Non-ideal models have gained considerable attention in the design stage for evaluating product functionality and performance considering the realistic conditions of the product surface. The performance evaluation generally involves deriving the statistical distributions of certain key characteristics, such as gaps and distances, based on numerous assembly process simulations, thus necessitating a large number of samples of non-ideal surfaces. The traditional practice for generating such samples is to model the systematic and random deviations of each point on the part surface. It is difficult, however, to represent the randomness of the real surface formation mechanism using this point-wise approach, thus leading to significant computational cost. As a result, this technique hinders the wider adoption of specified surface randomness representations in performance simulation and analysis.

The deviation modes that feature non-ideal surfaces are dominated by manufacturing error factors, which could be systematically represented by corresponding mode functions. Furthermore, the variations in the manufacturing process inevitably cause randomness in surface deviations. In this paper, this randomness is defined as the uncertainty of non-ideal surfaces and reflected by the randomness of deviation mode function coefficients. A conceptual non-ideal surface error model that characterises the uncertainty of non-ideal surfaces through the random distributions of mode function coefficients as represented in phase space is therefore proposed. The phase space is a multi-dimensional space, in which each point denotes a group of mode function coefficients that determines a certain non-ideal surface sample. Following the distribution law of coefficients, a number of non-ideal surface samples can be generated by phase space sampling. This method reduces the problem from modelling an infinite number of surface points to modelling a finite coefficient dimension of points in the compact phase space. It thus enables the efficient modelling of non-ideal surfaces that reflect realistic errors resulting from the manufacturing process and facilitates the product performance analysis under the effect of surface randomness. To verify the method, a case study involving a tapered surface manufactured by the taper-turning process is presented. The phase space and error model are discussed with respect to typical manufacturing error factors in this process.

考虑到产品表面的现实条件，非理想模型在评估产品功能和性能的设计阶段得到了相当多的关注。性能评估通常涉及基于大量装配过程模拟得出某些关键特征（例如间隙和距离）的统计分布，因此需要大量非理想表面的样本。生成此类样本的传统​​做法是对零件表面上每个点的系统性和随机性偏差进行建模。然而，使用这种逐点方法很难表示真实表面形成机制的随机性，从而导致显着的计算成本。因此，

以非理想表面为特征的偏差模式受制造误差因素的支配，这可以由相应的模式函数系统地表示。此外，制造过程中的变化不可避免地导致表面偏差的随机性。本文将这种随机性定义为非理想曲面的不确定性，通过偏差模态函数系数的随机性来体现。因此，提出了一种概念性非理想表面误差模型，该模型通过在相空间中表示的模式函数系数的随机分布来表征非理想表面的不确定性。相空间是一个多维空间，其中每个点表示一组决定某个非理想表面样本的模态函数系数。遵循系数的分布规律，可以通过相空间采样产生大量非理想表面样本。该方法将问题从对无限数量的表面点建模到对紧凑相空间中点的有限系数维进行建模。因此，它可以对非理想表面进行有效建模，以反映制造过程中产生的真实误差，并有助于在表面随机性影响下进行产品性能分析。为了验证该方法，介绍了一个涉及通过锥度车削工艺制造的锥面的案例研究。讨论了该过程中典型制造误差因素的相空间和误差模型。该方法将问题从对无限数量的表面点建模到对紧凑相空间中点的有限系数维进行建模。因此，它可以对非理想表面进行有效建模，以反映制造过程中产生的真实误差，并有助于在表面随机性影响下进行产品性能分析。为了验证该方法，介绍了一个涉及通过锥度车削工艺制造的锥面的案例研究。讨论了该过程中典型制造误差因素的相空间和误差模型。该方法将问题从对无限数量的表面点建模到对紧凑相空间中点的有限系数维进行建模。因此，它可以对非理想表面进行有效建模，以反映制造过程中产生的真实误差，并有助于在表面随机性影响下进行产品性能分析。为了验证该方法，介绍了一个涉及通过锥度车削工艺制造的锥面的案例研究。讨论了该过程中典型制造误差因素的相空间和误差模型。因此，它可以对非理想表面进行有效建模，以反映制造过程中产生的真实误差，并有助于在表面随机性影响下进行产品性能分析。为了验证该方法，介绍了一个涉及通过锥度车削工艺制造的锥面的案例研究。讨论了该过程中典型制造误差因素的相空间和误差模型。因此，它可以对非理想表面进行有效建模，以反映制造过程中产生的真实误差，并有助于在表面随机性影响下进行产品性能分析。为了验证该方法，介绍了一个涉及通过锥度车削工艺制造的锥面的案例研究。讨论了该过程中典型制造误差因素的相空间和误差模型。