切削力計算ツール

切断力はどこから来ますか?

ワークピースから取り外されたすべてのチップは、切削工具に測定可能な力を生み出します。この力は、スピンドルの消費電力、工具のたわみ、チャタリング振動、およびトルク要求の物理的な原因です。切断力がどのように発生するか、そしてそれらが3つの軸にどのように分散するかを理解することは、適切なツールホルダーを選択し、表面仕上げの品質を予測し、薄壁加工でのチャタリングを回避するために不可欠です。

The cutting force has three orthogonal components: Cutting force Fc (tangential, in the direction of cutting speed), 送り force Ff (axial, in the feed direction), and Passive force Fp (radial, perpendicular to both). Fc is always the largest — typically 60-70% of the resultant force. Ff accounts for 20-30%, and Fp for 10-20%. The ratio depends primarily on the tool's rake angle, the workpiece material, and the chip thickness.

カッティングフォースフォーミュラ

切断力は、力をチップ断面と材料の固有の切断抵抗に関連付けるKienzle-Victor方程式を使用してモデル化されます。

The specific cutting force kc is not a constant — it depends on chip thickness through the relationship kc = kc1 × h^(-mc), where kc1 is the specific cutting force at a reference chip thickness (typically 1 mm) and mc is the material-dependent increase exponent. Thinner chips have higher specific cutting forces because the material is subjected to greater strain in a smaller shear zone. This calculator applies the full Kienzle-Victor model, accounting for chip thickness effects.

切削力からのトルクとパワー

切断力Fcが知られると、スピンドルのトルクとパワーが直接続きます。

Torque Mc = Fc × (D/2) where D is tool diameter in meters.
Power Pc = Fc × Vc where Vc is cutting speed in m/s.

This direct relationship means that any parameter that increases cutting force — higher feed, deeper cuts, harder materials — also increases torque and power proportionally. The スピンドル馬力計算機 provides an independent check from the MRR perspective; comparing both tools helps validate your input parameters.

切断パラメータが各力コンポーネントにどのように影響するか

Depth of cut (ap) has a linear relationship with all three force components. Doubling ap doubles Fc, Ff, and Fp. This makes DOC the most direct lever for controlling cutting forces — and the fastest way to overload a tool or spindle.

送り per tooth (fz) has a sublinear effect on forces due to the chip thickness effect on specific cutting pressure. Doubling fz increases Fc by approximately 50-70% (not 100%), because the chip becomes thicker and the material offers proportionally less resistance per unit area. This is why increasing feed is more efficient than increasing DOC when you want to raise MRR without proportionally increasing forces.

Width of cut (ae) affects the number of teeth simultaneously engaged. For peripheral milling, increasing ae from 10% to 50% of tool diameter increases the engagement arc, raising the number of teeth in cut and proportionally increasing average force.

実用的な意味: たわみ、チャタリング、およびツールの選択

The radial force component Fp is responsible for tool deflection. A 12mm end mill with 50mm overhang deflecting under 1,500 N of radial force will produce a dimensional error of approximately 0.08-0.12 mm — enough to scrap a tight-tolerance feature. The deflection risk indicator in this calculator gives a qualitative assessment based on the ratio of cutting force to tool stiffness.

Chatter occurs when the cutting force excites the natural frequency of the tool-holder-spindle system. The most common fix is to reduce radial engagement (which reduces the number of teeth in cut, changing the excitation frequency) or to change RPM (which shifts the tooth engagement frequency away from the system's resonant peak). Using the 切削速度・送り計算ツール to find alternative RPM values is often the quickest chatter resolution.

For thin-wall machining, the passive force Fp pushes the workpiece away from the tool. Reducing radial engagement is the most effective strategy — at 10% ae, the cutting force drops by approximately 60% compared to 50% ae, allowing thin walls to be machined without deflection. The グレード相互参照 can help quantify the productivity trade-off.

材料による切断力のベンチマーク

Aluminum 6061: Low cutting forces (kc1 ≈ 700 N/mm²). A typical finishing pass with fz=0.05 mm, ap=1mm produces Fc ≈ 200-300 N — negligible for most machines and holders.

Mild Steel 1018: Moderate forces (kc1 ≈ 1900 N/mm²). A 12mm end mill in roughing (fz=0.10 mm, ap=3mm, ae=9mm) generates Fc ≈ 2,500-3,500 N. This is near the limit for ER collet holders; a solid shrink-fit holder is recommended.

Stainless Steel 304: High forces (kc1 ≈ 2300 N/mm²) with work-hardening that increases forces by 15-25% after the first pass. Expect Fc ≈ 3,000-4,500 N for moderate roughing parameters. Side loads above 3,000 N require hydraulic or mechanical milling chucks.

Titanium Grade 5: Extremely high specific cutting forces (kc1 ≈ 1700 N/mm² at reference thickness) combined with low recommended chip loads. The thin chip effect pushes the effective kc to 2500-3000 N/mm², resulting in Fc = 1,500-2,500 N even at conservative parameters. This high relative force is why titanium is notorious for chatter.

Inconel 718: The highest cutting forces of any common engineering material (kc1 ≈ 3200 N/mm²). At typical finishing parameters, Fc still reaches 2,000-3,000 N. Roughing forces can exceed 6,000 N — requiring robust tool holders with runout below 5 μm and machines with high static stiffness.

よくある質問

What is the cutting force formula for milling? The Kienzle-Victor model: Fc = kc × ap × fz × sin(κr), adjusted for chip thickness effect through kc = kc1 × h⁻ᵐᶜ. This calculator applies the full model automatically.

How does tool diameter affect cutting force? Larger tools distribute the cutting force across a longer cutting edge, reducing the specific force per unit edge length. However, larger diameters also mean higher torque at the same Fc — torque = Fc × D/2. A 25mm tool generates the same Fc as a 12mm tool at the same chip cross-section, but with double the torque demand on the spindle.

What is a safe cutting force for a 12mm carbide end mill? For a standard 12mm end mill with 40mm overhang: Fc below 2,000 N is safe for any operation. Fc between 2,000-4,000 N requires rigid setup and quality tool holders. Fc above 4,000 N risks tool breakage and should only be attempted with heavy-duty holders and stable machining conditions.

How do I reduce cutting force without changing feed? Increase the rake angle (positive rake tools reduce forces by 20-30%), use a tool with a larger helix angle (45° vs 30° reduces forces by 10-15%), or apply high-pressure coolant (reduces forces by 10-20% through improved chip lubrication).

What's the relationship between cutting force and spindle power? Direct: Power (kW) = Fc (N) × Vc (m/s) / 1000. Cutting force and spindle power are two sides of the same physical phenomenon. The スピンドル馬力計算機 approaches this from the MRR side; comparing both gives a cross-check on your parameter choices.

How does tool holder type affect force limits? ER collets (typically 8-10 Nm clamping torque) can safely transmit 1,500-2,500 N cutting force before the tool pulls down. Milling chucks (hydraulic or mechanical) handle 4,000-8,000 N. Shrink-fit holders handle 6,000-12,000 N. The tool holder is often the weakest link in the force transmission chain — exceeding its grip limit causes tool pull-out and catastrophic failure.