This orbital-riveting illustration shows a tilted forming tool precessing about a supported rivet, with a separate view of residual rotating unbalance. The calculator estimates the excitation from an eccentric mass at spindle speed. It does not calculate riveting force, joint strength or the vibration of the complete machine.
Balanced Riveting Machine Interactive Calculator
Vary residual mass, its radius and spindle speed to compare rotating excitation. Peen tilt provides a separate geometric comparison, not a forming-force prediction.
Equation Used
The calculator uses rotating unbalance to estimate the excitation magnitude m r ω². Balance Moment is the residual mass-radius product in g·mm, not torque. The separate tan(tilt) output describes geometry and does not solve contact or forming forces.
- Residual mass is treated as a point unbalance at the stated radius.
- Bearing and frame flexibility are ignored.
- Peen tilt supplies a tan(angle) geometric comparison only; actual side and axial forming forces are not calculated.
m·r·ω² is rotating imbalance excitation, not measured machine vibration. tan(tilt) is a geometric comparison, not a solved ratio of actual forming forces. The animation shows orbital peening with its contact tip held at the rivet.
Progressive forming and rotating unbalance
An orbital forming head holds a peen at an angle and moves its axis around the rivet. Contact progresses across the material as the head advances. Tool shape, material and the forming cycle influence the finished head; the work support closes the force path beneath the joint.
The inset represents a separate mass whose center is offset from the rotation axis. That offset creates a rotating force component at spindle frequency. Reducing residual unbalance can reduce this source of excitation, but it does not eliminate forming reactions or guarantee that a machine is vibration-free.
The tool’s contact geometry and the residual mass radius are different quantities. Changing the radius input changes the unbalance calculation; it does not specify the radius of the contact patch on the rivet.
Parts shown
- Spindle and peen: generate the illustrated precessing motion.
- Rivet and work support: carry the forming reaction.
- Balance-plane inset: locates an equivalent residual mass for the simple excitation estimate.
Choosing a forming process
Orbital forming is one way to upset a rivet or tenon progressively. Orbitform describes the tool’s sweeping contact and recommends application testing to determine required forming force. BalTec distinguishes orbital motion from radial riveting, which uses a different peen path. Those names should not be treated as interchangeable.
Whether a process suits a particular joint depends on material, fastener geometry, access, support, tooling and acceptance criteria. The calculator cannot qualify an aerospace or medical joint, select a production controller, or assign tool life.
Blind rivets, rivet nuts and clinch nuts also have different installation mechanisms. An orbital head is not a general substitute for their specified installation tooling.
Residual-unbalance excitation
Convert mass m from grams to kilograms and radius r from mm to meters. For spindle speed n rpm, angular speed ω = 2πn/60 rad/s. The ideal rotating excitation magnitude is F = mrω² in newtons.
Balance Moment U = mgrmm in g·mm. This is an unbalance mass-radius product, not a torque. Excitation frequency = n/60 Hz. Doubling speed quadruples excitation force; doubling mass or radius doubles it.
The fourth output is 100 tan(α), with tilt α entered in degrees. It is a geometric ratio displayed as a percentage. No constitutive material model or contact mechanics converts it into actual riveting forces.
Machine displacement and acceleration depend on stiffness, damping, mass distribution, supports and resonance. A single-plane point-unbalance estimate also does not determine all couple unbalance or a complete correction-weight arrangement.
Worked example: residual mass at spindle speed
Take a hypothetical residual mass of 5 g at 40 mm radius and 1500 rpm. The mass-radius product is 200 g·mm, angular speed is 157.0796 rad/s, excitation frequency is 25 Hz and force is 4.9348 N.
At 3000 rpm with the same mass and radius, frequency doubles to 50 Hz and excitation rises to 19.7392 N. At 1500 rpm with 20 g at 30 mm, the product is 600 g·mm and excitation is 14.8044 N.
At a 4° tilt, the geometric output is 6.9927%. Changing that tilt does not change the unbalance force in this model. It does not mean the actual side forming force is 6.9927% of axial force.
No forming force or acceptable imbalance limit follows from these examples. They cannot be used to approve a replacement peen, add a counterweight or determine whether a finished joint passes inspection.
Quantities that must remain distinct
| Quantity | What it means | Calculated? |
|---|---|---|
| Unbalance excitation | Rotating force from eccentric mass. | Yes, for the point model. |
| Machine vibration | Motion of the supported structure. | No dynamic response model. |
| Forming force | Reaction required to deform the rivet. | No material/contact model. |
| Forming work | Integral of force over displacement. | No. |
| Force-time integral | Impulse, with units N·s. | No; it is not work in joules. |
Manufacturer references
- Orbitform, Orbital forming.
- BalTec, Forming processes and monitoring.
Orbital-riveting calculation questions
Not necessarily. Residual unbalance is one excitation source, while forming reactions and the structure’s dynamic response also matter.
No. Here it is the radius of the equivalent residual mass in the spindle balance plane.
The ideal excitation contains angular speed squared. Doubling rpm therefore quadruples force at fixed mass and radius.
Not by itself. Tool contact, material behavior and the forming path are missing. The output is only a geometric comparison.
No. Force integrated over time is impulse. Mechanical work is force integrated along displacement.
No. Manufacturers distinguish their peen paths and process characteristics. Use the process description for the actual machine.
No. Tool compatibility, full mass distribution, balance, bearings and the manufacturer’s limits need evaluation.
No. Tooling, material, alignment and cycle conditions can contribute. The calculator cannot diagnose defects or replace joint inspection and process validation.
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