- Check supply against demand using a conservative lower bound for vacuum-source flow and a conservative upper bound for leakage flow. The acceptance threshold in this article is a ratio of at least 1.50.
- Enable lifting only after every required zone reaches the pressure threshold, remains stable for the specified window and satisfies the motion-permission logic.
- Verify normal holding capacity, tangential slip resistance and moment distribution over the complete motion trajectory, including the defined fault conditions.
- The holding time is based on the total emergency positioning time. Workpieces with insufficient holding or controlled positioning capabilities are directly judged as not applicable.
00Executive Summary
Cartons, corrugated board, bags and porous composites continuously admit air. Suction flow both evacuates the gas in the pipework volume and compensates for leakage through the cup lip and material pores. When incoming flow approaches the effective suction flow at the working vacuum level, vacuum may build slowly, fluctuate or fail to reach the permissive threshold. Selection must therefore account for leakage, evacuation time, friction, eccentricity, dynamic acceleration and local failure; the pressure-difference-times-area model for smooth steel alone is insufficient.
GB/T 41098—2021, Cranes—Safety—Load Lifting Attachments, is currently in force and is identical to ISO 17096:2015 [1][2]. Both apply only to non-fixed load-lifting attachments for cranes, hoists, and hand-controlled load-manipulating devices. ISO 17096 expressly excludes hazards from pneumatic components, so it cannot be extended directly into a complete safety basis for a robot end effector or pneumatic circuit. GB/T 32293—2015 is currently in force and is used only to select a leak-test method for hardware leakage Q_H in vacuum equipment; it does not establish standards conformity for carton porosity flow Q_P or process inflow at the cup lip Q_E [3]. ISO 4414:2010 applies to design, isolation, residual energy, and maintenance of pneumatic systems on machinery, but excludes factory air-supply systems, gas cylinders, and air receivers [4].
This report defines engineering release of the vacuum-gripping subsystem. Complete-machine risk assessment, validation of safety-related controls, robot-integration compliance, and air-receiver compliance require formal prerequisite records. After the subsystem tests pass, complete the machine-level safety release as well. This method uses a load safety factor of 2.5, flow reserve factor of 1.5, establishment limit of 2.0 s, and four-zone fault tolerance as its selected research baseline for calculation and verification.
Common Research Baseline
| Item | Study Baseline | Pass Conditions |
|---|---|---|
| Minimum Holding Differential During a Fault | Δp_min,LB = 45 kPa | Use the measurement lower bound; every healthy zone remains at or above it until the load reaches support |
| Normal Lifting-Permission Differential | Δp_pick,LB = 50 kPa | Each zone has 20 consecutive samples at 100 Hz with lower bounds≥50 kPa and window peak-to-peak variation≤2 kPa |
| Load Safety Factor | S_L = 2.5 | Capacity/design-demand ratio≥1.00 for every path orientation, acceleration, and eccentricity |
| Leakage Flow Reserve Factor | K_Q = 1.5 | Study coefficient applied to Q_S,LB/Q_L,UB |
| Conservative Flow Criterion | Q_S,LB/Q_L,UB ≥ 1.50 | Compare the source-flow lower bound with the leakage upper bound at the same reference state |
| Vacuum-Establishment Limit | t_pick ≤ 2.0 s | From cup contact until every zone reaches a 50 kPa lower bound and remains stable for 200 ms |
| Zoning | 4 mutually isolated zones | After complete failure of any one zone, the remaining system meets load and moment criteria |
| Backup Supply and Retention Time | t_1−t_0 ≤ 0.10 s | t_0: main-supply loss; t_1: supply-pressure lower bound at every zone-generator inlet≥0.40 MPa |
| Fault Confirmation | t_2−t_0 ≤ 0.50 s | t_2: controller confirms the fault and issues the set-down command |
| Controlled Set-Down | t_3−t_2 ≤ 4.00 s | t_3: load transfer to support is complete; t_res≥0.50+2×4.00=8.50 s |
| Sample Acceptance | Every test cell independently has zero failures at FAT and SAT | Any failure fails the entire item. After correction, repeat the item from its first trial. |
Key Conclusions
- Check pressure differential, effective area, load direction, friction and moments together. Rated suction force and cup count are only preliminary selection inputs.
- For a porous workpiece, measure the leakage-flow upper bound in the actual contact condition and verify it against the vacuum-source flow lower bound at a 45 kPa pressure differential and minimum supply gauge pressure of 0.40 MPa. If Q_S,LB/Q_L,UB<1.50, the condition fails.
- Suction permission shall come from a pressure switch or sensor in every zone. Lifting is permitted only when the pressure lower bound in every zone remains at least 50 kPa continuously for 200 ms and peak-to-peak variation is no greater than 2 kPa. A fixed delay alone shall not be used to declare suction established; doing so fails the criterion. SMC's official selection information likewise requires pressure-signal confirmation of established suction rather than reliance on a timer alone [5].
- A large central chamber’s average pressure must not conceal a single-zone fault. Provide separate pressure measurement, flow restriction or check-valve isolation, and identifiable alarms for every zone.
- For a high-leakage carton, an air receiver without validation of its discharge model and performance at minimum supply pressure shall not be treated as loss-of-air protection. Recalculate the backup vacuum source or compressed-air reserve using adiabatic discharge, the flow lower bound at minimum supply pressure, and the air-consumption upper bound, and verify it by a physical fault-injection test that shuts off the main energy supply.
- Release requires leakage records, a verified dynamic envelope, single-zone fault tests, and controlled set-down records. If any are missing, record not released; an experience-based signature is insufficient.
01Scope and Symbols
This article addresses corrugated cartons, uncoated board, permeable bags and similar workpieces gripped from the top or a designated suction surface, using pneumatic industrial manipulators, robots or dedicated handling machines. Assessment starts at cup contact and covers vacuum generation, distribution, monitoring, movement, isolation and safe placement. Equipment classified as a non-fixed load lifting attachment uses GB/T 41098—2021/ISO 17096:2015. Robot end effectors require separate system integration and control safety validation.
