　　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.

　　测量原理基于振动学中的动刚度定义，即动态力与动态位移的比值。当丝杠受到周期性外力作用时，其响应位移与激励力的相位差及幅值关系可反映动态刚度特性。具体而言，通过激振设备施加正弦扫描激励，利用传感器捕获力与位移信号，经频谱分析后，可绘制动刚度随频率变化的曲线。当激励频率接近丝杠固有频率时，系统发生共振，此时动刚度达到较小值，该参数对评估设备抗振性能具有决定性意义。

　　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.

　　测试设备需满足高精度、高带宽的要求。核心组件包括激振器、力传感器、位移传感器及数据采集系统。激振器通常采用电磁式或压电陶瓷式，可输出可控频率与幅值的动态载荷。力传感器需具备亚牛顿级分辨率，以准确捕捉微小动态力变化。位移测量则多采用激光干涉仪或电容式传感器，其线性度需优于0.01%。数据采集系统应支持同步多通道采样，采样率少覆盖激励频率的10倍以上，以确保信号完整性。

　　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.

　　操作流程分为准备阶段、测试阶段与分析阶段。在准备阶段，需对丝杠进行预处理，包括清洁、润滑及安装调试。安装精度直接影响测试结果，需确保丝杠轴线与激振方向重合，支承轴承的刚度需远大于被测丝杠，以符合“结合部刚度较弱原则”。测试阶段进行设备校准，通过静态标定验证传感器灵敏度。随后实施正弦扫描激励，频率范围通常从1Hz逐步升丝杠一阶固有频率的3倍，步长依据分辨率需求设定。每个频率点需采集多个周期的时域信号，以计算平均幅值与相位。

　　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.

　　数据分析需结合时域与频域方法。时域分析用于验证信号稳定性，通过观察力与位移波形的重复性，排除偶然干扰。频域分析则通过傅里叶变换提取幅频特性，计算动刚度模值与相位角。典型动刚度曲线呈现“V”型特征，共振频率处动刚度较低，相位角发生90°突变。此外，需结合阻尼比参数，通过半功率带宽法计算等效黏滞阻尼，该参数反映系统能量耗散能力，对抑制持续振动关重要。

　　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.

　　影响因素需在测试中予以控制。丝杠结构参数如直径、导程、螺旋升角对动态刚度有显著影响。实验表明，直径增加20%可使动刚度提升40%以上，而导程增大则可能降低刚度。预紧力作为关键可调参数，需在测试中保持恒定，其波动超过5%将导致动刚度测量误差超10%。环境因素方面，温度变化会引起材料弹性模量改变，需在恒温实验室进行测试，温度波动控制在±1℃以内。此外，支承方式对结果影响显著，一端固定一端自由配置与两端固定配置的动刚度差异可达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.

　　测试结果的应用具有多维度价值。在设备选型阶段，动刚度数据可辅助优化丝杠规格，例如在高加速工况下，需选择动刚度高于静态刚度3倍以上的型号。在故障诊断中，动刚度频谱可识别结构缺陷，如局部裂纹会导致特定频率点动刚度异常下降。在性能优化方面，通过对比不同润滑条件下的动刚度曲线，可确定润滑参数，使动刚度提升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%.

　　随着测试技术发展，非接触式测量与在线监测成为新趋势。激光多普勒测振技术可实现无损检测，避免传感器附加质量对测试的影响。基于物联网的在线监测系统可实时采集运行数据，通过机器学习算法建立动刚度退化模型，实现预测性维护。这些技术革新将进一步拓展丝杠动态刚度测试的应用场景，为高端装备制造提供关键数据支撑。

　　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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