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Science in China Series E: Technological Sciences ? 2008 Science in China Press Springer-Verlag Study of utilizing differential gear train to achieve hybrid mechanism of mechanical press HE YuPeng1?, ZHAO ShengDun2, ZOU Jun2 & ZHANG ZhiYuan2 1 School of Mechanical Engineering, Nanjing University of Science & Technology, Nanjing 210094, China; 2 School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China The problems of hybrid input of mechanical press are studied in this paper, with differential gear train as transmission mechanism. It is proposed that “adjustable- speed amplitude” or “differential-speed ratio” is the important parameters for the hybrid input mechanism. It not only defines the amplitude of the adjustable speed, but also determines the ratio of the power of the servomotor to the power of the conventional motor. The calculating equations of the ratio of transmission in all axes, the power of two motors, and the working load distribution are deduced. The two kinds of driving schemes are put forward that the servomotor and the conventional motor simultaneously drive and the servomotor and the conventional motor separately drive. The calculating results demonstrate that the latter scheme can use much lower power of the servomotor, so this scheme makes manufacture and use cost much lower. The latter scheme proposes a feasible way to apply the hybrid mechanism of mechanical press in practice engineering. mechanical press, hybrid mechanism, differential gear train, adjustable-speed 1 Introduction At present there are many research papers about the hybrid mechanism of mechanical press, and it has become a hot research topic. The hybrid mechanism is a mechanism with 2-degree-of freedom (also called differential speed mechanism), and when two independent motions are input at the same time, the output that can satisfy some motion requirements is obtained through the motion composition of the mechanism. The hybrid mechanism is also called controllable mechanism, or hybrid machine. The purpose of research on hybrid mechanism of mechanical press is using conventional motor with big power carrying flywheel to finish stamping work pieces; and uses ser —vomotor with low power to adjust the slider speed. The advantages of the hybrid mechanism applied in the mechanical press are that it not only can reduce much lower manufacturing cost than servo press, but also has a flexible working velocity of slider[1]. So the mechanical press of hybrid mechanism arouses many researchers’ interest in working on it; and these studies are mainly focused on the multi-bar hybrid mechanism. Du and Guo[1, 2] have comprehensively discussed the seven-bar hybrid mechanism of mechanical press, including the feasible conditions of composition of the linkage mechanism, the slider motion analysis, and the torque and power distribution between the two motors as well as the optimal design. The trajectory planning based on polynomial interpolation is also investigated, and the computer simulation shows that the result is indeed attractive. In addition, Meng[3] has also investigated the kinematical analysis of the seven-bar mechanism, and the optimal design has been completed based on the minimum power of the servomotor motor, and Meng has proposed that the hybrid mechanism is a research direction of the mechanical press. Tokuz[4] first put forward of the hybrid mechanism and analyzed the velocity synthesis by using the differential gear train. His experiment confirmed the feasibility of his conception. The concepts of the adjustable-speed amplitude and differential-speed ratio are not mentioned in their works, and the relationship between the velocity variation and the power of the two motors were not clearly given[5―8]. But these concepts are very important and absolutely necessary for the hybrid mechanism to select the two motors’ power and determine the working load distribution between conventional motor and the servomotor. In refs. [1―3] they used linkage mechanism to implement the hybrid input of mechanical press. The method is very complex