R1 checks five records: carton structural design, air-receiver vessel compliance, complete machine risk assessment, control-system safety integrity and equipment selection for explosive atmospheres. Subsystem engineering release may proceed only when all record identifiers are available and entered in R1. Any missing record causes R1 to fail.
| Symbol | Meaning | Unit |
|---|---|---|
| Δp_LB | Measurement lower bound of atmospheric pressure minus cup-cavity absolute pressure | Pa or kPa |
| A_eff,LB,i | Cup i effective-area lower bound at the specified compression, after deducting uncertainty | m² |
| C_i | Normal capacity of the i-th suction cup, C_i=Δp_min,LB A_eff,LB,i | N |
| Q_S,LB | Source extraction-flow lower bound at the specified differential and minimum supply pressure | NL/min |
| Q_L,UB | Leakage-flow upper bound across the specimen, orientation, compression, and contamination conditions | NL/min |
| μ_LB | Contact-pair friction lower bound at the specified contamination and wear states, after deducting uncertainty | — |
| N_i、T_i | Normal tensile force carried by suction cup i and the two-dimensional tangential-force vector in the suction plane | N |
| m_UB、g | Workpiece mass upper bound and gravitational acceleration; this report uses g=9.81 m/s² | kg、m/s² |
| a_n,UB、a_t,UB | Upper bounds of normal and tangential acceleration during normal motion, fault braking, and controlled set-down | m/s² |
| S_L、K_Q | Load safety factor and flow reserve factor | — |
| V_Z,UB | Upper bound of the volume evacuated by one zone | L |
| p_N、T_N | Reference state; fixed in this report at 101.325 kPa and 293.15 K | kPa、K |
| U_x | Expanded measurement uncertainty for quantity x, k=2 | Same as x |
Effective area shall be derived from suction-cup geometry, the locked compression range of 5–9 mm, and measurement uncertainty; the outer-contour area shall not be used directly as effective area. This report requires U_A/A≤2% and uses A_eff,LB=A_eff,meas−U_A in calculations. Schmalz's official technical information expresses theoretical holding force as F=ΔpA and notes that porous, rough workpieces reduce the achievable vacuum [6][7]. Supplier-catalog holding force is used for preliminary selection; subsystem engineering release consistently uses the pressure-differential lower bound, effective-area lower bound, and this report's safety factor.
02Porosity, Edge Sealing, and Leakage Mechanisms
Before measurement, distinguish three sources of incoming air: material-pore flow Q_P, leakage through microchannels between the cup lip and surface Q_E, and hardware leakage through fittings, valves and pipework Q_H.
Q_L = Q_P + Q_E + Q_HPaper fibers, creases, coatings, adhesive seams, tape and local warping affect material flow resistance; cup compression, lip hardness and contact location affect edge sealing. Piab's corrugated-board information identifies board porosity and cup sealing as causes of cycle-to-cycle leakage variation and uses F = AP to explain load support with low vacuum and a large area [8]. These sources support identification of leakage mechanisms and selection of configurations.
Tiwari and Persson used rough substrates and suction-cup tests to analyze how interface leakage, cup volume and stiffness affect detachment time [9]. Gabriel et al. incorporated surface roughness, cup diameter and cup count into leakage and energy-consumption models [10]. In project applications, measure leakage for the actual contact pair and compression condition rather than assigning a fixed coefficient solely from the material name.
Leak testing shall distinguish hardware leakage from process leakage through the workpiece. First seal every suction cup against an impermeable standard plate and measure Q_H at a 45 kPa pressure differential; then install the actual workpiece and measure Q_L. The fixed hardware gate is Q_H,UB/Q_S,LB≤0.05. If exceeded, stop and repair the system; increasing source capacity shall not mask a failed fitting or valve. Actual-workpiece measurement uses the ten numerical boundary cells in Chapter 08; labels such as worst, similar, or typical do not replace a numerical cell.
02.1 Defined Leakage Test Procedure
For every test, approach the surface normally at 0.10 m/s and set compression to 5 mm, 7 mm, or 9 mm for the test cell. Activate the zone source and record pressure and normalized flow from 0 to 12 s. Use a stability window of 10.0–12.0 s: every pressure lower bound must be ≥50 kPa and indicated peak-to-peak variation ≤2 kPa. Take the greatest 100 ms moving-average leakage in that window and add U_Q to obtain Q_L,UB. If the cup fails to reach a 50 kPa lower bound within 2.0 s after contact and remain stable for 200 ms, R4 fails for that cycle. Retain the raw data.
The contamination boundary is fixed at 23±2 °C and 50±10% relative humidity. Prepare and sieve material from the same carton batch into 75–150 μm paper dust and apply 0.50 g/m² uniformly to the suction surface. Cartons above that areal density or containing liquid water, oil, or adhesive contamination are outside this release boundary. The service-life boundary is reached when a suction cup has completed 100000 rated compression cycles or its sealing lip has worn 0.50 mm relative to a new cup, whichever occurs first. Friction, effective-area, leakage, and dynamic tests shall cover both new cups and cups at this service-life boundary.
The cycle fails immediately and the suction-cup placement point is added to the prohibited-zone map if the paper surface tears, the cup lip crosses an opening in the carton lid, the lid pulls up, or the minimum distance from the sealing lip to a crease, indentation, or tape step with height difference/depth ≥0.50 mm is <10 mm. The prohibited-zone map uses tooling coordinates, with boundary coordinates specified to 1 mm.
A workpiece family may share leakage data only when material grade, flute type, layer count, coating, print coverage, taping arrangement, permitted cup locations and upper mass limit are all identical. Create a separate dataset for any difference, so low-leakage samples do not conceal high-leakage batches.
03Suction Capacity, Friction, and Dynamic Loads
For cup i, calculate its normal-capacity lower bound and total capacity as:
C_i = Δp_min,LB A_eff,LB,i
F_N,cap,LB = ΣC_iWhen the suction surface rotates through θ from horizontal, calculate normal and tangential design demands using the following equations. Use measured upper bounds for mass, acceleration and eccentricity. The acceleration envelope must include per-axis peaks during production movement, braking after a single-zone fault, travel to the safe position and placement; average speed cannot substitute for these values.
