of the combution chamber volume i caued by the change of the poition of TDC, we have dvc 1 dytdc (0) = πd dθ 4 dθ From (1) and (9) we know dytdc dybdc (1) > dθ dθ From (7) and (0) we know dytdc () < 0 dθ Thu we have dybdc dytdc () < < 0 dθ dθ Thi indicate that when the control haft angle increae, both TDC and BDC poition will move lower, and BDC will move lower at a bigger rate than that of TDC. Subtitute (9) and (0) into (6), and alo note (), it i derived dybdc dytdc (4) 1 < < ε dθ dθ With imilar analyi, it i found that Scenario II give the ame reult a in (4). Thi i expected becaue Scenario I and II are in eence the ame and they only differ by how we define the poitive direction of the control action θ. The condition hown in (4) indicate that in order the multiple-link mechanim can realize the deired compreion ratio and diplacement behavior, when the control haft angle change, both TDC and BDC poition need to move in the ame direction; the change rate with repect to the control haft angle for the BDC poition hould be bigger than that of the TDC, but maller than ε time that of the TDC.
To implify the calculation, intead of finding the compreion ratio correponding to each control haft angle, for the condition in (4) we can chooe to ue the minimum compreion ratio ε 0 the mechanim need to realize, and thu get: dy BDC dytdc (5) 1 < < ε 0 dθ dθ Thi i a tronger condition for a deign to fulfill the requirement. In the following ection we will ue thi condition a a criterion for election of the mechanim geometric dimenion. 4. Deign of Experiment The previou ection preent the condition for a mechanim deign to give deirable compreion ratio and diplacement characteritic. However, it can be een from Section that the individual and combined influence of the geometric parameter and the control parameter on the motion of the piton, pecifically TDC and BDC poition, i not traightforward. How they affect the compreion ratio and diplacement could be complicated and may not be eaily determined. Thi place a challenge on the deign and optimization of the multiple-link mechanim dimenion. In thi ection, a DoE method i ued for creating a erie of multiple-link mechanim parameter combination, which are invetigated to obtain the mechanim deign that fulfill the deign requirement. Refering to Figure 1, the multiple-link mechanim geometric deign parameter include the following: l l, l, l, l, l,, X, Y, l 1, 4 5 6 δ Firt, a pecific range for each parameter i et up baed on experience, including reaonable phyical cotraint or limit. Table 1 how the geometric parameter range adopted for thi tudy. Then, in the pace panned by all the parameter, DoE i ued to generate a erie of parameter combination, and the propertie of the mechanim for each combination are calculated. For thi tudy, we et the range of the control parameter θ to be from -45 to 45, and chooe the mechanim propertie when θ i 0 a the bai for calculation. The targeted compreion ratio range i from about 8 to about 14. The combution chamber volume i et in uch a way that when θ i 0, the compreion ratio realized i the deigned value, which i choen to be 11 for thi tudy. For each parameter et, the piton motion i calculated for the whole range of θ. At each control haft angle, TDC and BDC poition are determied, and the combution chamber volume i calculated baed on how the TDC poition change from when θ i 0. The diplacement i calculated uing the TDC and BDC poition information. The compreion ratio and other characteritic are calculated ubequently. Table 1 Geometric Parameter and Their Range Parameter Minimum Maximum (mm) (mm) l 4 5 1
