Viscoelastic measurements made with a stress-controlled rheometer are affected by system inertia. Of all contributors to system inertia, motor inertia is the largest. Its value is usually determined empirically and precision is rarely if ever specified. Inertia uncertainty has negligible effects on rheologic measurements below the coupled motor/plate/sample resonant frequency. But above the resonant frequency, G' values of soft viscoelastic materials such as dispersions, gels, biomaterials, and non-Newtonian polymers, err quadratically due to inertia uncertainty. In the present investigation, valid rheologic measurements were achieved near and above the coupled resonant frequency for a non-Newtonian reference material. At these elevated frequencies, accuracy in motor inertia is critical. Here we compare two methods for determining motor-inertia accurately. For the first (commercially-used) phase method, frequency responses of standard fluids were measured. Phase between G' and G" was analyzed at 5-70 Hz for motor inertia values of 50-150% of the manufacturer's nominal value. For a newly-devised two-plate method (10 mm and 60 mm parallel plates), dynamic measurements of a non-Newtonian standard were collected. Using a linear equation of motion with inertia, viscosity, and elasticity coefficients, G' expressions for both plates were equated and motor inertia was determined to be accurate (by comparison to the phase method) with a precision of ± 3%. The newly developed two-plate method had advantages of expressly eliminating dependence on gap, was explicitly derived from basic principles, quantified the error, and required fewer experiments than the commercially used phase method.

中文翻译：

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确定应力控制流变仪的电机惯性

使用应力控制流变仪进行的粘弹性测量受系统惯性的影响。在所有影响系统惯性的因素中，电机惯性最大。它的值通常是根据经验确定的，如果有指定的话，精度很少。在耦合电机/板/样品共振频率以下，惯性不确定度对流变测量的影响可以忽略不计。但是在共振频率之上，由于惯性不确定性，软粘弹性材料（例如分散体、凝胶、生物材料和非牛顿聚合物）的 G' 值会出现二次误差。在本研究中，对于非牛顿参考材料，在耦合共振频率附近和之上实现了有效的流变测量。在这些升高的频率下，电机惯量的准确性至关重要。在这里，我们比较了两种准确确定运动惯性的方法。对于第一种（商业上使用的）相位方法，测量了标准流体的频率响应。G' 和 G" 之间的相位在 5-70 Hz 下分析，电机惯量值为制造商标称值的 50-150%。对于新设计的两板法（10 毫米和 60 毫米平行板），动态测量收集了非牛顿标准的 。使用具有惯性、粘度和弹性系数的线性运动方程，两个板的 G' 表达式相等，并确定电机惯性是准确的（通过与相位方法相比） ± 3% 的精度。新开发的两板法具有明确消除对间隙依赖性的优点，明确源自基本原理，量化误差，