Predicting Individual Die Loads in Multi-Stage Forging
Accordingly, we endeavored to develop a method of determining individual die loads, their fluctuation and their significance to process variables. Our new method differs from traditional tonnage monitors, which use the sum of four strain-gage measurements to arrive at conclusions. Rather, our research utilizes, for the first time, the extra information generated by the four individual sensor (strain-gage) signals as a diagnostic tool. Observations and data in support of this project were gathered from the operation of a five-station Kurimoto press at HHI FormTech in Royal Oak, Mich.
Our approach was to adopt a two-step analytical method of estimating the individual loads on each (die source signals). These signals are taken from the combined die force signals measured by each strain gage installed on the press columns, where the measured press-tonnage force signals are assumed to be linearly proportional to individual die forces but with different unknown parameters. Then, two analytical techniques – Independent Component Analysis (ICA) and Sparse Component Analysis (SCA) – are integrated into the model. In the first step, the ICA method is used to separate the combined sensor signals into individual source signals. In the second step, the SCA method is used to separate the dominant source signals from the remaining combined sensor signals obtained from Step 1.
Forging TrialsThe developed methods were applied to and tested on the Kurimoto press in a multi-stage forging process illustrated in Figure 1. A billet of rectangular cross section enters the press, is struck five times and emerges as a near-net-shape part. At each press stroke, five operations are performed simultaneously by five embedded dies, with each die striking a different intermediate part at each station. The five hits (stations) are sequenced as follows: station 1 – preforming; station 2 – blocker; station 3 – finisher; station 4 – piercing; and station 5 – trimming.
Figure 2 shows the source signals generated by the five die operations, which were obtained by off-line tests using either station-by-station tests or progressive feed-in and feed-out tests (which have been explored in another research paper). Based on the design of the process, it is known that the two independent source signals generated by station 4 (piercing) and station 5 (trimming) and three dependent source signals generated by stations 1 through 3 are included. The three source signals generated by stations 1 through 3 are considered dependent because each is a shape-forming operation and the tonnage force at a later forming stage (die) depends on what occurred at a previous forming station. In contrast, stations 4 and 5 are considered independent because they are related to removing some material at different portions of the part. From Figure 2, it can be seen that the magnitudes of the independent source signals (stations 4 and 5) are much smaller than those of the dependent source signals from stations 1 through 3. Therefore, neither the ICA method nor the SCA method can be used alone to fully separate the die source signals from the combined tonnage sensing signals.
Strain-gage sensors can be easily installed on the linkages or columns of the forging press to measure the press-tonnage forces. The measurements from the gage sensors on the press columns can be reasonably considered to be a linear combination of the individual die forces on each station. In practice, sensor installation and calibration are done based on this principle. In this case study, however, in order to fully separate the five die forces, five strain-gage sensors must be installed. Otherwise, only four die forces can be separated.
To avoid confusion, it is worthy of note here that the concept of five die-force signals is different from that of five sensing signals. The former are unmeasurable signals, while each of the latter sensing signals is a linear combination of five die signals. However, we do not know the linear proportion parameters of the die source signals, which is the intent of our research method to determine.
Testing the ModelIn order to demonstrate the proposed methodology, our first step was to simulate the five sensors’ measurements (X) as the combined signals of the five dies’ true force signals (true S) obtained by off-line station-by-station tests. At this step, the linear relationships between the sensor measurements and the individual die forces are mathematically represented by a pre-assumed matrix (A) that, in practice, is dependent on the sensor locations. Thus, a different matrix can be used to test if the estimated die-force signals are robust to the sensor locations.
The second step is a validation process in which we apply our method to estimate the five dies’ force signals (to get the estimated S) based on the sensor measurements (X) simulated in the first step. In this second step, we apply our method to obtain estimates of die loads (S). Then we compare the estimated die load values (S) to independently measured values (true S). If the values are consistent, our method is validated.
If a hypothetical abnormality was detected, let’s say on the first and fourth dies, the corresponding faulty die signals would yield curves different than the baseline data of Figure 2. These differences are illustrated in Figure 5. Comparing Figure 5 to Figure 6, it can be seen that both the independent faulty die signal (at station 4) and the dependent faulty die signal (at station 1) are successfully estimated. This result can help operators quickly notice the change of individual die forces and decide whether or not to make an immediate process correction. Alternatively, product formed during significant signal variation can be automatically placed into a bin for further inspection.
SummaryThis research project suggested a new method of estimating the individual die signals and, consequently, individual die loads from a standard tonnage monitor of a forging press. The proposed analytical tool combines the methods of Independent Component Analysis (ICA) and Sparse Component Analysis (SCA) with engineering knowledge to detect potential die overload or material fill problems in individual stations.
The method consists of two major steps. First, the ICA method is applied to multiple tonnage-sensor signals. The impacts of the independent die signals on the measured sensor signals are then eliminated. Secondly, the reduced sensor signals are separated using the SCA method in the time and frequency domains. Furthermore, two statistical rules are developed to check the sparse property and to monitor the individual operations based on the estimated source signals.
Actual forging process trials were run to demonstrate the predictive capability of the developed method. The case study showed that by using both ICA and SCA analytical methods the independent/dependent die signals can be successfully approximated by the proposed estimation method. However, the use of the ICA method or the SCA method alone could not deliver satisfactory predictive results. The estimation of the source signals offers efficient monitoring and quality assessment of the individual die operations, thus enhancing the diagnostic capability of the tonnage monitoring system.
Author Jionghua (Judy) Jin is associate professor in the Department of Industrial and Operations Engineering at the University of Michigan, Ann Arbor, Mich. She was assisted in this research by graduate assistants Qingyu Yang and Qiang Li. Dr. Jin has been serving as FIERF Professor in the Magnet School Program of the Forging Industry Educational and Research Foundation (FIERF) since 2006. She may be reached at 734-763-0519 or at firstname.lastname@example.org