在机械制造与自动化领域，丝杠作为实现直线运动的核心传动部件，广泛应用于数控机床、工业机器人、精密仪器等设备中。丝杠的动态刚度直接影响着机械系统的运动精度、稳定性和可靠性。当丝杠在动态载荷作用下工作时，若其动态刚度不足，可能导致运动部件产生振动、位移误差，进而影响整个设备的加工精度和使用寿命。因此，准确测量丝杠的动态刚度，对于优化设计、保障设备性能关重要。

　　In the field of mechanical manufacturing and automation, screw as the core transmission component for achieving linear motion is widely used in CNC machine tools, industrial robots, precision instruments and other equipment. The dynamic stiffness of the screw directly affects the motion accuracy, stability, and reliability of the mechanical system. When the screw operates under dynamic loads, if its dynamic stiffness is insufficient, it may cause vibration and displacement errors in the moving parts, which in turn affect the machining accuracy and service life of the entire equipment. Therefore, accurately measuring the dynamic stiffness of the screw is crucial for optimizing design and ensuring equipment performance. 

　　一、丝杠动态刚度测量原理

　　1、 Principle of measuring dynamic stiffness of screw

　　丝杠的动态刚度是指在动态载荷作用下，丝杠抵抗变形的能力，通常用单位位移变化所对应的动态力来表示。其测量原理基于动力学方程，当对丝杠施加一个动态激励力时，丝杠会产生相应的振动响应，通过测量激励力和响应位移，根据力学关系即可计算出动态刚度。

　　The dynamic stiffness of a screw refers to its ability to resist deformation under dynamic loads, usually expressed in terms of the dynamic force corresponding to a unit displacement change. The measurement principle is based on dynamic equations. When a dynamic excitation force is applied to the screw, the screw will produce corresponding vibration response. By measuring the excitation force and response displacement, the dynamic stiffness can be calculated based on the mechanical relationship. 

　　从本质上来说，丝杠可视为一个复杂的弹性振动系统，其动态特性受到自身结构参数（如直径、长度、导程）、材料属性（弹性模量、密度）以及工作条件（转速、润滑状态）等多种因素的影响。在动态测量过程中，需要考虑这些因素对测量结果的综合作用，以获取准确可靠的动态刚度数据。

　　Essentially, the screw can be regarded as a complex elastic vibration system, whose dynamic characteristics are influenced by various factors such as its own structural parameters (such as diameter, length, lead), material properties (elastic modulus, density), and working conditions (speed, lubrication state). In the process of dynamic measurement, it is necessary to consider the comprehensive effect of these factors on the measurement results in order to obtain accurate and reliable dynamic stiffness data. 

　　二、常用的丝杠动态刚度测量方法

　　2、 Common methods for measuring the dynamic stiffness of lead screws

　　（一）激振法

　　（1） Excitation method

　　激振法是一种较为常用的测量丝杠动态刚度的方法。该方法通过对丝杠施加特定频率和幅值的激振力，使其产生受迫振动。常用的激振设备有激振器、力锤等。

　　Excitation method is a commonly used method for measuring the dynamic stiffness of lead screws. This method applies a specific frequency and amplitude of excitation force to the screw to induce forced vibration. Common vibration excitation equipment includes exciters, force hammers, etc. 

　　以激振器为例，将激振器与丝杠刚性连接，通过控制系统调节激振器输出不同频率的正弦激励力。同时，在丝杠上安装位移传感器（如激光位移传感器、电容式位移传感器），实时测量丝杠在激振力作用下的位移响应。利用数据采集系统记录激励力信号和位移响应信号，通过傅里叶变换等信号处理方法，将时域信号转换为频域信号，进而分析丝杠在不同频率下的动态刚度特性。

　　Taking the exciter as an example, the exciter is rigidly connected to the screw, and the exciter outputs sinusoidal excitation forces of different frequencies through the control system. At the same time, displacement sensors (such as laser displacement sensors and capacitive displacement sensors) are installed on the lead screw to measure the displacement response of the lead screw under excitation force in real time. Using a data acquisition system to record excitation force signals and displacement response signals, the time-domain signals are converted into frequency-domain signals through signal processing methods such as Fourier transform, and the dynamic stiffness characteristics of the screw at different frequencies are analyzed. 

