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2008屆本科生畢業(yè)設(shè)計
Abstract Rubber rollers and conveyor belts transport flexible sheet-type media. With high-speed belt transporting systems such as mail sorters, demand for an increase in speed may cause the belt to come off. Therefore, we have examined the effects of belt transport speed and other factors that may cause belt mis-tracking fora basic belt conveyor system, consisting of one flat belt and two crown-face rollers. Experiments were conducted and we have formulated an experimental expression of the amount of belt mis-tracking using the roller misalignment parameters. As for transport speed, a speed increase did not enlarge belt mistracking. This tendency was explained by
ASME/JSME Joint Conference on Micromechatronics for
Information and Precision Equipment (MIPE 2006) Santa Clara,
CA, June 21–23, 2006.
Y. Kobayashi (&) _ K. Toya
Toshiba Corporation, 1, Komukai-Toshiba-cho,
Saiwai-ku, Kawasaki 212-8582, Japan
e-mail: yuko.kobayashi@toshiba.co.jp
1 Introduction
A great deal of research has been reported on transport simulation technology for flexible sheet-type media in office automation equipment and labor saving machines such as copiers, ATMs and mail-sorters. The development of simulation tools may help to shorten the development period of these kinds of products. Cheng et al. (2004) simulated belt skew for a basic belt conveyor system, consisting of one flat belt and two cylindrical rollers using MSC (Marc commercial finite element analysis software). The belt skew or mis-tracking was caused by angular misalignment of rollers. The mechanism of belt skew, the relationship of other factors with belt skew, and the effect of tensioning rollers on reducing belt skew were studied. The qualitative tendencies of belt skew obtained by simulation were in good agreement with experimental results. However, the quantitative results did not seem to be in good agreement with experimental results. Also, the effect of belt transport speed was not mentioned be-cause of the cylindrical roller system.
2 Belt transport system
Experiments were carried out using a belt transport system consisting of two crown-face rollers (diameter/ = 30 mm, roller width B = 10 mm, crown height H= 0.3 mm, roller distance L = 205 mm) and one flat belt as shown in Fig. 1. The near roller is the driven roller and the far roller is the drive roller. The coordinate axis origin is set at the drive roller center of gravity. The driven roller direction is the x-axis, the right-hand direction of the diagram is the y-axis and the upward direction is the z-axis. The parameters of the roller misalignments are given by the driven roller with a local coordinate system set at the driven roller center of gravity. The in-plaeen the initial belt position and the final steady position along the y-axis will be called a ‘‘belt sliding distance’’ in this paper. The belt sliding distance Y was measured by detecting the top edge of the belt by a laser sensor placed at about x-axis 70 mm. The belt tension was controlled by belt expansion rate ε (when a belt length of 100 mm is expanded to 101 mm, the expansion rate is 1%), or practically speaking, the belt tension was controlled by the roller distance.
Fig. 1 Belt transport system
3 Mechanism of the belt mistracking
The belt mis-tracking is generated by the misalignment of the rollers. Figure 2 shows the case for cylindrical Rollers with in-plane misalignment angle β of the driven roller. When the belt touches the driven roller, the belt and the ally the belt will come off. As for a crown-face roller, it has a self-aligning effect. Figure 3 shows a crown-face roller without misalignment angles of roller, and the belt center is not in the center of the roller. When the roller rotates, the belt edge point X1 will not lead to point X3 but trace a new tracking line to point X2. This makes the belt slide toward the centerline. Therefore, if crown-face rollers have misalignment angles, the belt will not fall off but stay somewhere on the roller where mis-tracking force and self-aligning force balance.
Fig. 2 Belt mistracking on cylindrical roller
Fig. 3 Self aligning effect of crown-face rollers
4 Experimental results
Figure 4 shows the effect of the in-plane roller angle β on the belt sliding distance, and that of the out-of-plane roller angle α.As for the in-plane roller airmed experiment -ally that these roller misalignment angles a and b affected the belt sliding distance independently and the effect of angle b was twice as large as the effect of angle a. The parallel gap y of the driven roller generated the belt sliding distance of about half the amount of y as shown in Fig. 5.These mis- alignments of rollers α,β and y are the main factors that generate the belt mis-tracking and they affect the belt sliding distance independently. As for the belt expansion rate, the belt sliding distance increased as the belt expansion rate was enlarged. The belt sliding distance decreased when the crown heights H of the rollers were enlarged and when the belt width B was widened. From these experimental results, we have achieved an expression of the belt sliding distance by empirical formula (1). The belt sliding distance Y can be de- scribed by the in-plane roller angle β, the out-of-plane roller angle α, the belt expansion rate e and the driven roller gap y as independent variables, where as constant K1, K2, K3 and K4 are dependent on crown height H and belt width B.
