ZL15型輪式裝載機(jī)工作裝置設(shè)計含5張CAD圖
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外文文獻(xiàn)
Proof that hinged four-bar mechanism will cause unstable motion
The unstable mechanism has two equilibrium points within its range of motion, and they are important in many systems, such as valves, switches and beats. The unstable mechanism is difficult to design because of the combination of energy storage and action characteristics. This paper studies unstable mechanism, such as four-bar mechanism, which has torsional elastic force at the joint. In theory, rigid mechanism has been improved to ensure the rotation of unstable mechanism. With this knowledge, designers can solve the problem of motion and energy demand of a large number of unstable mechanisms. An example is given to illustrate the theoretical role in the design of an unstable machine.
introduce
An activity agencies within the scope of its movement is two equilibrium position, it is required by many organizations, but there are many problems in the design activities institutions, especially the mechanism motion and energy accumulation characteristics. Moreover, motion and energy storage usually occur on a flexible rotating part. This paper discusses the necessity of designing a simple rotating mechanism to study the basic relationship between the motion of the mechanism and the unstable mechanism.
Many people have discussed a lot of characteristics of rotating mechanism, including the design of motion mechanism. Recently, they have been particularly interested in micro-rotating mechanisms, which require that the power needed to control the switch is provided by the rotating mechanism and not maintained. Unstable micro-valves, micro-switches, micro-relays, even a small fiber switch have all proved this. It has been suggested that a rotating system be used to provide the elastic force for assembling small parts. This paper is an example of the structure of research institutions to ensure the implementation of unstable institutions.
Problem study
Above each of the rotating mechanism are stored in the process of movement and release energy, in fact, all of the unstable system requires some form of energy storage, because of the stable point occurred in the place of minimum energy. Unstable mechanical systems typically rely on the energy stored during tension to obtain unstable motion. The compliant manner in which the unstable mechanism behaves is subjected to an unstable execution of the motion, since the moving member allows the moving member to merge with the energy storage. In addition, there are many advantages, such as reducing the number of parts, reducing friction, recoil and loss.
Unstable mechanical design, however, is not a mechanical, needs to analyze mechanism of rotation and storing energy, to solve this problem, many of the above mentioned mechanical with a simple beam for unstable motion. However, this method is simple, can let the designers flexible control sliding power or the location of the steady state, especially for small beams often rely on the rest of the bending strain and change a lot of parameters to reduce a little.
The hinge model provides a simple way to simulate complex non-linear deflection mechanisms. It can roughly describe the force deflection characteristics of a mechanism connected by one or more bolts. The torsional elastic force of the joint simulates the stiffness of the component, as shown in figure 1. This type of model is bolted with short, curved spindles, ends bolted, or straight members bolted. The length of the connecting rod and the stiffness of the spring are transported in combination.
Hinge model on accurate analysis and rotating mechanism and characteristics of energy storage using has been fully proved, but in order to study the current problems, people have realized that many types of institutions may be bending spring said connecting rod bolt coupling. Therefore, this paper will remind us to check the rotation and operation of the mechanism at one or more joints with fixed structure with bending spring, and then this; The results of the operation may be used in fixed or unstable structures. This depends on the implementation of the results or the designer's requirements.
Stability of unstable mechanism. The bending or bending of a part of a machine requires a strong movement of the spring. When there is no external force to ensure the position of the force mechanism, the mechanism is in equilibrium. If the system returns to its original position after a small disturbance, the mechanism is stable, but if a small disturbance causes the system to change its original position, it will be unstable. The potential and the stability of the mechanism can be linked by Lagrange's theorem. If comply with the minimum potential, equilibrium position is stable, the theorem of led to more instability organization form, the definition of an unstable agencies within the scope of rotational including two minimum energy points.
The potential equation of the hinged fixed model can be established simply.