F_N,d = S_L m_UB max_t|g cosθ + a_n,UB(t)|
F_T,d = S_L m_UB max_t√[(g sinθ + a_x,UB(t))² + a_y,UB(t)²]
Rapid screening criteria:
F_N,cap,LB ≥ F_N,d
μ_LB F_N,cap,LB ≥ F_T,dFor the friction-coefficient test, use three carton batches with 10 independent specimens per batch. At pressure differentials of 45 kPa and 50 kPa, measure the tangential force at the onset of continuous 2 mm slip. Complete 30 trials for every combination of pressure differential, new/end-of-life cup, and clean/0.50 g/m² paper-dust state. Calculate μ_meas=F_slip/(ΔpA_eff,meas), take the minimum of all results, and subtract U_μ to obtain μ_LB; U_μ shall be ≤0.02. The baseline condition uses μ_LB=0.35. Schmalz design information requires suction tests on porous workpieces and lists safety factors of at least 2 for horizontal workpieces and at least 2.5 for rotated workpieces [6]; this report uses 2.5 for every load direction.
After rapid screening, verify combined loading and three-dimensional eccentricity. Place the coordinate origin at the workpiece center of gravity. r_i runs from that origin to cup i; n is the suction-surface unit normal; T_i is the in-plane tangential vector; and f_i=N_i n+T_i. M_external includes only independent couples not already represented by the resultant force at the center of gravity. At every 10 ms path sample, solve for cup forces satisfying:
N_i ≥ 0
N_i/C_i + ||T_i||/(μ_LB C_i) ≤ 1
Σf_i + f_external = 0
Σ(r_i × f_i) + M_external = 0The normal and friction capacities of a cup must satisfy a shared linear interaction envelope; both full capacities cannot be used simultaneously. A pass requires a force distribution satisfying every equilibrium equation and the interaction envelope; otherwise, the result is a fail. External-moment calculations must include three-dimensional cup and center-of-gravity coordinates, the lever arm due to workpiece thickness and peak fault-braking loads. Verify board crushing, facing delamination and carton-flap cracking separately against material bearing criteria.
03.1 Carton Contact Pressure and Deformation Criteria
Use Δp_min,LB as the average compressive stress over the suction-cup area, while recognizing stress concentration in the narrow cup-lip annulus. Perform static holding and dynamic cycling on the target carton and inspect the suction surface after acceptance testing. The hard acceptance conditions are: the lid does not pull open; the liner does not separate from the corrugated medium; and no through-damage occurs. At 60 s after unloading, the measurement upper bound of permanent indentation in the suction zone relative to the unloaded reference plane shall be ≤2.00 mm. Any structural damage makes R9 fail even if vacuum pressure, load, and cycle time all pass.
Run the material-bearing test for 10 min at each lower-bound pressure differential, 45 kPa and 50 kPa. For the dynamic test, run 120 cycles for each of the six dynamic-path cells in Chapter 08. More suction cups increase total load-bearing area but do not automatically reduce local stress beneath an individual cup; the placement and compression of every cup shall satisfy the gates above.
04Flow Balance and Vacuum-Establishment Time
Select the vacuum source from the combined performance of the generator with the actual pipework, valves and filters, using the lower flow bound at a minimum supply gauge pressure of 0.40 MPa and a pressure differential of 45 kPa. Convert source and leakage flows to the same reference conditions, p_N=101.325 kPa and T_N=293.15 K, before checking supply and demand for each zone. Catalog maximum suction flow or ultimate vacuum alone cannot replace this calculation.
Q_S,LB = Q_S,meas - U_QS
Q_L,UB = Q_L,meas + U_QL
Q_S,LB(45 kPa differential, 0.40 MPa supply) / Q_L,UB ≥ 1.50Use the maximum Q_L,meas indication in the complete test matrix, not the average, and do not discard a sample merely because suction succeeded despite high leakage. Include the combined expanded uncertainties from the flow meter, supplier curve, and piping conversion in U_Q; this report requires U_Q/Q≤2%. SMC's official information describes how to back-calculate leakage using the actual generator, suction cups, workpiece, and vacuum gauge, and explains that leakage through rough or porous workpieces can prevent the required vacuum from being reached [5]. GB/T 32293—2015 is used only to select the hardware Q_H leak-test method; Q_P, Q_E, and total process flow Q_L use the workpiece process tests in this report. Records shall state pressure, temperature, range, sampling rate, and reference state.
Across pressure differentials from 0 to 50 kPa, define Q_net,LB as the minimum normalized source-flow lower bound after subtracting leakage. A conservative evacuation time from atmospheric pressure p_0 to target absolute pressure p_1 is:
Q_net,LB = min[Q_S,LB(p) - Q_L,UB(p)]
t_ev = V_Z,UB (p_0 - p_1) / (p_N Q_net,LB)
t_pick = t_ev + t_stable + t_auxConvert Q to L/s and set target p_1=p_0−50 kPa. If Q_net,LB≤0, the condition fails immediately. Set t_stable=0.20 s and fix the combined upper bound for valve response, sensor response, PLC scan, and permissive output at t_aux=0.10 s. The total time from contact until every zone reaches a 50 kPa pressure lower bound, 20 consecutive samples pass, and window peak-to-peak variation is ≤2 kPa shall be ≤2.0 s. Inhibit lifting and horizontal acceleration if any zone times out, any sample falls below threshold, no new analog sample arrives within 30 ms, or discrete and analog signals conflict for more than 50 ms.
05Zoning, Check Valves, Flow Restriction, and Leakage Compensation
Provide each of the four zones with its own vacuum-generation branch, pressure measurement, isolation components, and diagnostic identifier. Cups in every zone must span both sides of the workpiece center of gravity. After any zone is lost, use actual three-dimensional coordinates to verify Chapter 03 combined-load equilibrium; cup count or a two-dimensional visual check is insufficient. Chapter 06 restricts its example to the x-z plane with all y inputs zero. Central-header pressure is diagnostic only and cannot replace zone-specific permission.
| Architecture Element | Required Function | Nonconforming Condition |
|---|---|---|
| Independent Zone Pressure Measurement | Detect local leaks, incomplete contact, and cup detachment | Only header pressure is measured |
| Check-Valve or Vacuum-Flow Isolation | Prevent a faulted zone from collapsing vacuum in healthy zones | An open line in one zone reduces any healthy-zone pressure lower bound below 45 kPa |
| Source Flow Reserve | Maintain pressure at the leakage upper bound | Q_S,LB/Q_L,UB＜1.50 |
| Pressure-Based Permission | Every zone’s pressure lower bound≥50 kPa for 200 ms, with peak-to-peak variation≤2 kPa | A timer or one common signal provides permission |
| Backup Energy Supply | t_1−t_0≤0.10 s and maintained until t_3 | Adiabatic holding time <8.50 s or Q_S,LB/Q_L,UB <1.50 at 0.40 MPa |
| Controlled Venting | Vent only after both supports are confirmed for 500 ms, speed≤0.01 m/s, and position error≤5 mm | Venting is possible while a required condition is unmet |
SMC's energy-saving valve information describes restricting leakage from uncovered cups to maintain vacuum in the remaining circuits [5], while Piab's foam-gripper information discusses check valves for materials with different porosities [11]. After selecting these components, fault injection must still include valve sticking, contamination, reverse leakage and response time to verify actual isolation performance.
