Following Energy Through a Hydrostatic Transmission: an interactive hydraulic dynamometer laboratory for fluid power instruction

Abstract

A self-contained browser-based laboratory activity built around a hydrostatic transmission. A prime mover drives a fixed-displacement pump, the pump drives a fixed-displacement hydraulic motor through a hose, and an eddy-current brake absorbs the motor's output. Both machines are carried on trunnions with a torque arm resting on a load cell at a measured radius, so the power crossing into the fluid and the power crossing back out of it are separately weighed and the efficiency of the hydraulic link is measured rather than inferred. Energy is followed through four conversions — electrical to mechanical in the prime mover, mechanical to hydraulic in the pump, hydraulic back to mechanical in the motor, and mechanical to heat in the brake — with the loss and its mechanism named at every stage. The activity is organised around the two statements the whole of fluid power rests on: that the load sets the pressure, because a motor can only make torque by developing pressure across itself, and that the valve sets the speed, because whatever flow reaches the motor must be swallowed one displacement at a time. Most students expect a valve to be the pressure control, and the brake sweep settles that in minutes. In the simulation nothing is assumed. Viscosity follows the Walther relation fitted to the stated ISO grade; leakage in both machines is laminar and therefore viscosity dependent; the bypass valve is a sharp-edged orifice that seals on its seat; the relief valve cracks at its setting and passes more the further it is pushed above it; motor speed is solved from the flow balance, distinguishing a motor starved of flow from one stalled against the relief; and the prime mover carries a torque curve and a droop governor. Because leakage rises and viscous drag falls as the oil warms, the volumetric and mechanical efficiencies move against each other and their product passes through a maximum, which is the argument for fixing oil temperature in a test standard. The motor is instrumented twice over. A torque arm on its casing gives the torque the shaft actually delivers; a pressure gauge on each side of it, with the nameplate displacement, gives the torque the pressure accounts for. The two disagree by the mechanical efficiency, and comparing them lets students quantify the error introduced by the cheap, portable, industry-standard method that has to take that efficiency from a catalogue. On the reference data supplied, the catalogue figure is accurate to a fraction of a per cent at peak power and wrong by twenty-two per cent at light load. The torque arms can be switched off in the simulation, at which point the reported torque becomes an assumption with nothing on the rig able to check it. A needle valve downstream of the motor demonstrates separately that a restriction anywhere in the line loads the pump and not the motor, raising every pressure in the circuit while reducing the difference the motor converts into torque. All three interactive tools switch between SI and US customary units. The conversion is treated as a teaching point rather than a convenience: the constant in the displacement-torque relation changes from 20 pi to 2 pi between the systems because psi times cubic inches is already pound inches, and the 231, 1714 and 63025 that appear throughout American fluid power practice are shown to be unit conversions in disguise. Everything is stored and computed in SI so that no rounding accumulates from switching, and the test suite verifies that all dimensionless results are identical in both systems. The package includes a printable student handout typeset as an article, an instructor answer sheet that recomputes every result, curve, energy chain and model answer from the bench measurements entered rather than storing them, and a grading tool that audits a group's reported values against per-feature tolerances and computes every answer twice, once from the bench master readings and once from what the group wrote down, so that measurement error and arithmetic error can be graded apart. Every file is self-contained: no CDN, no build step, no server, no network access. A headless suite of 253 checks verifies the physics identities, the viscosity model, the flow balance across every combination of the two controls, the valve models, the governor, and both instructor tools.