絲杠動態剛度是衡量機械系統在動態載荷下抵抗變形能力的關鍵指標，尤其在數控機床、精密定位設備及自動化生產線中，其數值直接影響加工精度、設備壽命及運行穩定性。本文將從測量原理、設備配置、操作流程及數據分析等維度，系統闡述絲杠動態剛度的測試方法。

　　The dynamic stiffness of a screw is a key indicator for measuring the ability of a mechanical system to resist deformation under dynamic loads, especially in CNC machine tools, precision positioning equipment, and automated production lines. Its value directly affects machining accuracy, equipment life, and operational stability. This article will systematically explain the testing method of dynamic stiffness of screw from the dimensions of measurement principle, equipment configuration, operation process, and data analysis.

　　測量原理基于振動學中的動剛度定義，即動態力與動態位移的比值。當絲杠受到周期性外力作用時，其響應位移與激勵力的相位差及幅值關系可反映動態剛度特性。具體而言，通過激振設備施加正弦掃描激勵，利用傳感器捕獲力與位移信號，經頻譜分析后，可繪制動剛度隨頻率變化的曲線。當激勵頻率接近絲杠固有頻率時，系統發生共振，此時動剛度達到較小值，該參數對評估設備抗振性能具有決定性意義。

　　The measurement principle is based on the definition of dynamic stiffness in vibration science, which is the ratio of dynamic force to dynamic displacement. When the screw is subjected to periodic external forces, the phase difference and amplitude relationship between its response displacement and excitation force can reflect the dynamic stiffness characteristics. Specifically, by applying sinusoidal scanning excitation through vibration equipment and capturing force and displacement signals using sensors, the curve of brake stiffness changing with frequency can be plotted after frequency spectrum analysis. When the excitation frequency approaches the natural frequency of the screw, resonance occurs in the system, and the dynamic stiffness reaches a small value. This parameter is of decisive significance for evaluating the anti vibration performance of the equipment.

　　測試設備需滿足高精度、高帶寬的要求。核心組件包括激振器、力傳感器、位移傳感器及數據采集系統。激振器通常采用電磁式或壓電陶瓷式，可輸出可控頻率與幅值的動態載荷。力傳感器需具備亞牛頓級分辨率，以準確捕捉微小動態力變化。位移測量則多采用激光干涉儀或電容式傳感器，其線性度需優于0.01%。數據采集系統應支持同步多通道采樣，采樣率至少覆蓋激勵頻率的10倍以上，以確保信號完整性。

　　The testing equipment needs to meet the requirements of high precision and high bandwidth. The core components include exciters, force sensors, displacement sensors, and data acquisition systems. Exciters are usually of electromagnetic or piezoelectric ceramic type, which can output dynamic loads with controllable frequency and amplitude. The force sensor needs to have sub Newtonian resolution to accurately capture small dynamic force changes. Displacement measurement often uses laser interferometers or capacitive sensors, and their linearity needs to be better than 0.01%. The data acquisition system should support synchronous multi-channel sampling, with a sampling rate covering at least 10 times the excitation frequency to ensure signal integrity.

　　操作流程分為準備階段、測試階段與分析階段。在準備階段，需對絲杠進行預處理，包括清潔、潤滑及安裝調試。安裝精度直接影響測試結果，需確保絲杠軸線與激振方向重合，支承軸承的剛度需遠大于被測絲杠，以符合“結合部剛度較弱原則”。測試階段首先進行設備校準，通過靜態標定驗證傳感器靈敏度。隨后實施正弦掃描激勵，頻率范圍通常從1Hz逐步升至絲杠一階固有頻率的3倍，步長依據分辨率需求設定。每個頻率點需采集多個周期的時域信號，以計算平均幅值與相位。

　　The operation process is divided into preparation stage, testing stage, and analysis stage. In the preparation stage, it is necessary to preprocess the screw, including cleaning, lubrication, and installation and debugging. The installation accuracy directly affects the test results, and it is necessary to ensure that the axis of the screw coincides with the excitation direction. The stiffness of the supporting bearing should be much greater than that of the tested screw to comply with the principle of "weaker stiffness at the joint". The testing phase begins with equipment calibration, which verifies sensor sensitivity through static calibration. Subsequently, sinusoidal scanning excitation is implemented, with the frequency range usually gradually increasing from 1Hz to three times the first natural frequency of the screw, and the step size is set according to the resolution requirements. Multiple cycles of time-domain signals need to be collected at each frequency point to calculate the average amplitude and phase.