l 115 15 l 10 140 l 58 7 4 l 15 155 5 l 150 170 6 δ -4 8 X -16-110 Y -16-10 l 0 40 EayDoE ToolSuite from IAV Automotive Engineering, Inc. i ued to etablih a tet plan, which i actually a deign plan for the geometric parameter in thi tudy. Uing thi utility program, range and tep are et for each parameter, and a model tructure i elected. Creation of the tet plan i alo dependent on the deign method elected. D-optimality minimize the generalized variance of the parameter etimate. V-optimality minimize the variance of the predicted repone. In thi tudy, the tet plan i created uch that 60% are D-optimal point, 0% are V-optimal point and 10% are pace-filling point. With the deign method elected, 158 parameter et are created for invetigation. For each of the created parameter et, it i checked whether the geometry give a truly operational multiple-link mechanim for the whole range of the control action. i.e., the deign need to atify the Grahof Condition. Figure how the DoE tet plan reult and the ditribution of l 1, l, l in three dimenion. Figure DoE Tet Plan Reult
5. Tet Plan Reult Analyi Behavior of the multiple-link mechanim i calculated for each parameter et of the tet plan over the whole range of the control action. Criterion obtained in Section i checked againt each parameter et. For the DoE plan created in Section 4, only a mall percentage of deign atify the condition. A feaible olution i elected from thoe deign for further tudy. Table lit the parameter value of thi olution. Table Selected Mechanim Parameter Parameter Value (mm) l 4 1 l 115 l 140 l 58 4 l 155 5 l 150 6 δ -4 X -110 Y -10 l 0 Propertie of the elected mechanim deign are preented a follow. Figure (a), (b), and (c) how the piton poition, velocity and acceleration during a crank revolution repectively, while the control haft angle change from -45 to 45 in 10 increment. The red line correpond to -45 control haft angle, while the black line correpond to 45. Thee Figure are typical for mechanim geometric dimenion that atify the deign condition. It can be een that when the control haft angle change, the TDC and BDC move in the ame direction but at different rate. When the control haft rotate counterclockwie, i.e., when θ increae, both TDC and BDC move lower; the maximum velocity and acceleration rate increae. Alo deerve note i that the crank angle location correponding to the TDC and BDC alo change.
(a) (b) (c) Figure Piton Poition, Velocity and Acceleration
Figure 4 how the TDC and BDC poition with repect to the control haft angle. It indicate clearly that when the control haft turn counterclockwie, both TDC and BDC poition are lowered, and the rate of change of the BDC poition i greater than that of the TDC poition. Figure 5 how that the deign criterion, i.e., the ratio of the rate of change of the BDC poition to that of the TDC poition, i between the compreion ratio and 1, which indicate that the deign atifie the deign condition. Figure 4 TDC and BDC Poition Figure 5 Deign Criterion Figure 6 and 7 how how the compreion ratio and troke length change with repect to the control haft angle, repectively. It i clear that thi cae belong to Scenario I decribed in Section. When the control haft rotate counterclockwie
from -45 to 45, the compreion ratio decreae from 1.74 to 7.98, and the troke length increae from 117.9 mm to 15. mm. Correpondingly, when the bore diameter of the cylinder i 89 mm, the diplacement increae from 0.75 liter to 0.840 liter, and the combution chamber volume increae from 0.0576 liter to 0.107 liter. Figure 8 how how the diplacement and combution chamber volume change with the control haft angle. Figure 6 Compreion Ratio Figure 7 Stroke Length
Figure 8 Diplacement and Combution Chamber Volume Figure 9 how how the crank angle range of the expanion troke change with repect to the control haft angle. When the control haft rotate counterclockwie, the curve baically follow a decreaing trend. The Figure how that when the mechanim i at the highet compreion ratio, the expanion troke cover 19.4 crank angle degree, while when the mechanim i at the lowet compreion ratio, the number reduce to 184.0 crank angle degree. Figure 9 Crank Angle Range of the Expanion Stroke Figure 10 and Figure 11 how the maximum piton peed and acceleration (abolute value) repectively. When the control haft rotate counterclockwie, they both baically follow the increaing trend in the range, with a mall deviation for the acceleration near the end of the range.
