Mechanical Engineering Suite

ValiCalc Mechanical Design Record
Method version: 2.2.0
Project: Example drive project
Revision: 0
Requirements: Define the required speed, load and operating conditions.
Assumptions: Review every example input before using this calculation.
Required output: 500 rpm; 100 N·m; life unspecified h
All numerical values below use SI. No overall safety/compliance approval.

DS01 — Mechanical Design Record
Input snapshot (SI): {"numbers":{},"choices":{},"rows":[]}
Project revision: 0 [none] 
Stored worksheets: 9 [none] 
PASSED: Requirements and assumptions — Recorded text is a design input, not an engineering approval.
UNKNOWN: Design life requirement — Life is recorded in hours; no lifetime analysis is included in DS01–DS09.
Method: Browser-local revisioned input record. Calculations are regenerated when reopened; stale result approval is never restored.
Method IDs: record
Source/method record: Requirement → input snapshot → method → result → criterion; Versioned browser-local records; no numerical sizing defaults.; Trịnh Chất & Lê Văn Uyển, Tập 1, Chapter 1, printed pp. 5–14 (PDF 4–13).
Limit: No approval is inferred from an incomplete check. Records contain your inputs; explicitly exported files may contain project information.

DS02 — Motor Load & Duty Design Sheet
Input snapshot (SI): {"numbers":{"force":2000,"velocity":0.5,"radius":0.1,"ratio":3,"efficiency":0.9,"loadInertia":0.1,"motorInertia":0.01},"choices":{"load":"rotary"},"rows":[{"torque":100,"startRpm":0,"endRpm":500,"duration":5},{"torque":100,"startRpm":500,"endRpm":500,"duration":20},{"torque":50,"startRpm":500,"endRpm":500,"duration":5}]}
Peak mechanical power at load: 5290.818891544596 [power] 
Transmission efficiency (entered): 90 [none] %
Required peak shaft power: 5878.687657271773 [power] 
Total mechanical peak demand (includes rotor acceleration): 5928.03567927722 [power] 
Required peak motor torque: 37.739047247283644 [torque] 
Duty RMS torque · mathematical summary: 34.77101202914298 [torque] 
Required maximum motor speed: 1500 [rpm] 
Reflected load inertia (ideal kinematics): 0.011111111111111112 [inertia] 
Case | Output RPM start → end | Duration (s) | Motor torque (N·m) | Motor RPM | Motor total peak demand (W) | Load peak power (W) | Model
1 | 0 → 500 | 5 | 37.739047247283644 | 1500 | 5928.03567927722 | 5290.818891544596 | Motoring
2 | 500 → 500 | 20 | 37.03703703703704 | 1500 | 5817.764173314432 | 5235.987755982989 | Motoring
3 | 500 → 500 | 5 | 18.51851851851852 | 1500 | 2908.882086657216 | 2617.9938779914946 | Motoring
PASSED: Motoring load-case model — Every case stays within the positive load-torque model.
UNKNOWN: Physical motor performance — Check the actual torque-speed envelope, starts, cooling, supply, duty and ambient conditions. No model has been selected.
Method: P = Tω; motor/output speed ratio i is positive. Transmission η is motoring mechanical efficiency, not electrical motor efficiency.
Method: Tmotor = (Tload + Jload·αout)/(iη) + Jmotor·i·αout. This constant-η model applies only while load-side torque is nonnegative.
Method: J reflected = Jload/i² (ideal kinematic inertia); motoring loss is accounted separately in load acceleration torque.
Method: Duty rows use constant torque and constant angular acceleration. Case peak power considers both speed endpoints. Delivered shaft power excludes motor rotor acceleration; total mechanical demand includes it.
Method IDs: power, inertia, duty
Source/method power: P = T·2πn/60; P = Fv; SI: P watts, T N·m, n RPM, F newtons, v m/s. Mechanical power at the same shaft/load point.; Tập 1, Chapter 2, printed pp. 16–20; independently derived work/time relationship. Existing ValiCalc power expressions retained.
