Analysis of grinding motion track and speed of the

Starting from the principles of kinematics and geometry, by simplifying the complex motion as: under the condition of a certain center distance, the rotary motion of the fixture around the central axis of the grinding disc and the rotary motion of the fixture itself, the motion trajectory and instantaneous speed of a point on the workpiece relative to the grinding disc are analyzed and calculated, and the corresponding calculation software is compiled, Show the motion trajectory curve and instant in the form of graphics. "Zhang Wei, deputy general manager of Jiangsu meiside Chemical Co., Ltd., introduced the size of the time speed, which provides a basic theoretical basis for further analyzing the trajectory type, improving the grinding efficiency and reducing the grinding cost

a large number of experimental studies show that the motion trajectory and speed of the workpiece relative to the grinding disc are not only related to the wear of the grinding disc, but also closely related to the flatness, surface roughness and material removal rate of the workpiece. Based on the principle of kinematics, this study studies the motion track of single-sided grinder through theoretical analysis, and analyzes the motion track and instantaneous speed of a point on the workpiece relative to the grinding disc from a geometric point of view. The simulation software is compiled with visual basic language, and the motion track and instantaneous speed of a certain point on the workpiece relative to the grinding disc are represented by graphics, which is helpful for further analyzing the track type, improving the grinding efficiency It provides a basic theoretical basis for reducing the grinding cost

analysis of motion types

Figure 1 motion schematic diagram of single-sided grinder

Figure 1 is the motion schematic diagram of single-sided grinder. The system has two independent motions. One is the rotation of the grinding disc around its center O1, with an angular velocity of ω 1. The second is the rotation of the central wheel around its center O1, and its angular speed is ω 3. At the same time, the central wheel drives the fixture to rotate around its center O2 through ring gear engagement, and its absolute angular speed is ω 2. The direction of each movement is shown in Figure 1

trajectory analysis

Figure 2 Schematic diagram of grinding speed calculation

plane grinding trajectory curve directly affects the quality and efficiency of grinding. It is a basic problem for in-depth understanding of the mechanism of the grinding process and has been concerned by the engineering community. The trajectory curve of the grinding process can be divided into two categories: one is the trajectory of a certain point on the workpiece relative to the grinding disc, and the other is the trajectory of a certain point on the grinding disc relative to the workpiece, This research mainly focuses on the first type (that is, the motion trajectory of a certain point on the workpiece relative to the grinding plate). According to the generation principle of trajectory, assuming that the grinding disc is stationary, the motion of the fixture should be the combination of the revolution motion around the O1 point in the center of the grinding disc and the rotation motion around the O2 point in the center of the fixture. From a geometric point of view, it is assumed that a certain point on the fixture is Q, and its initial position is shown in Figure 2, in which the initial phase angle (that is, the included angle between QO2 and the positive direction of X axis) is α， The distance from point Q to fixture center O2 (i.e. QO2) is R2, and the distance from grinding plate center O1 to fixture center O2 (i.e. center distance O1O2) is R1. In addition, the profit growth rate of cement products, light building materials, glass fibers, thermal insulation materials, sanitary ceramics, etc. in the fake building materials industry is higher than 12%. Set the fixture center O2 to move to the position of o2'at time t, as shown in Figure 2. At this time, Q moves to the position of Q', so, in the grinding plate coordinate system xo1y, Assuming that the angular velocity is positive in the counterclockwise direction and negative in the clockwise direction, o1q'is the vector sum of o1o2' and o2o ', that is,

(1)

according to figure 2, the components of o1o2'and O2' on the x-axis and y-axis can be calculated as follows:

then the trajectory equation of point Q can be obtained from formula (1): (2)

when the center distance is certain, the position of occurrence point Q (R2, α) When known, change the angular velocity ω 1 and ω The ratio of 2 will cause changes in the type of motion, and equation (2) will describe various types of trajectory curves

analysis of grinding speed

Figure 3 Schematic diagram of grinding speed calculation

the movement of the grinder is mainly the rotary movement of the grinding disc and the rotation movement of the clamp with a portable, safe and reliable safety net component. Assuming that the grinding disc does not move, the speed of a certain point Q on the fixture is the vector sum of speed V1 and speed V2, as shown in Figure 3, where V1 is the tangential speed of point Q around the center O1 of the grinding disc, V2 is the tangential velocity of point Q around the fixture center O2, and the components of V1 and V2 on the x-axis and y-axis are respectively:

from which can be obtained

therefore, the instantaneous velocity of point q is: (3)

calculate the coordinates (x (T), y (T)) of point Q at time t from formula (2), and substitute it into the velocity equation (3) to calculate the velocity size VQ (T) of point Q at time t

software programming

in order to intuitively describe the motion trajectory and motion speed of the workpiece relative to the grinding disc, for the convenience of analysis, the calculation software is compiled with visual basic language, which displays its motion trajectory curve and instantaneous speed in the form of graphics, and the rotation speed of the grinding disc is listed on the interface ω 1. Fixture speed ω 2. Initial position of a certain point Q on the workpiece (R2, α ) As well as parameters such as grinding time and grinding times, users can change the type of motion track and speed by adjusting the value of each parameter. In addition, the program can also calculate the motion track and speed when multiple composite pieces move at the same time, which can more realistically simulate the actual grinding situation

hypothesis ω 1/ω 2 = I, various types of trajectory curves (Fig. 4) and velocity curves (Fig. 5) can be obtained by changing the size of I value

Figure 4 trajectory curve

Figure 5 velocity curve

result analysis

from the calculation results, it can be seen that the value of I is different, and the type, shape and position of trajectory curve are also different, which shows the complexity of trajectory change, which is the main reason why plane grinding can obtain high accuracy

according to the analysis and calculation results, its motion trajectory and speed can be summarized into the following types:

when I = -1, the motion trajectory of point q is an eccentric circle, and its speed is a certain value, but the speed direction changes, which shows that at this time, the motion of the workpiece is relatively uniform and stable, the workpiece has high grinding accuracy, and at this time, the grinding disc can also be worn more evenly

when -10, the motion of point q is an epicycloid motion. At this time, the outer ring speed is greater than the inner ring speed. The grinding speed of this type of motion changes greatly, the difference between the inner and outer ring speeds is large, and the wear of the grinding disc is uneven, which is easy to cause serious wear of the outer ring of the grinding disc

it can be seen that reasonable selection of the speed ratio I value is the key to further analyze the track type, improve the grinding efficiency and reduce the grinding cost

conclusion

the single-sided grinder is a motion mechanism with two degrees of freedom, which can be transformed into the rotary motion of the fixture around the central axis of the grinding disc and the rotary motion of the fixture itself under the condition of a certain center distance

from the perspective of geometry, the trajectory curve equation of a certain point on the workpiece relative to the grinding plate and the calculation equation of relative motion speed are analyzed and calculated

the calculation software of motion trajectory and speed is compiled with visual basic language, and its trajectory curve and speed change curve are shown in the form of graphics. The change of speed ratio I value will cause the change of trajectory curve and speed curve to varying degrees

because the parameters that affect the machining accuracy, such as the cutting speed of the workpiece relative to the grinding disc, the direction of the cutting speed, and whether there is an area on the workpiece that cannot be machined, are closely related to different trajectory curves, and the trajectory curve has a great impact on the process of the zigzag experiment of the zigzag experiment machine of workpiece machining accuracy, which needs to stop in a stable motion