# Combining the Advantages of Different Processing Solutions Using a Novel Motion Processing Approach
## 4 Operating-Speed-Dependent Motion Processing Approach
### Model-Based Optimized Process Solution  
In the state of the art, a large amount of literature is available concerning motion profile optimization for automated machines. In this work, only the results of the optimization  
Figure 2: Behavior of the conventional process solution. (**a**) Motion principle, (**b**) velocity profile of the working tool and product, and (**c**) trends of the product’s positioning error [8]. (the optimized process solution) are of interest. For the interested reader, we refer to, e.g., the review article [14] or the Ph.D. thesis [15] and the references therein. The new transport approach discussed in [8] applies a new strategy for implementing the same technical task as the conventional approach mentioned in Section 1. Figure 3a shows the motion principle of tool and product for this process solution in the process stroke. The product is initially (I) located at the same starting point as in the conventional process. At this position, the product is accelerated by the comb's left time. During phase (II), the comb decelerates (Figure 3b, gray), and the product is entering into a free-sliding phase. While sliding, the product slows down by friction. In phase (III), the comb speeds up again, actively catches the product with the right time, and stops it at the end point of the motion. The principle of this process solution is based on the concept of partly removing the product's kinetic energy by its friction with the slide surface. The remaining energy is actively absorbed by the second time. In this process, the product is first accelerated and reaches a velocity at which it detaches from the time. This velocity is proportional to the operating speed. Afterwards, the friction with the sliding surface decelerates the product's motion. The breaking force is independent of the operating speed. In turn, the time available for the product to decelerate decreases with rising operating speeds. Therefore, at higher operating speeds, less product velocity is removed by friction than at lower operating speeds. As a result, the influence of friction on the process decreases with increasing operating speed. Thus, the process is sensitive to changing operating speeds, and the motion has to be optimized operating-speed-dependent for a given velocity \(f_{\text{opt}}\). The lowest optimizable operating speed was determined to be at 1.3 Hz in the optimization configuration used in the example. At this speed, the product obtains exactly the kinetic energy from the working tool that is removed by friction on the sliding surface. In this case, actively stopping the product with the second time is not required. The product's motion is identical to the motion of the conventional solution. At lower operating speeds, the product does not slide far enough to be positioned correctly. On the contrary, the upper limit for the optimal operating speed \(f_{\text{opt}}\) is mainly determined by the physical limitations of the test rig, e.g., by the achievable motor torques. In [7], operating speeds of 5 Hz were  
Figure 3: Behavior of the new process solution. (**a**) Motion principle, (**b**) velocity profile of the working tool and product, and (**c**) trends of the product’s positioning error [8]. implemented reliably. This represents a significant increase in operating speed of 285 % compared to the conventional process. Figure 3c illustrates the operating-speed-dependent positioning error associated with the new process. If the optimized motion specification is executed slower than \(f_{\text{opt}}\), the product is not accelerated enough to reach the target. From this, a lower critical speed \(f_{\text{lcr}}\) results. If the product is accelerated too much, it has too much energy and collides with the second time. In this case, it bounces off and is not positioned as required above an upper critical speed \(f_{\text{ucr}}\). For the optimal speed \(f_{\text{opt}}\), the position error is small.