Source/method inertia: J reflected = J load / i²; T acceleration = J·α; Rotational inertia in kg·m²; angular acceleration rad/s². Motoring transmission efficiency is separately applied to output-side torque.; Oriental Motor: Motor Sizing Basics Part 3 — https://blog.orientalmotor.com/motor-sizing-basics-part-3-acceleration-torque-and-rms-torque
Source/method duty: T RMS = √(Σ Tj²·tj / Σtj); Constant torque per case including modeled acceleration. RMS is a mathematical summary, not an automatic thermal or motor selection approval.; Oriental Motor: acceleration and RMS torque — https://blog.orientalmotor.com/motor-sizing-basics-part-3-acceleration-torque-and-rms-torque
Limit: Constant resisting torque and constant acceleration within each case. RMS torque is a duty summary, not thermal approval; dwell cooling and speed-dependent motor losses need manufacturer review.
Limit: Regenerating/braking load cases need a separate reverse-loss and drive/brake model; they are explicitly blocked.
Limit: No automatic catalog model recommendation or starting/thermal approval.

DS03 — Multi-Stage Powertrain Design Sheet
Input snapshot (SI): {"numbers":{"rpm":1500,"power":7500,"torque":50,"outputPower":5000,"motorCase":2},"choices":{"basis":"power"},"rows":[{"ratio":3,"efficiency":0.95,"reverse":0},{"ratio":2,"efficiency":0.9,"reverse":1}]}
Final shaft RPM · signed rotation: -250 [rpm] 
Final shaft power: 6412.5 [power] 
Final shaft torque · signed rotation: -244.93945741842694 [torque] 
Cumulative efficiency: 85.5 [none] %
Total loss: 1087.5 [power] 
Total reduction ratio: 6 [none] :1
Shaft | RPM · signed | Power (W) | Torque (N·m) · signed | Stage η | Cumulative η | Loss (W)
0 | 1500 | 7500 | 47.7464829275686 | 1 | 1 | 0
1 | 500 | 7125 | 136.07747634357054 | 0.95 | 0.95 | 375.00000000000034
2 | -250 | 6412.5 | -244.93945741842694 | 0.9 | 0.855 | 712.4999999999999
PASSED: Serial energy balance — Pin − Pout − Σloss = -2.2737367544323206e-13 W.
UNKNOWN: Shaft/component capacity — This kinematic shaft table does not rate the actual components.
Method: n out = n in / i; P out = η P in; T = P/ω. Negative RPM and torque denote rotation only; P remains positive in the entered stage sequence.
Method: In inverse power mode, P input = P output / Πη. Linked steady DS02 cases are recalculated from the same project on every input change. Transient cases require a coupled inertia model and are blocked here.
Method IDs: power, stage
Source/method power: P = T·2πn/60; P = Fv; SI: P watts, T N·m, n RPM, F newtons, v m/s. Mechanical power at the same shaft/load point.; Tập 1, Chapter 2, printed pp. 16–20; independently derived work/time relationship. Existing ValiCalc power expressions retained.
Source/method stage: n out = n in/i; P out = ηP in; η total = Πη; T out = ηiT in; Serial passive motoring power flow; 0 < η ≤ 1. Rotation signs do not imply a reversible loss model.; Tập 1, 2.15–2.18 and 3.23–3.25; independent conservation-of-energy derivation.
Limit: Serial steady positive power flow only. Reversed rotation does not model backdriving or regenerative efficiency. No branching, differential or planetary topology here.
Limit: Efficiencies are user-entered operating assumptions. Shaft-load, gear strength and lubrication checks remain separate.

