0 Overview The Isuzu automotive driveshaft three-way lug automatic machining production line is an automated machining production line that includes drilling, reaming, countersinking, rough boring, fine boring, automatic measurement, and roll extrusion processes. It is equipped with auxiliary equipment such as loading and unloading devices, front and rear lifting devices, and chip removal devices. Its process flow is shown in Figure 1. [img=524,169]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/27-1.jpg[/img] This automated machining production line uses a programmable logic controller (PLC) for centralized control. The PLC used is the OMRON C200H, which has a status display and measurement data display on the central control console. The automatic measuring device is installed at station C8. During the automatic cycle, it automatically measures the workpiece being processed, and the measurement results are displayed on station C8 and the central control console, determining whether to proceed with the next process and the wear status of the cutting tools. [b]1 Measurement Principle[/b] Figure 2 is a schematic diagram of the pneumatic measuring instrument's airflow path. Compressed air with a constant pressure P1 and a flow rate Q1 flows into the inner cavity of the tapered glass tube from the lower end, and flows upward through the gap between the float and the glass tube. Because the gap is very small, it acts as a throttling mechanism, thus creating a pressure difference across the float. Under this pressure difference, the float is lifted, and simultaneously, the gap between the float and the tube wall increases, the flow velocity decreases, and the static pressure increases. When the float is stationary at a certain position, the static pressure above the float is P2. At this time, the force acting on the float by the differential pressure is just balanced with the weight of the float. Then: (p1－p2)f＝W (1) Where: f——area of ​​the upper plane of the buoy W——weight of the buoy [img=357,251]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/27-2.jpg[/img] Assume that the gas is an ideal gas and the flow velocity through the tapered glass tube is relatively small, so the compressibility of the gas can be ignored (as shown in Figure 3). According to Bernoulli's equation for incompressible fluids, neglecting the weight of the gas itself, we have: [img=350,45]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-1.jpg[/img] Where: v1 ——— average gas velocity at section I-I ——— average gas velocity at section II-II r1 ——— specific weight of air at section I-I r2 ——— specific weight of air at section II-II g ——— acceleration due to gravity [img=242,162]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-3.jpg[/img] According to the continuity equation of fluids, the air flow rate through section I-I is equal to the air flow rate through section II-II. That is: [img=337,66]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-4.jpg[/img] Where: Ff ——— the area of ​​the inner cavity of the tapered glass tube at the position of the upper plane of the buoy F1 ——— the area of ​​the inner cavity of the glass tube at section I-I [img=200,36]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-5.jpg[/img] Substituting equation (3) into equation (2) and considering that r1 and r2 are very small, we can assume that r1＝r2＝r, then we can get: [img=337,129]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-6.jpg[/img] Considering that the actual gas is viscous, the actual flow velocity v2 of the gas stream through section II-II will be less than the flow velocity calculated by equation (4). Let: [img=337,106]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-8.jpg[/img] The flow rate of the air stream through section II-II is Q1 = v2(Ff - f). [img=334,186]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-9.jpg[/img] For the measuring instrument, g, W, f, and r in equation (5) can all be considered as constants, that is, the flow rate Q1 is only a function of c and F. The flow coefficient c is related to the shape of the buoy and the Reynolds number of the gas. If the Reynolds number is above a certain limit, the flow coefficient is independent of the Reynolds number, so the flow coefficient can be considered as a constant. In this way, the flow rate Q1 is only a function of the cross-sectional area F. The inner cavity of the glass tube is conical. Let the diameter of its small end be D1 and the taper be K. Then the area of ​​the inner cavity at a distance H from the lower end of the glass tube is: [img=351,97]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-10.jpg[/img] From equation (6), it can be seen that the flow rate Q1 through the glass tube is only a function of the buoy height. However, we need to measure the change in the size of the workpiece by the change in the flow rate. Let the nozzle diameter be d, and the gap between the nozzle and the baffle be S. When S is within a certain range, the outflow area F of the nozzle-baffle can be expressed as follows: [img=311,21]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/28-11.jpg[/img] Assume