wheel size and wheel diameter calculation for goliath crane

CT Wheel Shaft and Bearing Calculation

Disclaimer: This is a preliminary engineering calculation based on standard assumptions for an M8-duty crane. The final design, material selection, and safety factors must be verified by a qualified design engineer.

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1. 🧮 Wheel Shaft Diameter Calculation

The shaft must be designed to withstand a combination of high bending (from the wheel load) and torsion (from the motor torque). We will use the ASME code for combined stress (based on the Maximum Shear Stress Theory) to determine the required diameter.

Input Data & Assumptions:

• Max Wheel Load (P_max): 17.75 Tons (174,128 N)
• Wheel Diameter (D): 315 mm (0.315 m)
• Motor Power (P): 3.7 kW (One motor per driven wheel is assumed)
• Bearing Span (L): 400 mm
  * This is a critical assumption for the bearing-to-bearing distance supporting the wheel. The 4200 mm "wheel gauge" is the crab span (rail-to-rail) and is not used for this specific shaft calculation.
• Load Position: Assumed centered between bearings (simply supported beam).
• CT Speed (v): 20 m/min (A typical speed for an M8 CT motion)
• Shaft Material: C45 or EN8 (Yield Strength ≈ 360 MPa)
• Allowable Shear Stress (τ_allowable): 60 MPa (N/mm²) (Using a factor of safety of ≈3 on shear yield for M8)
• Shock & Fatigue Factors (for M8):
  • Km (Bending): 2.0
  • Kt (Torsion): 1.5

Step 1: Calculate Bending Moment (M)

The shaft acts as a simply supported beam with a concentrated load (P_max) at the center.

M = (Pmax × L) / 4
M = (174,128 N × 400 mm) / 4
M = 17,412,800 N-mm
    

Step 2: Calculate Torsional Moment (T)

We first find the wheel RPM and then the torque from the 3.7 kW motor.

RPM (N) = v / (π × D) = 20 m/min / (3.14159 × 0.315 m) = 20.2 RPM
Torque (T) = (P × 9550) / N
T = (3.7 kW × 9550) / 20.2 RPM
T = 1748 N-m = 1,748,000 N-mm
    

Step 3: Calculate Equivalent Torsional Moment (T_e)

This formula combines the bending and torsional moments, applying the shock factors.

Te = √[(Km × M)² + (Kt × T)²]
Te = √[(2.0 × 17,412,800)² + (1.5 × 1,748,000)²]
Te = √[(34,825,600)² + (2,622,000)²]
Te = √[1.213 × 1015 + 6.875 × 1012]
Te = 34,923,700 N-mm
    

(Note: The bending force is the dominant factor in this design, which is expected).

Step 4: Calculate Required Shaft Diameter (d)

τallowable = (16 × Te) / (π × d³)
d³ = (16 × Te) / (π × τallowable)
d³ = (16 × 34,923,700) / (3.14159 × 60)
d³ = 558,779,200 / 188.5
d³ = 2,964,345
d = (2,964,345)1/3 = 143.6 mm
    

Shaft Diameter Selection:

The minimum calculated diameter is 143.6 mm. A standard shaft size should be selected.

Recommended Shaft Diameter at Bearing Seat: 150 mm

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2. ⚙️ Bearing Selection and Details

For an M8 application with high radial loads and potential misalignment, Spherical Roller Bearings are the standard choice.

• Selected Shaft Diameter: 150 mm
• Bearing Type: Spherical Roller Bearing
• Bearing Series: 22200 or 22300 Series
• Example Bearing Designation: 22230 C3
  • Bore Diameter (d): 150 mm
  • Outside Diameter (D): 270 mm
  • Width (B): 73 mm
• Mounting:
  • The bearing would typically be mounted on an Adapter Sleeve (e.g., H 3130) for easy installation and removal.
• Housing:
  • The bearings will be housed in heavy-duty Plummer (Pillow) Blocks (e.g., SNL 530 series) bolted to the CT end carriage frame, or integrated directly into a custom-fabricated bearing housing.
• Bearing Life (L10h):
  • At this high load (8,875 kgf per bearing) and very low speed (20.2 RPM), the bearing's dynamic fatigue life (L_10h) is extremely long. The design is governed by the static load capacity (C₀) and the shaft's bending strength, not the bearing's fatigue life. The 22230 bearing has a static safety factor well over 10 in this application, making it a very robust and safe choice for M8 duty.

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3. 📐 Clarification on "Wheel Gauge 4200mm"

The 4200 mm wheel gauge you provided is the span of the crab (trolley)—the center-to-center distance between the two ISCR 60 rails.

• This dimension is NOT used to calculate the individual wheel shaft diameter.
• It IS a critical dimension for:
  1. Designing the crab's structural frame.
  2. Calculating the bending moment on the main gantry girders (the 40-ton crane's main beams) to determine their size.