Evaluate leakage compensation in sequence: effective suction area, cup locations and sealing, main-line length and diameter, vacuum-source distribution, and finally source flow. Zone isolation must be retained and cannot be replaced by continually increasing suction flow. A large local opening can consume the available flow and conceal cup detachment.
06Worked Baseline Calculation and Decision
Use the following assumed conditions for the worked calculation: the suction surface remains horizontal, θ=0; calculation is in x-z with a_y,UB=0, e_y,UB=0, M_x=0, and M_z=0. Relative to the array center, cup projections are x=±0.25 m and y=0, and the center of gravity is (0.060,0,−0.160) m. For the Chapter 03 vector equations, calculate r_i as cup coordinates minus center-of-gravity coordinates. Any nonzero y acceleration, eccentricity, or moment requires the complete three-dimensional equilibrium calculation.
| Input | Specified Value Including Uncertainty |
|---|---|
| Carton Mass Upper Bound m_UB | 18.0 kg |
| Cup Count and Zoning | 8 cups in 4 zones, 2 per zone |
| Single-Cup Effective-Area Lower Bound A_eff,LB | 0.0060 m² |
| Two-Dimensional Cup Projections | Relative to array center: x=±0.25 m, y=0; each zone has one cup on either side |
| Fault-Holding Differential Lower Bound Δp_min,LB | 45 kPa |
| Normal Lifting Differential Lower Bound Δp_pick,LB | 50 kPa |
| Friction Lower Bound μ_LB | 0.35 |
| Normal/Fault Upward-Acceleration Upper Bound a_z,UB | 1.50 m/s² |
| Normal/Fault Horizontal-Acceleration Upper Bound a_x,UB | 2.00 m/s² |
| Y Acceleration and Eccentricity | a_y,UB＝0；e_y,UB＝0 |
| Horizontal Center-of-Gravity Offset Upper Bound e_x,UB | 0.060 m |
| Center-of-Gravity Distance from Suction Plane h_UB | 0.160 m |
| Independent Roll and Yaw Moments | M_x＝0；M_z＝0 |
| Registered Safe Support | S1=(1.00, 0, −0.20) m; maximum fault-path length 1.20 m |
| Single-Zone Evacuated-Volume Upper Bound V_Z,UB | 1.80 L |
| Maximum Zone-Leakage Indication and U_QL | 55.0、1.1 NL/min；Q_L,UB＝56.1 NL/min |
| Minimum Zone-Source Flow Indication and U_QS | 90.0、1.8 NL/min；Q_S,LB＝88.2 NL/min |
| Source-Flow Test Conditions | Complete 0–50 kPa differential range; supply gauge pressure 0.40 MPa; filter at its service limit |
| Stabilization and Auxiliary Time | t_stable＝0.20 s；t_aux＝0.10 s |
| Air-Receiver Volume, Supply-Pressure, and Initial-Temperature Bounds | Effective-volume lower bound 25.0 L; initial gauge-pressure lower bound 0.70 MPa; minimum usable gauge-pressure upper bound 0.40 MPa; T_1,UB=298.15 K |
| Maximum four-zone air-consumption indication and U_Qair | 300、6 NL/min；Q_air,UB＝306 NL/min |
06.1 Normal Operating Load Capacity
Total area lower bound is 8×0.0060=0.0480 m². Individual cup capacity is C_i=45000×0.0060=270 N:
F_N,cap,LB = 45000 × 0.0480 = 2160 N
F_N,d = 2.5 × 18 × (9.81 + 1.50) = 508.95 N
Normal capacity ratio = 2160 / 508.95 = 4.24 > 1.00: pass
F_T,cap = 0.35 × 2160 = 756 N
F_T,d = 2.5 × 18 × 2.00 = 90 N
Tangential capacity ratio = 756 / 90 = 8.40 > 1.00: passTaking moments about the suction-array center, the horizontal acceleration and center-of-gravity offset create the following pitching moment:
M_d = F_N,d e_x + F_T,d h = 508.95 × 0.060 + 90 × 0.160 = 44.94 N·m
Normal-force difference between sides: ΔF = M_d / 0.25 = 179.76 N
High-load-side demand = (508.95 + 179.76) / 2 = 344.36 N
Low-load-side demand = (508.95 - 179.76) / 2 = 164.60 N
Capacity per side = 4 × 45000 × 0.0060 = 1080 N
Both sides passWith equal distribution among four cups per side, each high-side cup carries N_H=344.36/4=86.09 N and each low-side cup N_L=164.60/4=41.15 N. Tangential force per cup is T=90/8=11.25 N across eight cups. Check the linear interaction envelope:
η_H = 86.09/270 + 11.25/(0.35×270) = 0.44
η_L = 41.15/270 + 11.25/(0.35×270) = 0.27
max(η_H,η_L) = 0.44 ≤ 1.00: combined loading passes06.2 Flow and Establishment Time
The upper leakage bound is 56.1 NL/min and the source flow lower bound is 88.2 NL/min:
Source/leakage ratio = Q_S,LB / Q_L,UB = 88.2 / 56.1 = 1.572 ≥ 1.50: pass
Demand-capacity ratio = Q_S,LB / (1.5 Q_L,UB) = 88.2 / 84.15 = 1.048 ≥ 1.00: pass
Q_net,LB = 88.2 - 56.1 = 32.1 NL/min = 0.535 L/s
p_1 = 101.325 - 50 = 51.325 kPa
t_ev = 1.80 × (101.325 - 51.325) / (101.325 × 0.535) = 1.66 s
t_pick = 1.66 + 0.20 + 0.10 = 1.96 s ≤ 2.00 s: passSource/leakage ratio and demand-capacity ratio have different thresholds: 1.50 and 1.00 respectively. Every zone must reach a 50 kPa lower bound and remain stable for 200 ms. Any zone exceeding 2.00 s fails R4.