　　激振法能够地获取丝杠在宽频范围内的动态刚度数据，适用于对丝杠动态性能进行深入研究和分析。但该方法需要的激振设备和信号处理系统，测量成本较高，且对测量环境要求较为严格，需尽量避免外界振动干扰。

　　The excitation method can comprehensively obtain the dynamic stiffness data of the screw over a wide frequency range, and is suitable for in-depth research and analysis of the dynamic performance of the screw. However, this method requires professional excitation equipment and signal processing systems, with high measurement costs and strict requirements for the measurement environment. It is necessary to avoid external vibration interference as much as possible. 

　　（二）模态分析法

　　（2） Modal analysis method

　　模态分析法基于结构动力学理论，通过对丝杠进行模态试验，获取其固有频率、振型等模态参数，进而推算出动态刚度。在试验过程中，对丝杠进行自由振动或锤击激励，使其产生振动响应。利用多个加速度传感器布置在丝杠的不同位置，采集振动加速度信号。

　　Modal analysis method is based on structural dynamics theory. By conducting modal tests on the screw, its natural frequency, vibration mode and other modal parameters are obtained, and the dynamic stiffness is then calculated. During the experiment, the lead screw is first subjected to free vibration or hammering excitation to generate vibration response. Multiple acceleration sensors are arranged at different positions on the screw to collect vibration acceleration signals. 

　　通过对采集到的信号进行分析，运用模态参数识别算法（如频域分解法、随机子空间法等），提取丝杠的模态参数。根据模态参数与动态刚度之间的关系，结合丝杠的结构模型，计算出丝杠在不同工况下的动态刚度。

　　By analyzing the collected signals and using modal parameter identification algorithms such as frequency domain decomposition and random subspace method, the modal parameters of the screw are extracted. Based on the relationship between modal parameters and dynamic stiffness, combined with the structural model of the screw, calculate the dynamic stiffness of the screw under different working conditions. 

　　模态分析法不需要施加复杂的动态激励，测量过程相对简单，且能够反映丝杠的固有动态特性。但该方法依赖于精确的结构建模和模态参数识别技术，若模型不准确或识别算法存在误差，可能导致测量结果偏差较大。

　　Modal analysis method does not require complex dynamic excitation, the measurement process is relatively simple, and it can reflect the inherent dynamic characteristics of the screw. However, this method relies on precise structural modeling and modal parameter identification techniques. If the model is inaccurate or the identification algorithm has errors, it may lead to significant measurement result deviations. 

　　（三）工作状态测量法

　　（3） Work state measurement method

　　工作状态测量法是在丝杠实际工作过程中，实时测量其动态刚度。该方法通过在丝杠驱动系统中安装力传感器和位移传感器，直接获取丝杠在工作载荷作用下的力和位移数据。例如，在数控机床的进给系统中，将力传感器安装在丝杠与螺母之间，测量工作时的轴向力；同时，利用光栅尺等位移测量装置监测丝杠的位移变化。

　　The working state measurement method is to measure the dynamic stiffness of the screw in real time during its actual working process. This method directly obtains the force and displacement data of the screw under working load by installing force sensors and displacement sensors in the screw drive system. For example, in the feed system of a CNC machine tool, a force sensor is installed between the screw and nut to measure the axial force during operation; At the same time, displacement measurement devices such as grating rulers are used to monitor the displacement changes of the screw. 

　　根据测量得到的力和位移数据，通过计算即可得到丝杠在实际工作状态下的动态刚度。工作状态测量法能够真实反映丝杠在实际工况下的动态性能，对于评估设备运行状态和优化控制策略具有重要意义。然而，该方法受到工作环境和工况的限制，测量数据的稳定性和重复性可能较差，需要进行多次测量和数据处理以提高测量精度。

　　Based on the measured force and displacement data, the dynamic stiffness of the screw under actual working conditions can be obtained through calculation. The working state measurement method can truly reflect the dynamic performance of the screw under actual working conditions, which is of great significance for evaluating equipment operating status and optimizing control strategies. However, this method is limited by the working environment and conditions, and the stability and repeatability of the measurement data may be poor, requiring multiple measurements and data processing to improve measurement accuracy.

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