(1) Figure 6 shows the xperimental results for the rela tion between transport speed V and belt sliding distance (belt expansion rate e = 0.85%, roller distance L = 205 mm, b = 0.166). At low speeds (less than 2 m/s), the belt sliding distance becomes slightly larger by decreasing the speed. As the speed increases, t distance does not increase at high trans-porting speed (10 m/s). The cause will be mentioned in the following chapter.
Fig. 4 Effect of misalignment (experiment) (L = 205 mm,e = 0.85%, H = 0.30 mm, B = 10 mm)
Fig. 5 Effect of parallel gap
Fig. 6 Effect of transport speed (experiment).. (b = 0.166,L = 205 mm, B = 10 mm, H = 0.3 mm, e = 0.85%)
5 Effect of transport speed
Okubo et al. (1998) studied the forces that cause belt sliding on a cylindrical roller experimentally.They found that the belt sliding force was proportional to roller misalignment angle and the thrust friction force generated by rolling sideslip. In particular, the latter force is related to a cornering force that occurs in the opposite direction to centrifugal force, such as when a car makes a turn. The cornering force will be the key factor iheel is turned to the left and the car will move to the traveling direction with velocity V. The slip angle of the front tire a (an angle between tire running direction and tire surface of revolution) generates side force F which prevents the car from sliding to the right-hand direction of the diagram in Fig. 7. Side force F can be expressed by formula (2), whereas C is constant.
(2)
Also, the side force F can be divided into two vectors as shown in Fig. 7. The vector which makes a right angle with traveling direction is called cornering force Ff. If slip angle a is small, the cornering force Ff is almost equal to the side force F. Also, the slip angle of the front tire a can be expressed by formula (3) using slipping angle b (angle between the car direction and the traveling direction), velocity of car center of balance V, yaw rate r (angular velocity of car around the z-axis), actual steering angleaken from typical automotive engineering articles.Therefore,the relation between cornering force Ff and speed V can be expressed by
formula (4) by substituting formula (3) for formula (2), whereas parameters b, r, d and ‘ were replaced by constants C1 and C2.
(3)
(4)
The cornering force on a tire can be applied to the belt sliding force on a roller. That is, roller as a tire and belt as a road. Therefore, the effect of the cornering force generated on the roller will be added on the belt sliding distance. The experi -mental results of transport speed on belt sliding distance shown in Fig. 6 can be approximated by formula (4) by selecting appropriate values for constants C1 and C2. Therefore, the tendency of transport speed V on the belt sliding distance can be explained by applying the cornering force. Also,formula (4) indicates that the increase of transport speed does not enlarge the belt sliding distance.
Fig. 7 Cornering force of the tire
6 Analysis model
Simulation was conducted using LMS DADS (Dynamic Analysis and Design System), which is a software to predict the behavior of single or multi-body mechanical systems. Firstly, because the belt transport system contains software would be more interesting and constructive.
An analysis model was made for the belt transport system shown in Fig. 1. The crown-face roller (rigid body) was made by drawing an arc in the x–y-plane and rotating around the y-axis. The belt was made by dividing the belt width and length into solid body elements connected by springs and dampers. Each solid body element has five contact points (four points in the corners and one point in the center of the element). The contact points are sphere with diameter equal to the belt thickness t. The contact is decided by the distance between the center of contact points and the roller surface. If the distance is smaller than t/2, the belt element and the roller are in contact and the contact force is calculated by Hertz’s Contact theory. The reaction force calculated by Hertz’s Contact theory is given on the roller in the next time step to prevent the belt element from penetrating the roller. A prior examination was conducted for a suitable number of elements of the belt width. When the belt width was divided into five elemimulation was about 1.6 times longer. Cornering force of the tire three elements, and the belt length was divided so that ten elements contact half the circumference of the roller. The belt tension was controlled by expanding the belt elements by belt expansion rate e.
