# Chain Drive Selection and Factor of Safety Calculation Let's solve the problem step-by-step: --- ## **Step 1: Given Data** - **Power** (\(P\)): 60 hp - **Sprockets:** Both have 17 teeth - **Center Distance:** 12 ft - **Speed:** 400 rev/min (rpm) - **Service:** Medium shock (brickmaking) - **Shifts:** 2 per day (moderate usage) --- ## **Step 2: Convert Units to SI** - \(1 \text{ hp} = 0.746 \text{ kW}\) - \(P = 60 \text{ hp} \times 0.746 = 44.76 \text{ kW}\) - Center distance: \(12 \text{ ft} \times 12 = 144 \text{ in}\) --- ## **Step 3: Determine Service Factor (\(K_s\))** Referencing typical chain drive tables: - **Medium shock**: \(K_s \approx 1.3 - 1.5\) - **Two shifts/day**: \(K_s\) toward higher value Let’s pick \(K_s = 1.5\) --- ## **Step 4: Determine Required Power Capacity** \[ \text{Design Power} = P \times K_s = 60 \text{ hp} \times 1.5 = 90 \text{ hp} \] --- ## **Step 5: Select Chain Size** Use standard chain tables (ANSI B29.1). Let’s check if ANSI #80 chain (1" pitch) is suitable. **Typical Power Ratings for ANSI #80 at 400 rpm:** - At 400 rpm, #80 chain can transmit about 17 hp per strand, **per manufacturer's tables**. \[ \text{No. of strands needed} = \frac{90}{17} \approx 5.3 \] Even if using double-strand chain (\(2 \times 17 = 34 \text{ hp}\)), you need: \[ \frac{90}{34} \approx 2.65 \] **Conclusion:** A triple-strand (#80-3) chain transmits about \(3 \times 17 = 51 \text{ hp}\). Not enough. A quadruple-strand (#80-4) chain transmits \(4 \times 17 = 68 \text{ hp}\). Still not enough. For 90 hp, need at least a larger chain or more strands. **Try ANSI #100 (1.25" pitch):** - At 400 rpm, #100 chain transmits about 31 hp per strand. \[ \frac{90}{31} \approx 2.9 \] A triple-strand #100-3 chain transmits \(3 \times 31 = 93 \text{ hp}\) – slightly above requirement. --- ## **Step 6: Check Chain Length** Number of teeth (\(N\)) = 17 per sprocket \[ L = \frac{2C}{p} + \frac{N_1 + N_2}{2} + \frac{(N_2 - N_1)^2 p}{4\pi^2 C} \] - \(C\): Center distance (in pitches) - \(p\): Pitch (in) - \(N_1, N_2\): Sprocket teeth For #100 chain, \(p = 1.25\) in \[ C = \frac{144}{1.25} = 115.2 \text{ pitches} \] \[ L = 2 \times 115.2 + \frac{17 + 17}{2} + 0 \] \[ L = 230.4 + 17 = 247.4 \text{ pitches} \] Round to nearest even number: 248 pitches. --- ## **Step 7: Factor of Safety Calculation** - **Ultimate tensile strength (#100):** ~25,000 lbf (per strand) - **Working load (per strand):** ~3,200 lbf Calculate **working tension**: \[ \text{Power} = T \times v \rightarrow T = \frac{P}{v} \] \[ \text{Chain speed}, v = \pi D n \] - Pitch diameter for 17 teeth, #100 chain: \[ D = \frac{p}{\sin(\pi/N)} \] \[ D = \frac{1.25}{\sin(\pi/17)} \approx \frac{1.25}{0.184} \approx 6.79 \text{ in} \] Convert to ft: \(6.79/12 \approx 0.566\) ft \[ v = \pi \times 0.566 \times 400 \approx 712 \text{ ft/min} \] \[ T = \frac{33000 \times P}{v} \] \[ T = \frac{33000 \times 60}{712} \approx 2,780 \text{ lbf} \] **For triple-strand:** \[ \text{Tension per strand} = \frac{2,780}{3} \approx 927 \text{ lbf} \] \[ \text{Factor of Safety} = \frac{\text{Ultimate Tensile Strength}}{\text{Tension per strand}} \] \[ \frac{25,000}{927} \approx 27 \] --- ## **Step 8: Final Answers** ### **Chain Selection** - **Triple-strand ANSI #100 (1.25" pitch) chain** - **17-tooth sprockets** - **Chain length:** 248 pitches ### **Factor of Safety** - **Factor of Safety:** \(\approx 27\) --- ## **Summary Table** | Parameter | Value | |-------------------|-----------------------------| | Power | 60 hp (44.76 kW) | | Sprocket Teeth | 17 each | | Speed | 400 rpm | | Center Distance | 12 ft (144 in) | | Chain Type | ANSI #100-3 (triple-strand) | | Chain Pitch | 1.25 in | | Chain Length | 248 pitches | | Factor of Safety | 27 | --- ## **Explanation** - The design power was increased by a service factor to account for shock loading and shift schedule. - Chain size was selected using standard manufacturer's tables for transmitted power at the operating speed. - Triple-strand #100 chain is just adequate for this duty. - The factor of safety, based on ultimate tensile strength, is much higher than typical (usually 8–12), indicating the selection is safe. --- **If you need manufacturer-specific recommendations or a more conservative design, consider a quadruple-strand or next larger chain size.**