DS04 — Gearbox Ratio Allocation Design Sheet
Input snapshot (SI): {"numbers":{"inputRpm":1500,"targetRpm":250,"power":7500,"stageCount":2,"efficiency":0.95,"driver1":20,"driver2":20,"minTeeth":20,"maxTeeth":80,"candidate":1},"choices":{"allocation":"equal"},"rows":[{"r1":3,"r2":2,"r3":1,"r4":1},{"r1":2.5,"r2":2.4,"r3":1,"r4":1}]}
Required total ratio: 6 [none] :1
Selected total ratio: 5.999999999999999 [none] :1
Selected output RPM: 250.00000000000006 [rpm] 
Speed error: 2.220446049250313e-14 [none] %
Selected output torque: 258.5472050527839 [torque] 
Selected stage 1 ratio: 2.449489742783178 [none] :1
Selected stage 2 ratio: 2.449489742783178 [none] :1
Rank | Candidate | Stage ratios | Output RPM | Output torque (N·m) | RPM error (%)
1 | Equal allocation · continuous | 2.4495 × 2.4495 | 250.00000000000006 | 258.5472050527839 | 2.220446049250313e-14
Selected candidate shaft table
Shaft | RPM | Power (W) | Torque (N*m) | Cumulative efficiency | Stage loss (W)
0 | 1500 | 7500 | 47.7464829275686 | 1 | 0
1 | 612.3724356957946 | 7125 | 111.10679417579884 | 0.95 | 375.00000000000034
2 | 250.00000000000006 | 6768.75 | 258.5472050527839 | 0.9025 | 356.25000000000034
PASSED: Defined search objective — 1 candidate(s). Minimize absolute speed error within entered bounds; ratio imbalance breaks ties. This does not optimize size, cost or strength.
UNKNOWN: Physical gearbox layout and strength — Fixed-axis serial kinematics only. Check module, tooth interference, centers, bearings, housing and lubrication separately.
Method: i total = n input / n target = Πi stage. Equal allocation uses i total^(1/stages).
Method: Discrete search keeps the entered driver teeth; recomputes every candidate's actual ratio, speed, torque and loss using the shared serial engine.
Method IDs: allocation, stage
Source/method allocation: Πij = n input/n target; equal starting ratio = i total^(1/k); Continuous equal ratios or explicitly bounded integer tooth comparisons. Absolute RPM error is the stated objective; mechanical layout remains unverified.; Independent product-ratio derivation; Chapter 3 topology context, printed pp. 25–49. Historical optimization factors are not applied.
Source/method stage: n out = n in/i; P out = ηP in; η total = Πη; T out = ηiT in; Serial passive motoring power flow; 0 < η ≤ 1. Rotation signs do not imply a reversible loss model.; Tập 1, 2.15–2.18 and 3.23–3.25; independent conservation-of-energy derivation.
Limit: Supports serial fixed-axis stages. Equal ratios are a numerical starting point. Coaxial layout, gear interference, module, housing, lubrication and capacity are not inferred.
Limit: Tooth candidates are geometric proposals within entered bounds, not manufactured gears or approved designs. No historical ratio-optimization coefficients are used.

DS05 — Flat Belt Drive Design Sheet
Input snapshot (SI): {"numbers":{"driver":0.1,"driven":0.2,"center":0.5,"selectedLength":1.5,"rpm":1500,"power":1500,"slack":100,"mass":0.1,"slip":0,"requiredWrap":0,"friction":0.3},"choices":{"geometry":"center"},"rows":[]}
Actual center distance: 0.5 [length] 
Actual pitch/datum length: 1.476243077261245 [length] 
Theoretical length at preliminary center: 1.476243077261245 [length] 
Center adjustment: 0 [length] 
Actual reduction ratio: 2 [none] 
Driven RPM: 750 [rpm] 
Belt speed: 7.853981633974483 [velocity] 
Small-pulley wrap: 2.9412578112666736 [angle] 
Effective pull · total: 190.9859317102744 [force] 
Tight tension · per belt/rib: 290.9859317102744 [force] 
Slack tension · per belt/rib: 100 [force] 
Estimated span load on each shaft: 389.49461494160636 [force] 
Centrifugal tension · per belt/rib: 6.168502750680848 [force] 
Ideal capstan ratio limit: 2.416638061191326 [none] 
Required effective tension ratio: 3.0354138781650977 [none] 
State | Center (m) | Exact length (m) | Legacy approximate length (m) | Small wrap (rad)
Preliminary | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
Actual / recalculated | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
PASSED: Pitch/datum circle geometry — Positive, non-overlapping pitch/datum circles. Outside diameters, take-up and installation clearances remain unverified.
PASSED: Selected-length recalculation — Exact pitch-line residual 0.00e+0 m.
BLOCKED: Material stress and bending life — No current applicable product rating dataset. Operating load calculations do not establish allowable capacity.
UNKNOWN: Entered minimum wrap criterion — No applicable minimum wrap supplied.