The parameters same as those of experiment were, the in-plane roller angle b, the out-of-plane roller angle a, the crown height H, roller distance L, belt expansion rate e, belt width B and transport speed V. As for simulation, belt thickness t, Young’s Modulus E, roller-belt friction coefficient l and Poisson’s ratio v were added to the above parameters. Young’s Modulus E for simulation was calculated by formula (5), referring to the belt catalog, whereas P is belt tension (which is half the amount of the axial load 147 N), A is belt section area (A = B · t) and e is belt expansion rate (=0.01). Young’s Modulus E was calculated 600 N/mm2.
7 Simulation results
Figure 8 shows the simulation results of the effect ofthe in-plane roller angle b on the belt sliding distance,and that of the out-of-plane roller angle a. The belt sliding distance was linear for the in-plane roller angle
b and for the out-of-plane roller angle a and the ten-dency corresponded to the results achie shows factorial effects by conducting 27 simulations for 10 parameters measured in 3 levels.
The parameters are, out-of-plane angle a, in-plane angle b, crown height H, roller distance L, belt expansion rate e, belt width B, belt thickness t, Young’s Modulus E, friction coefficient between roller and belt l and Poisson’s ratio v. The vertical axis is sensitivities of control factors g, which can be expressed by formula (6), whereas Yi is the belt sliding distance. The value g shows the sensitivity of the belt sliding distance. For example, if g is large, the belt sliding distance is large.
Figure 9 shows that out of ten parameters, the in-plane roller angle b, out-of-plane roller anistance. That is minimizing the misalignment angles a and b, elevating crown height H, lengthening roller distance L, and widening belt width B. However, the length of roller distance L may affect the belt vibration, which will not
be discussed in the paper.
8 Appropriateness of analysis model
The qualitative tendencies of the simulation results were in good agreement with the experimental results. Simulation was conducted with parameters equal to in-plane roller angle b = 0.5_ (out-of-plane roller angle a = 0_), the belt sliding distance was 2.30 mm by experiment and 0.95 mm by simulation. The simulation result was about 40% of the experimental value.
There was a difference in axial load on rollers despitethe same belt expansion rate. According to the belt catalog, the flat belt (10 mm width) should generateaxial load of 147 N on flat rollers at belt expansionrate e = 1.0%. The simulation result of axial loadon rollers was only 91 N at e = 1.0%. One reason forthis difference may be caused by the difference in rollers, flat rollers and crown-face rollers. On the other hand, the experimental result of axial load was about214 N at e = 1.0% which was measured (indirectly forexperimental reason) with load sensor. One reason forthis difference may be caused by set up error of rollerdistance. The roller distance determines the beltexpansion rate and it is likely that a small error leads to a large difference in axial load on rollers. Second reason may be caused by variation of belt characteristics. Therefore, it would be better to control belt tension by axial load on rollers than by belt expansion rate.
Accordingly, axial load on rollers were made equalbetween simulation and experiment (the axial load 180 N, roller distance L = 205 mm). The belt sliding distance for an in-plane roller angle b = 0.5_ (out-ofplane roller angle a = 0_) was 1.64 mm by simulation and 2.30 mm by experiment. The simulation result was e experimental value. Therefore the simulation results generally agreed with the experimental results quantitatively. In existing machines, the allowable belt skew depends on where and how the belts are used. It is important to roughly grasp the belt sliding distance and make fine adjustments by the actual equipments. Consequently, simulation results agreed with the experimental results qualitatively and quantitatively. This indicates that the analysis model applied to the belt transport simulations by motion system analysis software was applicable.
9 Conclusions
We have examined the belt mis-tracking for a basic belt conveyor system, consisting of one flat belt and two crown-face rollers. Experiments and simulation using commercial motion system analysis software were conducted.
1. The belt sliding distance can be expressed by an empirical formula using in-plane roller mis roller gap.
2. Confirmation of the fact that increase of transport speed does not increase the belt sliding distance was achieved by experiments. The cornering force of automotive engineering explained the phenomenon.
3. The sensitivity of belt sliding distance for ten parameters was studied by simulation. Roller mis-alignments, crown height and roller distance had large effects on belt sliding distance.
4. The qualitative tendencies of the simulation results were in good agreement with the experimental results.Also,when theaxial load on roller sand the other parameters were made equal, the simulation results generally agreed with the experimental re-sults quantitatively. This indicates that the analysis model applied to the belt transport simulations by motion system analysis software was applicable.