because the change of the length and position of the each bar in linkage mechanism will have an effect on the motion of the slide of the mechanical press. So some principal problems are usually ignored in research hybrid mechanism course, and the research results don not always coincide with the practice engineering conditions[9―11]. The gear differential train has two freedoms, and the ratios of transmission between arbitrary two axes are a constant. In order to simplify the mechanical model and make the problems much projected, the differential gear train is used as transmission mechanism to study the hybrid problems of the mechanical press in this paper. This paper addresses the relationship between the adjustable-speed amplitude and the power of the two motors, the working load distribution between the two motors, and puts forward two drive schemes of the conventional motor and the servomotor simultaneously working, and two motors separately working. With the 200-ton mechanical press as the engineering background, a drive system of the hybrid mechanism of the mechanical press is designed, and the feasibility of the two drive schemes in mechanical press is analyzed. 2 The principle of the hybrid mechanism The working principle of the hybrid mechanism of the mechanical press with differential gear train is illustrated in Figure 1. The system consists of conventional motor (also called AC machine with constant speed), servomotor, reducing unit I, reducing unit II, differential gear train, and crank slide mechanism. The output axis of the differential gear train is connected with the crankshaft of the crank slide mechanism. One of the two input axes links the conventional motor through the reducing unit ?; the other input axis links the servomotor through the reducing unit II. Therefore the motion of the crankshaft is completely controlled by the motions of the conventional motor and the servomotor. The reducing unit ? and the reducing unit II are respectively installed between the two motors and the differential gear unit in the way of serial in order to bear a part of reducing velocity task of the all transmission system, because too big drive ratio of the differential gear train will make its driving efficiency decreased. The angular velocity of the conventional motor is constant, so its price is cheaper. The angular velocity of the servomotor is adjustable, so its price is expensive. In the system of the hybrid mechanism the constant speed of the output axis is provided by high power conventional motor; and the servomotor provides its adjustable speed. Therefore, in this way, it not only makes the output motion of the crankshaft of the mechanical press flexible, but also avoids using high power servomotor. Hence it could save both the machine manufacturing costs and the machine operating costs. Figure 1 Working principle of hybrid mechanism of differential gear train. 3 The velocity characteristics of the mechanical press slide The work of the mechanical press presents the regularity of the periodic change[12]. The displacement and velocity changes of the mechanical press slide in an ideal work circulation are illustrated in the Figure 2. The slide starts to move from top dead center to the working start point at high velocity (called quick feeding stage). When the slide of mechanical press approaches the working point, its high velocity is shifted to slow velocity and then it begins to stamp work piece at low velocity (called low working stage). The low velocity of the slide is to avoid great impact on the die, and benefit the plastic shaping of the work piece. After the slide finishes the stamping work and reaches the bottom dead center, the slide comes back at high velocity and stops at the top dead center (called quick back stage). Hence, the motion velocity of the mechanical press slide can be divided three kinds: high down velocity V1 , slow working velocity V2 , and high back velocity V3 . The velocity V1 and velocity V3 should be as possible as high and the velocity V2 should be slow and flexible in order to ensure high working times of the mechanical press per minute and satisfy the requirements of different technologies. Actually the mechanical press only works in a very short course before the bottom dead center, and in the other courses it does not do work to the work piece. 