# How to Size a Vacuum Cup? Cheat Sheet by Davidpol

### Introd­uction

 Vacuum cups grip a workpiece by evacuating air from the space inside the cup, creating a partial vacuum at a pressure below ambient. In simple terms one can size a vacuum cup based on the load, available vacuum and cup area. But engineers should consider several other factors when sizing vacuum cups for a given job.

### Theore­tical Holding Force

 Theore­tical suction force is the cup force acting perpen­dicular to the workpiece surface. Theore­tical holding force Ft is simply Ft = ΔP × A where ΔP is the difference between ambient and system pressure, and A is the effective area of the suction cup under vacuum. Theore­tical holding force of a cup increases with the difference between ambient pressure and cup interior pressure, and with cup footprint.

### Actual Ambient Pressure

 Most catalog data on vacuum cups assume ambient air pressure is about 1 bar (actually 1,013.25 mbar). And vacuum­-system manufa­cturers generally recommend vacuum levels of –0.6 to –0.8 bar for handling air-tight surfaces such as clean metal and plastic sheets; and vacuum levels of –0.2 to –0.4 bar for porous materials like cardboard boxes or particle board. Also keep in mind that ambient pressure depends on elevation. Air pressure tends to drop by about 12.5 mbar per 100 m increase in elevation, which can reduce the attainable ΔP and maximum holding force. Thus, more or larger cups may be needed to compensate for lower ambient pressure.

### Coeffi­cient of Friction

 How well a given suction cup grips and seals against a workpiece surface is another consid­era­tion. Friction coeffi­cient µ approx­imates the relati­onship between friction force and normal force. Engineers need to take it into consid­eration when sizing vacuum cups. Typical estimated values for µ from several manufa­cturers are: Oily surface = 0.1 Moist or wet surface = 0.2 to 0.4 Glass, stone and dry plastic = 0.5 Rough surfaces = 0.6 Note that these are just estimates. Engineers should test samples under actual operating conditions to get a better handle on µ. That’s because a given workpiece surface can be smooth, rough, wet, dry or oily; and suction cups vary by material, hardness, lip contact shape and so on. All these parameters will influence actual friction proper­ties.

### Safety Factor

 Never neglect a factor of safety. One can calculate theore­tical holding forces, but many external influences affect actual perfor­mance. Even in mundane applic­ations, calcul­ations should include a safety factor of at least 1.5. Many vacuum­-system manufa­cturers recommend a safety factor of at least 2.0. In high-speed swinging or swiveling operat­ions, a safety of 2.5 or higher might be needed to ensure a tight grip on work pieces and safety of nearby workers.

### Load, Orient­ation and Accele­ration Forces

 One can calculate the required diameter and effective gripping area of a vacuum cup. But it’s usually preferred to determine the necessary holding force. From there, users can choose from a range of cups that meet the requir­ements based on size, shape, material, cost and manufa­cturer. First, determine the workpiece mass, m, by multip­lying volume by material density. Then determine holding force based on these common config­ura­tions. For more complex motions or orient­ations, discuss the design with a manufa­ctu­rer’s applic­ation engineer, or rely on sizing software available from several vacuum­-system suppliers. For a horizontal vacuum cup with a vertical lifting force: F = m × (g + a) × S where F = holding force, N; m = mass, kg; g = accele­ration of gravity, 9.81 m/sec2; a = system accele­ration, m/sec2; and S = safety factor. For a horizontal vacuum cup moving a load in a horizontal direction: F = m × (g + a/µ) × S For a vertical vacuum cup moving a load in a vertical direction: F = (m/µ) × (g + a) × S. Typically, in such an orient­ation, the safety factor should be 2.0 or greater. After calcul­ating holding force, one can find approp­riate data for “pull off” or “break­away” force of different cups from catalogs or manufa­ctu­rers’ websites. (Note that catalog specs are typically listed for a specific vacuum, say –0.7 bar.) The listed breakaway force should exceed the calculated holding force. Depending on the applic­ation a single cup might suffice, or the total holding force may be distri­buted among several cups.

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