帶傳輸速度和其它因數(shù)對帶偏移的影響
摘要 橡膠滾子和傳送帶運輸柔性薄介質(zhì)。像郵件分類器那樣的高速的帶傳送系統(tǒng)，要求速度的增加可能導(dǎo)致皮帶脫落。因此, 我們已經(jīng)對由一個平帶和二個圓錐滾子組成的基本的帶式運送機系統(tǒng)，這趨向可由汽車工程學(xué)的回轉(zhuǎn)向心力解釋。同時，使用商業(yè)的動作系統(tǒng)分析軟件實施仿真。來自仿真和實驗的皮帶偏移的定性趨勢非常吻合，而且因數(shù)的結(jié)果也被簡化為十個參數(shù)。定量的，當(dāng)滾子的軸向載荷和其他的叁數(shù)被做的相等的時候，依照仿真的帶偏移與實驗值基本一致。
1 介紹
很多的研究關(guān)于柔性薄介質(zhì)的運輸仿真技術(shù)在辦公室自動化設(shè)備和節(jié)省勞動力的機器方面的應(yīng)用已經(jīng)被報導(dǎo),像是復(fù)印機，自動柜員機和郵件分類器。 仿真工具的發(fā)展也許會縮短開發(fā)這些種產(chǎn)品的周期。Cheng et al. (2004) 使用 MSC (馬可商業(yè)有限元分析軟件)為由一個平帶和二個圓錐滾子組成的基本的帶傳送系統(tǒng)仿真了帶隆起面. 皮帶的隆起面或偏移是由滾子的角度失準(zhǔn)所引起。帶的隆起面裝置, 皮帶隆起面的其他因數(shù)的關(guān)系, 及張緊輪在減少皮帶隆起面上的效果等，正在被研究。通過仿真獲得的皮帶隆起面的定性的趨向與實驗的結(jié)果吻合。然而, 定量的結(jié)果似乎與實驗的結(jié)果不是很一致。并且,由于圓錐滾子系統(tǒng)的因素，帶輸送速度的影響沒被提到。
2 帶傳輸系統(tǒng)
實驗被實施，使用由如圖 1 所顯示的圓錐滾子(直徑Φ=30 毫米，滾子寬度 B=10 毫米，圓錐高度 H=0.3毫米,滾子距離 L=205 毫米) 和平帶的一個帶傳輸系統(tǒng)。近的滾子是從動滾子，而且遠(yuǎn)的滾子是主動滾子。座標(biāo)軸原點被設(shè)定在主動滾子重心。從動滾子方向是 X軸,圖的右側(cè)方向是 Y軸，向上的方向是 Z軸。滾子偏心系數(shù)被給出，在從動滾子重心設(shè)置的有同樣的坐標(biāo)系統(tǒng)的從動滾子上。內(nèi)表面滾子角 β (Z軸的旋轉(zhuǎn)角), 外表面滾子角 α (X軸的旋轉(zhuǎn)角)，從動滾子間隙 y和Y軸平行。 滾子偏心引起皮帶向 Y軸的正負(fù)方向偏移, 然而滾子的隆起效果阻止皮帶滑離開。 最終，皮帶受到的壓力將會被平衡，并且它將會追蹤一個穩(wěn)定的位置。皮帶偏移的機構(gòu)將會在下列的章節(jié)被提到。在這篇論文中，沿著Y軸方向皮帶的初始位置和最后的穩(wěn)定位置之間的滑動距離被稱為“皮帶滑動距離''。皮帶滑動距離 Y 通過被放置在X軸大約 70 毫米的一個激光感應(yīng)器檢測皮帶的上邊緣而被測得。皮帶張力被皮帶膨脹率 ε (當(dāng)一個 100 毫米的皮帶長度被擴大為 101 毫米的時候, 膨脹率是 1%) 控制, 或者更確切地說,皮帶張力被滾子距離控制了。
圖 1 帶傳輸系統(tǒng)
3 皮帶偏移機構(gòu)
