Performance Analysis of Feed Servo Drive Systems
A comprehensive technical analysis of mathematical models, characteristics, and precision impacts in CNC machining systems
Table of Contents
I. Mathematical Models and Transfer Functions of Feed Servo Drive Systems
1. General Structure of Semi-closed Loop Feed Servo Drive Systems
The semi-closed loop feed servo drive system uses the rotation angle of the lead screw as a position feedback signal for indirect position feedback in CNC machine tools, rather than using the actual movement position of the machine table for direct feedback. In semi-closed loop systems, position detection elements measure from the servo motor shaft end or lead screw shaft end through encoders to indirectly calculate the actual displacement of the worktable, as shown in Figure 4-45 (for explanatory convenience, a DC servo motor model is used as the drive motor).
This configuration offers a balance between performance and cnc machine cost, providing sufficient accuracy for most industrial applications without the expense of full closed-loop systems that require linear scales. The indirect measurement approach reduces complexity and potential points of failure, contributing to lower overall cnc machine cost while maintaining acceptable precision levels.
The diagram illustrates the signal flow from CNC command input through position control, speed control, motor drive, mechanical execution components, and back through the detection and feedback units. This structure is widely adopted in modern CNC systems due to its favorable balance between performance characteristics and cnc machine cost.
When evaluating cnc machine cost factors, the semi-closed loop configuration presents an attractive option because it eliminates the need for expensive linear feedback devices mounted on the machine table. Instead, it utilizes more economical rotary encoders attached to the motor or lead screw, significantly reducing cnc machine cost while still providing adequate feedback for many machining applications.
2. Mathematical Model of the Position Control Unit
The position controller employs a proportional regulator, whose transfer function is a constant. Therefore:
Up = kN(xo - xi) = kNΔX
(4-23)
Where:
- xo — command position parameter
- xi — actual position parameter
- Up — position controller output
- kN — proportional coefficient
The simplicity of proportional control contributes to its widespread adoption, as it reduces system complexity and associated cnc machine cost. Implementing more advanced control algorithms would increase computational requirements and potentially raise cnc machine cost without providing proportional benefits for all applications.
When optimizing for cnc machine cost, manufacturers often select proportional control for position regulation in standard machine configurations. This approach provides sufficient performance for general purpose machining while helping maintain competitive cnc machine cost points in the market.
The proportional coefficient kN is a critical parameter that affects both system responsiveness and stability. Proper tuning is essential to balance performance requirements with economic considerations related to cnc machine cost.
3. Mathematical Model of the Speed Control Unit
The command speed is the output of the position regulator Up, and the actual speed feedback signal is -nf. The speed control unit is a proportional amplification环节, with proportional coefficient kv as its transfer function. The output of the speed control unit is Ua, therefore:
Ua = kv(Up - nf)
(4-24)
Here, both the position controller and speed controller adopt proportional control strategies, which is the control strategy used in most feed servo drive systems in actual use today. These controllers can also adopt PI control, PID control, or even other control strategies, although their transfer functions would then take different forms.
The choice between proportional, PI, or PID control involves trade-offs between performance and cnc machine cost. While PID control offers superior performance in terms of reducing steady-state errors and improving dynamic response, it increases system complexity and requires more sophisticated tuning, which can raise cnc machine cost.
For many standard machining applications, proportional control provides sufficient performance at a lower cnc machine cost. Manufacturers often reserve more advanced control algorithms for high-performance machine models where the added precision justifies the increased cnc machine cost.
When evaluating cnc machine cost, it's important to consider the total cost of ownership rather than just the initial purchase price. While proportional control may reduce upfront cnc machine cost, applications requiring higher precision may benefit from the long-term value provided by more advanced control strategies despite their higher initial cnc machine cost.
II. Characteristic Analysis of Feed Servo Drive Systems
1. System Gain
For the feed servo drive system shown in Figure 4-47, if we consider that the natural frequencies of each component of the system are often designed to be much higher than the natural frequency of the entire system, the system can be simplified to the structure shown in Figure 4-48. Thus, the transfer function of the system can be expressed as:
G(s) = K / (Ts² + s)
Where K represents the system gain and T represents the time constant
System gain is a critical parameter that directly influences both performance and stability. Properly setting the system gain is essential for achieving the desired dynamic response without compromising stability, which ultimately affects both machining quality and long-term operating costs beyond the initial cnc machine cost.
When optimizing system gain, engineers must consider the entire mechanical and electrical system, including the ball screw stiffness, servo motor characteristics, and load inertia. Incorrect gain settings can lead to performance issues such as overshoot, oscillation, or sluggish response, which reduce productivity and can increase operational costs despite a lower initial cnc machine cost.