(1)
Where k is the bending spring coefficient, and so is the turning Angle of the connecting rod, or the bending Angle of the rods. The potential of the mechanism is the sum of the potential stored in the rods. The equilibrium point can be found by determining the location of the machine. It is the first time that the offset is zero. The second offset at these points will determine the stability of the equilibrium position, and the positive value is consistent.
Methods analysis of institutions No hinged four-bar linkage is shown in figure 2, figure in each of the four pole length is r1, r2, r3 and r4, four torsional spring coefficient k1, k2, k3, k4, an Angle of theta every rod and ground 1, 2, theta theta 3, 4, theta define the ground as the first lever, don't think torsional spring is distorted, position in an organization depends on theta 20, 30, theta theta 40, unstable structure design to ensure there are unstable structure. Therefore, it may be necessary to check each spring separately to determine whether there is a spring in the mechanism to ensure that the mechanism can execute motion. It's going to take a non-zero parameter, and everything else is going to be zero, and this potential equation might be different, its offset is going to be zero, and the solution is going to be in equilibrium. Therefore, the solution to the problem can be described as follows: find the position of the torsion spring in the general four-bar hinge mechanism, which has two balance points during the rotation process.
Problem solution shows that simple design tool for processing unstable structure as a series of theorems guiding unstable structure, consists of a series of theorems of unstable institutions run results, proves theorem above solution.
The theorem guides the movement of unstable structures
According to the Grashof criterion, the four-bar mechanism is divided into Grashof mechanism and non-grashof mechanism, grof mechanism
The criteria can be described mathematically:
(2)
Where s,l,p and q are respectively the longest and the shortest, and two rods whose length is in the middle. Grashof criterion 2 divides the equation into
Where the inequality is satisfied is the mechanism, and vice versa. In addition, the side is the mechanism for the left and right sides of the equation. The transposition mechanism will be handled differently from other types of mechanisms, so there are three types of mechanisms: institutions, and the side is institutions and non-institutions.
The Grashof inequality mechanism
Theorem 1 if and only if the four-bar linkage of a torsion spring is located in the connection place opposite the shortest bar, and not bending spring instead of the opposite two inconsistent state in a straight line, its movement as unstable and the hinge bar model agency.
Rule 1.1 if and only if the four pole Grashof institutions have a torsion spring is located in the shortest across the bar, and not bending spring instead of the opposite two inconsistent state in a straight line, it will not balance.
Argument. Through to the general there is a connection of potential equation of four bar linkage analysis, prove theorem 1, the analysis on the solution of the equation of the minimum potential decide whether institutions rotation can reach each minimum value, because the previous demonstration of the accuracy of the hinge, the result is quite suitable for any organization. So rule 1 is the same argument as theorem 1.1.
The above theorem can be used to determine which bolt connection should be at the same Angle in two positions by considering the rotation of Grashof mechanism. However, more rigorous arguments give designers more information about the way nature and stability are set.
For any four-bar mechanism, the energy equation is the sum of each spring's potential
Type in the
Select delegate 2 as an independent variable, and the first offset is:
Because the agency may be reversed in order to make it of each bar is as fixed on the ground, there is only one spring position need analysis, select position because of simple equation, and theta. 2 the independent variables did not appear in the expression of bits of four equations, if k4 is not zero, equations as follows:
0 = (6)
Equation of the first part theta 40 = 0, 4 - theta conformed institutions have two assembly method, that is to say, any length r1, r2, r3r and r4 rod, the fourth lever of the initial Angle of theta 40, there are two different mechanical position, assuming theta 40 does not conform to the requirements, institutions can be configured, as shown in figure 3, according to the accurate position equation can be so
The solution to the equation is
Type in the
And the two sets of solutions will be the same, as in the case of the second and third rods, respectively.
The second part of equation (6) has an offset of
If the equation has two sets of solutions:
2 = theta 3 theta.
Theta 2 = theta 3 + PI.
Therefore, when the second lever and third lever on the same straight line, the offset is zero, according to the equation (10) of the offset is zero, the second, three pole, also in the same line that is agency is modified gear.