　　數據分析需結合時域與頻域方法。時域分析用于驗證信號穩定性，通過觀察力與位移波形的重復性，排除偶然干擾。頻域分析則通過傅里葉變換提取幅頻特性，計算動剛度模值與相位角。典型動剛度曲線呈現“V”型特征，共振頻率處動剛度較低，相位角發生90°突變。此外，需結合阻尼比參數，通過半功率帶寬法計算等效黏滯阻尼，該參數反映系統能量耗散能力，對抑制持續振動至關重要。

　　Data analysis requires a combination of time-domain and frequency-domain methods. Time domain analysis is used to verify signal stability by observing the repeatability of force and displacement waveforms to eliminate accidental interference. Frequency domain analysis extracts amplitude frequency characteristics through Fourier transform and calculates dynamic stiffness modulus and phase angle. The typical dynamic stiffness curve exhibits a "V" - shaped characteristic, with lower dynamic stiffness at the resonance frequency and a sudden 90 ° phase angle change. In addition, it is necessary to combine the damping ratio parameter and calculate the equivalent viscous damping through the half power bandwidth method. This parameter reflects the energy dissipation capacity of the system and is crucial for suppressing sustained vibration.

　　影響因素需在測試中予以控制。絲杠結構參數如直徑、導程、螺旋升角對動態剛度有顯著影響。實驗表明，直徑增加20%可使動剛度提升40%以上，而導程提升則可能降低剛度。預緊力作為關鍵可調參數，需在測試中保持恒定，其波動超過5%將導致動剛度測量誤差超10%。環境因素方面，溫度變化會引起材料彈性模量改變，需在恒溫實驗室進行測試，溫度波動控制在±1℃以內。此外，支承方式對結果影響顯著，一端固定一端自由配置與兩端固定配置的動剛度差異可達3倍以上。

　　The influencing factors need to be controlled during testing. The structural parameters of the screw, such as diameter, lead, and helix angle, have a significant impact on the dynamic stiffness. Experiments have shown that a 20% increase in diameter can increase dynamic stiffness by over 40%, while an increase in lead may decrease stiffness. As a key adjustable parameter, the preload force needs to be kept constant during testing, and fluctuations exceeding 5% will result in a measurement error of dynamic stiffness exceeding 10%. In terms of environmental factors, temperature changes can cause changes in the elastic modulus of materials, which need to be tested in a constant temperature laboratory with temperature fluctuations controlled within ± 1 ℃. In addition, the support method has a significant impact on the results, and the difference in dynamic stiffness between one end fixed and one end free configuration and two end fixed configuration can reach more than three times.

　　測試結果的應用具有多維度價值。在設備選型階段，動剛度數據可輔助優化絲杠規格，例如在高加速工況下，需選擇動剛度高于靜態剛度3倍以上的型號。在故障診斷中，動剛度頻譜可識別結構缺陷，如局部裂紋會導致特定頻率點動剛度異常下降。在性能優化方面，通過對比不同潤滑條件下的動剛度曲線，可確定潤滑參數，使動剛度提升15%-20%。

　　The application of test results has multidimensional value. In the equipment selection stage, dynamic stiffness data can assist in optimizing screw specifications. For example, under high acceleration conditions, it is necessary to choose a model with dynamic stiffness that is more than three times higher than static stiffness. In fault diagnosis, the dynamic stiffness spectrum can identify structural defects, such as local cracks that can cause abnormal decrease in dynamic stiffness at specific frequency points. In terms of performance optimization, by comparing the dynamic stiffness curves under different lubrication conditions, lubrication parameters can be determined to increase dynamic stiffness by 15% -20%.

　　隨著測試技術發展，非接觸式測量與在線監測成為新趨勢。激光多普勒測振技術可實現無損檢測，避免傳感器附加質量對測試的影響。基于物聯網的在線監測系統可實時采集運行數據，通過機器學習算法建立動剛度退化模型，實現預測性維護。這些技術革新將進一步拓展絲杠動態剛度測試的應用場景，為出眾裝備制造提供關鍵數據支撐。

　　With the development of testing technology, non-contact measurement and online monitoring have become new trends. Laser Doppler vibration measurement technology can achieve non-destructive testing and avoid the influence of additional sensor mass on testing. The online monitoring system based on the Internet of Things can collect real-time operational data, establish a dynamic stiffness degradation model through machine learning algorithms, and achieve predictive maintenance. These technological innovations will further expand the application scenarios of dynamic stiffness testing for lead screws, providing key data support for high-end equipment manufacturing.

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