Static balancing of mechanisms (1986)

High-speed train.

Cars driving down the street.

Combine harvester harvesting.

Weaving looms in a factory workshop.

Slider-crank mechanism in operation until it is balanced.

The resulting vibration is transmitted to the mechanism frame.

Balancing the mechanism with a correcting mass.

The frame becomes motionless because there is no vibration.

We remove the correcting mass and get vibration again.

A cartoon explaining what forces cause frame vibrations.

Frame vibrations are caused by an unbalanced force, which is equal to the product of the mass of all moving links of the mechanism and the acceleration of the center of this mass.

The concept of a statically balanced mechanism.

Formulas.

To determine the magnitude of the unbalanced force, it is necessary to find the coordinates, velocity and acceleration of the center of mass of the moving links of the mechanism.

In the practice of balancing mechanisms, the method of determining the coordinates of the center of mass of the moving links using the vectors of the main points has become widespread.

A cartoon explaining the method.

A cartoon showing the trajectory of the center of mass of the mechanism.

The study of the movement of the center of mass of the mechanism can be performed using various methods.

The film shows the graph method.

The speed and acceleration of the center of mass by this method are determined directly by the trajectory of point C. Graphs of functions are constructed, representing the laws of motion of the projection of the center of mass on the coordinate axes.

If the graphs of functions are differentiated by time, then graphs of speeds and accelerations can be obtained.

Formula for the modulus of the acceleration vector of the center of mass of moving links of a mechanism.

According to another method, the movement of the center of mass is studied using an auxiliary mechanism.

Cartoon showing two versions of auxiliary mechanisms.

The concept of static balancing of mechanisms.

Cartoon explaining balancing of mechanisms by the zero-vector method.

The zero-vector method ensures complete static balancing of mechanisms that allow the setting of the necessary correction masses.

Cartoon explaining balancing of mechanisms by the similarity method.

The similarity method for the slider-crank mechanism does not provide complete static balancing.

Here, only part of the connecting rod mass statically related to the crank and the crankshaft are balanced.

Even if the rotating masses are balanced, an unbalanced force acts on the machine frame along the geometric axis of the slider.

Cartoon explaining the action of an unbalanced force.

Forces of the first and higher orders can be balanced using a special balancing mechanism.

Sample of a slider-crank mechanism.

In multi-cylinder machines, mutual balancing of forces of different orders is achieved by choosing the number of cylinders and the arrangement of the cranks.

Cartoon explaining balancing in the mechanism of a two-cylinder compressor.

In a four-cylinder machine with cranks located at an angle of 90 degrees, the forces of the first and second order are completely balanced.

A cartoon explaining the balancing of mechanisms in which the trajectory of the center of mass approaches a circle.

Changing the module of the vector of unbalanced forces of the mechanism after installing the main correcting mass.

By selecting pistons, rings and other parts of the reciprocating links by mass, their parameters are brought into line with the specified ones.

The center of mass of the connecting rod is brought to a specified position.

Additional correcting masses are installed on the crankshaft.

Rotating masses are dynamically balanced on a special machine.

Equilibrated and balanced parts are sent for assembly.

The finished mechanism is sent to the test bench.

During the test, vibration levels are measured and their harmonic analysis is performed.

The mechanism meets the technical requirements for vibrations if they do not exceed the permissible values.

Samples of balanced mechanisms.