Figure 10 Maximum Piton Speed (Abolute Value) Figure 11 Maximum Piton Acceleration (Abolute Value) 6. Future Work The approach preented in thi paper give multiple-link mechanim deign that fulfill the deired compreion ratio and diplacement behavior. A hown in Section 5, major kinematic characteritic of the mechanim can be calculated. To further invetigate the engine performance when adopting pecific mechanim deign, variou imulation and teting tudie need to be performed. Detailed imulation of the engine performance involve variou ubytem, procee and control, uch a charging and dicharging procee, fuel delivery, combutible mixture formation, ignition timing, valve timing, combution propertie etc., which are related to the mechanim deign and piton kinematic directly or indirectly. Commercially available engine imulation oftware, uch a GT-Power, might be ued for thi purpoe, provided it could take into account the pecific piton motion and the ubequent influence on variou apect of the engine performance. Related tudy in thi area will be performed and preented in the future.
Beide performing neceary imulation, it i deirable to build prototype engine of variou multiple-link gemmetric deign parameter and carry out tet. However, thi approach would take a long time with high cot. To deal with thi challenge, A&D Co. Ltd. developed a highly flexible teting engine, whoe piton i electrohydraulically controlled and can realize arbitrary motion profile within the phyical limit of the ytem. Figure 1 how the configuration of the teting engine ytem. The ytem conit of two ADX controller, which are high performance real time hardware platform that realize pecific control function. One ADX erve a a univeral engine controller that implement uch function a ignition, injection etc. The other ADX mainly implement hydraulic control of the piton and intake and exhaut valve. Baed on the targeted engine teting condition, the hydraulic control ADX will create neceary encoder ignal that correpond to the rotational behavior of the engine emulated. Thee ignal are ent to the ignition/injection control ADX for engine operation control. The hydraulic control ADX ue the piton poition enor meaurement a feedback, and control the piton motion to deired trajectorie by manipulating the hydraulic actuator that i attached to it. During the teting engine operation, the hydraulic ytem will actuate or load the piton in order that it will follow the target curve of motion. Although greatly different from the mechanical deign of a real engine, by realizing the ame piton motion, the teting engine in a certain ene duplicate the operation and performance of the real engine. The teting reult will provide further inight for improving the mechanim deign. By changing the target piton motion curve, the ytem can be ued for tudying the characteritic of multiple-link mechanim engine of variou geometric deign. Preliminary teting how that the ytem give excellent performance in realizing deired piton motion trajectorie. Detailed work in thi area will be implemented and preented in the future. Figure 1 Highly Flexible Teting Engine Sytem 7. Concluion Thi paper preent an approach on how to achieve multiple-link mechanim deign that realize deirable behavior for both compreion ratio and diplacement. A condition i obtained on how the TDC and BDC poition hould change with
repect to the control action to fulfill the deign requirement. DoE methodology i ued for creating et of geometric deign of the mechanim, which are checked againt the condition. Selected deign that atifie the condition i further tudied in detail. The deign approach and obtained reult erve a a bai and provide inight for further analyi and optimization of the multiple-link mechanim. Reference [1] Charle Mendler, Roland Gravel, Variable Compreion Ratio Engine, SAE 00-01-1940 [] Martyn Robert, Benefit and Challenge of Variable Compreion Ratio (VCR), SAE 00-01-098 [] Amjad Shaik, N Shenbaga Vinayaga Moorthi and R Rudramoorthy, Variable Compreion Engine: a Future Power Plant for Automobile an Overview, Proc. IMechE Vol. 1 Part D: J. Automobile Engineering [4] Katuya Moteki, Shunichi Aoyama, Kenhi Uhijima, et al., A Study of a Variable Compreion Ratio Sytem with a Multi-Link Mechanim, SAE 00-01-091 [5] Naoki Takahahi, Shunichi Aoyama, Katuya Moteki, et al., A Study Concerning the Noie and Vibration Characteritic of an Engine with Multiple- Link Variable Compreion Ratio Mechanim, SAE 005-01-114 [6] Ryouke Hiyohi, Shunichi Aoyama, Shinichi Takemura, et al., A Study of a Multiple-link Variable Compreion Ratio Sytem for Improving Engine Performance, SAE 006-01-0616 Acknowledgement The author would like to thank IAV Automotive Engineering, Inc. for providing the EayDoE ToolSuite for the tudy.