FAILED: Ideal flat-belt traction estimate — Effective tension ratio 3.0354; capstan limit 2.4166 using entered μ. This is an ideal estimate.
Method: Actual dimensions control all downstream results. Ratio uses consistent datum/pitch diameters.
Method: Exact tangent geometry solves length and center; the established approximate ValiCalc kernel is retained in the comparison table.
Method: P/v gives total effective pull. 1 equal load-sharing belt/rib path(s); operating slack tension is entered rather than inferred from installation pretension.
Method: Entered speed loss 0% affects driven RPM only; tension uses driver pitch-line speed.
Method: Span-force vector estimate excludes weight and transient loads. No overall safety/capacity approval.
Method IDs: belt, exactBelt, tension, flatFriction
Source/method belt: L ≈ 2C + π(D+d)/2 + (D−d)²/(4C); small wrap = π−2 asin(|D−d|/(2C)); Open two-pulley drive, consistent pitch/datum diameters in metres. No crossed belt or idler. Existing approximate length/wrap kernels are reused.; Tập 1, Chapter 4; SDP/SI technical section 22 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method exactBelt: L = 2√(C²−δ²) + π(D+d)/2 + 2δ asin(δ/C); δ=|D−d|/2; Exact ideal tangent pitch-line geometry. A bounded bisection solves selected pitch length → physical center distance. No tooth deformation or installation tension correction.; Independent tangent geometry; SDP/SI equation 22-11 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method tension: ΔT = P/v; T tight = T slack + ΔT; R = √((Tt+Ts)²cos²α + (Tt−Ts)²sin²α); α = asin(|D−d|/(2C)). Steady span-force estimate using entered slack tension or operating tension ratio. Equal belt/rib sharing is an explicit assumption; no rated belt count is inferred.; Gates Heavy Duty V-Belt Drive Design Manual, tension ratio D18; independent vector sum — https://www.gates.com/content/dam/documents-library/catalogs/heavy-duty-vbelt-drive-design-manual-en.pdf
Source/method flatFriction: (Tt−Tc)/(Ts−Tc) ≤ exp(μθ); Tc = m′v²; Ideal flexible flat-belt friction estimate with user-supplied μ and mass/length. Static-friction limit and centrifugal allowance, not manufacturer capacity.; MIT FUNdaMENTALS of Design, Topic 5, belt/cable stress and capstan; independent force-balance derivation — https://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%205.PDF
Limit: Open two-pulley drive with no idler. Enter consistent actual datum/pitch diameters and lengths. Outside diameters, alignment and take-up travel still need checking.
Limit: Tensions are operating values; equal sharing across entered belts/ribs is an assumption. Shaft span-force estimate excludes pulley weight, bearing reactions and transient loading.
Limit: Capacity, fatigue, installation pretension and allowable speed require current product-specific evidence. No catalog dimensions or ratings are inferred.
Limit: The capstan check is an ideal engineering estimate using supplied friction and centrifugal tension. Passing it does not approve belt width, stress, bending life or adhesion.

DS06 — V-Belt Drive Design Sheet
Input snapshot (SI): {"numbers":{"driver":0.1,"driven":0.2,"center":0.5,"selectedLength":1.5,"rpm":1500,"power":1500,"slack":100,"mass":0.1,"count":1,"slip":0,"requiredWrap":0},"choices":{"geometry":"center"},"rows":[]}
Actual center distance: 0.5 [length] 
Actual pitch/datum length: 1.476243077261245 [length] 
Theoretical length at preliminary center: 1.476243077261245 [length] 
Center adjustment: 0 [length] 
Actual reduction ratio: 2 [none] 
Driven RPM: 750 [rpm] 
Belt speed: 7.853981633974483 [velocity] 
Small-pulley wrap: 2.9412578112666736 [angle] 
Effective pull · total: 190.9859317102744 [force] 
Tight tension · per belt/rib: 290.9859317102744 [force] 
Slack tension · per belt/rib: 100 [force] 
Estimated span load on each shaft: 389.49461494160636 [force] 
Centrifugal tension · per belt/rib: 6.168502750680848 [force] 
State | Center (m) | Exact length (m) | Legacy approximate length (m) | Small wrap (rad)
Preliminary | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
Actual / recalculated | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
PASSED: Pitch/datum circle geometry — Positive, non-overlapping pitch/datum circles. Outside diameters, take-up and installation clearances remain unverified.