4 The nomenclatures and equations of the hybrid mechanism 4.1 The relationship of the angular velocity in all axes There are three external axes in the differential gear train as illustrated in Figure 1. In order to conveniently express the relationship of the three axes, the axis connected with the conventional motor is called axis 1, the axis connected with servomotor is called axis 2, and the axis connected with crankshaft is called axis 0. The angular velocities of the three axes are respectively expressed as n1 , n2 and n0 . The torques of the three axes are respectively expressed as M1 , M2 and M0 . Because there are two freedoms in the differential gear train, only the third axis is fixed, such that the drive ratio of the other two axes can be determined. So the relationships of drive ratio and angular velocity of the three axes need to be expressed as the character with superscript and subscript. Figure 2 Ideal displacement cure of the slide. 4.1.1 The conventional motor’s influence on the output motion. When the servomotor stops, n2 = 0 , only the angular velocity of the conventional motor affects the output angular velocity n0 . 4.1.2 The servomotor’s influence on the output motion. When the conventional motor stops, n1 = 0 , only the angular velocity of the servomotor affects the output angular velocity n0 , where 1 n0 represents axis 0 angular velocity, and 1 i20 represents total drive ratio from axis 2 to axis 0 including differential gear train and reducing unit II when axis 1 (servomotor axis) is fixed. 4.1.3 The conventional motor’s and servomotor’s influence on the output motion. When the conventional motor and the servomotor run at the same time through the composition of the differential gear train, the output velocity can be expressed as . Because the servomotor can run at arbitrary angular velocity between the zero and specific velocity in both positive and negative directions, n2 can be expressed as .where K is the ratio of the actual angular velocity to the specific angular velocity of the servomotor; the value is arbitrary between ?1 and +1, including zero. n2e is the specific angular velocity of the servomotor. 4.2 Adjustable-speed amplitude and differential-speed ratio 4.2.1 Adjustable-speed amplitude. In order to correctly denote the variable velocity of the differential gear train of the hybrid mechanism, the concept of adjustable-speed amplitude is introduced. As shown in Figure 1, adjustable-speed amplitude is the ratio (or percentage) of absolute value of up and down adjustable amount to the base speed. In the differential gear train of the hybrid mechanism, the adjustable-speed amplitude equals the ratio value of axis 0 output speed of operating a single servomotor at the specific speed to axis 0 output speed of operating a single conventional motor[13]. In the differential gear train of the hybrid mechanism, the adjustable-speed amplitude is the most basic and the most important technology parameter. It not only determines the matching relationship of the speed of the two input axes, but also decides the matching relationship of the installed capacity of the servomotor and the conventional motor 4.2.2 Differential-speed ratio. The differential-speed ratio is usually used to express adjustable speed technology performance in the differential gear train. It is an important technology parameter of the differential effect in the differential system. The differential-speed ratio equals the reciprocal value of the adjustable-speed amplitude. It can be expressed as According to the fact that the angular velocity is in inverse proportion to its torque and that the same load is driven by conventional motor and servomotor, an equation expressed with the powers of the two motors can be deduced, where P1 is the power of the conventional motor, P1 = M1n1 . P2 is the power of the servomotor, P2 = M2n2e . 