Interpretation of the solution
It can be seen from the above analysis that the potential equation of the first offset of a spring on any member of a four-bar mechanism has four sets of solutions. The first two groups are given in equation (8), which indicates the stable position of the mechanism, and the other two groups of solutions are in equation (11), which indicates an unstable position, unless, as defined above, they are extreme values. At this point, equation (7) has a unique solution, the same as the total solution of equation (11). Therefore, the potential equation has at most two exact values during the entire rotation -- a stable position and an unstable position. This proves that the spring of a four-bar mechanism is stable if the opposite pole is coaxial.
Although a mechanism for any length of pole and the bending spring are likely to have two stable position, but the extreme value of in addition to the above discussion, some structures can not reach a steady state, that is to say, an organization can always in a stable position assembly. But it's not necessarily stable after assembly. To prove this, think of a mechanism in an unstable position, where the opposite pole connected to the spring is in a straight line. That is, when the delegate 2= delegate 3, the organization reaches its balance point,
And similarly, if there is a difference in the number of circles between now and tomorrow, the equation is zero
Equation (12) of the second condition and the conditions of equation (13) of the first can simultaneously with any proof of four bar linkage, known type of any two pole length less than or equal to the other two shots, and, to prove the inequality, can assemble an accord with inequality to institutions. The longest bar is also less than or equal to the sum of the other two bars
S + p + q > l (14)
Where SLPQ is defined in equation (2), the algebraic inequality is
L minus q is less than or equal to s plus p of 15.
L - p s + q or less
L - s p + q or less
In addition, since l is the longest rod, the following inequality can be obtained:
-s < p + q l (16)
Q -s < l + p
| | < p - q l + s
The above six inequalities prove that the difference between any two bar lengths of a four-bar mechanism is equal to the sum of the other two bars, which satisfies the second equation of equation (12) and the first equation of equation (3). However, an unstable mechanism must satisfy one of two conditions to get a consistent equilibrium position. In order to decide which mechanical structure is unstable, the length of the pole with no possible structure should be considered.
Individual results
Three useful relationships are described in detail before describing the conditions under which each mechanism can reach an unstable state. The first two are the length of the longest bar and the length of the middle bar is greater than or equal to the length of the middle bar,
Equation (17) (18) (19) is a supplement to the conditions for obtaining an unstable mechanism.
This proves that for a spring at any one connection, the four-bar mechanism may be assembled at one of two stable positions. However, if you can get one of two unstable positions, the spring can be inserted between them. These unstable positions correspond to the states of the same line on the opposite side of the spring, or in other words, the same or different angles between them. The first condition of equation (12) must be satisfied for the position of the same Angle between two bars opposite the spring:
Spring type and is in the connection of two rod length, and is the length as opposed to a spring, is one of the conditions of unstable four-bar linkage, in the same way, when the position of the organization in a relatively pole Angle difference of PI, it must meet the second condition in (13).
In this equation, the unstable mechanism caused by a spring connection is analyzed. Each spring must satisfy one of the above two conditions. If both conditions are satisfied, the unstable mechanism caused by the spring can reach a stable state when rotating in both directions. If only one condition is satisfied, two stable positions can be achieved by hanging rope rings in an unstable state. If neither condition is satisfied, the position of the spring will not cause instability.
For Grashof agencies, dislocation mechanism and Grashof institutions, organizations can form the kinematic chain of the two, or agencies may be set up the basic method, for example, figure 4, in figure (a), the longest and the shortest bar adjacent. Figure (b) is the opposite. Every basic chain has to be considered.
inference
The above discussion is suitable for any four-bar mechanism, but the last part of the argument only applies to ashgrof mechanism. We first consider the spring mechanism of position 1, the Grashof mechanism of type 4 (a) in figure 4:
Equation (22) is in violation, because the sum of the length of the adjacent two bars is less than that of the opposite bars only. Similarly, it is not satisfied for the Grashof type in figure 4 (b)
Equation (23) violates the equation (17), which is not satisfied. The Grashof structure of spring in position 1 is neither stable nor kinematic.