PASSED: Selected-length recalculation — Exact pitch-line residual 0.00e+0 m.
BLOCKED: Rated belt/rib count — No current applicable product rating dataset. Operating load calculations do not establish allowable capacity.
UNKNOWN: Entered minimum wrap criterion — No applicable minimum wrap supplied.
Method: Actual dimensions control all downstream results. Ratio uses consistent datum/pitch diameters.
Method: Exact tangent geometry solves length and center; the established approximate ValiCalc kernel is retained in the comparison table.
Method: P/v gives total effective pull. 1 equal load-sharing belt/rib path(s); operating slack tension is entered rather than inferred from installation pretension.
Method: Entered speed loss 0% affects driven RPM only; tension uses driver pitch-line speed.
Method: Span-force vector estimate excludes weight and transient loads. No overall safety/capacity approval.
Method IDs: belt, exactBelt, tension
Source/method belt: L ≈ 2C + π(D+d)/2 + (D−d)²/(4C); small wrap = π−2 asin(|D−d|/(2C)); Open two-pulley drive, consistent pitch/datum diameters in metres. No crossed belt or idler. Existing approximate length/wrap kernels are reused.; Tập 1, Chapter 4; SDP/SI technical section 22 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method exactBelt: L = 2√(C²−δ²) + π(D+d)/2 + 2δ asin(δ/C); δ=|D−d|/2; Exact ideal tangent pitch-line geometry. A bounded bisection solves selected pitch length → physical center distance. No tooth deformation or installation tension correction.; Independent tangent geometry; SDP/SI equation 22-11 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method tension: ΔT = P/v; T tight = T slack + ΔT; R = √((Tt+Ts)²cos²α + (Tt−Ts)²sin²α); α = asin(|D−d|/(2C)). Steady span-force estimate using entered slack tension or operating tension ratio. Equal belt/rib sharing is an explicit assumption; no rated belt count is inferred.; Gates Heavy Duty V-Belt Drive Design Manual, tension ratio D18; independent vector sum — https://www.gates.com/content/dam/documents-library/catalogs/heavy-duty-vbelt-drive-design-manual-en.pdf
Limit: Open two-pulley drive with no idler. Enter consistent actual datum/pitch diameters and lengths. Outside diameters, alignment and take-up travel still need checking.
Limit: Tensions are operating values; equal sharing across entered belts/ribs is an assumption. Shaft span-force estimate excludes pulley weight, bearing reactions and transient loading.
Limit: Capacity, fatigue, installation pretension and allowable speed require current product-specific evidence. No catalog dimensions or ratings are inferred.
Limit: Rated belt count is BLOCKED without applicable power rating, correction factors, service conditions and matched-set guidance. A flat-belt friction coefficient is not reused for V-groove capacity.

DS07 — Poly-V Belt Drive Design Sheet
Input snapshot (SI): {"numbers":{"driver":0.1,"driven":0.2,"center":0.5,"selectedLength":1.5,"rpm":1500,"power":1500,"slack":100,"mass":0.1,"count":6,"slip":0,"requiredWrap":0},"choices":{"geometry":"center"},"rows":[]}
Actual center distance: 0.5 [length] 
Actual pitch/datum length: 1.476243077261245 [length] 
Theoretical length at preliminary center: 1.476243077261245 [length] 
Center adjustment: 0 [length] 
Actual reduction ratio: 2 [none] 
Driven RPM: 750 [rpm] 
Belt speed: 7.853981633974483 [velocity] 
Small-pulley wrap: 2.9412578112666736 [angle] 
Effective pull · total: 190.9859317102744 [force] 
Tight tension · per belt/rib: 131.83098861837908 [force] 
Slack tension · per belt/rib: 100 [force] 
Estimated span load on each shaft: 1384.1452957890128 [force] 
Centrifugal tension · per belt/rib: 6.168502750680848 [force] 
State | Center (m) | Exact length (m) | Legacy approximate length (m) | Small wrap (rad)
Preliminary | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
Actual / recalculated | 0.5 | 1.476243077261245 | 1.4762388980384689 | 2.9412578112666736
PASSED: Pitch/datum circle geometry — Positive, non-overlapping pitch/datum circles. Outside diameters, take-up and installation clearances remain unverified.