4.3 The working load power distribution Supposing that the working load power of the mechanical press is P0 , the power relationship between the conventional motor, the servomotor and working load can be expressed as below: Figure 3 Physical sense of the adjustable-speed amplitude. From eqs. (9)―(11), the output powers of the conventional motor and the servomotor are determined by the value of factor K, which is actually equal to the change ratio of angular velocity of the servomotor. Hence when the output angular velocity runs in different working region, the ratio of bearing load of the two motors is different, too. 4.3.1 The output axis running at the basic speed. When the output angular velocity of the servomotor equals zero, that is, K = 0 , P2 = 0 , from eq. (9), we have .Here the conventional motor bears all the loading power. 4.3.2 The output axis running in the increasing speed region. The servomotor runs in the positive direction, 0≤K≤1 , and both P1 and P2 are positive values, so both the conventional motor and the servomotor bear a part of the working load. Thus the conventional motor bears 90.9%―100% working load and the servomotor bears only 0―9.1% working load. The value of the adjustable-speed and the differential-speed ratio deter-mine the load distribution between the two motors. 4.3.3 The output axis running in the decreasing speed region. In the decreasing speed region, the servomotor runs in negative direction, and the range value of K is ?1≤K≤0 . By eqs. (9) and (10), the P1 is positive, and the P2 is negative. The negative value of the servomotor power shows that the servomotor power is already the working resistance. Hence the conventional motor is not only doing work to the working load, but also doing work to the servomotor power, When the angular speed is in the region 0―n2e, the load of the conventional motor is Thus when the output angular speed is in the decreasing region, the conventional motor consumes more energy than in the other regions. The decrease of the output speed is at the price of consuming the servomotor input power. In order to save energy, the output angular speed should avoid or reduce running in the decreasing region. 4.4 The two drive schemes of the hybrid mechanism of the mechanical press According to eq. (3), the output angular velocity of the hybrid mechanism is equal to the reduced value of their sum of the angular velocities of both the conventional motor and the servomotor. As shown in Figure 1, the output angular velocity of the differential gear train is connected with the crank axis of the mechanical press, so the two axes have the same angular velocity. When either of the conventional motor or the servomotor is driven, or when both of them are driven, the different angular velocity of the crankshaft of the mechanical press can be obtained. Therefore, two kinds of the schemes of the hybrid mechanism of the mechanical press are proposed: (i) the conventional motor and the servomotor are simultaneously driven; and (ii) the conventional motor and the servomotor are separately driven. 4.4.1 The conventional motor and the servomotor being simultaneously driven. This scheme shows that the angular velocity of the crankshaft of the mechanical press is composed of the angular velocity of the conventional motor as the basic speed and the angular velocity of the servomotor as the adjustable speed (Figure 3). The angular velocity and the powers can be calculated by using eqs. (1)―(18). 4.4.2 The conventional motor and the servomotor being separately driven. This scheme shows that only one motor is driven in the hybrid input course and at the same time another motor is braked, i.e. when the crankshaft is in differential running stage, the conventional motor and the servomotor are separately operated; thus the different angular velocity of the crankshaft can be obtained. The flexible low speed operation .When the conventional motor is braked and the servomotor is operated, n1 = 0，the below equation can be obtained from eq. (5) Because ?1≤K≤+1 , the output angular velocity of the crankshaft is adjustable and the crankshaft has two rotating directions; therefore it