皮帶偏移通過滾子的偏心發(fā)生。圖 2 顯示了從動輪的內(nèi)表面偏心角 β 的圓柱滾子的情況。當(dāng)皮帶接觸滾子的時候，如果在他們之間沒有滑動，那么皮帶和滾子將會一起隨著從動滾子的旋轉(zhuǎn)而運動。在那里在前面皮帶邊緣點 X1 將不采取行動來磨利 X3 但是將會向前追蹤一個新的追蹤線磨利 X2,然而一個新的追蹤線用滾子橋線來制造一個直角。逐漸地, 皮帶將會滑動到那正的發(fā)生皮帶偏移的線圖的手方向和最后皮帶將會脫落。 美國標(biāo)準(zhǔn)對于一個隆起-面的滾子, 它有自己，自動的意義排列影響。沒有滾子的失準(zhǔn)角的圖 3 表演一個隆起-面的滾子, 和皮帶中心不在滾子的中心。當(dāng)滾子使旋轉(zhuǎn)的時候，皮帶邊緣點 X1 將不帶領(lǐng)磨利 X3 但是追蹤一個新的追蹤線磨利X2 。這做皮帶滑動向中線。因此，如果隆起-面的滾子有失準(zhǔn)角,皮帶將不下跌但是停留在排列力平衡的偏移強迫的滾子和自己，自動的意義上的某處。
圖 2 圓柱滾子上帶的偏移
4 實驗結(jié)果
從動滾子的平行間隙 y 產(chǎn)生了如圖 5 所顯示的大約y 一半數(shù)量皮帶滑動距離。滾子的這些失偏心度a、b 和 y 是產(chǎn)生皮帶偏移的主要的因數(shù)，而且他們獨立地影響皮帶滑動距離。對于皮帶膨脹率，當(dāng)皮帶膨脹率被擴大的時候，皮帶滑動距離增加。皮帶滑動距離減少當(dāng)滾子的隆起高度 H 增大和皮帶寬度 B 被加寬。從這些實驗的結(jié)果，我們已達(dá)成由實驗驗式得到的皮帶滑動距離的一個［表達(dá)］式。(1) 皮帶滑動距離 Y 能被描述通過作為獨立變量的內(nèi)平面滾子角 b,外平面滾子角a，皮帶膨脹率ε和從動滾子間隙 y, 然而常數(shù) K1，K2, K3 和K4 則依賴隆起高度 H 和皮帶寬度 B。 (1)
圖 6 顯示了傳輸速度 V 和皮帶滑動距離之間的關(guān)系的實驗結(jié)果(帶膨脹系數(shù) ε=0.85% ，滾子距離L=205mm,β=0.166°).在低速下(低于2 m/s),皮帶滑動距離變得輕微增大通過速度的遞減。隨著速度的增大，皮帶的滑動距離變成一個恒定的值2。因此，皮帶滑動距離不以高的運輸速度(10 m/s)而增加。原因?qū)诤竺娴恼鹿?jié)中提到。
圖 4 偏心度的影響 (實驗) (L = 205 mm,e = 0.85%, H = 0.30 mm, B = 10 mm)
圖 5 平行間隙的影響
圖 6 傳輸速度的影響 (實驗). (b = 0.166,L = 205 mm, B = 10 mm, H = 0.3 mm, e = 0.85%)
5 傳輸速度的影響
同時,邊力F能被分解為如圖7所顯示的二個矢量. 做一個與移動方向成直角的矢量被叫旋回向心力Ff。如果側(cè)滑角a很小,旋回向心力 Ff 也幾乎與邊力F相等.同樣地前輪的側(cè)滑角α能被使用滑動角β(車方向和移動方向之間的角)公式(3)表達(dá)，平衡 V的汽車中心的速度，橫擺角速度 r(車?yán)@Z軸的角速度)前輪帶實際轉(zhuǎn)向角度δ 和車中心和前面輪帶之間的距離l,公式(2)和(3)從典型的汽車工程制品中被提出。因此,旋回向心力 Ff 和速度 V 之間的關(guān)系能被由公式(3)代入公式(2)且叁數(shù) b,r,δ 和 l 被常數(shù) C1 和 C2 代替得到的公式(4)表達(dá)。
(3)
(4)
在一個輪帶上的旋回向心力能被應(yīng)用到在滾子上的皮帶側(cè)滑力。 那是, 像一個輪的滾子和像路一樣的皮帶。因此，在滾子上產(chǎn)生的旋回向心力對的影響將會被加上皮帶滑動距離。 在圖 6 被顯示的傳輸速度對皮帶滑動距離的實驗結(jié)果能被近似通過對公式(4)中常數(shù) C1 和 C2 選擇適當(dāng)?shù)闹?。因此，在皮帶滑動距離方面的傳輸速度 V 的趨向能被加旋回向心力解釋。同樣,公式(4)指出傳輸速度的增大不擴大皮帶滑動距離。