PASSED: Selected-length recalculation — Exact pitch-line residual 0.00e+0 m.
BLOCKED: Rated belt/rib count — No current applicable product rating dataset. Operating load calculations do not establish allowable capacity.
UNKNOWN: Entered minimum wrap criterion — No applicable minimum wrap supplied.
Method: Actual dimensions control all downstream results. Ratio uses consistent datum/pitch diameters.
Method: Exact tangent geometry solves length and center; the established approximate ValiCalc kernel is retained in the comparison table.
Method: P/v gives total effective pull. 6 equal load-sharing belt/rib path(s); operating slack tension is entered rather than inferred from installation pretension.
Method: Entered speed loss 0% affects driven RPM only; tension uses driver pitch-line speed.
Method: Span-force vector estimate excludes weight and transient loads. No overall safety/capacity approval.
Method IDs: belt, exactBelt, tension
Source/method belt: L ≈ 2C + π(D+d)/2 + (D−d)²/(4C); small wrap = π−2 asin(|D−d|/(2C)); Open two-pulley drive, consistent pitch/datum diameters in metres. No crossed belt or idler. Existing approximate length/wrap kernels are reused.; Tập 1, Chapter 4; SDP/SI technical section 22 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method exactBelt: L = 2√(C²−δ²) + π(D+d)/2 + 2δ asin(δ/C); δ=|D−d|/2; Exact ideal tangent pitch-line geometry. A bounded bisection solves selected pitch length → physical center distance. No tooth deformation or installation tension correction.; Independent tangent geometry; SDP/SI equation 22-11 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method tension: ΔT = P/v; T tight = T slack + ΔT; R = √((Tt+Ts)²cos²α + (Tt−Ts)²sin²α); α = asin(|D−d|/(2C)). Steady span-force estimate using entered slack tension or operating tension ratio. Equal belt/rib sharing is an explicit assumption; no rated belt count is inferred.; Gates Heavy Duty V-Belt Drive Design Manual, tension ratio D18; independent vector sum — https://www.gates.com/content/dam/documents-library/catalogs/heavy-duty-vbelt-drive-design-manual-en.pdf
Limit: Open two-pulley drive with no idler. Enter consistent actual datum/pitch diameters and lengths. Outside diameters, alignment and take-up travel still need checking.
Limit: Tensions are operating values; equal sharing across entered belts/ribs is an assumption. Shaft span-force estimate excludes pulley weight, bearing reactions and transient loading.
Limit: Capacity, fatigue, installation pretension and allowable speed require current product-specific evidence. No catalog dimensions or ratings are inferred.
Limit: Required rib count and allowable rib load are BLOCKED until current profile-specific catalog ratings, wrap corrections and installation guidance are available. V-belt wedge factors are not transferable.

DS08 — Timing Belt Drive & Engagement Sheet
Input snapshot (SI): {"numbers":{"pitch":0.005,"z1":20,"z2":40,"center":0.2,"teeth":110,"rpm":1500,"power":500,"slack":100,"requiredMesh":0},"choices":{"profile":"htd5"},"rows":[]}
Actual center distance: 0.19936438561580416 [length] 
Actual pitch/datum length: 0.55 [length] 
Theoretical length at preliminary center: 0.5512671844270792 [length] 
Center adjustment: -0.0006356143841958484 [length] 
Actual reduction ratio: 2 [none] 
Driven RPM: 750 [rpm] 
Belt speed: 2.5 [velocity] 
Small-pulley wrap: 2.98176021531901 [angle] 
Effective pull · total: 200 [force] 
Tight tension · per belt/rib: 300 [force] 
Slack tension · per belt/rib: 100 [force] 
Estimated span load on each shaft: 399.04290234138034 [force] 
Theoretical belt teeth: 110.25343688541584 [none] 
Selected belt teeth: 110 [none] 
Driver pitch diameter: 0.03183098861837907 [length] 
Driven pitch diameter: 0.06366197723675814 [length] 
Small-pulley teeth in mesh · geometric: 9.491237547655492 [none] 
State | Center (m) | Exact length (m) | Legacy approximate length (m) | Small wrap (rad)
Preliminary | 0.2 | 0.5512671844270792 | 0.5512665147955292 | 2.9822692532676136
Actual / recalculated | 0.19936438561580416 | 0.55 | 0.5499993239350083 | 2.98176021531901
PASSED: Pitch/datum circle geometry — Positive, non-overlapping pitch/datum circles. Outside diameters, take-up and installation clearances remain unverified.
