Explore a rotating stone-polishing lap guided across the work by a swivel handle. The illustration shows the sliding upper shaft and two universal joints, while the calculator compares rim speed, revolutions, circular guide-path length and nominal lap area.
Stone Grinding and Polishing Machine Interactive Calculator
Explore direct geometry and timing for the documented annular cast-iron lap. The calculator reports rim speed, revolutions, guide path and nominal area.
Equation Used
- Entered lap speed is constant.
- Guide path is assumed circular for the path-length output. Its radius and the lap diameter use the same drawing scale.
- Elevation and plan inset show the fixed-axis feathered slide, two universal joints, rigid intermediate shaft, swivel guide and sand/water feed schematically.
The drawing follows a single guided lap. Its circular guide orbit is illustrative; the results do not predict finish, removal rate or the time needed to polish a stone.
How the Guided Lap Works
In Hiscox movement 1465, printed page 353, the grinding lap consists of concentric cast-iron rings, with sand and water fed through the spaces. A connecting shaft has a universal joint at each end, and a swivel handle guides the lap.
The upper shaft is feathered so it can slide through the driven gear hub while transmitting rotation. The joints allow the connecting shaft to incline as the lap moves across the surface. The illustration uses a circular guide path; it does not reproduce an individual operator's motions.
What You Can Compare
Use the calculator to separate lap rotation from movement of the lap centre. Diameter and RPM determine rim speed. RPM and run time determine revolutions. Guide radius sets the distance around one assumed circular guide orbit.
These are motion and geometry quantities. Abrasive type, contact pressure, stone properties, slurry, surface finish and material removal are outside this tool. The historical guided lap shown here is different from a modern multi-head conveyor polishing line.
Rim Speed, Revolutions and Area
n = Nt
L = 2Ï€r
A = πD²/4
D and r are lap diameter and guide radius in metres, N is RPM, and t is minutes. The results are rim speed v in m/s, lap revolutions n, guide-path length L in metres per orbit, and nominal disk area A in m².
The nominal area includes the gaps between the concentric rings. It is not abrasive contact area. Guide-path length is for one orbit and is not multiplied by lap revolutions, because lap spin and operator guidance are separate motions.
Worked Motion Example
For a 700 mm diameter lap at 80 RPM, with a 180 mm circular guide radius and 8 minutes run time:
- Rim speed: π × 0.7 × 80/60 = approximately 2.93 m/s.
- Lap revolutions: 80 × 8 = 640.
- Guide path per orbit: 2π × 0.18 = approximately 1.13 m.
- Nominal disk area: π × 0.7²/4 = approximately 0.385 m².
These results describe the entered scenario. They do not specify a suitable polishing speed, processed area, required dwell time or expected gloss.
Rotation, Guidance and Contact
| Quantity | Meaning | Limit |
|---|---|---|
| Rim speed | Speed at the outer radius from lap rotation | Does not include local motion from hand guidance |
| Lap revolutions | Turn count at constant entered RPM | Does not determine abrasive removal |
| Guide path per orbit | One circumference of the assumed lap-centre path | Does not determine how many guide orbits an operator makes |
| Nominal area | Area inside the outer lap diameter | Does not subtract feed grooves or calculate contact pressure |
Use the specific machine and abrasive documentation for operating conditions. The illustration is a motion explanation, not a modern machine specification or process-setting guide.
Frequently Asked Questions
Is the guide orbit the same as lap rotation?
No. Lap rotation is spin about its own centre. The guide orbit represents movement of that centre across the stone.
Why is guide path not multiplied by the run time?
The tool reports distance for one circular guide orbit. No operator guide-orbit speed is entered, so total guided distance cannot be calculated.
Why does the upper slide stay at one height in this animation?
The chosen circular guide path keeps the horizontal offset from the upper axis constant. With a fixed connecting-shaft length, the vertical separation stays constant too.
Does the animation run at the entered RPM?
Playback is slowed so the mechanism remains visible. The numerical rim speed and revolution count use the entered RPM.
Does nominal lap area equal abrasive contact area?
No. It is the full disk area inside the outside diameter, including the spaces between rings.
Can this predict gloss or select abrasive pressure?
No. It does not model abrasive action, loading, removal rate or surface finish.
Does this describe a multi-head slab-polishing line?
No. It explains the historical single guided lap described by Hiscox. Its calculator does not represent conveyor feed or multiple polishing heads.
References
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