在機械制造與自動化領域，絲杠作為實現直線運動的核心傳動部件，廣泛應用于數控機床、工業機器人、精密儀器等設備中。絲杠的動態剛度直接影響著機械系統的運動精度、穩定性和可靠性。當絲杠在動態載荷作用下工作時，若其動態剛度不足，可能導致運動部件產生振動、位移誤差，進而影響整個設備的加工精度和使用壽命。因此，準確測量絲杠的動態剛度，對于優化設計、保障設備性能關重要。

　　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、絲杠動態剛度測量原理

　　1、 Principle of measuring dynamic stiffness of screw

　　絲杠的動態剛度是指在動態載荷作用下，絲杠抵抗變形的能力，通常用單位位移變化所對應的動態力來表示。其測量原理基于動力學方程，當對絲杠施加一個動態激勵力時，絲杠會產生相應的振動響應，通過測量激勵力和響應位移，根據力學關系即可計算出動態剛度。

　　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. 

　　從本質上來說，絲杠可視為一個復雜的彈性振動系統，其動態特性受到自身結構參數（如直徑、長度、導程）、材料屬性（彈性模量、密度）以及工作條件（轉速、潤滑狀態）等多種因素的影響。在動態測量過程中，需要考慮這些因素對測量結果的綜合作用，以獲取準確可靠的動態剛度數據。

　　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、常用的絲杠動態剛度測量方法

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

　　（一）激振法

　　（1） Excitation method

　　激振法是一種較為常用的測量絲杠動態剛度的方法。該方法通過對絲杠施加特定頻率和幅值的激振力，使其產生受迫振動。常用的激振設備有激振器、力錘等。

　　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. 

　　以激振器為例，將激振器與絲杠剛性連接，通過控制系統調節激振器輸出不同頻率的正弦激勵力。同時，在絲杠上安裝位移傳感器（如激光位移傳感器、電容式位移傳感器），實時測量絲杠在激振力作用下的位移響應。利用數據采集系統記錄激勵力信號和位移響應信號，通過傅里葉變換等信號處理方法，將時域信號轉換為頻域信號，進而分析絲杠在不同頻率下的動態剛度特性。

　　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. 

　　激振法能夠地獲取絲杠在寬頻范圍內的動態剛度數據，適用于對絲杠動態性能進行深入研究和分析。但該方法需要的激振設備和信號處理系統，測量成本較高，且對測量環境要求較為嚴格，需盡量避免外界振動干擾。

　　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）模態分析法

　　（2） Modal analysis method

　　模態分析法基于結構動力學理論，通過對絲杠進行模態試驗，獲取其固有頻率、振型等模態參數，進而推算出動態剛度。在試驗過程中，對絲杠進行自由振動或錘擊激勵，使其產生振動響應。利用多個加速度傳感器布置在絲杠的不同位置，采集振動加速度信號。

　　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. 

　　通過對采集到的信號進行分析，運用模態參數識別算法（如頻域分解法、隨機子空間法等），提取絲杠的模態參數。根據模態參數與動態剛度之間的關系，結合絲杠的結構模型，計算出絲杠在不同工況下的動態剛度。

　　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. 

　　模態分析法不需要施加復雜的動態激勵，測量過程相對簡單，且能夠反映絲杠的固有動態特性。但該方法依賴于精確的結構建模和模態參數識別技術，若模型不準確或識別算法存在誤差，可能導致測量結果偏差較大。

　　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）工作狀態測量法

　　（3） Work state measurement method

　　工作狀態測量法是在絲杠實際工作過程中，實時測量其動態剛度。該方法通過在絲杠驅動系統中安裝力傳感器和位移傳感器，直接獲取絲杠在工作載荷作用下的力和位移數據。例如，在數控機床的進給系統中，將力傳感器安裝在絲杠與螺母之間，測量工作時的軸向力；同時，利用光柵尺等位移測量裝置監測絲杠的位移變化。

　　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. 

　　根據測量得到的力和位移數據，通過計算即可得到絲杠在實際工作狀態下的動態剛度。工作狀態測量法能夠真實反映絲杠在實際工況下的動態性能，對于評估設備運行狀態和優化控制策略具有重要意義。然而，該方法受到工作環境和工況的限制，測量數據的穩定性和重復性可能較差，需要進行多次測量和數據處理以提高測量精度。

　　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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