PASSED: Selected-length recalculation — Exact pitch-line residual 1.11e-16 m.
BLOCKED: Tooth load, width and torque capacity — No current applicable product rating dataset. Operating load calculations do not establish allowable capacity.
UNKNOWN: Entered engagement criterion — Required engagement is unspecified; consult product guidance.
Method: Actual dimensions control all downstream results. Ratio uses integer pulley teeth / circular pitch.
Method: Exact tangent geometry solves length and center; the established approximate ValiCalc kernel is retained in the comparison table.
Method: P/v gives total effective pull. 1 equal load-sharing belt/rib path(s); operating slack tension is entered rather than inferred from installation pretension.
Method: Matching profile htd5; pitch 0.005 m. Selected 110 teeth gives 0.55 m pitch length.
Method: Span-force vector estimate excludes weight and transient loads. No overall safety/capacity approval.
Method IDs: timing, exactBelt, tension
Source/method timing: d pitch = zp/π; L pitch = N belt p; teeth in mesh = z small θ small/(2π); Circular pulley pitch convention for selected matching profile. Engagement is fractional geometric contact; entered required engagement is a separate user criterion.; SDP/SI timing profiles and technical section 22 — https://sdp-si.com/resources/beltdesignsuggestions.php
Source/method exactBelt: L = 2√(C²−δ²) + π(D+d)/2 + 2δ asin(δ/C); δ=|D−d|/2; Exact ideal tangent pitch-line geometry. A bounded bisection solves selected pitch length → physical center distance. No tooth deformation or installation tension correction.; Independent tangent geometry; SDP/SI equation 22-11 — https://sdp-si.com/D820/PDFS/Technical-Section.pdf
Source/method tension: ΔT = P/v; T tight = T slack + ΔT; R = √((Tt+Ts)²cos²α + (Tt−Ts)²sin²α); α = asin(|D−d|/(2C)). Steady span-force estimate using entered slack tension or operating tension ratio. Equal belt/rib sharing is an explicit assumption; no rated belt count is inferred.; Gates Heavy Duty V-Belt Drive Design Manual, tension ratio D18; independent vector sum — https://www.gates.com/content/dam/documents-library/catalogs/heavy-duty-vbelt-drive-design-manual-en.pdf
Limit: Open two-pulley drive with no idler. Enter consistent actual datum/pitch diameters and lengths. Outside diameters, alignment and take-up travel still need checking.
Limit: Tensions are operating values; equal sharing across entered belts/ribs is an assumption. Shaft span-force estimate excludes pulley weight, bearing reactions and transient loading.
Limit: Capacity, fatigue, installation pretension and allowable speed require current product-specific evidence. No catalog dimensions or ratings are inferred.
Limit: HTD 3M/5M pitch conventions are supported by SDP/SI product documentation; catalog belt availability, tooth shape, width, torque capacity and tooth-jump resistance are not validated.
Limit: Teeth in mesh is fractional geometric contact, not a count of fully load-bearing teeth. Required engagement is user supplied. No automatic tooth-width or allowable load selection.