06.3 Complete Loss of One Zone
Isolating any zone leaves 6 cups and 0.0360 m² effective area. Each zone has one cup on either side of x, so 3 cups remain on each side after a single-zone fault.
F_N,1fail = 45000 × 0.0360 = 1620 N
Normal capacity ratio = 1620 / 508.95 = 3.18: pass
F_T,1fail = 0.35 × 1620 = 567 N
Tangential capacity ratio = 567 / 90 = 6.30: pass
Remaining capacity per side = 3 × 45000 × 0.0060 = 810 N
810 > 344.36 N and 810 > 164.60 N: moment distribution passesAfter one-zone failure, three cups remain on each high- and low-load side. Tangential demand per remaining cup is T=90/6=15 N:
N_H,1fail = 344.36/3 = 114.79 N
N_L,1fail = 164.60/3 = 54.87 N
η_H,1fail = 114.79/270 + 15/(0.35×270) = 0.584
η_L,1fail = 54.87/270 + 15/(0.35×270) = 0.362
max(η_H,1fail,η_L,1fail) = 0.584 ≤ 1.00: passWith the fixed inputs in this article—a mass upper bound of 18 kg, a horizontal suction surface, specified normal/fault acceleration envelopes and a two-dimensional eccentricity envelope—both the normal state and complete failure of any single zone pass the rapid screening and combined-load calculations. This is a calculation result for the baseline operating condition.
06.4 Main-Supply Loss and Controlled Set-Down
The example uses a compressed-air reserve with effective-volume lower bound 25.0 L, initial gauge-pressure lower bound 0.70 MPa, and minimum usable gauge-pressure upper bound 0.40 MPa. With p_N=0.101325 MPa, absolute pressures are P_1=0.801325 MPa and P_2=0.501325 MPa. Use adiabatic discharge from a rigid tank with γ=1.4, reference temperature T_N=293.15 K, and initial tank-temperature upper bound T_1,UB=298.15 K. Four-zone consumption upper bound is 306 NL/min=5.10 NL/s. At minimum supply gauge pressure 0.40 MPa, each zone provides Q_S,LB=88.2 NL/min and passes the 1.50 flow criterion.
m_2/m_1 = (P_2/P_1)^(1/γ) = (0.501325/0.801325)^(1/1.4) = 0.7153
V_N,use = 25 × (0.801325/0.101325) × (293.15/298.15) × (1 - 0.7153) = 55.34 NL
t_res = 55.34 / 5.10 = 10.85 s
t_required = (t_2-t_0)_max + 2(t_3-t_2)_max = 0.50 + 2 × 4.00 = 8.50 s
10.85 > 8.50 s: passThe calculations in this section pass R2, R3, vacuum build-up time, single-zone failure and backup-duration checks, allowing the configuration to proceed to the FAT/SAT process in Sections 08 and 09. Engineering release of the vacuum gripping subsystem requires zero-failure FAT and SAT records for every boundary-condition cell and fault injection, together with complete documentation for the complete machine prerequisite gate.
07Single-Zone Faults, Supply Loss, and Controlled Set-Down
Provide separate response chains for alarms and safety actions. Apply the following state logic to the operating permissive; do not share a delay that postpones protective action:
Lift_Enable =
Workpiece_Present ∧ Zone_A_OK ∧ Zone_B_OK ∧ Zone_C_OK ∧ Zone_D_OK
∧ Δp_LB per zone ≥ 50 kPa continuously for 200 ms
∧ Peak-to-peak variation in the 200 ms window ≤ 2 kPa
∧ Motion_Envelope_OK
Single_Zone_Fault →
Inhibit continuation of the production path
∧ |a_z,UB| ≤ 1.50 m/s²
∧ √(a_x,UB²+a_y,UB²) ≤ 2.00 m/s²
∧ Prohibit turning
∧ Set down at registered support S1
Main_Supply_Loss →
Backup supply established: t_1-t_0 ≤ 0.10 s
∧ Fault confirmed: t_2-t_0 ≤ 0.50 s
∧ Maintain every healthy zone
∧ Load transferred to support: t_3-t_2 ≤ 4.00 sThe four timestamps use the same 1 ms time base. t_0 is the earlier of the first instant when the main-supply inlet-pressure lower bound falls below 0.55 MPa gauge or the main-valve-open signal is lost. t_1 is the first instant when the inlet supply-pressure lower bound at all four zone generators reaches 0.40 MPa gauge. t_2 is when the controller sets the energy-supply fault and issues the set-down command. t_3 is the first instant when both independent support sensors are ON and the support-force lower bound has reached 0.95m_UBg continuously for 500 ms. The 4.00 s interval begins at t_2; the total upper limit from loss of main energy to transfer onto support is 4.50 s.
Register safe support position S1=(1.00,0,−0.20) m with ±5 mm tolerance. Maximum path length from any point in the motion envelope to S1 is 1.20 m. The support-force lower-bound threshold is 0.95×18×9.81=167.75 N. Record support coordinates, path limit, and force threshold in R1. Unregistered locations must not be used as safe supports.
Do not command venting after a fault until every release condition is met: position within S1±5 mm; speed≤0.01 m/s continuously for 500 ms; both independent support sensors ON continuously for 500 ms; support-force lower bound≥0.95m_UBg; and a manual release command maintained for 500 ms. Pressure recovery must not automatically restart production. Complete t_3, inspect the workpiece, and reset manually before a new cycle.
Verify the backup energy supply by shutting off main energy under the combined conditions of initial gauge pressure 0.70 MPa, leakage upper bound, air-consumption upper bound, filter service-life boundary, and 1.20 m fault path. From t_0 through t_3, controlled set-down fails if any healthy-zone pressure lower bound is <45 kPa, any fault-acceleration upper bound is exceeded, any t_1/t_2/t_3 time gate is exceeded, or a person supports the workpiece manually.