the gas is an ideal gas and the gas flow is adiabatic. Thus, the compressed air flowing out from the upper end of the glass tube flows into the atmosphere through a throttling orifice equivalent to the outflow area of ​​the nozzle-baffle with diameter d (as shown in Figure 4). Take sections III-III and IV-IV. Let the static pressure at section III-III be p3≈p2, and the flow velocity be v3. Let the static pressure at section IV-IV be p4≈1 atmosphere, and the flow velocity be v3. According to Bernoulli's equation for compressible fluids, we have: Where: k — the adiabatic constant of air, k＝1.41; r0 — the specific weight of air. Because the flow process is adiabatic, the relationship between pressure and specific weight is as follows: [img=138,53]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-1.jpg[/img] [img=211,192]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-2.jpg[/img] Furthermore, according to the continuity equation for compressible fluids, the weight flow rates of the gas flowing through sections III-III and IV-IV are equal, i.e.: [img=347,252]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-3.jpg[/img] If the velocity coefficient is also ξ, then the mass flow rate of the gas flowing through section IV-IV is: [img=347,190]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-4.jpg[/img] [img=347,156]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-5.jpg[/img] If we consider atmospheric pressure p4 as zero and p2 as relative pressure, then: [img=346,29]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-6.jpg[/img] The gas flowing through the downpipe must all flow into the atmosphere through the nozzle, so: Q1=Q, that is: [img=346,101]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/29-7.jpg[/img] Equation (11) is a function expressing the position H of the buoy and the gap between the nozzle baffle. It shows that when the gap between the nozzle baffle changes, it will cause the position H of the buoy to change. Conversely, the position of the buoy can be used to determine the gap between the nozzle baffle. This is the working principle of the buoy-type pneumatic gauge for measuring workpieces. From equation (11), it can be seen that when the inner cavity of the glass tube is conical, the relationship between H and S is nonlinear. In fact, the value of p2 is not a constant either, and it also changes slightly with the value of S. When the inner cavity of the glass tube is designed with a composite shape of conical and quadratic curve, the linear relationship between H and S can be guaranteed. 2. Composition of the Measuring Instrument Figure 5 is a block diagram of the measuring instrument. First, the pneumatic signal from the nozzle is converted into an electrical signal by a pneumatic-to-electric converter for easy processing. Then, the electrical signal is amplified, organized, and sent to an analog-to-digital converter (A/D) for conversion into a digital quantity, which is then sent to a single-chip computer for processing. The measuring nozzle is mounted on a moving slide. When the measuring nozzle reaches the measuring position, the measuring position control switch closes. Simultaneously, the host computer (OMRON PLC) sends a control command to the lower-level computer (measuring device) via the RS-232 communication port to initiate the measurement. Since the processing cycle of the automated production line is 4-5 minutes, while the measuring station only needs 15-20 seconds to move from its original position on the measuring slide to the measuring position, perform the measurement, and return to the original position, the measurement process takes only 15-20 seconds. To reduce measurement errors, after the host computer issues the measurement command, the measuring device repeats the measurement 10 times. The arithmetic average of the measured results is used as the current measurement result, displayed in the measuring device's display window, and sent back to the host computer via the communication port. The measurement result determines whether the next processing step should proceed. If the measurement result is within the allowable error range of the workpiece, the next processing step—rolling extrusion—will proceed. If the measurement result is outside the allowable error range of the workpiece, the next processing step—rolling extrusion (C7 station)—will not proceed, and an audible and visual alarm will be activated to remind the operator to handle the situation. [img=338,189]http://zszl.cepee.com/cepee_kjlw_pic/files/wx/zdhyyqyb/2002-1/31-1.jpg[/img][align=left][b]3 Conclusion[/b] This automatic machining production line is a special production line designed and manufactured by our institute specifically for a certain transmission shaft factory. It was delivered in July 1995 and has been operating well ever since. Because this measuring device adopts pneumatic non-contact measurement, there is no damage to the machining and measuring surface, ensuring the machining accuracy. Measuring range of the measuring device: 0～200μm; Measuring gap: 0.2～0.3mm; Measuring accuracy: ±1μm. [/align]