DS09 — Chain Drive Design Sheet
Input snapshot (SI): {"numbers":{"pitch":0.01905,"z1":25,"z2":75,"center":0.762,"links":132,"rpm":300,"power":3000,"mass":1,"slack":100,"allowable":0,"requiredWrap":0},"choices":{"family":"roller","selection":"even","joint":"even"},"rows":[]}
Reduction ratio: 3 [none] 
Driven RPM: 100 [rpm] 
Mean link-advance speed: 2.38125 [velocity] 
Effective working pull: 1259.8425196850394 [force] 
Centrifugal tension estimate: 5.6703515625000005 [force] 
Estimated tight-span tension: 1365.5128712475394 [force] 
Theoretical links: 131.58314349441153 [none] 
Selected physical links: 132 [none] 
Actual center distance: 0.7660502867456284 [length] 
Center adjustment: 0.004050286745628351 [length] 
Nominal chain pitch length: 2.5146 [length] 
Driver pitch diameter: 0.15199480184340802 [length] 
Driven pitch diameter: 0.4549182712034071 [length] 
Small sprocket wrap · pitch-circle estimate: 2.743534344257981 [angle] 
Fixed-pin articulation at driver: 0.25132741228718347 [angle] 
Ideal fixed-pin chordal variation: 0.7885298685522124 [none] %
Links | Actual center (m) | Adjustment (m) | Selection
130 | 0.7466097172674523 | -0.015390282732547722 | compare
132 | 0.7660502867456284 | 0.004050286745628351 | selected
PASSED: Actual integer-link recalculation — 132 links; residual 0.00e+0 pitches using the established two-sprocket approximation.
PASSED: Link assembly — Even count permits alternating-link assembly in the modeled geometry; actual connecting hardware remains to be verified.
BLOCKED: Rated capacity, lubrication and life — No applicable current supplier dataset; breaking strength is not treated as permissible working load.
UNKNOWN: Supplied steady working-pull criterion — No allowable working-pull criterion supplied.
UNKNOWN: Supplied minimum wrap criterion — Ideal pitch-circle wrap comparison only; actual engaged tooth count and product rating are separate.
Method: Mean speed = pitch × driver teeth × RPM / 60; pull = power / mean speed. No pitch-circle speed substitution.
Method: Mass/length and slack-span tension are user inputs. Centrifugal estimate m′v² is added separately; no historical sag or impact coefficients.
Method: Chain construction: roller. No overall capacity approval.
Method: Theoretical 131.58314349441153 pitches → selected 132 → actual center 0.7660502867456284 m. Each size change reruns the inverse and forward residual.
Method: No automatic 0.2–0.4% center shortening from historical guidance; required installation slack is a separate physical adjustment.
Method: Chordal variation = 1−cos(π/z), relative to ideal maximum pitch-circle speed, for the fixed-pin polygon only.
Method IDs: chain, chainForce, polygon
Source/method chain: d = p/sin(π/z); L pitches ≈ (z1+z2)/2 + 2C/p + (z2−z1)²p/(4π²C); Two-sprocket fixed-pitch roller/bush chain approximation. Larger quadratic root is checked after selecting actual integer links. Sprocket OD/tooth profile is separate.; Tập 1, 5.12–5.17, printed pp. 84–86; Renold chain design guide; existing ValiCalc chain kernels reused. — https://www.renold.com/media/165418/transmission-i-and-m-ren12-eng-10-10.pdf
Source/method chainForce: v mean = pzn/60; F effective = P/v; F centrifugal = m′v²; Mean link-advance speed differs from pitch-circle peripheral speed. Working pull is not breaking strength or permissible load.; Renold chain design guide; Ramsey engineering formulas — https://ramseychain.com/download/literature/support_documentation/other_documentation/Silent-Chain-Drives-Operating-and-Servicing-Manual.pdf
Source/method polygon: Articulation ≈ 2π/z; ideal chordal variation = (1−cos(π/z))×100%; Fixed-pin regular polygon model relative to its maximum pitch-circle speed. Not a vibration/noise prediction; rocker-joint silent chains need their own model.; Independent regular-polygon kinematics; Tập 1 Chapter 5 chain context.
Limit: Two sprockets, no idler; link-count and center equations are geometric approximations. No automatic center shortening or sag allowance is applied. Actual OD, take-up travel and installation tension need separate verification.
Limit: Roller and bush chains use the fixed-pin pitch-polygon model. Silent fixed-pin geometry needs a matching supplier convention. Rocker-joint silent chain retains mean speed and pull only; center/articulation/chordal predictions are BLOCKED pending its product model.
Limit: Capacity, fatigue, wear life, shock load, lubrication and allowable speed are BLOCKED without current applicable product data. A steady working-pull comparison does not establish chain-strength approval.
Limit: Mean link-advance speed differs from instantaneous pitch-circle peripheral speed. Ideal chordal variation is not a vibration or noise prediction.