Overview
ISO 8426-1:2025 - "Hydraulic fluid power - Determination of derived displacement of positive displacement pumps and motors - Part 1: Two-step Toet method" specifies a standardized laboratory method to determine the derived displacement (derived capacity) of positive-displacement hydraulic pumps and motors under steady-state conditions. The standard defines how to collect flow and speed data across multiple shaft speeds and differential pressures and prescribes the two-step Toet regression procedure to compute the derived displacement value.
Key technical topics and requirements
- Scope and definitions: Applies to hydraulic fluid power positive-displacement pumps and motors. Terminology follows ISO 5598.
- Test planning:
- Use five or more shaft speeds and five or more differential pressures (≥25 measurement points total).
- Shaft speeds and differential pressures should be increased in approximately equal increments; targeted values must meet a ±5% tolerance to avoid clustering.
- Guidance for maximum targeted differential pressure is provided relative to rated pressure (different rules for ≤50 bar and >50 bar).
- Measurement requirements:
- Follow ISO 4409:2019 for basic steady-state testing, flowmeter placement, fluid properties, temperature, and measurement accuracy classes.
- Special considerations for variable displacement units, reverse-flow operation, and whether the unit is tested as a pump or motor (results can differ).
- Computation - Two-step Toet method:
- Step 1: For each targeted differential pressure, perform ordinary least squares (OLS) regression of high-pressure flow rate versus shaft speed to obtain slopes (α_i).
- Step 2: Regress the obtained slopes α_i versus differential pressure Δp; the intercept at Δp = 0 is the derived displacement V (slope of flow vs speed at zero Δp).
- Formulae and fitting guidance are provided in Annex B; test report examples are in Annex A.
- Reporting:
- Required test report information includes unit ID, test date/location, speed and pressure ranges, fluid properties, raw measured values (p_in, p_out, Δp, n, flow, temperature), derived displacement, coefficients and correlation statistics.
Practical applications and users
ISO 8426-1:2025 is intended for:
- Test laboratories and certification bodies performing hydraulic component characterization.
- Manufacturers of hydraulic pumps and motors for product development, quality control and datasheet validation.
- R&D and engineering teams assessing volumetric performance and design changes.
- Specifiers and procurement engineers who need comparable, traceable derived displacement data for system design and component selection.
Using this standard ensures repeatable, comparable derived-displacement measurements that support performance verification, troubleshooting, and compliance with industry best practices.
Related standards
- ISO 4409:2019 - Methods of testing and presenting basic steady-state performance for positive-displacement pumps and motors (referenced for test setup and measurement accuracy).
- ISO 5598 - Fluid power systems and components - Vocabulary (terms and definitions used).
Open preview (PDF)Hydraulic fluid power — Determination of derived displacement of positive displacement pumps and motors — Part 1: Two-step Toet method
