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The application of rigid body fixed-point motion theory in mechanical continuously variable transmission system

[Abstract] this paper introduces a new type of mechanical continuously variable transmission system, which comprehensively utilizes the gyroscopic effect of rigid body fixed-point motion and the kinematic characteristics of planetary gear train; The working principle of the CVT system is preliminarily studied, and the relationship between the parameters and performance of the CVT system is preliminarily clarified. It is considered that the new mechanical system has the characteristics of simple structure, constant power, high efficiency, self-adaptive, stepless speed change and so on. It has broad application prospects in the fields of automobiles, ships, machine tools and so on

key words: fixed-point motion gyro effect planetary gear train stepless speed change

1 introduction

in the mechanical system, in order to meet the requirements of driving different loads at different speeds when the engine works at the economic speed, the transmission is often an essential subsystem. A simple transmission subsystem, usually composed of gears and clutches, can be switched manually or automatically between several fixed transmission ratios to meet the requirements of ordinary mechanical systems. This kind of simple transmission subsystem with different gears not only produces impact with step change in the process of speed change, but also affects the stability of the whole mechanical system; Moreover, because the simple step-by-step transmission can not form the most appropriate fit between the engine and the load, the design of an economic, reliable and energy-saving mechanical continuously variable transmission subsystem has always been a competitive research topic in the mechanical field

in order to overcome the above problems, on the basis of theoretical research and prototype experiments, it is found that a new type of mechanical stepless speed change system with extremely simple structure can be constructed by comprehensively utilizing the gyroscopic effect of rigid body fixed-point operation and the kinematic characteristics of planetary gear train

2 principle

the mechanical structure of the system is shown in Figure 1. In Figure 1, 1 is the input shaft, 2 is the planetary gear, 3 is the central wheel, 4 is the output shaft, 5 is the special gyro, and 5 'is the "child moving body" of the gyro

1 - input shaft 2 - planetary gear 3 - central wheel 4 - output shaft 5 - special gyro 5 '- the "sub moving body" of the gyro

to study its mechanical principle, the oxyz coordinate frame attached to the special gyro 5 body is selected, and the origin is the geometric center O of the gyro body; The x-axis coincides with the rotation axis of the planetary gear 2, pointing above the paper in the state shown in the figure; The y-axis coincides with the center line of input shaft 1, pointing to the left of the paper in the state shown in the figure; The z-axis can be determined according to the spiral direction of the right hand. In the state shown in the figure, it points to the direction outside the paper

according to the symmetry, the X, y and Z axes are the three inertia principal axes of the special gyro 5

as shown in the figure, when the system input shaft 1 rotates, it will drive the special gyro 5 to rotate around the y-axis, and at the same time make the special gyro 5 rotate around the x-axis because of the meshing relationship between the gear 2 and the gear 3, that is, make the special gyro 5 move at a fixed point

according to the rigid body fixed-point motion theory, if the three inertia axes of the rigid body are taken as the reference system, the angular acceleration, rotation moment and external moment of the rigid body in the spindle coordinate system comply with the following Euler dynamic equation relationship, that is,

in the formula, the first term on the right is the rotation moment term reflecting the so-called gyro effect

in the following discussion on the system shown in Figure 1, it can be agreed that -

the input dynamic torque added to input shaft 1 is Mi, and the positive direction of the torque is the same as the y-axis direction

the speed of input shaft 1 is constant ω i. The positive direction of rotation is the same as the y-axis direction

the load torque on the output shaft 4 is lo, and the positive direction of the torque is opposite to the direction of the Y axis

the speed of output shaft 4 is ω o. The positive direction of rotation is the same as the y-axis direction

the rotation speed of special gyro 5 is ω x. Its positive direction is the same as the x-axis direction

the external moment of force driving the rotation of the special gyro 5 is MX, and its positive direction is the same as the x-axis direction

special gyro 5 revolution speed is ω y. Its positive direction is the same as the y-axis direction (obviously, ω y= ω i）；

the external moment of force driving the special gyro 5 revolution is my, and its positive direction is the same as the y-axis direction (obviously, my=mi)

at a point where the planetary gear 2 meshes with the center gear 3, the force exerted by the planetary gear 2 on the center gear 3 is F. in the state shown by the measured elongation value in Figure 1, its positive direction points within the paper

r refers to the vector radius from the center of the center gear 3 to the meshing point a

r refers to the vector radius from the circle center of planetary gear 2 to the meshing point a

through the action point a, the driving torque applied by the planetary gear 2 to the center gear 3 is mo, and its positive direction is the same as the y-axis direction

then, when the gyroscopic effect is not taken into account, the following relationship holds for the system shown in Figure 1:

② ÷ ① is combined into:

it can be seen from equation (11): when the gyroscopic effect is not taken into account, when the acceleration of the output shaft 4 is zero (including the stationary output end), the driving torque Mo applied by the

planetary gear 2 to the center gear 3 through the meshing point a is equal to 0. That is, if the gyro effect is not considered, the mechanism in Figure 1 has no output force

distance - no output power, which is a useless mechanism, which is completely consistent with the conclusion in mechanism design ①

to simplify the theoretical analysis, it is assumed that the mass of the special gyro 5 in Figure 1 is completely distributed on the sub moving body it contains, and when the gyro effect of the sub moving body is taken into account, the above equations should be revised to the following form:

② ÷ ① will be consolidated as follows:

it can be seen from formula ⒀: when the gyro effect of the sub moving body is taken into account, when the acceleration of the output shaft 4 is zero (including the output end always stationary), Although the first term on the right in the formula is zero, since the moment of inertia JY of each sub moving body revolution with the special gyro body is constrained in the cavity with the sub moving body, the moment of inertia JZ of rotation that can only be realized in the form of micro rotation is not equal (JY> JZ), and the second term on the right in the formula is generally not zero. Therefore, the driving torque Mo ≠ 0 applied by the planetary gear 2 to the center gear 3 through the meshing point a, that is, If the gyro effect of the sub moving body is taken into account, the mechanism in Figure 1 has output torque - output power, which means that there is power flow between the input shaft and the output shaft. It is a useful mechanism

in addition, equation (1) also contains a theoretical explanation for the facts seen in the following comparative experiments in the prototype experiments: in the comparative experiments, due to ω Z is limited to zero, and the second term on the right in the corresponding formula is also zero at this time. Therefore, the output torque of the comparative experimental device is zero, and the success rate flow cannot be formed between the input shaft and the output shaft

3 prototype experiment

Figure 2 is the photo of the principle prototype for the experiment

figure 2

1 - motor 2 - O-frame that can rotate around the vertical axis 3 - special gyroscope horizontally supported in the frame of "O-frame" 2

4 - output shaft 5, 6, 7, 8 - pulley 9 - generator 3 '- ordinary gyroscope

Figure 2, 1 is motor; 2 is the "O-frame" that can rotate around the vertical axis; 3 is the special gyroscope horizontally supported in the frame of "O-frame" 2, 4 is the output shaft, 5, 6, 7 and 8 are the belt pulley, and 9 is the generator

the particularity of the special gyroscope is that there are multiple cavities uniformly distributed on the circumference with the same radius from the center of the gyroscope, and each cavity contains a ball

the relationship between the above components is: the motor 1 can drive the "O-frame" 2 to rotate around the vertical axis through the pulley; As a system load, the generator 8 adds a resistance moment to the output shaft 4 through the pulley 8, so that the pulley 7 coaxial with the pulley 8 tends not to rotate. Therefore, when the "O-frame" 2 rotates around the vertical axis, there is a relative movement between the pulley 7 and the "O-frame" 2. Therefore, through the pulleys 6 and 5, the gyro 3 can be driven to rotate around the horizontal axis in the "O-frame" 2, forming that the gyro 4 rotates around the horizontal axis It also moves around the vertical axis

experimental results:

when the motor 1 drives the "O-frame" 2 to rotate around the vertical axis at an approximately constant speed (expressed as the voltage at both ends of the motor is approximately constant), the pulley 8 will rotate, and its speed is inversely proportional to the load carried by the generator, and the load carried by the generator is directly proportional to the motor working current. It is shown that the mechanism between the motor output shaft and the pulley 8 in Experiment 1 has the function of adaptive stepless speed change

in order to find out the function of the ball bearing, a child moving body that can rotate freely relative to the gyro body in the cavity of the special gyro 3 shown in Figure 2, under the condition that other parameters are completely the same, only the gyro 3 is changed from a special gyro to an ordinary gyro (as shown in Figure 2 Photo 3 '). The material and size of the ordinary gyro are exactly the same as those of the special gyro. The only difference is that the ball in each cavity is cemented in the cavity with only a small gap and cannot move relative to the gyro body

what we have seen in the comparative experiment:

when the motor 1 drives the "O-frame" 2 to rotate around the vertical axis at an approximately constant speed (expressed as the voltage at both ends of the motor is approximately unchanged), the system vibrates strongly, and the pulley 8 can rotate slowly and weakly initially (it is estimated that it is due to the large static friction). After carrying a very light load, the pulley 8 turns to a static state, and there is no power output at the pulley 8. It is reflected that no power flow occurs between the motor output shaft and the pulley 8

4 efficiency analysis

on the premise of affirming that there is power flow between the input shaft and output shaft of the system shown in Figure 1, we can further consider whether the power input from the input shaft is diverted or intercepted and consumed, and calculate the energy budget corresponding to each degree of freedom of motion of components in the system: for the revolution motion of special gyro 5 and planetary gear 2, due to the input speed ω i = ω Y is constant. Therefore, during the normal operation of the whole system, the kinetic energy of the special gyro 5 and planetary gear 2 due to the revolution movement does not increase or decrease, and there is no interception and consumption of the energy input to the system; Considering that the output power moment Mo is equal to the load moment lo, the output shaft drives the load to rotate at a uniform speed, according to the kinematic relationship in the system:

it is known that under the above preconditions, ω X is the fixed value, that is, the large kinetic energy in the experimental space of the experimental machine possessed by the special gyro 5 and planetary gear 2 due to rotation does not increase or decrease, and there is no interception and consumption of the energy input to the system

furthermore, considering the nutation of the sub moving body in the cavity in the form of micro rotation, the energy source can only be the kinetic energy of the input system. From the Euler equations, if the nutation of the sub body in the form of micro rotation is not restricted by the resistance moment, it can be infinitely accelerated by the rotation moment and become an energy storage well in the system, in which part of the energy input to the system is stored; However, in fact, the nutation of the sub moving body in the form of micro rotation cannot be restricted by the resistance moment, which is the friction moment, so that when the friction moment increases with the increase of the micro rotation speed and reaches the same value as the rotation moment of accelerating the micro rotation of the sub moving body, the micro rotation speed of the sub moving body will not continue to increase. It can be seen that the nutation kinetic energy stored due to the micro rotation of the sub moving body is also limited

to sum up, in addition to the expected power output path, there is only one inevitable shunt power vulnerability in the system - overcome

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