Trochoidal Milling and High Efficiency Machining (HEM/HSM): Engagement Angle, Parameters and MRR Calculation

Trochoidal milling and High Efficiency Milling (HEM) form an approach that reconfigures the engagement geometry rather than raising the cutting parameters one by one. The basic idea is to reduce the radial engagement and increase the axial engagement, so that the load on the cutting edge is spread over both time and length. This article covers the logic of the strategy, the calculation of the engagement angle and the feed correction, the material removal rate comparison, the naming conventions on the CAM side and the machine tool requirements.

1. The limit of full slotting

In full slot milling the radial engagement equals the tool diameter: ae = D. In this case the cutting edge remains inside the material along a 180° arc. The consequences fall under three headings:

• Heat build-up. The time the edge spends inside the material is long; the arc left for cooling is short. Instead of being transferred to the chip, heat accumulates in the tool.
• Load concentration. Since the axial engagement is necessarily kept small (typically 0.25–1.0 × D), wear is concentrated only in the lower band of the length of cut. The remainder of the tool is never used.
• Chip evacuation. Inside a slot the only route for the chip to escape is the tool flute. If the flute clogs, the chip is recut and the tool breaks. The rules specific to slotting are covered separately under slotting, plunging and helical interpolation.

The radial force is also high and the engagement angle grows abruptly at corners. This produces both vibration and a risk of sudden breakage.

2. The logic of the trochoidal strategy

In trochoidal milling the tool performs a circular movement while at the same time being translated in the feed direction. The resulting path is a series of overlapping circles, and a thin slice is taken from the material on each cycle. In this way a slot wider than the tool diameter can be opened with a low radial engagement.

The parameter set-up is the inverse of the conventional approach:

Sandvik Coromant states that the controlled arc of engagement produces low cutting forces, that this permits high axial depths of cut, and that having only a single tooth in cut at any one time limits the tendency to vibrate. The same source reports that the strategy makes it possible to work with markedly higher cutting speeds compared with conventional methods.

Axial engagement: Increasing the axial engagement is not an optional detail of this strategy but the very element that carries the productivity. If ae is reduced while ap is left unchanged, the material removal rate falls and the strategy becomes meaningless.

3. Engagement angle and chip thinning correction

The radial engagement determines the arc over which the cutting edge stays inside the material. The angle of this arc is called the engagement angle and is calculated with the following relation:

θ = arccos(1 − 2 × ae / D)

When the radial engagement falls below the tool radius, the maximum chip thickness produced stays below the feed per tooth. This phenomenon is termed radial chip thinning. In order to maintain the target chip thickness, the feed per tooth is multiplied by a correction factor:

RCTF = 1 / √(1 − (1 − 2 × ae / D)²), from which fz = RCTF × fz(nominal)

Neglecting the correction is the most frequently seen application error of the strategy. If the feed is not increased, the chip thickness drops to the order of the edge radius of the cutting edge; burnishing begins instead of cutting, the heat cannot be carried away with the chip and passes into the tool. The axial chip thinning aspect of the subject, together with the ball nose side, is detailed under chip thinning and feed correction. For the basic relations of spindle speed and feed, the cutting speed, spindle speed and feed calculation page is used.

4. Material removal rate comparison

The material removal rate (MRR) is found with the following relation:

Q = ap × ae × vf / 1000 (Q: cm³/min, ap and ae: mm, vf: mm/min)

The example below compares two strategies in general structural steel with a D = 10 mm carbide end mill. The values are chosen from typical application ranges.

Conventional full slot

• Z = 3, vc = 80 m/min → n = 1000 × 80 / (π × 10) = 2,546 rpm
• fz = 0.04 mm/tooth (reduced because of full engagement)
• vf = 0.04 × 3 × 2,546 = 306 mm/min
• ae = 10 mm, ap = 5 mm
• Q = 10 × 5 × 306 / 1000 = 15.3 cm³/min

Trochoidal

• Z = 4, vc = 200 m/min → n = 1000 × 200 / (π × 10) = 6,366 rpm
• ae = 1 mm (10% × D) → RCTF = 1.67 → fz = 0.05 × 1.67 ≈ 0.08 mm/tooth
• vf = 0.08 × 4 × 6,366 = 2,037 mm/min
• ae = 1 mm, ap = 15 mm (1.5 × D)
• Q = 1 × 15 × 2,037 / 1000 = 30.6 cm³/min

The doubling of productivity in the example does not originate from a single parameter: the threefold increase in axial engagement together with the increase in cutting speed more than compensates for the tenfold reduction in radial engagement. Because of the air-cutting portions of the trochoidal path, the actual cycle time gain remains somewhat below this ratio; on the other hand, the tool life gain is added on top of it.

