Whether for sports or equipment operation and control, "core strength" is crucial. In this issue, we will seriously analyze the impact of the stiffness characteristics of the transmission chain, which is the "waist" of the operation and control system, on the operation and control system.
The rigidity of mechanical transmission refers to the speed at which the force of motion is transmitted from the power source to the load. The faster the response, the better the rigidity. Conversely, poor rigidity indicates that there is a delay and lag in the transmission of force (or torque) between the power source and the load, and the load cannot obtain the power required for motion in time.
The delay and hysteresis in force transmission of a drive train typically manifest in two forms: backlash and elasticity. In practical applications, they often coexist, but in analysis and adjustment, they are usually treated separately.
Let's talk about the return journey first.
Backlash refers to the "gap" between the drive side and the driven side of the transmission system, within which relative displacement occurs during movement and operation.
A typical example of backlash is what is referred to as tooth backlash (or backlash) in gear transmission.
As shown in the diagram above (the black gear is the driving side, and the gray gear is the driven side), if the driving side needs to apply rightward (CCW) power to the driven side, it is necessary to first go through the relative displacement of the return gap to make the right side of the black gear and the left side of the gray gear fit together and mesh. This usually occurs when the gray gear needs to be driven to run in the CCW direction and accelerate or run in the CW direction and decelerate.
The backlash directly impacts motion control applications by affecting the positioning accuracy at the load end. The reason is simple: the backlash prevents adjustments made on the drive side within a very small range from being transmitted to the load end.
In fact, the impact of backlash on dynamic response characteristics and system stability may be more worthy of our attention.
The most prominent characteristic of a high-dynamic motion control system is the need for frequent acceleration, deceleration, and directional adjustments. As mentioned above, the relative displacement between the driving and driven sides due to the backlash often occurs during directional adjustments and acceleration/deceleration. During this relative displacement process of acceleration, deceleration, or reversal, there is no stress contact between the driving and driven sides; that is, the motor on the power side is in an unloaded state. Once the relative displacement is complete and the driving side "gears" switch "engage" with the other side, the motor immediately returns to a loaded state.
Therefore, in a high-speed dynamic motion control system, the backlash means that the "teeth" of the drive and driven sides need to "collide" frequently, while the motor on the power side needs to switch repeatedly between the working state of being under load and being unloaded. For the control system, this means that the system inertia is constantly changing.
We know the importance of system inertia to the motion control system. The motion control system needs to determine the output based on the size of the system inertia. Changes in system inertia caused by backlash, as shown above, will directly affect the control output. As shown in the diagram above, when the speed change begins, the motor is in an unloaded state, but its output is based on normal load output. As a result, the feedback speed, position, and acceleration deviations of the motor increase, causing the system to reduce its output. When the drive side and the driven side teeth collide on the other side, a reverse impact force is generated on the motor. Combined with the already reduced output, lag in speed, position, and acceleration is inevitable. Once the teeth mesh smoothly and the system inertia stabilizes, the motor continues to accelerate in this direction, and the motion control system will automatically adjust and restore the lag error gradually. However, if the high-dynamic acceleration and deceleration motion continues repeatedly, the system needs to repeatedly experience the above-mentioned sudden changes in system inertia and make "extra" adjustments to the feedback error caused by this. This "extra" adjustment increases the output power consumption of the drive and motor. Furthermore, because it is a repeated sudden "adjustment," it will cause rotational vibration during motor operation. In severe cases, the excessive vibration amplitude may cause the motor to overheat.
If we understand the frequent abrupt changes in system inertia caused by the return backlash, and the resulting disturbances to the dynamic control system, we can then discuss the "spring effect" in the transmission system.
The spring effect doesn't mean there's actually a soft "spring" connecting the driving and driven sides. Rather, it means that mechanical transmission mechanisms, as the means of transmitting motion, possess a spring-like "soft elasticity." Given sufficient stress, any transmission connection will appear "soft." Therefore, the data used to quantify the stiffness of a mechanism is the stress value required to produce a unit displacement deformation. For example, we see stiffness values marked on couplings as xxx Nm/deg, which indicates the amount of rotational torque stress required to twist the coupling by one degree. The larger this value, the higher its stiffness; conversely, the smaller the value, the softer it is.
When a "spring effect" occurs in the transmission chain, the torque (force) output by the motor according to the system inertia cannot be directly applied to the load. During dynamic acceleration and deceleration, the "tension of the spring" will affect the transmission of the force (torque). When the "spring is relaxed", the system inertia decreases, and the output acceleration, speed and position will exceed the given values. When the "spring is tense", the system inertia increases, and the output will be lower than the given values. Since it is a closed-loop control, the motor must adjust for such output deviations. In fact, this deviation does not come from the load itself, but is a disturbance to the motor caused by the "elasticity" of the transmission mechanism.
The mechanism of this disturbance is very similar to the backlash mentioned earlier. Both are caused by the lag in force (torque) transmission when acceleration or deceleration is required, resulting in a change in the system's inertia. However, under the influence of the backlash, the inertia is a sudden change, while under the "spring effect," the inertia range shows a periodic, gradual change trend.
Similarly, this spring effect produces virtually no disturbance in a constant load system operating at a uniform speed for a long time. However, in high-dynamic motion control applications, due to the need for frequent acceleration, deceleration, and positioning adjustments, the system requires "extra" adjustments to the disturbance errors caused by inertia fluctuations. This increases the output power consumption of the drive and motor, and the repeated high-frequency "adjustments" to disturbances can cause rotational jitter during motor operation. In severe cases, excessive jitter can lead to motor overheating. During actual debugging, to avoid this jitter, we have to reduce the response gain of the motion control system, making the system "softer." However, although the system is relatively stable and has little "jitter," its dynamic characteristics and accuracy are obviously greatly reduced.
For motion systems, the rigidity of the drivetrain affects more than just control precision. Modern servo drive systems can easily achieve frequency responses of over 1000 Hz, meaning they can respond extremely quickly to load changes to achieve high dynamic control performance. However, when drivetrain rigidity is insufficient, the high-frequency dynamic performance of motion control products must respond to additional load disturbances caused by power transmission lag. To reduce the interference of this "variable load" on system stability, we sometimes have to sacrifice high-frequency dynamic characteristics and reduce the servo frequency response to "preserve" system stability first. This is undoubtedly a waste of resources for servo products that could otherwise improve motion control performance.
Therefore, to make the best use of motion control products and give full play to their due motion control performance, it is necessary to first ensure the rigidity of the system.
Over the years, with the development of the industry, many motion control products have incorporated response parameters to address transmission rigidity issues. These parameters reduce the response amplitude to load disturbances with specific frequency characteristics, ensuring that the overall system response frequency is not forced to decrease due to poor mechanical rigidity and maintaining sufficient dynamic response capability. We will gradually cover this topic in the future.
In my opinion, these product parameters regarding transmission rigidity are merely compensation measures for the machinery from an electrical control perspective. They mitigate the adverse effects of transmission rigidity issues to a certain extent, but they cannot fundamentally change the performance of motion control equipment. To fundamentally improve the dynamic characteristics of a motion control system, the rigidity of the transmission must first be increased.
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