08Test Matrix, Measurement Chain, and Records
Run the complete matrix separately at FAT and SAT for every carton specification; FAT data cannot be credited against SAT. The coordinate origin is the carton's design suction center. Fix permitted suction-cup placement offset at ±20 mm in both x and y and compression at 5–9 mm. Use independent cartons for every boundary cell: three incoming batches × 10 cartons/batch × 5 cycles/carton = 150 cycles. Save four zone curves per cycle, giving 600 zone curves per cell.
| Test Cell | Suction-Cup Placement Point / State | Compression | Contamination and Service Life | Samples per Stage |
|---|---|---|---|---|
| E1 | (0,0) mm; unprinted central area | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E2 | (+20,0) mm | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E3 | (−20,0) mm | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E4 | (0,+20) mm | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E5 | (0,−20) mm | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E6 | 100% print coverage; sealing lip 10 mm from the tape edge | 7 mm | Clean, new cup | 150 cycles/600 curves |
| E7 | (0,0) mm | 5 mm | Clean, new cup | 150 cycles/600 curves |
| E8 | (0,0) mm | 9 mm | Clean, new cup | 150 cycles/600 curves |
| E9 | (0,0) mm | 7 mm | 0.50 g/m² paper dust; new cup | 150 cycles/600 curves |
| E10 | (0,0) mm | 7 mm | 0.50 g/m² paper dust; cup at 100000 cycles or 0.50 mm lip wear | 150 cycles/600 curves |
For each carton specification at each stage, complete 1500 leakage/establishment cycles and 6000 zone curves; FAT and SAT together total 3000 cycles and 12000 zone curves. If carton material, flute type, number of layers, coating, tape, or upper mass limit changes, treat it as a new specification and repeat the full quantities.
Use six dynamic path cells. D1: 18 kg, a_z,UB=+1.50 m/s², a_x,UB=0. D2: 18 kg, a_x,UB=+2.00 m/s², a_z,UB=0. D3: 18 kg, a_x,UB=−2.00 m/s², a_z,UB=0. D4 combines a_z,UB=+1.50 m/s² and a_x,UB=+2.00 m/s². D5 combines a_z,UB=+1.50 m/s² and a_x,UB=−2.00 m/s². D6 follows the 1.20 m maximum fault path to S1 after a single-zone fault. All cells use E10 contamination and wear conditions, with three batches × 10 cartons × 4 cycles=120 cycles per cell. Each stage totals 720 dynamic cycles; FAT and SAT together total 1440.
At each stage, independently complete: effective area: 8 cups × 3 compression levels × 2 life states × 10 trials = 480 trials; coefficient of friction: 2 pressure differentials × 2 life states × 2 contamination states × 30 trials = 240 trials; and, with generator supply gauge pressure at 0.40 MPa and filter pressure drop at 5 kPa, 4 zones × 10 curves from 0 to 50 kPa = 40 curves. These counts may not be credited against E1 to E10 or D1 to D6.
| Measurement | Instrumentation and Sampling | Required Records | Criterion |
|---|---|---|---|
| Zone Pressure | Independent absolute or differential pressure sensor per zone; ≥100 Hz and U_p/p≤2% | Δp_meas、U_p、Δp_LB | Before lifting, Δp_LB≥50 kPa; during faults, every healthy zone Δp_LB≥45 kPa |
| Leakage and Source Flow | Normalized-flow meter ≥100 Hz; U_Q/Q≤2% | Q_meas, U_Q, and reference state | Q_S,LB/Q_L,UB≥1.50 |
| Mass and Coordinates | Calibrated scale U_m≤0.10 kg; three-dimensional measurement U_r≤1.0 mm | m_meas, U_m, and cup, center-of-gravity, and support coordinates | m_UB=m_meas+U_m; take the absolute value of eccentricity and moment arm plus U_r |
| Dynamic Load | Independent three-axis accelerometer ≥200 Hz, U_a≤0.05 m/s² | Per-axis readings, U_a, and fault-braking peaks | a_UB = max|a_meas| + U_a; does not exceed the calculated envelope |
| Displacement / Slip | ≥100 fps visual measurement, U_s≤0.20 mm | Start, peak, and end positions with the measurement scale | s_UB＝s_meas+U_s≤2.00 mm |
| Support Force | Calibrated force transducer; U_F/F≤2% | F_support,meas, U_F, and both support signals | F_support,LB＝F_meas−U_F≥0.95m_UBg and maintain for 500 ms |
| Volume, Stored-Air Pressure, and Temperature | Volume U_V/V≤2%; pressure U_P≤0.005 MPa; temperature U_T≤1 K | Zone/receiver volumes, P_1, P_2, T_1, and corresponding uncertainties | Use the upper bound for evacuated volume; use the lower bounds for air-receiver volume and P_1, and the upper bounds for P_2 and T_1. |
| Effective Area | Calibrated imaging or dimensional measurement; U_A/A≤2% | Compression, inner seal boundary, and area | Use only A_eff,LB=A_meas−U_A in calculations |
| Friction Coefficient | Calibrated force gauge; U_μ≤0.02 | Force at continuous-slip onset, differential pressure, area, and contact condition | Use only μ_LB=min(μ_meas)−U_μ in calculations |
| Backup Energy Supply | Pressure, flow and 1 ms event time base | t_0, t_1, t_2, t_3, and minimum zone pressure | ≤0.10 s, ≤0.50 s, ≤4.00 s, and healthy-zone Δp_LB≥45 kPa |
Use pressure lower bounds for permission. At U_p/p=2%, a 50 kPa lower bound requires an indication of at least 51.02 kPa; a 45 kPa lower bound requires at least 45.92 kPa. Sampling-clock skew must be ≤10 ms. Supplement a discrete pressure switch with recordable analog pressure. A pass/fail bit without the original pressure trace fails R10.
The release-pressure window is 0≤Δp_UB≤5 kPa continuously for 500 ms. A change in analog pressure below 0.50 kPa within 300 ms of valve actuation, or no new sample for 30 ms, indicates a frozen signal. A discrete/analog conflict lasting more than 50 ms is a diagnostic fault.
Retain timestamps, zone identifiers, sample identifiers, batch identifiers, cup-location identifiers, pressure, flow, acceleration, valve states and permissive states in the raw data, with units in the fields or metadata. Archive processing scripts and parameters alongside them so every calculated result is traceable to original rows. Images cannot replace raw data. Only clearly established instrument failures may be excluded, with the reason, failure evidence and retest records retained. Deleting high-leakage or slow-build-up cycles as “outliers” causes R10 to fail directly.