is flexible. A big value of the drive ratio 1 i20 can be designed, so a very small output angular velocity 1 n0 can be achieved. Hence in this course the output angular velocity is flexible and low. When the servomotor is braked and the conventional motor is operated, n2 = 0 , from eq. (5), we have. Crankshaft has two rotating directions; therefore it is flexible. Figure 4 Physical sense of the comparison of the two output angular speed. Because drive ratios 2 i10 and 1 i20 are independent of each other, and the operation and the servomotor operation of the conventional motors are independent of each other too, the values of the two drive ratios can be assigned a very different value (one is very small, and the other is very big), so the two output angular velocities may differ greatly. So doing can satisfy the motion requirements of the mechanical press slide in different stages. The physical sense of comparison of the two output angular speed is illustrated as in Figure 4. 5 Conclusion According to the velocity characteristics of the mechanical press, the differential gear train is applied in the hybrid mechanism of the mechanical press. Through the above analysis and calculation, the following conclusions can be reached: (1) The adjustable-speed amplitude and differential-speed ratio are important parameters of the hybrid mechanism. They are not only the ratio of the adjustable speed to the basic speed, but also the ratio of the power of the servomotor to the power of the conventional motor. (2) With the scheme of the conventional motor and the servomotor being simultaneously driven, the power of the two motors has to be assigned high value in order to satisfy the velocity requirements of the mechanical press. So doing increases the manufacturing cost and the operation cost of the mechanical press, and therefore is valueless in practical application. (3) With the scheme of the conventional motor and the servomotor being separately driven, the power of the servomotor can be assigned low value in order to satisfy the velocity requirements of the mechanical press. So doing decreases the manufacturing cost and the operation cost of the mechanical press. Therefore, this scheme proposes a feasible way in practical industrial engineering. 中國(guó)的科學(xué)系列E：技術(shù)科學(xué) ? 2007 中國(guó)科學(xué)出版社 施普林格出版社 研究利用差動(dòng)齒輪系實(shí)現(xiàn)機(jī)械混合壓力 何宇鵬，趙勝敦，周軍&張志遠(yuǎn) 1、 中國(guó)，南京210094，南京大學(xué)科學(xué)與技術(shù)，機(jī)械工程學(xué)校 2、 中國(guó)，西安710049，西安交通大學(xué)，機(jī)械工程學(xué)校 本文對(duì)機(jī)械壓力混合輸入的問(wèn)題進(jìn)行了研究，用差動(dòng)輪系作為傳動(dòng)機(jī)構(gòu)。它建議將“調(diào)速幅度”或“差動(dòng)速比”作為重要參數(shù)混合投入機(jī)械研究中。它不僅規(guī)定了可調(diào)節(jié)幅度速度，而且還決定了伺服電動(dòng)機(jī)功率比的傳統(tǒng)電機(jī)。所有傳動(dòng)軸計(jì)算的傳輸功率，兩個(gè)電機(jī)的功率和工作負(fù)載的分布得到了推斷結(jié)果。它提出了伺服電機(jī)和傳統(tǒng)電機(jī)同時(shí)驅(qū)動(dòng)，伺服電機(jī)和傳統(tǒng)電機(jī)單獨(dú)驅(qū)動(dòng)兩種驅(qū)動(dòng)方案。計(jì)算結(jié)果表明后者的方案能比伺服電機(jī)使用更低的功率，因此這種方案能使得制造和使用成本低得多。后一個(gè)方案提出了一個(gè)可行的途徑在實(shí)際工程中來(lái)使用混合機(jī)械壓力。 機(jī)械壓力，混合機(jī)制，差動(dòng)輪系，調(diào)速 1、引言 目前有許多關(guān)于機(jī)械壓力的混合機(jī)制的研究報(bào)道，并且已經(jīng)成為一個(gè)熱門的研究話題。混合動(dòng)力機(jī)制是一種有2個(gè)自由度的機(jī)制（也稱為差速機(jī)制），當(dāng)兩個(gè)獨(dú)立的運(yùn)動(dòng)同時(shí)輸入時(shí)，輸出的運(yùn)動(dòng)能夠滿足一些運(yùn)動(dòng)要求，這些要求通過(guò)機(jī)械的運(yùn)動(dòng)組成來(lái)獲得的。混合動(dòng)力機(jī)制也可稱為可控機(jī)制，或者稱作混合機(jī)器。研究機(jī)械壓力機(jī)的混合機(jī)械的目的是使用大功率常規(guī)電機(jī)利用飛輪來(lái)完成工件的沖壓；并使用低功率的伺服電機(jī)來(lái)調(diào)整滑塊速度。應(yīng)用在機(jī)械壓力中的混合機(jī)制的優(yōu)勢(shì)在于它不僅可以比伺服壓力機(jī)降低更多的制造成本，而且還有一個(gè)靈活的工作速度滑塊。所以混合動(dòng)力機(jī)械壓力機(jī)在機(jī)制上的工作引起了許多研究者的興趣；并且這些研究主要集中在多桿混合機(jī)械中。杜和郭已經(jīng)全面討論了七桿的機(jī)械壓力機(jī)的混合機(jī)制，包括組成連桿機(jī)構(gòu)的可行條件，滑塊機(jī)構(gòu)的動(dòng)力分析，和兩臺(tái)電機(jī)之間轉(zhuǎn)矩和功率的分配以及它們之間的優(yōu)化設(shè)計(jì)?；诙囗?xiàng)式的軌跡規(guī)劃也需要調(diào)查，且計(jì)算機(jī)模擬表明結(jié)果的確吸引人。此外，孟也調(diào)查了七桿機(jī)構(gòu)的運(yùn)動(dòng)學(xué)分析，基于最低功率的伺服電機(jī)的優(yōu)化設(shè)計(jì)已經(jīng)完成，然后孟建議混合機(jī)制是機(jī)械壓力機(jī)的研究方向。Tokuz 首次提出了混合機(jī)構(gòu)并且使用差動(dòng)齒輪系分析了合成速度。他的實(shí)驗(yàn)證實(shí)了他的理論的可行性。 調(diào)速幅度和差速比的概念在他們的作品中沒(méi)有提到，并且兩電機(jī)的速度變化和功率之間的關(guān)系也沒(méi)有清楚的給出。但是這些概念對(duì)混合動(dòng)力機(jī)械選擇兩個(gè)電機(jī)的功率、決定傳統(tǒng)電機(jī)和伺服電機(jī)之間的工作負(fù)載分