5. Heat distribution and tool life

The contribution of the strategy to tool life comes from two mechanisms. The first is the contact time: as the engagement angle narrows, the cutting time of the cutting edge per revolution shortens, the time it spends in air lengthens and the edge finds an opportunity to cool on every revolution. The second is the spreading of the load along the edge: when the axial engagement is raised to 1–2 times the diameter, wear is not concentrated in the lower band but distributed over the entire length of cut. Equalising heat and wear along the edge provides longer tool life compared with conventional slot milling.

In the application examples published by Harvey Performance Company it is reported that in 17-4PH stainless steel the number of parts machined with a single tool rose from 15 to 40 compared with a conventional roughing path, and that in 6061 aluminium 900 parts were machined with a single tool, an increase of over 150% compared with the conventional method. Since these values depend on the machine, the workholding and the coolant, they are not to be expected identically; the trend they show, however, is consistent. The distinction between wear forms and the criteria for tool life are covered under tool wear mechanisms and tool life. The standard method for comparative tool life trials is defined by ISO 8688-2.

The gain comes not only from the path geometry but from the entire clamping chain. Since the work is carried out at high spindle speeds, runout and balancing become decisive; the holder type, the clamping quality and the runout tolerance directly affect the tool life obtained.

6. Naming conventions on the CAM side

The same underlying logic is offered under different trade names in CAM software. The difference lies in how the engagement is measured and how the feed is adapted.

The common point is preventing the engagement angle from growing at corners and narrow transitions. In conventional contour-parallel roughing the engagement increases abruptly at an internal corner; adaptive algorithms keep the load constant by adding extra trochoidal cycles in that region.

7. Machine tool and control unit requirement

The strategy produces far more and far shorter NC blocks than a conventional path. For this reason the determining factor is not only the spindle power but the ability of the control unit to process these blocks fast enough and maintain the feed.

• Look-ahead depth and block processing time. If the control unit cannot resolve the speed profile in advance by looking ahead, it slows down at every change of direction. The programmed feed is not achieved and the calculated material removal rate cannot be reached.
• Axis acceleration. In short circular cycles the axes accelerate and decelerate continuously. On machines with low acceleration capacity, a high programmed feed remains merely on paper.
• Rigidity and spindle balance. Although the radial force is low, the axial engagement is large and the spindle speed is high; the spindle bearings and the balance of the holder are decisive.
• Chip evacuation and coolant. A high volume of chips is produced in a deep slot. Pressurised coolant or air is required in order to prevent the chips from returning to the cutting zone.

For the assessment of vibration-related limits, the chatter in milling: causes and solutions article is used.

8. Cases where it is not suitable

The strategy does not produce a gain in every job. In the following cases conventional paths are preferred:

• Shallow pockets and light roughing. If the axial engagement stays below 0.5 × D, the basic lever of the strategy disappears; since the proportion of air-cutting movement increases, the total time can become longer.
• Face milling of wide open surfaces. For this work, operation with high ae and low ap using a face mill or shell mill is more productive.
• Tools with a short length of cut. The axial engagement cannot exceed the length of cut of the tool; a high ap cannot be set up with a short tool.
• Weakly clamped or thin-walled parts. A high axial engagement stresses the part through a long force arm. The risk of wall deflection and chatter increases.
• Control units with low acceleration or a short look-ahead buffer. The calculated performance cannot be obtained.
• Finishing operations. The trochoidal path is a roughing strategy; surface quality is provided separately by a finishing pass.

In work with high axial engagement, tools with a long length of cut and a large core diameter offer an advantage; geometries of this type can be examined in the square end mill category.

Sources

• Sandvik Coromant — Slicing and trochoidal milling
• Sandvik Coromant — Entering angle and chip thickness in milling
• Harvey Performance Company / Helical Solutions — Introduction to High Efficiency Milling
• Sandvik Coromant — Milling formulas and definitions (vc, n, vf, fz and Q relations)
• Celeritive Technologies — VoluMill: How It Works
• ISO 8688-2:1989 — Tool life testing in milling — Part 2: End milling
• ISO 3685:1993 — Tool-life testing with single-point turning tools (tool life criteria definitions)
• Machinery's Handbook, Industrial Press — Milling / Speeds and Feeds sections