09FMEA-Based Fault-Injection Matrix
Convert FMEA failure modes into repeatable fault injections, including low-occurrence faults. Use an 18 kg upper mass, E10 contamination/wear state, and 1.20 m fault path. FAT and SAT each complete the full table. For faults other than main-supply loss, t_F is the physical injection time and fault confirmation must meet t_2−t_F≤0.50 s. Main-supply loss retains the Chapter 07 t_0–t_3 definitions.
| Failure Mode | Injection Method | Trials per Stage | Required Control Response | Pass Criterion |
|---|---|---|---|---|
| Uncovered Suction Cup | Apply a calibrated 6.0 mm opening at each cup | 8 cups × 10 = 80 | Alarm for the affected zone and move the load to S1 | Healthy-zone Δp_LB≥45 kPa, t_2−t_F≤0.50 s, t_3−t_2≤4.00 s |
| Disconnected Zone Line | Completely disconnect each zone’s quick coupling | 4 zones × 10 = 40 | Isolate the faulted zone and set down at S1 | All 40 trials meet the time, pressure, acceleration, and slip gates |
| Check Valve Stuck Open | Bypass each zone check valve with a fully open flow path | 4 zones × 10 = 40 | Healthy zones retain independent diagnostics; execute S1 set-down | Any healthy-zone Δp_LB below 45 kPa fails the complete item |
| Pressure Sensor Stuck High | Inject full-scale high level into each channel: 5 trials before lifting and 5 during motion | 4 channels × 10 = 40 | Inhibit lifting before pickup; execute S1 set-down during motion | No false Lift_Enable; motion tests meet t_2 and t_3 limits |
| Pressure Sensor Stuck Low | Inject 0 kPa into each channel: 5 trials before lifting and 5 during motion | 4 channels × 10 = 40 | Inhibit lifting before pickup; execute S1 set-down during motion | Bypass operation is prohibited; healthy-zone pressure remains within the acceptance limit |
| Main Compressed-Air Loss | Close the main valve at a point with 1.20 m of path remaining to S1 | 10 | Establish backup supply and confirm the fault at t_1/t_2, then set down at S1 | t_1−t_0≤0.10 s，t_2−t_0≤0.50 s，t_3−t_2≤4.00 s |
| Low Backup-Reserve Pressure | Initial gauge pressure fixed at 0.39 MPa | 10 | Inhibit startup | No Lift_Enable in any of 10/10 trials |
| Local Carton Collapse | Prepare a 30 mm-diameter, 5.0 mm-deep indentation in the suction area | 10 | Execute S1 set-down after the pressure fault | No tearing, no drop, and s_UB≤2.00 mm |
| Premature Timer Permission | Set fixed delay to 0.50 s | 10 | Pressure interlock continues to prevent movement | No lifting while any zone has Δp_LB<50 kPa |
| Unintended Venting Command | Inject a vent-output request at the path midpoint | 10 | Each of the five release conditions blocks venting when unsatisfied | The vent valve must remain de-energized before t_3 |
Perform 290 fault injections at each stage, totaling 580 across FAT and SAT. Before testing, install a load-catching device and clear the hazardous area. Record a failure for any unintended movement, pressure below its lower bound, exceeded time limit, acceleration above its upper bound, slip above its upper bound, unintended venting or manual support of the workpiece. After corrective action, repeat that failure mode in that stage from the first test; repeating only the failed trial is not sufficient.
10FAT, SAT and vacuum grabbing subsystem engineering release standards
The release process checks the prerequisite gate, design documentation, factory acceptance testing (FAT) and site acceptance testing (SAT) in sequence. All four gates must pass before a subsystem engineering conclusion is issued. Calculations do not replace physical acceptance tests, FAT does not reduce SAT requirements, and testing must use the target cartons rather than the supplier's generic samples.
| No. | Release Gate | Pass Criteria |
|---|---|---|
| R1 | Prerequisite Gate and Input Freeze | Complete-machine risk assessment passes; validated PL/SIL for Lift_Enable, fault detection, exhaust inhibition, and controlled set-down is ≥ the risk-assessment requirement; robot integration, air-receiver compliance, and environmental compliance pass; and mass/center of gravity/three-dimensional coordinates/acceleration/safe position/A_eff,LB/μ_LB/Q_L,UB/Q_S,LB and all U values are version-controlled |
| R2 | Static and Dynamic Load Capacity | Normal and single-zone-fault rapid capacity ratios≥1.00; a three-dimensional solution with η_i≤1.00 exists at every 10 ms sample |
| R3 | Flow Reserve | Every zone: Q_S,LB(45 kPa, 0.40 MPa supply)/Q_L,UB≥1.50 |
| R4 | Vacuum-Establishment Time | For every E1–E10 cell, all 150/150 cycles and 600/600 zone traces reach the 50 kPa lower bound within 2.0 s and remain stable for 200 ms |
| R5 | Dynamic Handling | Each D1–D6 cell completes 120/120 cycles: no drop, s_UB≤2.00 mm, and acceleration upper bounds within the calculation envelope |
| R6 | Single-Zone Fault | Disconnect each zone 10 times and bypass its check valve 10 times; healthy-zone Δp_LB≥45 kPa and every load reaches S1 within the time limit |
| R7 | Main-Supply Loss | All 10/10 trials satisfy t_1−t_0≤0.10 s, t_2−t_0≤0.50 s, t_3−t_2≤4.00 s, and healthy-zone Δp_LB≥45 kPa throughout t_0–t_3 |
| R8 | Fault Injection | Chapter 09: 290/290 trials per stage; no false permission or venting and no exceeded time, pressure, acceleration, or slip limits |
| R9 | Carton Structure | No opened lid, liner separation, or through-damage; permanent-indentation upper bound≤2.00 mm at 60 s after unloading |
| R10 | Record Integrity | Traceable original pressure, flow, acceleration, and displacement curves; t_0–t_3 logs; instrument uncertainties; configuration; and decision |
FAT and SAT use the same thresholds and independently complete the full required quantities. If the vacuum generator, suction-cup model/hardness, pipe diameter, filter, valve, control program, carton material, coating, tape, mass, center of gravity, or path acceleration changes on site, the existing release boundary expires immediately and R1–R10 shall be repeated in full. Conditional release is not permitted: if any item is not met, the vacuum gripping subsystem fails engineering release.
