The coupled simulation of numerical and real subsystems is sometimes called ‘hybrid substructuring’, ‘hardware in the loop (HIL)’, ‘cyberphysical simulation’, or ‘hybrid simulation’, and is an active field of research. In this publication, an iterative algorithm for a coupled simulation of a numerical subsystem and a real (experimental) one is presented. The term ‘iterative’ means that the subsystems are not computed or tested simultaneously but in loops one after the other. After each loop run, new control signals are computed so that the deviation of the coupling forces and displacements becomes smaller with each iteration. If the coupling quantities are equal, then the systems are coupled in a mechanical sense because of the cutting force principle. The proposed method works for quasi-static (slow speed) and dynamically reacting systems as well as for subsystems with moderate nonlinearities. The iterative character has several consequences: (1) No controllers are necessary. (2) The speed of the data exchange is not critical. (3) The method can only be applied to components whose properties do not change during the simulation (e.g. due to damage). Privacy between the two domains is guaranteed, as no explicit mathematical models in the sense of Finite Element (FE) structures or the like, but only frequency response functions, have to be exchanged. A possible application scenario could look as follows: An original equipment manufacturer (OEM) provides a web interface to a complex overall simulation model. A (geographically distant) supplier starts an iterative co-simulation with a somehow modified component (e.g. a bearing). Both sides can thus estimate the impact on the overall system. After explaining the theory, two examples are presented. The first concerns the coupled simulation of two pure numerical systems. In the second example, mixed numerical and experimental subsystems are coupled. Hence, a simple wheel suspension is considered, where the shock absorber is the real part on a test bench.

数值子系统和实际子系统的耦合模拟有时被称为“混合子结构化”、“硬件在环 (HIL)”、“信息物理模拟”或“混合模拟”，是一个活跃的研究领域。在本出版物中，介绍了一种用于数值子系统和真实（实验）子系统耦合仿真的迭代算法。术语“迭代”意味着子系统不是同时计算或测试的，而是一个接一个地循环。每次循环运行后，都会计算新的控制信号，以便每次迭代时耦合力和位移的偏差都变小。如果耦合量相等，则由于切削力原理，系统在机械意义上耦合。所提出的方法适用于准静态（低速）和动态反应系统以及具有中等非线性的子系统。迭代特性有几个后果： (1) 不需要控制器。(2) 数据交换的速度并不重要。(3) 该方法仅适用于在模拟过程中特性不发生变化（例如由于损坏）的组件。两个域之间的隐私是有保证的，因为不需要交换有限元 (FE) 结构等意义上的明确数学模型，而只需要交换频率响应函数。一个可能的应用场景如下所示： 原始设备制造商 (OEM) 为复杂的整体仿真模型提供 Web 界面。一个（地理上遥远的）供应商开始与一个以某种方式修改的组件（例如轴承）的迭代联合仿真。双方因此可以估计对整个系统的影响。在解释了理论之后，给出了两个例子。第一个涉及两个纯数值系统的耦合模拟。在第二个例子中，混合数值子系统和实验子系统是耦合的。因此，考虑了一个简单的车轮悬架，其中减震器是测试台上的真实部件。