Every spring in the same way, after decide whether could be unstable structure analysis, the results for Grashof agencies, are shown in table 1, 1 a according to figure 4 (a) the location of 1, 1 b in figure 4 (b) in the spring position 1. Table shows that if, when the spring in position 3 or 4 institutions is not stable, it shows that the spring if the spring is not the shortest bar adjacent location, Grashof institutions meet the conditions of the same will also meet the conditions of 2, agency can get the second stable position in the unstable position, above is the proof of theorem 1 and rule 1.1
The Grashof institutions
Theorem 2 if and only if a lack of mechanism in the hinge bar model bending spring instead of the opposite two inconsistent state in a straight line, its movement and any connection with torsion spring Grashof four-bar linkage as unstable.
Criterion 2.1 when and only if the unbending torsion spring of a non-grof four-bar mechanism does not conform to the state of two opposite rods on a straight line, the spring will not be balanced at any position.
The proof of the hinge bar model has been proved accurately. We will also prove the conclusion and criterion 2.1. Except the last part, all the above proofs are suitable for Grashof mechanism and non-grashof mechanism. Therefore, it can be proved that the conclusion and criterion 2.1 indicate that the spring satisfies at least one condition in equations (20) and (21) at any position of the mechanical mechanism. The above material proves that the mechanism is unstable if the two rods opposite the spring are coaxial in a tortuous position.
For example, the spring is at position 1 in FIG. A. According to the used criteria, the Grashof inequality is:
This formula proves that the non-grashof mechanism satisfies, but according to equation (19), it does not. If the spring is placed at position 1 in FIG. B, equation (17) proves that it is not satisfied, and Grashof has an inequality:
Proved to satisfy the type, as shown in table 2 for all other springs as a result, there is only one of the two conditions satisfy any springs, which springs in any of the four position will make the Grashof imbalance, except in the case of rod in the same line of spring. Therefore, theorem 2 and criterion 2.1 have been proved.
An other on the content of the Grashof institutions. Spring in consistent connection of Grashof mechanism can get one of two unbalanced position, table 2 shows that don't meet another equilibrium position, because each spring only meet one of the two conditions. The contents of the figure decide in which direction to insert the plug of the organization, note 1 b, 2 a, 2 b and 3 a in spring, they meet, means that the spring on the Angle of the pole must be a difference of PI radians, the location of the other 1 a, 3 b, 4 a and 4 b requirements for two rod equal Angle with the ground. Figure 4 shows each position that satisfies condition 1 and the longest bar adjacent, but satisfies condition 2 and the longest bar adjacent. This is useful in many designs, since condition 2 requires two relative rods to cross each other, in the case of two coplanar rods, as with MEMS surfaces, it is usually impossible.
Modified gear
Theorem 3. The hinge bar model movement and in any place have a torsion spring displacement of four bar mechanism, if and only if the spring did not bend inconsistent state and institutional position, namely spring for rod with a straight line when imbalance.
Rule 3.1 torsional spring at any connection of four-bar linkage is not stable, if and only if the spring did not bend inconsistent state and institutional position, namely the spring to imbalance when rod with a straight line.
Arguments to prove theorem 3 and rule 3.1, again to position 4 in spring, as shown in figure 3, used to excessive rod 2 and 3 is the same straight line, the offset may molecular denominator in the equation of 10 are zero, this is because all of the rod in the modified gear with straight line when there is only one position. The mechanism can move in two ways. If it goes in one direction, it goes up, if it goes in the opposite direction, it goes down. So, rotating in one direction means that the offset symbol is changing, and in the other direction it's not changing. Symbol has changed, if single position is the maximum potential, but said symbolic constant potential continue to increase, regardless of which longest lever which lever at this time the shortest, because it is modified gear shift. When the mechanism i
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