11Engineering Controls and Maintenance
- Suction cups and placement points: the sealing lip shall not cross a carton-lid opening, damage, or a crease, indentation, or tape step with height difference/depth ≥0.50 mm. Its minimum distance from those boundaries shall be ≥10 mm. Mechanical guidance limits compression to 5–9 mm.
- Filtration and drainage: Monitor differential pressure across each zone filter. At an upper-bound pressure drop of 5 kPa or 500 h of service, whichever occurs first, inhibit use and replace the filter. Repeat the Q_H pre-shift test afterward.
- Zone checks: Before each shift, measure hardware leakage against an impermeable standard plate at 45 kPa differential. If any zone has Q_H,UB/Q_S,LB>0.05, remove it from service for repair.
- Sensor diagnostics: before suction, 0≤Δp_UB≤5 kPa continuously for 500 ms. Set a fault if the change is <0.50 kPa within 300 ms after valve actuation, no new sample arrives for 30 ms, or the discrete and analog signals conflict for >50 ms.
- Pressure monitoring: During normal motion, every zone requires Δp_LB≥50 kPa. If any healthy zone records a 100 Hz sample with Δp_LB<45 kPa, the controller sets a fault on its next scan while still meeting t_2≤0.50 s.
- Change control: Version-control cups, sealing materials, valves, hose lengths, vacuum sources, program parameters, and carton materials. Recalculate and perform the required retests before using a substitute.
- Personnel protection and energy isolation: Before maintenance, first confirm that the support-force lower bound reaches 0.95m_UBg continuously for 500 ms. Then isolate and lock the air supply and release residual pneumatic energy. Permit entry only after support confirmation and energy isolation are complete. ISO 4414:2010 covers design, installation, operation, and maintenance of machinery pneumatic systems, excluding compressors, factory distribution, gas cylinders, and air receivers [4]. Air-receiver compliance remains an R1 prerequisite.
12Conclusions
Assessment of porous-workpiece handling must cover load capacity, leakage, dynamics, zone isolation and response to loss of air. This article expresses these as six engineering criteria that must be met together:
- Verify normal and single-zone-fault operation using Δp_min,LB, A_eff,LB, μ_LB, and a 2.5 load factor. Rapid capacity ratios must be ≥1.00, with a three-dimensional equilibrium solution satisfying η_i≤1.00 at every 10 ms sample.
- Each zone must satisfy Q_S,LB/Q_L,UB≥1.50 at 45 kPa differential and minimum supply gauge pressure 0.40 MPa.
- Every zone reaches a 50 kPa lower bound within 2.0 s; 20 consecutive samples pass and window peak-to-peak variation is ≤2 kPa; the permissive comes from per-zone pressure signals.
- After complete loss of any zone, healthy-zone pressure lower bounds remain ≥45 kPa, fault accelerations remain within the verified envelope, and the load reaches its registered safe support.
- Require t_1−t_0≤0.10 s, t_2−t_0≤0.50 s, and t_3−t_2≤4.00 s. The backup adiabatic-discharge model with γ=1.4 and initial-temperature upper bound 298.15 K must give t_res≥8.50 s.
- FAT and SAT independently complete, for each specification, ten boundary cells, six dynamic cells, and 290 fault injections, all with zero failures and complete R1 prerequisite-gate records.
Chapter 06 gives a single calculation-pass conclusion for the 18 kg carton baseline: normal and tangential rapid capacity ratios are 4.24 and 8.40, respectively, with a maximum interaction coefficient of 0.44; after one-zone failure, the rapid capacity ratios are 3.18 and 6.30, with a maximum interaction coefficient of 0.584; Q_S,LB=88.2 NL/min and Q_L,UB=56.1 NL/min; source/leakage ratio is 1.572 and demand-capacity ratio is 1.048; establishment-permissive time is 1.96 s; and adiabatic backup-energy duration is 10.85 s, greater than 8.50 s. This calculation result proceeds to the specified FAT/SAT verification process.
The subsystem result is “Pass” only when R1—R10 all have independent zero-failure FAT and SAT records. Any missing item results in “Fail.” Release of the complete machine additionally requires risk assessment, control safety validation, robot integration and air-receiver vessel compliance records.
References
[1] State Administration for Market Regulation and Standardization Administration of China. GB/T 41098—2021 Cranes — Safety — Load lifting attachments. Published on 2021-12-31; implemented on 2022-07-01; status: current.
[2] International Organization for Standardization. ISO 17096:2015 Cranes—Safety—Load lifting attachments. The official ISO page states that this edition was reviewed and confirmed in 2026 and remains current.
[3] National Standards Open System of the State Administration for Market Regulation. GB/T 32293—2015 Vacuum technology — Selection of leak-testing methods for vacuum equipment. Published on 2015-12-10; implemented on 2016-07-01; status: current.
[4] International Organization for Standardization. ISO 4414:2010 Pneumatic fluid power—General rules and safety requirements for systems and their components. The official ISO page states that this edition was reviewed and confirmed in 2021.
[5] SMC Corporation. Vacuum Equipment: Model Selection and Common Precautions. Official vacuum-component selection reference covering leakage estimation, response time, pressure confirmation, throttling, and check-valve applications.
[6] J. Schmalz GmbH. Design of the Suction Cup. Official vacuum-technology knowledge base.
[7] J. Schmalz GmbH. Technical Data of Suction Cups. Official vacuum-technology knowledge base.
[8] Piab AB. Handling Corrugated Cardboard: Advantages through Optimized Pressure Regulating of Air-driven Vacuum Pump. Official technical reference on vacuum handling of corrugated cardboard.
[9] A. Tiwari, B. N. J. Persson. Physics of suction cups. Soft Matter, 2019, 15: 9482–9499. Original research article.
[10] F. Gabriel, S. Baars, M. Römer, K. Dröder. Grasp Point Optimization and Leakage-Compliant Dimensioning of Energy-Efficient Vacuum-Based Gripping Systems. Machines, 2021, 9(8):149. Original research article.
[11] Piab AB. piCOBOT Foam Grippers. Official product technical page, including guidance on check-valve applications for materials with different porosities.