圖7 輪的旋回向心力
6 模型分析
模擬進行使用的LMS DADS（動態(tài)分析與設(shè)計系統(tǒng)） ，這是一個軟件對單一或多重體機械系統(tǒng)進行預(yù)測的行為。首先，由于帶的交通運輸系統(tǒng)包含皮帶和滾子，系統(tǒng)分析軟件似乎是合適的。其次，由于模擬斜帶與商業(yè)有限元分析（有限元法）分析軟件已經(jīng)報道說，進行模擬與不同類型的軟件會更有趣和有建設(shè)性的。
分析模型為帶的交通運輸系統(tǒng)中顯示的圖 1 。對軋輥（剛體）是由繪畫的一個弧形在X - Y型和旋轉(zhuǎn)靠近Y軸。帶是由帶的寬度和長度通過彈簧和阻尼器而結(jié)實連接在一起的。每一個剛體元素有5個聯(lián)絡(luò)點（ 4點在彎道中和1點在該中心）。聯(lián)系點是決定于中心聯(lián)絡(luò)點和輥表面的距離。如果距離小于t/ 2 ，帶元素和軋輥是通過赫茲的接觸理論計算的。該通過赫茲的接觸理論計算出來的給出了對輥以防止在下一時間帶從滾筒上跑偏。事先檢查，進行適當(dāng)帶的寬度。當(dāng)帶的寬度分成五個要素，滑動距離所取得的模擬是相同的情況一樣，當(dāng)帶的寬度被分成三個要素。在另一方面，總時間為模擬的1.6倍?；剞D(zhuǎn)強度的三個要素，并帶長度劃分，分開10個接觸半的圓周輥。該帶的緊張局勢受到控制時，擴大帶元素帶膨脹率e.
這些實驗是在這些參數(shù)相同的情況下：平面軋輥的角度b，出平面滾子的角度a ，高度h，軋輥的距離L，腰帶膨脹率e，法帶的寬度B和輸送速度v，帶厚度t ，模量E ，滾子帶的摩擦系數(shù)和泊松比等上述參數(shù)。楊氏模量E的模擬計算公式（ 5 ），而P是帶張力（這是二分之一的數(shù)額軸向負(fù)荷147 n ）的，一個是帶截面面積（a = b ? T ）和E是帶擴展率（ = 0.01 ） 。楊氏模量E為600 n/mm2 。
7 結(jié)果仿真
圖 8 所示的模擬結(jié)果是平面滾子在帶滑動距離上按某一角度 b 轉(zhuǎn)動,而且那外面者平面滾子按某一角度 a 轉(zhuǎn)動?；瑒泳嚯x呈線性為在平面軋輥的角度 b 和出平面滾子的角度 a 和10個參數(shù)對應(yīng)所取得的實驗結(jié)果如圖4所示。然而,模擬值同實驗值不符合。下一個章節(jié)將討論原因。圖 9 所示因子的影響，參數(shù)來衡量，對于 10個叁數(shù)的模擬在 3個水平中測量了。
參數(shù)在出平面的角度來 a ，在平面的角度 b，隆起高度 H ，滾子距離 L ，帶膨脹率 e ，帶寬度 B ，帶厚度 t標(biāo)識, 模量 E, 滾子和帶之間的磨擦系數(shù)l 和浦松氏比 v。 垂直軸是感度控制因數(shù) g, 能表示為公式 (6), 然而 Yi 是帶滑動距離。G表示帶滑動距離的感度。例如, 如果 g 是大的,帶滑動距離是大的。
圖9顯示出10參數(shù)，在平面軋輥的角度b ，出平面滾子的角度來看， 隆起高度H 和滾子距離 L 在滑動距離對帶有大的影響。此外，數(shù)字顯示的有效途徑，減少帶滑動距離。這是盡量減少失調(diào)的角度A和B，增大加冠高度 H, 延長滾子距離 L, 擴大帶的寬度 B, 然而滾子的長度距離 L 可能影響帶振動, 這不將會在該文中討論
圖8 偏心角的影響(L = 205 mm, B = 10 mm, H = 0.3 mm, e = 0.85%)
圖9 參數(shù)的影響
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