Effects of Low System Gain
- Slower response to command signals
- Increased following error
- Reduced machining accuracy
- Potential for increased cycle times
Effects of High System Gain
- Increased susceptibility to oscillation
- Potential for mechanical resonance
- Higher energy consumption
- Increased wear on mechanical components
The relationship between system gain and performance directly impacts the total cost of ownership beyond the initial cnc machine cost. A system with properly tuned gain settings will maintain accuracy over longer periods, reduce scrap rates, and minimize maintenance requirements, all of which contribute to lower operating costs compared to a machine with poorly tuned gains, even if the initial cnc machine cost is higher.
Manufacturers often invest in systems with better gain tuning capabilities to balance performance and long-term costs. While this may increase the initial cnc machine cost, the return on investment becomes evident through improved productivity and reduced waste, making it a worthwhile consideration when evaluating cnc machine cost factors.
The chart above illustrates the relationship between system gain, response time, and stability margins. Optimal performance occurs in the "sweet spot" where gain is sufficient for responsive operation without compromising stability. This balance is crucial for maximizing productivity while protecting the machine from excessive wear, ultimately affecting the true cnc machine cost over its operational lifetime.
III. Impact of Feed Servo Drive System Characteristics on Machining Accuracy
This section analyzes the machining errors caused by speed errors and acceleration errors in the feed servo drive system when machining straight lines, circular contours, or corner parts of workpieces with two-axis linkage on CNC machine tools. These errors directly affect part quality and can influence production costs through increased scrap rates and rework, factors that must be considered alongside the initial cnc machine cost when evaluating overall manufacturing economics.
1. Impact of Speed Errors on Machining Precision
In the feed system of CNC machine tools, the lead screw and nut convert the motor's rotational speed into the displacement of the executive component, which is equivalent to an integral link. The remaining parts of the system can be simplified into a proportional link with gain K, so the feed system shown in Figure 4-47 can be simplified into the structure shown in Figure 4-48. From the perspective of control systems, this is a Type 1 system.
A key characteristic of Type 1 systems is that they have no steady-state error in response to step position command inputs. For step speed inputs, i.e., ramp position command inputs, the steady-state position error Ess, also known as the speed error, is the necessary command position error between the command position and the actual position to establish the speed.
In CNC machine tool feed systems, the input is not a step position command but a ramp position command, so there must be a position error Ess. The steady-state movement speed of the system is the same as the step command speed, but the actual position always lags behind the command position, resulting in a steady-state position error.
This speed error directly affects machining accuracy, particularly in contouring applications where multiple axes must move in precise coordination. The magnitude of this error is influenced by system gain, as discussed earlier, and represents a critical performance parameter that impacts the true value derived from a CNC machine beyond its initial cnc machine cost.
When evaluating cnc machine cost, it's essential to consider the level of speed error that can be tolerated for specific applications. High-precision machining tasks require servo systems with minimal speed error, which typically increases cnc machine cost. For less demanding applications, machines with higher allowable speed errors may provide adequate performance at a lower cnc machine cost.
The relationship between speed error and machining accuracy becomes particularly critical in applications such as aerospace component manufacturing, where tight tolerances are required. In these cases, the higher cnc machine cost associated with low-speed-error servo systems is justified by the quality requirements.
Speed errors become most problematic during contour machining, where two or more axes must maintain precise positional relationships. For example, when machining a circle, any mismatch in speed errors between the X and Y axes will result in a non-circular contour. This effect increases with feed rate, making high-speed machining particularly sensitive to speed error characteristics, which in turn influences the required cnc machine cost for such applications.
Manufacturers often provide specifications on maximum speed error for different feed rates, allowing buyers to match machine capabilities with application requirements. This information is crucial for making informed decisions about appropriate cnc machine cost investments based on specific production needs.
Reducing speed error typically involves increasing system gain, improving feedback resolution, and implementing more sophisticated control algorithms—all factors that can increase cnc machine cost. However, the resulting improvements in part quality and reduction in scrap can provide significant returns on this investment, especially in high-value manufacturing environments where the cost of errors exceeds the additional cnc machine cost.
When calculating the true economic impact of speed errors, manufacturers must consider not just the initial cnc machine cost but also factors such as: part rejection rates, rework costs, inspection requirements, and customer quality penalties. In many cases, the higher cnc machine cost associated with better servo performance is offset by these downstream savings.
Modern CNC systems often include advanced compensation features to mitigate the effects of speed errors, such as look-ahead control and feed-forward algorithms. These technologies, while increasing cnc machine cost, provide significant improvements in contour accuracy, making them valuable investments for precision-critical applications.